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Content MODELS OF SPATIAL ACCURACY AND CONDITIONAL BEHAVIOR IN OCULOMOTOR CONTROL by Peter Ford Dominey A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Computer Science) August, 1993 UMI Number: DP22863 All rights reserved INFORMATION TO ALL USERS T he quality of this reproduction is d ep en d en t upon the quality of the copy subm itted. In the unlikely event that the author did not sen d a com plete m anuscript and th ere are m issing pag es, th e se will be noted. Also, if m aterial had to be rem oved, a note will indicate th e deletion. Dissertation Publishing UMI D P22863 Published by P roQ uest LLC (2014). Copyright in the Dissertation held by th e Author. Microform Edition © P roQ uest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United S ta tes C ode P roQ uest LLC. 789 E ast Eisenhow er Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 -1 3 4 6 UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90007 This dissertation, written by * under the direction of h.t.&..... Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of re quirements for the degree of o m m DOCTOR OF PHILOSOPHY D ean of G raduate Studies Date vluns..Ifr,..!S33 DISSERTATION COMMITTEE Chairperson Acknowledgments The spirit of graduate life is heavily influenced by that of the thesis advisor. I have been quite fortunate to have Professor Michael A. Arbib as my advisor, through thick and thin. In 19871 took his "Brain Theory and Artificial Intelligence" on closed-circuit television, while working at the Jet Propulsion Laboratory (JPL) in Pasadena, and was excited to learn how the study of motor control provides an intermediate step on the way to understanding biological intelligence. The following summer I approached him to do a directed research project, related to autonomous navigation and visual attention. We investigated a number of issues, settling on a model of visual attention via the saccadic eye movement system. Thinking that this was just a short term project, I was continually surprised when the latest draft came back to me, filled with new questions and ideas. I had no idea at the time that this area could be a career in itself. I Not only did Arbib provide me with excellent food for thought and intellectual j freedom (tempered by periodic lectures, to this day, about pulling in the reigns of wild imagination with the steady hand of rigor), but he also introduced me to his colleagues, who in turn became my colleagues. One day, at Arbib's suggestion, I called Professor Thomas H. McNeill to ask if he had time to do a sanity check on our basal ganglia model. After we got warmed up, the ideas were flying in a common language - as if we had known each other for years. By the end of the day we were well on the way to a cure for Parkinson's disease (or so it seemed to me), and I had an NIH [ Multidisciplinary Training Grant in Gerontology. For the next year, I had the unique experience of a one-on-one tutorial with Tom in all aspects of basal ganglia function - priceless. Here I met John Walsh and have gained much from his perspective. For the rest of my Ph.D. I also attended each week a seminar in gerontology that covered j everything from the biochemistry of environment mediated stress responses, to J psychological studies demonstrating that elderly people are happier if they have a plant j to take care of. I thank Professor Vem Bengston, for financial support and for the j exposure to the "living" part of our science. Around this time Arbib took me one day | to UCLA to meet John and Madeline Schlag who had developed an oculomotor paradigm that occupies much of Chapter 4 of this volume, and with whom I continue to enjoy a quite lively exchange of ideas and collaboration. Their kindness, extreme patience and free flow and exchange of ideas have provided some of my highlights. Dr. Arbib also introduced me to Dr. George Bekey, who has provided valuable insight from the robotics perspective. I want to thank Doctors Bekey, McNeill and Schlag for their respective roles on my thesis committee. In a strange "small world" way, Arbib also introduced me to Professor Marc Jeannerod and Dr. Jean-Paul Joseph, colleagues on a Human Frontiers project. Ten years earlier, Jean-Paul had been trained by the Schlags, and now I would go to Lyon, France to learn from Jean-Paul. He didn't realize it at the time, but Arbib was also helping lay the groundwork for my family, as during that year I would meet and marry the wonderful Dr. Jocelyne Ventre, also from Jeannerod's lab. Jocelyne, and now our daughter Emilie, have more than anything else in my life turned my blurred eyes away from the mirror and out into the world. Life is so much more when we finally see that we are part of something, and not alone. What fun we have already had, and will have together. Thinking of my small family, and being with them, has been my major fuel through these final laps, and will continue to be for the rest of them. One of my greatest pleasures has been to experience the little intellectual explosions that happen when people who have been thinking about the same problems sit down and talk, and make plans. What more than to do this with the woman you love! For the first time I will leave USC without a date marked on my calendar for the return. Our lab here has been a second home. From the "old days" (I am an old man here now) Deliang Wang, Reza Shademehr and Bruce Hoff all left their mark on me and have gone off to do great things. I miss them. My good friend Alfredo Weitzenfeld (Father of NSL) remains to continue in the great tradition and will probably be the department chair some day. I have enjoyed the intellectual and personal stimulation from Jim Liaw, Fernando Corbacho, Hung-Bong Lee, Joseph Fiser and Irwin King who receives extra-special mention for making the style sheets available that produced this gleaming copy. Jean-Marc Fellous is not only a great Frenchman, but has also been an inspiration in his leadership in teaching and i developing his field of "emotion." Nicholas Schweighofer, my office-mate and iii Frenchman, who had the strength to read my French e-mail, has become a good friend and heir to the saccade model to which he adds the much needed cerebellum. Andy Fagg and Tony Lewis have been outstanding in their creation of the robotics lab, complete with autonomous walking and flying creatures, and in grasping the underlying theory as a mighty sword. Lucia Simo has been a good friend and colleague through double and colliding saccade story which continues to unfold. In France, I "profited from life" and from knowing and working with Professor Marc Jeannerod, Jean-Paul Joseph, Claude Prablanc, Yves Rossetti, Denis Pelisson, Driss Boussaoud, Laurent Goffard, Pascal Barone, Bruno Tadaiy and others who I am happy to return to work with, and I especially thank Professor Jeannerod for welcoming me to his lab. While at JPL, I enjoyed working with a number of talented people and thank Jeff Leising for my start; Lewis Boydstun, Jesse Jackson, Frank Parker, Dick Coffin, Jay Holladay, Bob Polansky, Jeff Jones, Gil Dawson, Ron Slusser, the "elite runners," and especially Peter Poon and Don Sweetnam for intellectual and financial support in making the transition from professional engineering back into academia. Craig Chambers introduced me to J.D. Salinger "the Kierkegaard of Buddhism," and talked almost as much as me on some long runs in the Santa Monica mountains. My adopted father, David Newton Dominey, used to help me wind electromagnets and was the inspiration in my first feeble steps towards science. He taught me that anyone can paint a painting; build an electric skateboard, or a rocket to the moon. My mother always said we could do anything, and was always happy when we did. My brother Doug has inspired me since I can remember, and he and his wife Andrea and their kids Eric and Elise have been like my own family. Education has always been important in our family and I thank my grandfather William Roy Carrick for all of his I support, and my father, Dr. Paul H. Ford for leading the way. This work was also supported in part by NIA under Multidisciplinary Research Training in Gerontology Grant 2T32AG0037 (V. Bengston PI), a Chateaubriand I Fellowship from the French Government, NIA Grant 7R01 NS24926 from NINCDS j I (M. Arbib PI), and a grant from the Human Frontier Research Program. Contents Acknowledgments ii List of Figures ix List of Tables xi Abstract xii 1 Introduction 13 1.1 M otivation.....................................................................................13 1.2 Overview of the Oculomotor System ....................................... 15 1.3 Modeling Methodology...........................................................17 1.4 Organization of the Thesis and Summary of Contributions...............................................................................19 2 Spatiotemporal Transformation in the Brainstem Saccade Generator 21 2.1 Introduction.................................................................................21 2.2 Neurophysiology and Models................................................... 22 2.3 An Updated M odel.................................................................. 25 2.4 Superior Colliculus as a Spatial Integrator............................34 3 A Model of Cortico-Subcortical Function in Voluntary Saccade Generation 37 3.1 Introduction...................... 37 3.2 The Model and its Biological Substrate................................41 3.2.1 Frontal Eye Fields.............................................................. 43 3.2.2 Basal Ganglia.......................................................................49 3.2.3 Superior Colliculus............................................................. 56 3.2.4 Cortico-striato-thalamo-cortical interactions............... 58 3.3 Simulation Results.................................................................... 59 3.3.1 Simple and Memory Saccades................................. 59 3.3.2 Simulated Lesion Studies................................................... 64 3.4 Discussion.................................................................................... 66 4 Shared and Interacting Mechanisms for Double-Step and Colliding Saccades 68 4.1 Introduction..................................................................................68 4.2 Cortical Dynamic Remapping.................................................72 4.3 Brainstem Dynamic Remapping............................................. 82 4.4 Interacting Mechanisms.............................................................. 87 4.5 Simulation Results.................................................................... 90 4.5.1 Double Saccades..................................................................90 4.5.2 Compensatory and Colliding Saccades......................... 91 4.6 Predictions and Experimental Design.......................................93 4.7 Discussion......................................................................................96 5 Sensorimotor Convergence and Stimulus-Response A ssociations • Dopamine and C orticostriatal Plasticity 98 5.1 Introduction - Context and Behavior........................................ 99 5.2 The Role of Basal Ganglia in the "Base" Model.................... 100 5.3 Formation of Visuomotor Associations..................................103 5.4 Model performance and single unit activity 5.5 Discussion........................................................ 110 120 6 Internal State Transitions and Sequential Behavior - Connected Associations 124 6.1 Introduction - Connected Contexts and Sequences............. 124 6.2 Sequence Learning..................................................................... 125 6.3 Model performance and single unit activity.......................... 130 6.4 Discussion....................................................................................139 7 Generalization of Associative and Spatial Relations 141 7.1 Introduction Generalization Requires a Structured Environment .............142 7.2 Generalization on Stim uli.........................................................143 7.3 Generalization on Response Formation of a Spatial Gradient............................................... 145 7.4 Generalization on Stimuli and Responses in Sequence Learning.................................................................................... 149 7.5 Structure-Function Relations Architectures and Generalization..............................................150 7.6 Discussion From Habits to The Wisconsin Card S ort............................... 151 8 Dissociable Models of Early and Late Onset Huntington's Disease 153 8.1 Introduction................................................................................ 153 8.2 Saccade Deficits in H D ..............................................................154 8.3 Implicated Brain Regions 156 j 8.4 Parametric Analysis of Simulated Lesions and HD..............157 j vii 8.5 Clinical Dissociation of Two HD M odels...............................160 8.6 Discussion....................................................................................161 9 Conclusion and Prospectus 163 9.1 Summary of Results, Lessons Learned..................................163 9.2 Extensions and Prospects for Future Research....................164 Appendices 167 Appendix A Brainstem Saccade-Generator Model Specification...............167 Appendix A1 Cortico-Subcortical Saccade Model Specification.................169 Appendix B Association and Sequence Model Specification...................... 173 References 179 List of Figures 2.1 Classes of Saccade Generator Models.................................................23 2.2 Independent Velocity and Amplitude M odel.....................................27 2.3 Brainstem Saccade Generator Simulation..........................................35 3.1 Saccade task protocols...........................................................................39 3.2 Multiple brain regions involved in saccade generation..................... 40 3.3 FEF Sustained response during Memory saccade task..................... 48 3.4 Caudate sustained memory response.................................................. 52 3.5 SNr and SC visual saccade response................................................... 54 3.6 SNr Memory-contingent sustained response.................................. 55 3.7 Simple Saccade Task simulation......................................................... 61 3.8 Memory Saccade Task Simulation........................................ 62 4.1 Double Step Saccade............................................................................. 70 4.2 Colliding Saccade............................................................................. 70 4.3 Shared and Cooperating Spatial Accuracy Mechanisms.................. 71 4.4 Mechanism for Dynamic Remapping Using Eye Position.............. 75 4.5 Dynamic Spatial Remapping Simulation............................................78 4.6 Damped Signal Effect...........................................................................81 4.7 Colliding Saccades Modify Fixed Vector Saccades......................... 83 4.8 Colliding Saccade Simulation.............................................................. 85 | 4.9 Mechanism B - Double Saccade Simulation............................. 86 | 4.10 Double step memory saccade....................................................... 95 5.1 Cue-saccade Association T ask............................................................99 ! 5.2 The Role of Basal Ganglia................................................................ 101 5.3 Corticostriatal Plasticity for Selective Disinhibition.....................102 5.4 Schematic of Association M odel........................................................105 5.5 Dopamine Regulation of Corticostriatal Activity........................... 106 5.6 Changes in caudate response due to learning...................................112 5.7 Simulated saccade preparation cell................................................114 5.8 Saccade preparation cell...................................................................... 117 5.9 Cue-guided memory saccade..............................................................118 6.1 Sequence Task and Connected Contexts........................................... 126 6.2 Schematic of Sequencing M odel........................................................127 6.3 Activity differences in Sequences RUL and R L U .......................... 129 6.4 Comparison of Simulated and Real Visual-Tonic Cells............... 133 6.5 Comparison of Simulated and Real Context Cells......................... 134 6.6 Comparison of Tonic and Phasic paradigms on PFC activity 137 6.7 PFC activity before each saccade..................................................... 138 7.1 Spatial Generalization Tasks..............................................................146 7.2 Spatial Gradient Implements Spatial Generalization........................146 7.3 Neural Implementation of Spatial Gradient................................... 147 List of Tables 3.1 Observed (OBS) and simulated (SIM) neural activities in saccade tasks............................................................... .....60 3.2 Simple Saccades................................................................................. 63 3.3 Memory saccades.................................................................................64 3.4 Lesion Effects..........................................................................................65 4.1 Comparison of Compensation Model Configurations....................... 89 4.2 Double saccades...................................................................................91 4.3 Compensatory saccades......................................................................... 92 4.4 Colliding Saccade.................................................................................. 93 4.5 Predictive Experiment...........................................................................94 6.1 Number and classification of prefrontal cortex cells..................... 135 7.1 Generalization on Stimuli for Structured and Unstructured Environments....................................................................144 8.1 Summary of HD saccade deficits..................................................... 156 8.2 Saccade metrics for normal and HD lesion m odels........................159 Abstract The real-time production of spatially accurate conditional behavior requires the nervous system to accommodate neural transmission delays and multiple coding frames for perception and action, and to adapt to changing environmental contingencies. The oculomotor system provides a rich domain in which to explore these and related nervous system functions. The philosophy employed is to develop neural network models whose architectures are based on known anatomy in order to explain and predict behavioral and electrophysiological results, and to provide a coherent computational framework in which to understand nervous system function. We present a new model for the spatiotemporal transformation required for the production of reflexive, high-velocity eye movements (saccades) to peripheral targets. We then build up a model of cortical and basal ganglia function in order to provide voluntary control of this reflexive system. A dual-mechanism theory for maintenance of spatial accuracy is introduced to provide a coherent explanation for a controversial body of experimental data. Voluntary control over saccade generation is further developed by the introduction of (cortico-striatal) synaptic plasticity. Via this mechanism, sensory cortical activity becomes causally associated with striatal activity that selects the correct saccade in a conditional learning paradigm. The ability to learn and reproduce sequences of saccades is provided by allowing the combination of current sensory input with efferent copies of previous saccades in cortex, providing the required temporal link between saccades in a sequence. The capability to generalize these spatial-cognitive functions is demonstrated, and a distinction between generalization on stimuli and responses is introduced, in order to compare different forms of generalization. An analysis of parameter sensitivity is performed in order to suggest two possible brain mechanisms responsible for dissociable saccade dysfunction in two age-onset groups of patients with Huntington's disease. Chapter 1 Introduction We consider the nervous system as an analog computational device that controls sensory, cognitive and motor functions. We are concerned with how the nervous system selects, encodes and executes orienting eye movements to fixed targets in space. The rich experimental history of investigation in the oculomotor system has yielded an extensive body of sometimes conflicting data which we characterize in terms of constraints on neural network models. Our goal is then to develop a coherent explanation that reconciles these constraints in the form of neural a network model that generates testable predictions._________________________________________________ 1.1 Motivation A famous artificial intelligence (AI) researcher once explained that the study of neurons was a waste of time in the pursuit of understanding intelligence, citing an apocryphal story about the failure of early aviation researchers who had decided to j study feathers. Yet the field of AI has largely failed to keep its early promise of I revealing and exploiting the basis of NI (natural intelligence). This thesis is based on the belief that intelligent behavior is a progressive development that has grown step by | I step from the most simple visually guided motor behaviors. Our study and modeling of the oculomotor system (OMS) allows us to retrace this progressive development, starting with a reflexive orienting mechanism, gradually introducing more voluntary control that culminates (in this thesis) with generalized conditional and sequential behavior. 13 While fairly simple when compared with the skeletomotor systems, the OMS must solve many of the same problems using similar organizing principles. Thus, some of the results that we develop here for the oculomotor system, including some theories about mechanisms for spatial accuracy should have application to better understanding of the skeletomotor system. In addition, a major underlying theme in this thesis is the functional anatomy of the cortico-basalganglio-thalamo-cortical circuits that are involved in voluntary behavior and in the inter-modal combination of information required for such behavior. Our modeling allows the investigation and prediction of intact function of this system in new experimental paradigms, as well as explanations for behavioral deficits seen in its aging-related disease. The oculomotor saccade system has been studied and modeled extensively at the level of the brainstem control of oculomotor neurons (e.g. Robinson 1975, Jurgens et al. 1981, Scudder 1988). At the same time, extensive anatom ical and electrophysiological investigations have been performed in many cortical and subcortical structures that act on the brainstem and participate in saccades. The list of such structures is now quite long, and includes posterior parietal cortex, the frontal eye fields (FEF), thalamic nuclei, the basal ganglia and superior colliculus (SC). These studies have produced an extensive body of data, and thus a corresponding challenge to develop a theory or theories to explain this data. The oculomotor system is interesting in and of itself but, in addition, it is a prototypical brain sub-system that provides insight into general theories of sensorimotor organization, and voluntary, cognitive sensorimotor function. Such a theory can be judged on two criteria - first, its ability to explain an extensive body of data based on a straightforward model, and second, its ability to make precise predictions that can be tested by future experiments. Towards this end, we have taken an incremental approach in the construction of a theory of spatial accuracy and j cognitive control of saccades, starting with a model of the spatiotemporal transformation, building finally to a mechanism for learning and reproducing sensorimotor sequences. At each step in the progressive development of this model, | we respect existing data, introducing minimal, realistic changes to the model in order to i account for experimental results. At the same time, the architectural features that ' account for existing data must also be verified by the validity of their predictions, and we suggest the corresponding experiments. 14 1.2 Overview of the Oculomotor System In order to appreciate the details of accurate eye movement, we look to the design of the oculomotor system. The primate retina provides the front end of the visual interface between the animal and the world. The functional organization of the retina reflects many of the information processing strategies that are employed in primate vision. Retinal ganglion cells are densely packed in the foveal region, and their density falls off exponentially with the distance from the fovea. The result of this organization is that the fovea has the highest acuity, which quickly drops off away from the fovea (Perry and Cowey 1985). There are two broad functional classes of ganglion cells which define two parallel visual systems. The magnocellular system is primarily concerned with object position and motion, while the parvocellular system is primarily concerned with object form and detailed. As part of the "what" system, the X cells have medium-sized bodies and small dendritic fields and participate in high acuity vision, including object recognition. These cells define the front end of the parvocellular system, which can be traced from retina, through the lateral geniculate nucleus (LGN), visual cortical area 1 (VI), V2, V3, V4 and finally to inferotemporal cortex (IT), an area known to be involved with object recognition (Anderson and Van Essen 1989, Kandel 1985). The "where" system is subserved by the type Y and W retinal ganglion cells. The type W cells have small cell bodies and project almost exclusively to the superior colliculus (SC), a subcortical structure that contains a map of ocular motor error, and is known to be a major player in the normal generation of saccades (Sparks 1986). As we will see later, it is likely that it is this direct path from retina to SC that subserves reflexive saccades. The type Y ganglion cells have large cell bodies (giving rise to the "magnocellular" pathway) and are thought to be involved in processing crude form, j location and movement information. The Y cells project to distinct portions of LGN j and from there to V I, V2, V3, the mediotemporal and medial superior temporal cortex I (MT and MST), posterior parietal cortex (PP) and to the frontal eye fields (FEF). About 80% of the cells in MT are sensitive to motion and selective for the direction of motion (Maunsell & Van Essen 1983), and the optimal visual stimuli for activating MT | cells are similar to the properties of visual motion that initiate pursuit. All of these cortical motion processing areas project to the pontine nuclei (Glickstein et al. 1980, L 15 Brodal 1978) which relay these signals to the areas of the cerebellum that are concerned with pursuit eye movement (Brodal 1979, Langer et al. 1985). Eye movements can be broadly classified by two related functions involving the "where" system directing the eyes so that the "what" system can do its job. The first function is to shift gaze to a new location, centering a peripheral target onto the fovea (saccadic eye movement). An extensive body of experimental, clinical and theoretical literature exists describing the behavior and neurobiology of saccades (see Leigh and Zee 1991). In its simplest form, a saccade is a reflexive shift of gaze, at velocities up to 1000°/sec, to a peripheral target. With increasing reliance on voluntary control, saccades can be made to the remembered location of a target that is no longer visible, and even to a sequence of targets that are remembered. We will see how this voluntary control comes from exerting cortical influence on the older subcortical superior colliculus (SC), via the basal ganglia. Of particular interest is the ability to maintain an accurate representation of a target's location in space, while representing targets in a motor error map. This is interesting because in order to remain accurate, the remembered motor error for a spatial target must necessarily change to reflect the updated motor error as the eyes move to another target. The second class of eye- movement function is to hold an image steady on the fovea. These movements typically compensate for head and body movements with respect to the target (vestibulo-ocular reflex), as well as for object movement with respect to the eyes (smooth pursuit). Whereas a saccade typically is generated to move the eyes to center a stationary peripheral target, smooth pursuit occurs in response to moving stimuli, and the resulting smooth movement keeps the fovea centered on the moving stimulus. Smooth and saccadic eye movements appear to be generated, at least in part, by separate neural systems, as indicated by their different latencies, and the different effects of cortical and cerebellar lesions (Lisberger et al, 1987). Pursuit movements generally have a shorter i latency than saccades, 130 vs. 200 ms. ! j Deno, Keller and Crandall (1989) describe three classes of existing pursuit models. | j The first class is a simple proportional error feedback servo that simply attempts to reduce the retinal slip velocity of the selected target image. This class of controller fails j to produce the steady-state tracking where eye and target velocity are equal. In the I second class of pursuit models, the efferent copy feedback model, a copy of the neural j command for desired eye velocity is passed through a central model of the plant dynamics to produce an internal copy of the eye velocity. This is combined with the retinal slip velocity to produce a replica of the target velocity (Robinson et al. 1986). The third class of models, exemplified by Lisberger et al. (1987) uses the retinal motion signal as input to a parallel network which produces weighted combinations of retinal position, velocity and acceleration errors, which are then combined and fed through a velocity memory integrator. Deno et al. (1989) determined that in the linear case, the second and third classes can be shown to be equivalent The vestibulo-ocular reflex (VOR) produces eye movements that compensate for head rotations to keep a stationary target stabilized on the retina while the head moves. Each of the three fluid filled canals of the vestibular organ detect angular acceleration in one of three quasi-orthogonal planes, and influence a pair of extraocular muscles that move the eyes in approximately the plane of the respective canal (see Leigh and Zee 1991 p. 33) A three neuron arc has been studied that includes the vestibular ganglion, the vestibular nuclei and the oculomotor nuclei. Anastasio (1991) notes that in the mammal, the time course of the horizontal VOR is longer than the that of the vestibular canal signals that drive it, thus revealing the presence of a mechanism for velocity storage. While we are not addressing the VOR in this work, the concept of velocity storage will be re-appearing in a mechanism for spatial accuracy. 1.3 Modeling Methodology A major thesis of the models we present is that a functional topography of saccade direction and amplitude is maintained through multiple projections between brain regions until it is finally transformed into a temporal pattern of activity that drives and holds the eyes on the target. The preserved topography is a map coding for amplitude and direction of an eye movement vector that, when combined with the current eye location, will center the eye on the saccade target. The models are implemented in the Neural Simulation Language NSL (Weitzenfeld 1990) on a Sun 3/260. The major neural elements are 2-dimensional neural surfaces, representing cortical and subcortical oculomotor structures. We refer to these neural surfaces as layers. We can think of 17 these layers as representing the corresponding brain region with the topographic mapping of the region flattened into a plane. The individual units that make up these layers interact via their "firing rates," while the firing rate of a cell depends only on its own membrane potential. Computer simulation cycles through two steps: Step 1. Updating the Membrane Potentials: The membrane potential of each cell is described by a differential equation of the form Xjji \F(dm (t),dt) = -m (t) + Sm(t). Here the subscript m indicates the specific cell type, while m(t) denotes the membrane potential of that cell at time t. xm is the time constant for the rate of change of this potential. Sm(t) represents the total input that the cell of type m receives from other cells. Our computer simulations use the Euler method, the simplest approach to solving differential equations. We choose a small time step At (5 milliseconds) and approximate dm(t)/dt by the ratio (m(t+At) - m(t))/At to obtain the difference equation m(t+At) = 1 - — m(t) + — Sm (t) In what follows, we simply specify the membrane time constant, and the input Sm for each layer m of cells of interest to us. Step 2. Updating the Firing Rates: Rather than model spike generation, we use a coarse approximation: instantaneous average firing rate. The firing rates are determined by a function of the membrane potential, e.g. M = sigmoid(m, minjnput, max_input, min_output, max_output) where M is the firing rate, m is the membrane potential, and for min_input<m< max_input, the firing rate is a sigmoid (non-linear) function of m. For m<min_input or m>max_input, the firing rate is min_output or max_output respectively. In addition to the sigmoid function, we also use step, ramp, and saturation functions. M = step(m, low_input, low_output, high_output). 1 M = ramp(m/ low_input, low_output, high_output). M = saturation(m, minjnput, maxjnput, min_output, max_output) i For step, if m < low_input, M = min_output; else M = high_output. For ramp, if m < low_input, M = low_output; else M = max(m, high_output). Saturation operates 18 as sigmoid, but with a linear rather than sigmoid relation for m and M when min_input<m<max_input. Connections between these two dimensional arrays of neurons are defined in terms of interconnections masks which describe the synaptic weights, and are applied via a spatial convolution. Consider the following equation where A,B and C are layers of neurons and M l is a 3x3 connection mask: Ta = 10 ms Sa = C + B*M1 A = sigmoid(a,100,500,0, 500) (0) This states (a) that the membrane time constant for A, - ta, is 10 milliseconds, (b) that for each cell i,j in layer "a" the input to the membrane potential, Sa, is the sum of the firing rate of the i,jth cell in C, plus the sum of the firing rates of the 9 cells in B centered at i,j times their corresponding weights in M l. SA(id) = C(i,j) + \i\su(k;1 = .!,!,) M l (k,l)B(i+k,j+l) That is, the * operator in ”B*M1" indicates that mask M l is spatially convolved with B. Note that if M l were just a scalar value then "B*M1" would simply be a layer in which each member of B is multiplied by the constant value of M l. Finally, the resulting firing rate is a sigmoid function of the membrane potential, where 100<m<500 is mapped into 0<M<500; m < 100 produce M =0, and m > 500 produce M = 500. i f 1.4 Organization of the Thesis and Summary of Contributions In Chapters 2 and 3 we lay the foundation for the rest of the thesis by constructing a model of saccade generation that includes both the brainstem oculomotor system, and the cortio-subcortical circuits that provide voluntary control over this system. In I i j Chapter 2 we present a new variation of the intemal-feedback model of the brainstem j saccade generator for the spatiotemporal transformation required for the production of reflexive, high-velocity eye movements (saccades) to peripheral targets. This model addresses the emerging view that saccade amplitude and velocity are coded respectively by location and firing rate of activity on saccade motor-maps. We then build, in Chapter 3, a model of cortical and basal ganglia function in order to provide voluntary control of this reflexive system. For the first time, the interactions of cortex, basal ganglia and thalamus and colliculus are integrated in a computer model to explain a variety of anatomical, electrophysiological and behavioral data. In Chapter 4, a dual mechanism theory for maintenance of spatial accuracy is introduced to provide a coherent explanation for a controversial body of experimental data. For the first time, an extensive and controversial body of data related to double (e.g. Mays and Sparks 1980, Goldberg et al. 1990, Dassonville et al. 1992) and colliding saccades (Schlag and Schlag-Rey 1990) is addressed in a single, coherent fashion. Voluntary control over saccade generation is further developed in Chapter 5 by the introduction of (cortico-striatal) synaptic plasticity. Via this mechanism, sensory cortical activity becomes causally associated with striatal activity that selects the correct saccade in a conditional learning paradigm. While the computational mechanism used is a straightforward associative memory, it is implemented in the context of known neurophysiological details, and offers specific predictions and novel interpretations of existing data. The capability to learn and reproduce sequences of saccades is developed in Chapter 6, by allowing the combination of current sensory input with efferent copies of previous saccades in cortex, providing the required temporal link between saccades in a sequence. The capability to generalize these spatial-cognitive functions is demonstrated in Chapter 7, and a distinction between generalization on stimuli and responses is introduced, in order to compare different forms of generalization. In Chapter 8, an analysis of parameter sensitivity is performed in order to suggest two possible brain mechanism responsible for dissociable saccade dysfunction in two age- onset groups of patients with Huntington's disease. In Chapter 9, we summarize the thesis, and suggest future research that will test and advance these principles. Chapter 2 Spatiotemporal Transformation in the Brainstem Saccade Generator In order to produce changes in extraocular muscle activation required to fixate a peripheral target, the nervous system must transform the target specification from a 2- dimensional spatial code of retinal- or motor-error into a temporal code of muscle activation. For primate saccade generation, this spatiotemporal transformation occurs in part in the brainstem reticular formation. Here we review neurophysiological data that provides insight into the precise mechanisms supporting this function. We consider existing models of the brainstem saccade generator and present a variant of the Scudder model in which saccade amplitude is coded by the location of activation on a motor error map, and saccade velocity by its firing rate.___________________________ 2.1 Introduction I The essential function of a saccade is to bring a target projected on the peripheral retina into the foveal region of the retina. The fovea-to-target "vector" specifies a displacement that, when added to the current eye position will yield the desired final position. During a saccade, oculomotor neurons change their firing rate to produce a change j in eye position, and then assume a steady firing rate producing muscle activation ! appropriate for holding the eye in its new posture (Robinson 1970). For almost 20 | years a debate has continued concerning the neural implementation of this or an j 21 equivalent function. One of the original points of discussion involved the question - is the control of saccades open-loop or closed-loop? An open loop system produces a preprogrammed response and does not monitor the execution of the program in order to adjust its execution (Fig 2.1 A). Mounting evidence concerning the on-line modification of saccades has lead to a general acceptance that the system is closed-loop, but another question remains open concerning whether the feedback loop operates in terms of eye displacement or eye position. A final point involves the role of the superior colliculus and its position inside or outside the loop. 2.2 Neurophysiology and Models We first consider how eye position and velocity are controlled by oculomotor neurons in saccade generation. During a saccade, oculomotor neuron (OMN) firing follows a stereotyped pulse/step activity profile: the eye velocity is coded by a rapid, brief increase in firing rate (the pulse), and the new eye position is coded by the steady level of firing (the step) (Robinson 1970). Clearly, the OMN firing rate is in a coordinate system related to muscle activation and thus, eye position and its derivatives. Any model of saccade generation must explicitly state at what point retinal-position signals are transformed into eye position signals. In 1975, Robinson proposed an "internal feedback" model of the saccade generator based on neuroanatomy, neurophysiology and control theory (Fig. 2.IB). In this model the target in space impinges on the retina as a function of the eye position (visual feedback), yielding a retinal error. The target's spatial location is then reconstructed by i combining the retinal error with an efference copy eye position (efference copy). Local | feedback (eye position) then controls pulse generation by continuously comparing the desired target goal with the current efference copy eye position, yielding a "motor error" pulse or burst, which produces the saccade velocity. The saccade burst is integrated (NI) to produce the eye position efferent that when compared with the desired eye position forms the local feedback loop. When these efferent and desired eye position signals are equal, the saccade is terminated. ! ! 22 | A Target £ ^ Retina Visual feedback Pulse Program ■ T O — OMN PL Eye Position Visual feedback Efference copy Local feedback (eve position! Target + Stei OMN PL Pulse Generator Eye Position Target Position Reconstruction Retina Pulse c Visual feedback Local feedback (eye displacement) Target + Eye Position Motor Error Retina OMN PL IM Pulse Generator Pulse D Visual feedback Target Local feedback (IFN) Pulse OMN PL IM (LLBN) Eye Position Pulse Figure 2.1 Classes of Saccade Generator Models. A. Open Loop: For a given retinal error, a preprogrammed pulse is produced. B. Robinson's Local Feedback Model. C. Jurgens' et al. Model. D. Scudder Model. OMN - oculomotor neuron; PL - plant; NI - neural integrator; IM - integrator model; TN - tonic neuron; EBN - excitatory burst neuron; LLBN - long lead burst neuron; See text for details. 23 The concept of saccade control via internal feedback was a conceptual success, that was verified experimentally. In purely feedforward mechanism, a saccade program would be selected and executed in a ballistic fashion. If the program's normal execution were modified, i.e. if the velocity were reduced, then appropriate errors would be seen in the resulting saccade. Jurgens et al. (1981) observed that under normal conditions, saccade duration and velocity could vary by up to 60% while saccade amplitude remained accurate to 90%. Additional changes in duration and velocity could be induced pharmacologically, again leaving accuracy almost intact. They argued, in the spirit of Robinson, that this data favors a local feedback mechanism. The question remained, however, does the feedback operate in retinal or spatial error coordinates? While Robinson (1975) called for a specification of saccades in terms of final position, a major input to the brainstem saccade generator, the subcortical SC was shown to code saccade metrics in terms of displacement or change in position rather than final position (Robinson 1972, Sparks and Mays 1980). Jurgens et al. (1981) proposed a model in which the saccade is specified in terms of retinal error rather than spatial location, eliminating the need for reconstruction of the target location in space. This simplification, however, required the introduction of a resettable model of the neural integrator (IM) that represents just the displacement due to the ongoing saccade, rather than the actual eye position (Fig 2.1C). The output of IM is compared with the retinal error to specify the motor error. IM is suggested to have a smaller time constant than the neural integrator that feeds the oculomotor neurons. This allows an explanation of their observation that slower saccades were slightly longer than faster saccades. They also suggested that operating in retinal error removes the extra computation of "internal reconstruction" of the target's location in space, and is thus inherently more accurate than a head centered system. This model is more compatible with the knowledge that microstimulation of brainstem input areas FEF (Bruce and Goldberg 1984) and SC (Robinson 1972) produce fixed vector, rather than goal directed movements, implying that at this level, the OMS operates in terms of displacements rather than final positions. However, coding in displacement rather than position does require the introduction of a resettable ! integrator that accurately models the change in eye position generated by the neural pulse. Thus, it must model not only the neural integrator, but the whole chain of elements downstream, including the mechanics of the plant. The gain of the integrator could be modified according to the position of the eye in the orbit, in order to account 24 for the position dependent relation between oculomotor activation and displacement. This gain control may operate via the cerebellum, as lesions of the vermis produce large difference between the amplitudes of centripetal and centrifugal saccades (Ritchie 1976). Both the target position signal required by Robinson's model, and the resettable integrator required by Jurgens et al. (1981) have yet to be clearly demonstrated. Addressing these issues, Scudder (1988) uses SC input to specify the saccade size and direction, similar to the approach of Jurgens et al. Instead of a separate resettable integrator, however, Scudder has the LLBNs take over the function of the explicit resettable integrator. In this model (Fig 2. ID), the LLBNs code a form of motor error, with their firing rate computed as the temporal integral of the difference between excitatory SC inputs, and inhibitory velocity feedback from IFNs which represent the internal feedback loop. When these integrated signals cancel, the LLBN output ceases, and the saccade is terminated. In order to perform the spatio-temporal transformation, Scudder suggests that collicular inputs to LLBNs are spatially weighted such that collicular regions representing larger saccades will have stronger projections to LLBNs. He also suggests that FEF and SC inputs can be combined in such a model as inputs to the saccade generator. 2.3 An Updated Model As Scudder himself points out, all models of the saccade system have their own strong and weak points. Scudder’ s model accounts for a variety of electrophysiological and anatomical data, however there is one weakness upon which we now focus. In j Scudder's saccade generator model, the SC and FEF inputs represent a hybrid of : spatial and temporal coding, since the number of FEF and SC spikes (the integrated { input waveform) precisely specifies the saccade amplitude. If this is the case, then by varying the duration or frequency of bursting activity at a given SC site, saccades of arbitrary amplitude could be produced. However, in driving saccades by collicular ! stimulation, Robinson (1972) found that stimulation of a deep SC site evokes a saccade ! _____________________________________________ 2 5 j of fixed amplitude and direction whose amplitude does not vary with frequency, strength (above saccade threshold) nor with duration of the stimulation, for durations from slightly over 25 ms to slightly under 135 ms. "Above threshold, a conjugate saccade was evoked of a fixed amplitude and direction which depended almost not at all on stimulus parameters. Specifically, neither the size or the direction of the movement could be changed by further increasing stimulus intensity, or changing pulse width, rate or train length" (Robinson 1972 p. 1797). This argues strongly that the saccade amplitude is not coded by the sum of collicular spikes. Thus, contrary to Scudder's scheme, it is the location of activity in SC, not the number of SC spikes, that specifies saccade amplitude and direction. Whereas for Scudder the eccentricity weighted number of SC spikes determines the amplitude, we believe the topographic location of SC and FEF activity, as expressed in the eccentricity-dependent projection strength of FEF and SC onto LLBNs, determines the amplitude and direction of the saccade, independent o f the number or rate o f spikes. The combined eccentricity-weighted discharge rate of the cortical and collicular inputs along these projections determines the velocity of the saccade, and hence its duration. That is, the velocity and amplitude are specified independently by the firing rate and map location of SC/FEF activity, respectively. Along these lines, Sparks and Mays (1990) note a correlation between saccade velocity and collicular burst rate, in agreement with the idea that saccade size and direction is coded by collicular location, and velocity is coded by collicular firing rate. A similar conclusion can be drawn from a study by Choongkil, Roher and Sparks (1988) in which saccade amplitude is left intact, while the velocity is reduced and duration increased following a reversible pharmacological inactivation of a subpopulation of SC cells for saccades similar to those produced by stimulation at the injection site. We simulate this reduction in activity of an SC population by reducing output threshold of SC at the corresponding site. Thus, the map location is still correct, with a reduced firing rate, producing accurate but slower saccades. Jurgens et al. (1981) argue that variations in saccade velocity may be due to changes in the pulse generator. It also appears that changes well j j upstream from the pulse generator, i.e. in the SC can effect saccade velocity while J leaving the amplitude unchanged. I i In our modification of Scudder's model, we retain his assumption that more i i ! eccentric SC and FEF loci have stronger projections to LLBNs (Edwards and Henkel j 26 I 1978). Our SG circuits include excitatory burst neurons (EBNs), tonic position related neurons (TNs), medium and long lead burster neurons (MLBNs, and LLBNs) (Fig. 2.2). The saccade generator and oculomotor plant are driven by input from FEF and SC. Because SC, FEF and LLBN can fire at subthreshold rates without eliciting an eye movement, our EBNs require MLBN - which receives LLBN input - to reach a threshold before they begin to burst. The EBN firing rate is a non-linear function of MLBN firing rate, thus allowing FEF and SC firing rate to specify saccade velocity. The pause neuron (OPN) responds to a two phase triggering. The initial SC/FEF burst turns the pause neuron off, then the velocity-independent code for saccade amplitude is maintained in the A neuron. During the course of the saccade, the resettable integrator, RI, accumulates the EBN output. When this becomes equal to A, the saccade is complete; the OPN neuron is reactivated, resetting A and RI and inhibiting EBN (see simulation in Fig. 2.3). Visual feedback trigger amplitude Local feedback (eye displacement) Retina FEF, LLBN, SC MLBN T • L Step Pulse NI, OMN Generator, (TN) PL (EBN) _ J Pulse Eye Position Figure 2.2 Independent Velocity and Amplitude Model. Retinal Input: The external visual world, analogous to the viewing screen in front of the monkey, is represented in the simulation by a 27x27 array, Vislnput. The retina is | a 9x9 array, RETINA. In each iteration of the simulation, the function Eyemove j extracts RETINA as the sub-array of Vislnput centered on the values of 0 r and 0 y (horizontal and vertical components of eye position). We also implement an inhibition of retinal input so that when the eye velocity is over 200°/sec, retinal output is gated J off. The notation in the following equations was described in section 1.3 of Chapter 1. 27 xretina = 6 ms ^retina = Eyemove(VisInput, O r, 0y) A SACCADEMASK RETINA = retina (la ) The small time constant for retina allows for perception of short-duration targets. The delays associated with retinal and visual system processing are described in Eqn 2 (Chapter 3, and Appendix A l). To generate the retinal input, eye position is combined with the visual input to yield the retinal error, where Eyemove (Vislnput, a, b)(i,j) = Vislnput(a+i,b+j) for -4 < i,j < 4. Thus, the 9x9 sector of Vislnput centered at eye position ( 0 r , 0 u ) is projected onto the retina. SACCADEMASK is a 9x9 mask whose elements are 1 when the eye velocity is less than 200°/sec, and 0 otherwise; and the point-wise multiplication operator "A " acts componentwise, (A A B)(i,j) = (A(i,j)* B (iJ» . O culom otoneuron behavior: During a saccade, firing follows a pulse/step activity profile: the eye velocity is coded by a rapid, brief increase in firing rate of EBNs (the pulse) and the new position is coded by the level of firing (the step) of TNs, which are hypothesized to integrate the bursts to code for eye position. Robinson (1970) determined that in rhesus monkey, the firing rate of individual oculomotor neurons in abducens nucleus depends linearly on both eye position and eye velocity. In the model, we provide four (left, right, up, down) oculomotor units with motoneuron discharge rate MN = k0 + r0+c (2a) where 0 is the eye displacement in degrees from the "dead ahead" position, 0 is the eye velocity, and k, r and c are constants that vary for individual neurons.1 From Robinson (1970) we chose typical values of k as 2.75, r as 0.90, c as 154, and -56° as the eye position at which the cell begins to respond, for each of our four oculomotor units. Each of these neurons is responsive to displacements ranging from 1 approximately -56° to +56° in the left, right, up and down directions respectively. Eqn. 1 Moving the eyes an equal displacement to increasingly eccentric positions requires non-linearly increasing increments of muscle innervation. However, at the single motoneuron level, the j linear relation between position and firing rate holds. The nonlinear relationship appears to be j implemented by the recruitment of successively more motoneurons for increasingly eccentric positions (Sparks and Mays, 1990). 28 2a provides the basis for describing position-velocity relations in eqns. 9a and 10a; motoneuron activity in eqn. 1 la; and eye position in eqn. 12a. In order to achieve the characteristically high saccade velocities, approaching 1000°/second (Robinson 1970), primate oculomotor neurons generate saccadic bursts with peak rates in excess of 800/sec. (Fuchs, Kaneko and Scudder 1985). In our simulations, maximum EBN firing rates are just in excess of 900/sec, yielding maximum velocities of approximately 900° /sec. Fig. 2.2, the saccade burst generator, represents only one of four similar elements that generates motoneuron activity. We provide the equations below for the horizontal right case. Thus in the actual NSL code, each of LLBN, MLBN, EBN, OPN, TRIG, RI, A, TN, MN, and 0 will appear 4 times, once each with subscripts or prefixes L, R, D and U for left, right, up and down respectively. In p u t to the Saccade B urst G enerator; In this model, we provide input to SG in the form of topographic maps SC and FEFsac, corresponding to the brainstem- projecting cells of superior colliculus and frontal eye fields, respectively (the biology and modeling of these are described in the Chapter 3). Mcllwain (1982) reported that saccades resulting from focal stimulation in the intermediate gray layer of the SC (admittedly in the cat) are preceded by a lateral spread of discharge throughout a significant portion of that lamina, leading to his suggestion that populations of SC movement cells contribute to the final saccade metrics via their projections to this pulse generation center. We thus follow Scudder's (1988) proposal that the weighting of each collicular neuron's projection to the horizontal burst generator is proportional to the horizontal distance from the fovea to the center of the collicular neuron's movement field. In our model, each SC and FEF unit represents a population of cells, and the eccentricity-weighted projections to brainstem specify the saccade amplitude and direction, while the eccentricity-weighted firing rate along that projection specifies the saccade velocity (see eqns. 3a, 4a, 5a). Lesion studies (Sparks 1986 [review],Schiller and Sandell 1983, Keating and ! Gooley 1988) show that superior colliculus is not essential for saccades. Ablation of SC increases latency up to 200 ms, accuracy is reduced due to reduced amplitude, and fewer saccades are made to distracting stimuli (simulations provided in Chapter 3). This suggests a complementary non-collicular pathway for saccades. The one that we study is from FEF to brainstem eye movement areas. The brainstem's saccade 29 generator located in the paramedian-pontine reticular formation (PPRF) receives a projection from FEF, independent of the superior colliculus (Bruce and Goldberg 1984). This direct path may allow cortical control to generate strategic saccades, bypassing the direct influences of the sensory modalities that converge on the SC. FEF and SC may cooperate in specification of a saccade via projections to brainstem long lead burst neurons (LLBNs). When one of these areas is silenced, the strength of the saccade specification is correspondingly weakened, leading to a delay in the LLBNs’ reaching the threshold required to initiate the saccadic excitatory burst neuron (EBN) bursts. Spatio-Temporal Transformation: In the Scudder model (1988), activity at a given location in SC can generate saccades of arbitrary size. Collicular stimulation studies indicate that this is not the case (see Robinson 1972). Thus, we modify the Scudder model so that eccentric location of collicular/FEF input (above threshold) alone determines the saccade amplitude, and the firing rate of collicular and FEF cells determines saccade velocity. Like the Scudder model we show an increase in saccade velocity with saccade amplitude, but because we use non-linear thresholding elements, we avoid Scudder’ s problem of excessive velocity for large saccades. Long- and M edium Lead B urst neurons: LLBNs of the PPRF are innervated by both the FEF and SC, and form a motor map of saccade vectors (Hepp and Henn 1983). Moving from rostral to caudal in the PPRF there is transition from spatial to temporal coding of saccade metrics (Hepp and Henn 1983). In our model, spatially coded LLBN activity leads to activation of medium lead burst neurons (MLBN) that combine spatial and temporal code as a function of saccade amplitude. The time j constants for LLBN and MLBN produce a gradual increase and "long lead" presaccadic j j activity in LLBNs, and a shorter lead in MLBNs (Hepp and Henn 1983.) For normal j visual or memory guided saccades (see Chapter 3), FEF and SC will be in agreement. As we will see in Chapter 4, however, in cases where the inputs are not in agreement, the stronger of two conflicting inputs will dominate and gain control of the subsequent saccade (e.g. FEF and SC collisions, Ch. 4.) We capture this behavior with a 30 WinnerTakeAll strategy (Didday and Arbib 1975; Koch and Ullraan 1985) for selection of the strongest saccade input from multiple sources, like the winner-take-all competition modeled for frog tectum by Didday (1970, 1976). In our model, WinnterTakeAll selects the strongest input - corresponding to a population of activity - and suppresses the weaker inputs. % bn = 4° m s s Ubn = WinnerTakeAll(2.67*SC + 5.4*FEFsac)2 LLBN = sigmoid(llbn, 0,950, 0,950) (3a) xmlbn = 8m s Smlbn = LLBN*Kstt MLBN = sigmoid(mlbn, 0,1500,0,950) (4a) The components to the right of center in LLBN contribute to the MLBN map, proportional to their distance from the fovea, implementing the concept that more peripheral target inputs will have a greater influence in the brainstem. This is achieved by multiplying the input with a 9x9 "right" mask Kstt. In this mask, only components to the right of center are non-zero, and they increase in value as the distance from center increases. Formally, for j = -4 to 4: for i = 1 Kstt(i,j) = 1.425, for i = 2 Kstt(i,j) = 2.85, for i = 3 Kstt(i j) = 4.265, for i = 4 Kstt(i,j) = 5.7. Similar considerations apply for left, up and down directions. By this method we ensure that the left, right, up and down MLBNs are influenced by the eccentricity weighted input only from the appropriate neurons in left, right, up and down FEF and SC, respectively. The amplitude of these inputs to MLBNs - and hence the saccade velocity input to the EBNs - is directly related to the firing rate of the inputs from FEF and SC, and their topographic location via Kstt. For large saccades with FEF and SC intact the weighted inputs to LLBN would exceed 950, so we make the upper limit on the sigmoid output 2 The max FEF output is 90 spikes/sec, and SC is 500 spikes/sec. The numbers 2.67 and 5.4 were determined under the FEF and SC lesion studies to be the minimum for each of these two areas to elicit any movement in the absence of the other area. 31 function equal to 950 which corresponds to maximal LLBN rates. This threshold contributes to the increase in saccade duration as amplitude increases (Fuchs 1967). The pure amplitude information, independent of velocity; is specified by the movement fields of the active MLBNs. In order to extract this code in the model, "A" neurons receive the spatially coded MLBN input (via the step function) and use the mask Kstt to translate the spatial code (that has velocity information removed by the step function) into a temporal one. Taking the maximum value from the resulting 2 dimensional layer as a scalar value produces a temporal coded specification of saccade amplitude, independent of velocity. The OPN influence resets this value when the saccade is completed. ^ = 6018 s 8 = step(MLBN, 120, 0, 120)*Kgtt A = max(8) - 3*OPN (5a) Hepp and Henn (1983) describe "direction burster (D-burster)" neurons whose integrated firing rate is tightly coupled with saccade amplitude in the cell's preferred direction, and is fairly independent of saccade velocity. Two such populations in left and right PPRF would cover the full horizontal saccade range. Our A neurons provide a similar specification of saccade amplitude, independent of velocity. Four A neurons would then represent a minimal set of D-bursters for spanning the positive and negative horizontal and vertical directions. When the value of the resettable integrator RI is equal to A then the saccade is complete (see eqn. 7a). Excitatory burst neurons: T ebn = 6 ms s ebn = MatrixToScalar (MLBN) - k*OPN j EBN = ramp(ebn, 120,0,120) (6a) The MLBN activity at the locus transmitted from LLNB is transformed to a scalar value 1 by the function MatrixToScalar. The constant k = .5 sets the threshold for the pause neurons to shut down the EBNs even when MLBNs maintain a residual activity. We 32 use the ramp output function so that these bursting EBNs do not fire unless their input is > 120, at which point they fire also at 120 and increase with the input Pause neurons: xopn = 6 ms sopn = - kl* RI + A + 0.5TRIG OPN = step(opn; k2,300,0) (7a) When opn < k2, OPN is 300, and once opn >= k2, OPN = 0. The initial input from TRIG turns OPN off, then A is set to specify the saccade amplitude, and opn continues to be > k2 until the -kl*RI term cancels A. In the current simulations, k l = 1.1, and k2 = 8. These parameters were chosen to produce small saccade undershoots, and can be manipulated to tune the accuracy of saccades. Here, TRIG is innervated by superior colliculus and FEF neurons that code for a rightward saccade component. xtrig= 6 ms S trig = (FEFsac + SC)*Kstt TRIG = max(trig) (8a) where the function max() takes the maximum value in the 2-d layer trig, and returns a scalar value in TRIG. Resettable integrator: These neurons integrate the corresponding burst neuron's output, computing the current saccade amplitude, and are reset to 0 when the pause neuron resumes firing. The constant k = 0.031 used to integrate the EBN velocity signal into a displacement signal was determined based on the simulation time constant (5 ms), and the relation of EBN firing rate to velocity as described in Eqn 2a. The ramp function here simply ensures that for ri<0, RI = 0, else RI = ri. s ri = RI + k*EBN - OPN RI =ramp(ri, 0, 0, 0) (9 a) I I Tonic neurons: The tonic neuron is a non-resettable integrator, and continuously describes the current position of the eye in its orbit. The push-pull organization of TN activity is captured by the -LEBN term, so that leftward eye movements will lead to a decrease in activity for this TN for the rightward component. Again, based on Eqn 2a, | k = 0.015, and the initial value of TN is 154. 33 s tn = TN + k*(REBN - LEBN)3 TN = tn (10a) Motoneurons and displacement o f the eye: The motoneuron is driven by the sum of the burst and tonic outputs, yielding the pulse/step activity of the saccade, xmn=6ms V i = EBN + TN MN = mn (11a) To produce the eye position, we recall that the tonic neurons integrates the velocity component of the burst neuron, and so codes for eye position, with the constants reconstructed from Eqn 2a. Figure 2.3 displays the activity the major components of the saccade generator during execution of a saccade. % = 0.364* RTN -56. (12a) 2.4 Superior Colliculus as a Spatial Integrator It is not clear whether a) the initial SC input to the brainstem completely specifies the saccade or b) the SC continuously specifies the ongoing motor error as suggested by Waitzman et al. (1988) and Pelisson et al. (1991). Waitzman et al. (1988) observed a qualitative correlation between the spike density of intermediate SC cells and the motor error during a saccade, suggesting that SC codes ongoing motor error, rather than the change in position for the complete saccade. The results of Pelisson (et al. 1991, Munoz et al. 1991) in cat indicate that during a saccade collicular activity shifts continuously from the initial caudal representation of the desired eye displacement rostrally to the fixation related cells in the rostral pole of the colliculus. This suggests that during a gaze shift, in cat, the SC is continuously specifying motor error. 3 We do not model the inhibitory burst neurons directly, assuming instead that, e.g., RIBN = LEBN. 34 Brains temActivity Brainstem LongLead MediumLead Bursters Pause Delta Resettablelnt MotorNeuron Figure 2.3 Brainstem Saccade Generator Simulation. Activity for LLBN, MLBN, EBN, Pause (OPN), Delta (A), Resettablelnt (RI) and Motomeuron (MN) for a rightward saccade. Note how RI builds up, and OPN resumes once j RI and Delta cancel. Also see that there remains a small activation in LLBN after the saccade. Triggering another saccade at this time would produce some residual effect, as described by Sparks and Mays (1983). | In this sense, the SC would act as a neural integrator, but operating in a spatial rather than temporal domain. When the spatial (rather than temporal) error is reduced to zero - i.e. activity shifts to the fixation zone, the saccade is terminated. This eliminates the need for the resettable integrator of Jurgens' et al. (1981) and related models, including our own. On the other hand, this explanation would indicate that in the absence of SC, saccade termination and thus accuracy would be severely impaired, 35 which is not the case (Schiller et al. 1987). If FEF is expected to take over the role of spatial integrator in the absence of SC, we now have problems of a very long control loop and the associated delays that would lead to greater inaccuracies. In fact, it appears that the activity of FEF neurons specifies the amplitude and direction for an impending saccade, and the time to initiate the saccade, but not to the dynamic aspects of the saccade during its execution (Segraves and Park 1993). In discussing the problem of how accurate saccades are made following SC lesions, these authors consider that the dynamic signal in SC may not be necessary, and may be the result of a corollary discharge generated by SC. In Chapter 4 we will consider a related explanation - that the dynamic signal may be generated in parietal cortex and transmitted from there to both FEF and SC, producing the shifting effect both in FEF (Goldberg et al. 1990), and SC (Pelisson et al. 1991, Munoz et al. 1991). This shift, in our model, is used for keeping track of the second target in double saccades, but not for the dynamic aspects of an ongoing saccade. Control of gaze typically involves both eye and head movement. The caudal to rostral shift in collicular activity has only been observed in the colliculus of cats during head free gaze shifts. To date, a shifting of activity specifically in the presaccadic brainstem-projecting cells of primate SC in the head-fixed saccade paradigm has not been reported. The segregation of collicular control of head and eye movement commands in primate may be such that the specification of saccade error is encoded and commanded in the initial collicular burst, while the ongoing trajectory of gaze error is specified in the shift of activity from caudal to rostral SC. In addition, a potential explanation due to species differences in the neural architecture of these two animals could derive from the greater ocular range in primates and the greater neck flexibility in cat. 36 Chapter 3 A Model of Cortieo-Subcortical Function in Voluntary Saccade Generation In the previous chapter we specified a model that transforms saccade targets in a 2- dimensional motor map into the appropriate commands to produce a saccade. Here, we provide the upstream control structures that implement voluntary control over saccade generation. An important aspect of voluntary oculomotor control is the capability not to orient, that is to inhibit saccades to distracting targets. A second control function is the ability to remember target locations for subsequent saccade generation. We develop here the coordination of cortex, basal ganglia and thalamus in providing these voluntary functions, and lay the foundation for the subsequent chapters.______________________ 3.1 Introduction In this chapter we consider saccade experiments in which the monkey is seated in a primate chair with its head fixed and eyes free to move. Illuminated fixation points and saccade targets are presented on a visual screen in front of the primate (see Fig. 3.1). Microelectrodes record (and stimulate) neural activity during the tasks, while eye movements are concurrently monitored and recorded. Our modeling is based on an effort to identify relevant constraints from anatomy, electrophysiology and lesion studies within the context of primate oculomotor behavior, and then to implement these constraints in a computer model and simulation. We model the control of voluntary saccades to visual and remembered targets in terms of interactions between posterior parietal cortex (PP), frontal eye fields (FEF), the basal ganglia (caudate and substantia 37 nigra), superior colliculus (SC), mediodorsal thalamus, and the saccade generator of the brainstem. Interactions include the modulation of eye movement motor error maps by topographic inhibitory projections; and sustained neural activity that embodies spatial memory. Models of these mechanisms implemented in NSL (our Neural Simulation Language described in Chapter 1) simulate behavior and neural activity described in the literature, and suggest new experiments. The model was initially developed to address the work of Hikosaka (1989, Hikosaka and Wurtz 1983, Hikosaka et al., 1990) on the role of the basal ganglia in the disinhibition of SC and thalamus (Ilinsky et al. 1985) for saccades and spatial memory (Fuster and Alexander 1973, Goldman-Rakic 1987) respectively. We use the variation of Scudder's saccade generator (1988) model described in Chapter 2. It receives input from FEF and SC and generates eye movements as a function of activity in tonic position cells and excitatory burst neurons (Robinson 1970). The results from anatomical studies and single unit recordings made during saccadic eye movement tasks provide insight into at least two major elements of brain function: 1) Topographic relations between sensory and motor areas, including the inhibitory projections that manage motor field activities during the implementation of saccades; 2) the cortical and sub-cortical activity that sustains spatial memory during delay saccades. We study the functional neuroanatomy that implements these capabilities, and offer a corresponding simulation that generates neural and behavioral performance as seen in primates as they perform saccades to visual and remembered targets, as described in the following paragraphs. 1. Simple saccade (Hikosaka and W urtz 1983a): In the sim ple saccade task, the monkey fixates a spot of light (fixation point) which later disappears as another spot of light (target point) appears in another location. The monkey is rewarded for making a saccade to the new target at its onset. A time trace of the fixation point, the target, and the horizontal and vertical components of the saccade are illustrated in Fig. 3.1 A. 38 2. M em ory saccade (Hikosaka and Wurtz 1983c): In the m em ory saccade task, during the display of the fixation point, a peripheral saccade target point is briefly illuminated. The monkey is trained to make a saccade to the location of the previously flashed target following the removal of the fixation point, as illustrated in Fig. 3.IB, thus showing that it has remembered the location of this target during the period between the removal of the target and the removal of the fixation point. A. Simple Saccade B. Memory Saccade o o Target Target O O Fixation Fixation point point Fixation point Target Horizontal eye move Vertical eye move 1 I ______ I :zi / ------- / -------- — > - time Fixation point Target Horizontal eye move Vertical eye move I ' I _____ _ n ________ r ~ i — — > - time Figure 3.1 Saccade task protocols. Time runs from left to right. Traces indicate time course of presentation of fixation point, target(s), and eye movements. 3. Lesion Studies (Schiller and Sandell 1983; Keating and Goo ley 1988): In these studies, the respective roles of FEF and SC are studied by combinations of cooling and ablation of both structures and then attempting compensatory and simple saccades respectively. Cooling has the advantage of disabling the region temporarily, thus preventing physiological compensatory changes from occurring. MD CAUDATE VisCx ■ ck'lay m em T H m e m mem eye movement Brainstem Saccade Generator Retina VisCx LGN V islnput FEF - Frontal Eye Fields PP - Posterior Parietal cortex CD - Caudate nucleus SNR - Substantia Nigra pars Reticulatta SC - Super Colliculus TH - Thalamus (mediodorsal) FOn - Fovea On (foveation) vis - Visual response mem - Memory (sustained) sac - presaccadic (phasic) qv - Quasi-Visual wta - Winner Take All PPctr - central element of PPqv Figure 3.2 Multiple brain regions involved in saccade generation. 40 a) Anatomical localization of brain regions involved in sequential saccade generation (modified from Hikosaka 1989). Visual cortex (VisCx), posterior parietal cortex (PP), frontal eye fields (FEF), caudate and substantia nigra pars reticulata (SNr) nucleus of die basal ganglia, mediodorsal thalamus (MD), superior colliculus (SC) and the brainstem saccade generator (SG). b) A block diagram showing the interactions between these regions as employed in our model. Connections between arrays preserve topography of saccade dimensions. The labeled layers represent two dimensional surfaces of neurons that form an interdigitated mosaic of task related response types within the topography of saccade dimensions. The FEF to SC path includes both an excitatory topographic projection of saccade dimension, and a distributed inhibitory fovea-on (FOn) projection that inhibits SC and prevents saccades while a target is fixated. FOn is activated by the central element of PP, that is, PP(4,4). Output from FEF and SC drives the brainstem saccade burst generator which in turn drives a linear oculomotor plant, moving the retina with respect to the visual input projection screen (Vislnput), thus updating the visual image as the result of a saccade. We provide a detailed cellular model to expand the SG of part (a). For further explanation, see text 3.2 The Model and its Biological Substrate In this section, we introduce our model for two major functional components of the saccadic eye movement system, namely topographic organization that preserves saccade dimensions, and spatial working memory. Our strategy will be to offer, for each component of the model, a brief review of the biological literature followed by a formal description of the component. As shown in Fig. 3.2a (anatomically) and Fig. 3.2b (in terms of simulated neural computations), our model involves the topographic relations between posterior parietal cortex (PP), the frontal eye fields (FEF), the caudate nucleus (CD) and substantia nigra pars reticulata (SNr) of the basal ganglia, superior colliculus (SC), the mediodorsal nucleus of the thalamus (MD), and oculomotor regions of the brainstem responsible for saccade burst generation (SG). Both SC (Sparks 1986) and FEF (Bruce and Goldberg 1984) contain "maps" coding for motor error, the eye movement required to attain the target with respect to its offset from the fovea, regardless of the eye's position in its orbit. The FEF interacts with the rest of the oculomotor system via multiple pathways. We will emphasize the topo graphic projections to caudate, SC, thalamus and brainstem. A major thesis of this model is that a functional topography that preserves saccade direction and amplitude is maintained through multiple projections between brain 41 regions until it is finally transformed into a temporal pattern of activity that drives and holds the eyes on the target. The preserved topography is a map coding for amplitude and direction of an eye movement vector that, when combined with the current eye location, will center the eye on the saccade target. The major neural elements are 2- dimensional neural surfaces, layers, representing retina, PP, FEF, caudate, substantia nigra, superior colliculus, and thalamus. Multiple functionally distinct neuronal response types (corresponding, for example, to phasic visual, tonic memory and phasic movement components of the saccade tasks) are distributed in a topographic mosaic in each of PP (Gnadt and Anderson 1988), FEF (Segraves and Goldberg 1987), CD (Hikosaka et al. 1989a), SNr (Hikosaka and Wurtz 1983a-c), and SC. We model this effect by using separate neural layers for each of the functionally distinct response types without implying an anatomical separation into layers in the brain. In addition, we model non-retinotopic populations of neurons in the brainstem involved in saccade generation. Our simulated retina is the interface between the world and the brain, and our simulated eye movements remap external visual information onto the retina. Retinal Input: As we saw in Chapter 2, the external visual world, analogous to the viewing screen in front of the monkey, is represented in the simulation by a 27x27 array, Vislnput (Fig. 3.2), whose elements we turn on and off in a time sequence corresponding to the equivalent sequence of fixation and target points presented to the primate in the tasks we model. The retina is a 9x9 array, RETINA. The topographic brain regions (e.g. PP, FEF) are also modeled by 9x9 arrays, representing the visual field. Each model neuron represents a population of real neurons. In each iteration of the simulation, the function Eyemove extracts RETINA as the sub-array of Vislnput centered on the values of and Gy (horizontal and vertical components of eye position). We also implement an inhibition of retinal input so that when the eye velocity is over 200°/sec, retinal output is reduced. T retina = 6 ms ^retina = Eyemove(VisInput, 0R, 0u) A SACCADEMASK RETINA = retina (1) Here, Eyemove (Vislnput, a, b)(i,j) = Vislnput(a+i,b+j) for -4 ^ i,j < 4; SACCADEMASK is a 9x9 mask whose elements are 1 when the eye velocity is less than 200°/sec, and 0 otherwise. The saccade burst generator of Chapter 2 (SG in Fig. 3.2a) performs the spatiotemporal transformation from the motor error maps of SC and FEF into motoneuron firing rates to reposition the eye and hold it at a new 0jj, 0y. On the way to the posterior parietal cortex (PP), retinal output passes through 5 layers corresponding to LGN, V I, V2, V4 and MT, each with a time constant of 6 ms, in order to produce the latency from retina to PP. Here will summarize these five layers LGN, V I, V2, V4 and MT as VisPath and write: xVisPath = (5x6) ms s VisPath = RETINA (2) X PP ms Spp= VisPath PP = PP (3) 3.2.1 Frontal Eye Fields Bruce and Goldberg (1984) found that stimulation at a particular location of FEF yields saccades of a particular direction and amplitude, largely independent of stimulation parameters and the position of the eyes in their orbit when the stimulation is applied. The FEF projects with a topography of saccade amplitude to multiple saccade related areas including perioculomotor regions in the midbrain and pons responsible for eye movements, the caudate nucleus which inhibits the inhibitory pathway between SNr and superior colliculus (Alexander et al. 1986), mediodorsal thalamus, an area associated with spatial memory (Stanton et al. 1988a, Goldman-Rakic 1987), and the intermediate and deep layers of the SC (Sparks 1986; Stanton et al. 1988b). Bruce and Goldberg (1984) identify three classes of pre-saccadic cells in the FEF: visual cells respond to visual stimuli, with enhanced response for saccade targets; movement cells have a brisk response before all voluntaiy saccades; visuomovement cells have combined visual and movement response, including sustained activity during the delay of a memory saccade. Of these three types, only the movement and visuomovement are cortico-tectal cells (Segraves and Goldberg 1987). In addition to 43 the presaccadic cells, Bruce and Goldberg (1987) also reported the presence of postsaccadic cells that discharged after spontaneous and voluntary saccades of particular dimensions. Interestingly at least 16% of the presaccadic FEF cells show a post saccadic discharge for saccades of opposite direction from the saccades with the presaccadic discharge - thus they are well suited for the often used behavior of retracting the previous saccade, which we consider further in Chapter 4. Among the different types of response cells distinguished in FEF in relation to saccade tasks are neurons that have on or off responses to visual stimulation of the fovea. These foveal cells are not localized to a particular location of the topographic map of FEF, and they were antidromic ally excited from a wide range of locations within the topographic representation of the SC (Segraves and Goldberg 1987). One role these cells may play is to inhibit the SC from producing saccades while a target is fixated. It is possible that these cells influence the fixation related tecto-reticular fixation cells in the rostral pole of the cat SC (Munoz et al., 1991). Functionally, the SC is harder to stimulate for a saccade when a target is currently fixated (Sparks 1986). In our simulations it is this fixation related inhibition that prevents saccades from being visually triggered during the presence of a fixated target Cortico-reticular projections from these foveal cells may provide cortical control over the omnipause neurons in the brainstem saccade generator. Hikosaka et al. (1989a) detected a caudate neuron whose response to the target in a delay saccade task increased when the fixation point was removed, suggesting a projection of the foveal neurons to the caudate as well as the SC. Foveal On fFOri) cell: The contents of the central element of the PP layer is projected to all elements of the 9x9 layer FOn, that is used to provide inhibition to elements of caudate, SC and the FEF itself. In each of the tasks we model, the stimulus that signals the animal to initiate the saccade is the removal of the initial fixation point T fon= 6 ms Sfon = project_sca!ar_to_matrix ( PP[X_Center,Y_Center] )* FOn = sigmoid(fon,0,50,0,90) (4) ^This function simply takes a takes a scalar value and applies it to every element of a 2 dimensional Many of the areas that we consider are functionally partitioned into a topographical mosaic, so that distinct functional regions are interspersed within the topography of motor error for a given layer. In particular, we consider the visual, sustained memory and movement response types in FEF (Bruce and Goldberg 1984, Segraves and Goldberg 1987, Funahashi et al. 1989)2. It is likely that these response types are derived in part from the prominent cortico-cortical projection from posterior parietal cortex (areas 7a, 7b, 7ip, and 7m) to the dorsolateral prefrontal cortex (principal sulcal and FEF regions) (Petrides and Pandya 1984; Anderson et al. 1985; Selemon and Goldman-Rakic 1988) since multiple response types are also seen in PP (Gnadt and Anderson 1988). This modeling strategy of functional segregation reflects the possible organization of the projections from parietal to frontal cortex into functionally discrete modalities or "labeled lines" (Goldman-Rakic 1987). This segregation is continued in the model as corticostriatal, striatonigral, nigrothalamic and thalamocortical projections form segregated mosaics within the overall topography of saccade amplitude and direction. We model three classes of saccade task-related cells in FEF. Visual cells are responsive to all visual stimulus, including targets for saccades (Bruce and Goldberg 1984). Memory cells have sustained activity during the delay period of the memory saccade (Funahashi et al. 1989), and movement cells discharge before all voluntary saccades corresponding to the cell's preferred dimensions (Segraves and Goldberg 1987). FEF visual response (FEFvis): Roughly half of the visually driven FEF cell investigated by Bruce and Goldberg (1984) were most active to visual stimuli that were targets for impending saccades. Based on the cortico-cortical projections from posterior parietal to dorsolateral prefrontal cortex (Petrides and Pandya 1984; Anderson et al., 1985; Selemon and Goldman-Rakic 1988), we describe the FEFvis layer as: xfef_vis = 6 ms %ef_vis = PPqv FEFvis = sigmoid(fef_vis/ 0, 90, 0, 90) (5) 2 Although Stanton and Goldberg (1988) distinguish two FEF regions 1FEF and sFEF, with large and small receptive fields, responsible for large and small saccades, respectively, we do not employ this subdivision in the present model. 45 The 6ms time constant gives these neurons a fast reponse to parietal input The sigmoid parameters map parietal inputs into the range 0-90, approprite for visually guided activity. Note that we use the PPqv as input to these visually guided saccade neurons. This cell type displays a spatial accuracy mechanism that is described in detail in Chapter 4. For now, we can simply consider that PPqv specifies retinal locations of targets in its 2-d map. FEF memory response (FEFmemV. Funahashi, Goldman-Rakic and Bruce (1989) describe a class of directionally selective cells in FEF that show sustained activity during the delay period of the memory saccade task, implementing working memory (Goldman-Rakic 1987) in the memory saccade. Tracing the origin of this response, we see that FEF is innervated by, and closely related to, the cortical tissue surrounding the principal sulcus (PS) (Goldman-Rakic 1987). These areas have parallel but distinct connections with areas including mediodorsal thalamus and posterior parietal cortex (PP) (Selemon and Goldman-Rakic 1988). Similar sustained tonic activity has been seen in FEF neurons that code for the location of a remembered target (Bruce and Goldberg 1984; Segraves and Goldberg 1987). A similar sustained activity has been found in PP of the macaque (Gnadt and Andersen 1988, Andersen et al. 1990). Like the FEF neurons, these PP neurons have receptive fields tuned for saccades of a particular amplitude and direction, and show a sustained activity in the memory saccade task. Both areas show sustained activity in tasks that require memory of a spatial location (Goldman-Rakic 1987). An interesting distinction is that dorsolateral prefrontal lesions impair spatial memory, where PP lesions do not (Goldman-Rakic 1987). In a related set of studies Fuster and Alexander (1973, Alexander and Fuster 1973) showed that in a delayed response task, mediodorsal thalamus (MD) and dorsolateral prefrontal cortex (DLPFC) showed sustained activity during the delay, and that cooling DLPFC abolished both the sustained activity in MD, and the animal's ability to perform the task. We suggest that interaction between PP, FEF/PS and mediodorsal thalamus provides a basis for memory of target locations in the FEF. As we will discuss in a later section, we believe that selective release of the normal tonic inhibition from SNr on mediodorsal thalamus allows reciprocal connections between FEF and MD to , maintain sustained activity for spatial memory. This would also allow a projection from FEF back to PP to generate the sustained response seen there (Gnadt and 46 Anderson 1988). To terminate the sustained activity, we suggest that a projection from SC to dorsal thalamus (Ilinsky 1985) provides a signal that terminates this memory in thalamus once the saccade has taken place, presumably via inhibitory intemeuron in MD. Figure 3.3a illustrates the sustained response in a primate FEF neuron while Fig. 3.3b shows our simulated result. The increase in activity at removal of the fixation point in the simulation derives from the .2 * FOn" term in eqn. 6. Fig 3.3c isolates the structures of the model that are involved in the sustained activity in FEF. xfef_mem = 8 ms Sfef mem = THmem + FEFvis - .2* FOn FEFmem = sigmoid(fef_mem,0, 90, 0,90) (6) FEF saccade cells fFEFsac): Finally we simulate the cortico-tectal and cortico-reticular presaccadic movement cells which made up 53% of the cortico-tectal cells antidromically stimulated from SC by Segraves and Goldberg (1987). Because these cells were found to respond to both visually and memory guided saccades, we describe them as follows: xfef_sac = ^ ms %ef_sac = FEFvis + 2*FEFmem - 3*FOn FEFsac = sigmoid(fef_sac, 0, 90, 0,90) + kl*ElectricalStim (7) In the memory saccade, FEFmem will be active during the delay, but the FOn" term here insures that the FEFsac presaccadic response will not be generated until after the removal of the fixation point. ElectricalStim is another 9x9 matrix into which we can place values that code, for a given time in a task, electrical stimulation corresponding to that used in colliding and compensatory saccades. A similar term appears in eqn. 15 for SC. By changing the k l values we can stimulate one, or the other or neither of these areas to reproduce the intervening (Sparks and Porter 1983) and colliding saccades (Schlag Schlag-Rey 1990) in Chapter 4. 47 b) a) SACCAJDE:MemorySaccade « ■ > u k i i h n a m a t i n - 911 l a it id 1 a I I lilt i n t i w M i a a a | m i a l l l a a w i a * a t | al u m aasiai 1 lilt I til IMMI | I IK 1 U | F i x a ti o n _ P o in t H orizon ta I _ E y e_ Pos t1:5.00 c) FEF vis PP m em fFOn; PPctr vis sac THmem Figure 3.3 FEF Sustained response during Memory saccade task. 48 a) Spike histogram of a directionally sensitive sustained response FEF cell. The vertical lines labeled C indicate the presentation of the target. The portion labeled D represents the delay period, and R indicates the response period signaled by the offset of the fixation point. This neuron had significant excitatory tonic activity during the delay period of the memory saccade when the target was presented in its visual field, and was suppressed when the target was away from the cells visual field (Funahashi et al. 1989, Fig 15b). b) Simulation of the sustained response in the delay task. The upper trace shows the fixation point, the second trace shows the target, the third shows the sustained FEF cell and the last two traces show the eye displacement Note that while there is fluctuation in the activity of the FEF cell in a), our FEFmem cell shows fairly constant activation. The spike at the end of the delay period indicates this FEF cell may have some presaccadic increase in activity. In our simulation, this response results from the reduction of FOn activity in eqn. 6. We model average firing rates, not individual spike generation. Further, our cell represents the average activity over a population of cells, rather than a single cell, c) Cortical and thalamic structures involved in the sustained response. 3.2.2 Basal Ganglia Two inhibitory nuclei of the basal ganglia, caudate (CD) and substantia nigra pars reticulata (SNr), are arranged in series and provide an additional, indirect link between FEF and SC (Chevalier et al. 1985). This link allows FEF to selectively modulate the tonic inhibition of SNr on SC and thalamus (Deniau and Chevalier 1985, Alexander et al. 1986) through caudate nucleus. Without the inhibition of SNr on SC, gaze would be uncontrollably distracted to targets appearing in the periphery while a subject tries to fixate. This distractibility is prominent in Huntington's disease and is thought to result from decreased activity in SNr (Lasker et al. 1987). In contrast, hyperactivity of SNr would lead to impairment in voluntary saccade generation. This is seen in Parkinson's disease (Crawford et al. 1989), in which the inhibition of SNr by caudate is compromised, leaving the SNr overactive. In addition, the basal ganglia pathways provide a mechanism for the initiation of cortico-thalamic interactions via the removal of SNr inhibition on the mediodorsal thalamus (MD). As expected, then, we see an impairment in memory guided saccades in Parkinson's disease (Crawford et al. 1989). Thus, while the retina, FEF and SC alone appear capable of all saccade functions, we see that in reality, some of the more subtle elements of saccade gaze control including 49 the ability to fixate, to initiate voluntary movements and to remember targets require the functions of the basal ganglia. The striatum (caudate, putamen and accumbens nuclei) is composed of two distinct types of functional area - patches and matrix - that are arranged in a mosaic pattern and can be distinguished both pharmacologically and by distinct segregation in both cortical inputs as well as their subeortical targets (Gerfen 1986, 1989). The patch cells project to dopamine-producing cells including those in SNc, whereas the matrix cells project to GABA producing cells in SNr and globus pallidus (Gerfen 1986). While it is the matrix cells with which we are concerned in this model, the activity of the patch cells modulates the dopamine activity in the striatum, thus influencing the effects of corticostriatal projections. See Chapter 5 for our details of dopamine function related to regulation of corticostriatal activity, and plasticity. The mosaic interdigitation of cortical projections to neostriatum again suggests that specific functional inputs remain segregated from input to output, representing a "labeled line" (Goldman-Rakic 1987) extending from cortex through neostriatum to SNr, and from there, diverging in one path to SC, and another through thalamus back to cortex. We suggest that within the macroscopic topography of saccade metrics in these corticostriatal projections and their terminal sites there is a microscopic functional segregation of task-related response types. As mentioned earlier, we see the functional segregation in FEF, caudate and SNr with respect to at least two types of saccade related response types: pre-saccade and memory sustained response types. The FEF has an excitatory projection to caudate (a topographical projection that preserves saccade amplitude and direction) that can trigger the selective release of SNr's inhibition on SC (Bruce and Goldberg 1984; Segraves and Goldberg 1987; Stanton et al. 1988a). Hikosaka et al. (1989a-c) found a large number of caudate neurons that were responsive to visual saccade targets and to remembered targets. To provide cortical control while a target is foveated, foveal cells in FEF could gate activity j in caudate and SC, preventing saccades while a target is fixated. We represent these by the subtraction of FOn in the appropriate equations. This tends to keep the system stable when targets are foveated (Bruce and Goldberg 1984; Segraves and Goldberg 1987), by preventing peripheral targets from exciting caudate and SC. As in FEF, we see multiple task dependent response types in caudate. We simulate two types of task dependent caudate cells. _____________________ 50 Caudate Saccade (CDsac) Response: The majority of the saccade related cells found in the caudate by Hikosaka et al. (1989a) are phasically active before and during saccades (presaccadic activity). Roughly one third of these cells had presaccadic activity for both visual and memory guided saccades. This phasic activity is attributable to the corticostriatal projection (Stanton et al. 1988a), which would correspond to our FEFsac cells. The parameters of the sigmoid function that describe the excitability of these cells are fixed here. In Chapter 5 we introduce a regulatory mechanism involving dopamine that adjusts striatal excitability as a function of cortical input strength. T cd_sac = 8 ms ^cd_ .sac = FEFsac CDsac = sigmoid (cd_sac,0,50,0,60) (8) Caudate Sustained Memory fCDmem) Response: These cells, described by Hikosaka et al. (1989c) are tonically active following the presentation of a target that is to be remembered for a subsequent saccade until the offset of the fixation point (Fig. 3.4a). This tonic activity is attributable to the corticostriatal projection (Stanton et al. 1988a) which we describe as the FEFmem memory cells (see eqn. 9). (See Fig. 3.4b for the simulation trace of these cells). T cd_mem = 10 ms Scd_mem = FEFmem CDmem = sigmoid(cd_mem, 50,90,0,60) (9) Caudate inhibits SNr via a topographic pathway, controlling SNr’ s inhibition of SC (Chevalier et al. 1985, Alexander et al. 1989). Hikosaka and Wurtz (1983a) showed that the SNr provides a tonic (50 to 100 spikes/sec) inhibitory topographic projection to the SC, preventing SC from generating saccade signals, thus forming an inhibitory mask on SC. Visual and memory related decreases of SNr firing rate release collicular inhibition and facilitate initiation of saccades. We simulate two classes of SNr cells, related to saccade and memory responses. These cells are influenced by the CDsac and CDmem cells, respectively. 51 a) kit .. i c) FEF P P q v v is PPctr ’ O n ; m e m CD b) SACCADE:MemorySaccade Targe t_ A n . C D m e m H 0 r1 2 o rtta L .E y e._ P 0 s t1:5.00 F igure 3.4 Caudate sustained memory response, a) Sustained activity during the fixation period of the delay saccade in response to a briefly exposed contralateral target (Hikosaka et al. 1989c, Fig. 4a) b) Simulation of the caudate sustained memory response in the delay task. TTie upper trace shows the fixation point, the second trace shows the target and the third shows sustained memory response caudate cell, c) Components of the model that implement the corticostriatal projection responsible for transient (light shading) and sustained (darker shading) responses to memory targets in caudate. Substantia nigra pars reticulata saccade (SNRsac) response; Hikosaka and Wurtz (1983c) describe SNr cells whose phasic reduction in discharge is temporally correlated with saccades to visual targets (SAC/VIS), memory targets (SAC/MEM), and to both. About half of the cells classified as SAC/MEM also showed a visually contingent saccade response. Fig. 3.5 shows the decrease in SNr activity and corresponding increase in SC activity for experimental and simulated simple saccades. We model this single presaccadic neuron type: T snr_sac = 20 ms Ssnr_sac = 50 - CDsac SNRsac = sigmoid(snr_sac, 0,50,0,100) (10) Substantia nigra pars reticulata memory (SNRmem) response: Hikosaka and Wurtz (1983c) describe a class of SNr cells that maintain a decrease in their tonic firing rate during the delay period of the memory saccade task. These neurons have a tonic baseline activity of 100 spikes/s, and are inhibited by the sustained memory cells (CDmem) in caudate (Deniau and Chevalier 1985). This represents a separate “labeled- line” from the CDmem input to the SNRmem cells. We speculate that these SNRmem cells usually inhibit the thalamus (ventromedial and mediodorsal nuclei) (Hinsky et al. 1985, Deniau and Chevalier 1985), so that while they are not active the thalamocortical memory loop can show sustained activity, implementing the spatial memory of the target location. Figure 3.6 shows experimental and simulated SNr cells that show a sustained decrease in firing during the delay period of the memory saccade. Based on the anatomy outlined above we describe this neural layer as follows: xsnr_mem = 40 ms ^snr_mem = 50 - CDmem SNRmem = sigmoid(snr_mem, 0,50,0,100) (11) 53 a) a t A .__________ P /fv m te fc w z m a c H ---------- - V 2 [ 1 c) sac CD SNR iem. sup qv sac wta SA C C A D E :Sim pi< Saccade H o rizo n t i l 7£ye_'tfo's V 9 rti< ai.ty « _ P o * Figure 3.5 SNr and SC visual saccade response, a) A visually contingent saccade response in an SNr cell that was antidromically stimulated from SC, and the corresponding SC cell in the visual saccade task. The SC cell discharged before the visual, memory and spontaneous saccades, whereas the SNr cell deceased its discharge rate only before the visually contingent saccade. Top: Fixation and target, horizontal and vertical eye movement. Middle: SNr spike histogram. Bar on left 100 spikes/sec. 200 ms bins. Bottom: SC presaccadic burst. (Hikosaka and Wurtz 1983d Fig. 7a) b) Simulation of the SNr and SC response in the simple saccade task. The upper trace shows the fixation point, the second trace shows the target the third shows SNr activity and the bottom shows the SC presaccade burst, c) Cortical and basal ganglia influences on the superior colliculus. a) H V • _R_ b) I SACCADE:MemorySaccade T r a a tio n .lS o in t 1 cos-i: ^Rmem c) FEF PPctr *FOn; THmem CD S N R Hori^ontaL£/e_Pos V8ru c a L ty e _ P o s Figure 3.6 SNr Memory-contingent sustained response, a) This cell shows sustained decrease in firing in response to a target in the contralateral visual field that is to be memorized for the delay saccade task. The decrease usually follows the target presentation and remains until the saccade onset (Hikosaka and Wurtz 1983c, Fig. 7). b) Simulation of the memory contingent sustained response (SNRmem). TTie sustained suppression of SNr allows the thalamus (mediodorsal) to participate in the reciprocal activity with FEF that instantiates a spatial memory. This SNRmem is inhibited by CDmem which in turn is tonically excited by FEFmem in the delay period of the memory saccade. c) Cortico-striato-nigro-thalamo-cortical path subserving spatial memory. 55 3.2.3 Superior Colliculus Neurons in deeper layers of the SC discharge in bursts before saccades of a particular direction and amplitude, regardless of initial eye position (see Sparks 1986, Sparks and Mays 1990 for a review). Hence, deep SC can be considered to be a map of ensuing change in eye position rather than a map of absolute (head centered) location or of strictly retinotopic position. Each deep SC neuron has a movement field, and a topographic organization of movements fields within the SC that is aligned with the visually responsive superficial layer has been described (Robinson 1972). Within both left and right SC, upward saccades are coded for by activity in medial SC, downward saccades are coded for by activity in lateral SC. Small lateral saccades are mapped to rostral SC, and larger saccades are mapped to caudal SC (Robinson 1972, Munoz et al. 1991). In our model, the SC receives input to the superficial layers from RETINA, to intermediate layers from PPqv, and inputs from FEF and SNr representing presaccadic activity. SC brainstem projection cells convey saccade metrics to the LLBNs as seen in Chapter 2. Superior colliculus superficial laver visual (SCsup) responses: These cells receive direct input from the retinal ganglion cells, and are active in generating reflexive saccades to visual targets. It is important to note that these cells will generate short latency reflexive saccades only when a target has not been recently fixated, that is, in the simple saccade task, these cells will continue to receive residual inhibition from the FOn cells and will not decrease the latency in this task. If a fixation target is not present, however, these cells will drive the SC prior to the longer loop through cortex, generating short latency saccades (Braun and Breitmeyer 1988, Fischer and Boch 1983) via the transcollicular pathway (Sparks 1986). The threshold parameters ensure that SCsup does not trigger express saccades in the standard visual saccade paradigm. T sc_sup = 8 ms Ssc_sup = RETINA - 2*FOn SCsup = sigmoid(70,90,0,90) (12) [ Superior colliculus OV activity: While the details of QV (quasi-visual) function are provided in the next chapter, we note here that the model accounts for the QV cells in 56 intermediate layers of the SC (Mays and Sparks 1980) by recalling that intermediate layers of SC receive a prominent direct projection from the inferior bank of the intraparietal sulcus (Lynch et al. 1985). Cells in or near this region have been found to display QV properties (Gnadt and Anderson 1988), and project to the intermediate layers of SC, leading to the observation of QV activity there. The intermediate layer SC QV cells in the model (SCqv) simply receive the posterior parietal projection of QV activity. Although antidromic stimulation of the SCqv cells from PP has not yet been demonstrated, our model suggests that it should be found. These cells thus display the shifting of activity seen by Munoz et al. (1991). xsc_qv = 10 ms ®sc_qv = PPqv SCqv = sigmoid(sc_qv/ 0,90,0,100) (13) Superior colliculus saccade (SCsacl response: These cells generate presaccadic bursts before voluntary saccades. Experimental data indicate that SC receives an excitatory topographic projection from presaccadic cells in FEF (Segraves and Goldberg 1987), FEFsac. This topography preserves the amplitude and direction of the intended saccade (Stanton et al. 1988). In addition, Hikosaka and Wurtz (1983a) show that the SNr provides tonic inhibition to intermediate and deep SC, preventing SC from producing excitatory saccade bursts. The sigmoid threshold parameters ensure that these cells have a bursting characteristic, rather than gradual onset. xsc_sac = 10 ms Ssc_sac = FEFsac - l.l*SNRsac SCsac = sigmoid(sc_sac, 0,80,0,80) (14) Superior colliculus motor activity: It has been postulated that SC employs a winner take all (Didday and Arbib 1975; Koch and Ullman 1985) strategy for selection of a saccade from multiple targets, like the winner-take-all competition modeled for frog tectum by Didday (1970, 1976). Our deep SC model selects the strongest component of the superficial and intermediate layers, as in the winner-take-all model. These are the eollicular cells that project to the saccade burst generator of Chapter 2. Note that we used a similar WinnerTakeAll function in the brainstem in Chapter 2. T sc = 38 ms ^sc = WinnerTake All(4*SCsup + 1.5*SCqv + SCsac - 2*FOn) + ElectricalStim SC = sigmoid(sc, 85,99,0,500) (15) The final SC output is affected by the influences of visual stimulation, memory and QV shifting, as well as a signal coding the presence of a stimulus on the fovea. The threshold and time constant parameters again ensure that this cell has a phasic, bursting characteristic. 3.2.4 Cortico-striato-thalamo-cortical interactions: spatial memory As we have seen, cortical interactions with the basal ganglia are implicated in the formation of spatial memory that is required for the memory saccade task. Ilinsky et al. (1985) found in the nigrothalamocortical system of the rhesus monkey, a topographic pathway from SNr, to ventral anterior magnocellular (VA) and mediodorsal paralaminar (MD) nuclei of the thalamus (TH), and from these thalamic nuclei to the FEF. The MD projection to FEF is topographic and reciprocal. In addition, Fuster and Alexander (1973) determined that mediodorsal neurons show a sustained activity during the delay period of a delay response task, and that cooling the prefrontal cortex in the principal sulcal area caused a reversible disruption of the sustained response in the MD neurons during the delay period (Alexander and Fuster 1973). Based on similar deficits in memory saccade and delay response tasks from prefrontal lesions, we follow the assumption that the memory saccade task and the delay response tasks employ at some level the same thalamocortical mechanism for storage of visuospatial targets (Goldman-Rakic 1987). The activity of this spatial memory could be regulated by the inhibitory topographic projection from SNr to MD. Absence of SNr inhibition allows reciprocal connections between FEF and thalamus (MD) to generate a spatial "memory" cycle or loop (Hikosaka 1989). Once a saccade has been made to a remembered target the memory trace must be erased to prevent generation of further saccades of equal magnitude and direction. The SC projects to the dorsal thalamus (Ilinsky et al. 1985), possibly erasing the remembered target location. This erasure is modeled by the “4* SC_Delay” term in j the equation 16. In the memory saccade task, while the fixation point is still present 58 and the target briefly appears, the memory contingent sustained SNr cell (SNRmem) reduces its inhibition on the thalamus which allows the initiation of the thalamus«-»FEF cyclic excitation that embodies the memory function. The caudate participates by inhibiting SNr, setting up the conditions for the thalamocortical memory to be instantiated. Cordco-Thalamic interactions: We repeat the equation for the FEF memory response to memory saccade which represents half of the reciprocal connection between FEF and MD thalamus that implements the spatial memory. See Fig. 3.8 for simulation results. xfef_mem = 8 ms %ef mem = THmem + FEFvis - .2* FOn FEFmem = sigmoid(fefLmem,0, 90,0,90) We see here that the mediodorsal thalamus and FEF participate in a memory loop that is initiated by the phasic visual response of the FEFmem layer. Once this loop is established, it remains intact until the saccade burst of SC "erases" i t This erasure may occur via inhibitory intemeurons in the thalamus. T th_mem = 6 ms ®th_mem = FEFmem - SNRmem - 4* SC_Delay THmem = sigmoid(th_mem,0,45, 0,10) (16) We simulate the saccade system starting with retinal input, through cortical and subcortical areas, the brainstem, and finally the oculomotor plant that moves the eye to generate a new retinal input (Fig. 3.2). Table 1 provides the firing rate ranges that are used for some of the neurons in the simulations. W e note that the neural populations we model carry information in terms of their discharge frequencies, the durations of discharge, and the latencies both between stimulus and firing, and between 3.3 Simulation Results 3.3.1 Simple and Memory Saccades 59 neural events in connected regions. Our simulated results correspond well along these dimensions with the reported dynamics in the literature. T able 3.1 O bserved (OBS) and sim ulated (SIM ) n eu ral activities in saccade tasks. Background rate Task Related Reference OBS / SIM OBS / SIM Neuron a. FEF 0-20 0 100 100 (Segraves and Goldberg 1987) b. CD 0 0 50 50 (Hikosaka et al. 1989a,b,c) c. SNr 50-100 80 0 0 (Hikosaka and Wurtz, 1983a,c) d. SC 0 0 500 500 (Hikosaka and Wurtz, 1983d) e. FOn 0-20 0 50 50 (Segraves and Goldberg ,1987) f. thalamus 0 0 10 10 (Fuster and Alexander, 1973) Simple saccade (Fig. 3.71: During initial fixation, the foveation signal, FOn keeps caudate inhibited. At fixation loss and target onset, the central element of PP is no longer activated, and the FOn foveation signal is released, releasing its inhibition on caudate. At the same time, the FEFsac element corresponding to the location of the new target projects topographically to the caudate. This excitation, combined with the loss of the FOn inhibition activates the corresponding CDsac element, which projects an inhibitory signal to SNRsac, resulting in the release of SNRsac's SCsac inhibition. The topographic excitatory FEFsac projection to SCsac, combined with the release of the SNRsac inhibition activates the SCsac element that generates motor burst signal of saccade direction and amplitude corresponding to the target location on FEFsac. Fig. 10 illustrates the relation between SNr and SC that we see here. The SC and FEF output drives the burst generator in the brainstem as described in Chapter 2, repositioning the "virtual eye" such that the target is now foveated, centered in the FEF. The foveation signal returns, inhibiting the caudate, setting the network back into the state of tonic SCsac inhibition from SNRsac. SACCADE:SimpleSaccade Fixation_Point \ Target_ft F FOn J L J FEFsac n CDsac n SNRsac SC n _ Horizon tal_Eye_Pos r t 1 : 1 .0 0 Figure 3.7 Simple Saccade Task simulation. The simulation has a time course of 1000 ms. The graphs labeled FEFsac, CDsac, SNRsac and SC represent the activity in each of these layers of a cell whose visual/movement field corresponds to the location of the visual target. Following onset of target, T, 30 degrees right, 30 degrees up, and offset of fixation point, F, the FOn becomes inactive, allowing the FEF visual saccade cells, FEFsac to initiate the disinhibition of SC via the caudate visual saccade layer's (CDsac) inhibition of SNr visual saccade layer (SNRsac). SC indicates the SC burst that drives the eyes to new horizontal and vertical positions indicated by H and V respectively. 61 SACCADE:MemorySaccade Fixation.Point 1 L T a rg e t. A - 1 FEF m e m 1 1 — SNRmem THmem Horizontal..E y e.P o s r~ V ertical.Eye.Pos ... __ _ _ _ _ _ _ r ~ t1:5,00 Figure 3.8 Memory Saccade Task Simulation. Time runs from left to right. The fixation point (F) is present for 570 ms. After the initial 20 ms of fixation point presentation, a peripheral target (T) (40° up and 30° right) is presented for 50 ms. For the remaining 500 ms of fixation, the target is memorized. Following fixation offset a saccade is made to the remembered target. FEFmem shows the time course of the sustained activity that encodes the memory for the location. CDmem is the sustained memory caudate cell that inhibits SNRmem. SNRmem is the sustained memory SNr cell whose default tonic activity inhibits SC and thalamus. When this activity is blocked by caudate, the cortico thalamic memory is enabled, and SC is only inhibited by the activity of the FOn neurons. THmem shows the sustained activity of the mediodorsal thalamus. Note how this cell is co-active with FEFmem, and also how it abruptly cuts off after the SC burst. SC, excited by the FEFms activity, shows the collicular burst that takes place when the fixation point is removed. 62 In table 3.2 we summarize data on the latency, duration, size and velocity of a number of visual saccades. Note that as in primates, the saccade velocity and duration increase semi-linearly with the amplitude of movement. The velocity increases due to the increased strength of projection from increasing eccentric locations in SC and FEF to LLBNs. The saturation of LLBN activity at high input rates yields the desired increase in duration with increasing amplitude. Also note that, while the saccades all maintain good accuracy, there is a tendency towards overshoot on the largest saccades, due in part to the cooperation of FEF and SC to LLBNs, Table 3.2 Simple Saccades H V beg end latencv duratn actual ampl velocitv 10 0 .165 .200 .145 .035 10,0 10 285 20 0 .135 .180 .120 .045 21,0 21 466 30 0 .130 .180 .110 .050 32,0 32 640 40 0 .125 .180 .105 .055 43,0 43 781 10 10 .165 .200 .145 .035 10,10 14 400 20 20 .135 .180 .120 .045 21,21 29 659 30 30 .130 .180 .110 .050 32,32 45 900 30 40 .125 .180 .105 .055 32,43 52 945 Memory saccade (Tig- 3.81: The Memory saccade requires, in addition to the machinery needed for the visual saccade, the thalamus as a mechanism for storing spatial location memories via reciprocal excitatory connections with FEF . When the target disappears, it is held in FEF memory (FEFmem) by the reciprocal excitatory connection between MD of the thalamus and FEF. The removal of the fixation point causes the FOn signal to be reduced which allows the FEFsac to fire and removes a j source of inhibition from the SC. The combination of these events allows the stored ! spatial memory to command a saccade. The effect of the spatial memory is to keep the target position in the FEF active after it is extinguished. At fixation offset the system responds, in terms of FEF, as if it were in the visual saccade mode. Table 3.3 summarizes timing and movement metrics for 2 sample memory saccades. 63 Table 3.3 Memory saccades Protocol: 0.0 - 0.02 fixation MS.I MS.H ( 0, 0) ( 0, 0) (20,20) (-30,20) ( 0, 0) ( 0, 0) 0.02 - 0.07 fixation & target 0.08 - 0.58 fixation(memory) 0.58 - fixation offset Begin Latncy End Am pi Vel MS.I .700 .120 .755 30[21,21] MS.II .700 .120 .750 36[-30,20] 539 721 3.3.2 Simulated Lesion Studies Keating and Gooley (1988) produced reversible cold lesions of both FEF and SC. Reversible lesions have the advantage of preventing postoperative compensation by the remaining area when either FEF or SC is lesioned. Cooling the FEF increased saccade latency by an average of 68 ms and shortened the amplitude of the initial saccade. Saccades following the initial one successfully acquired the target. Cooling SC increased the saccade latency by and average of 98 ms and shortened the first saccade's amplitude as in the FEF cooling. Unlike FEF cooling, a subsequent corrective saccade brought the eyes closer to the target, but ultimately fell short by some 3 degrees. Sparks (1986) reports that following a recovery period, animal with SC lesions regain normal saccade amplitude and velocity. Schiller and Sandell (1983) note that deficits in the guidance of saccades due to FEF ablations are substantially recovered within 24 days. Table 3.4 summarizes our SC and FEF cold lesion experiments. W e simulate SC lesion by reducing the output of eqn. 22 to zero; and FEF lesion by setting the output of eqn. 10 to zero. In our simulations, when the SC is first lesioned, saccade latency is ! increased by up to 105 ms, and amplitudes fall just short of the target, similar to the j results reported by Keating and Gooley (1988). Simulated lesion of FEF leaves the i parietal cortex projection to SC intact. Again, in our FEF simulations we see increased latency (in this case up to 45 ms) and reduced amplitude of the initial saccade resulting in multiple saccades required to fixate the target. Table 3.4 Lesion Effects SC Lesion: Tgt beg end latency duratn ampl velocity 20 .245 .315 .225(+.105) 30 .160 .250 .140(+.030) 40 .140 .245 .120(+.015) .070 .090 .105 19 271(194)3 29 322(317) 39 371(409) FEF Lesion: Tgt beg end latency duratn ampl velocity 10 .210 .240 .190(+.045) 20 .165 .215 .125(+.035) 30 .160 .210 .140(+.030) 40 .160 .220 .140(+.035) .03 .05 .05 .06 7 233(51) 16 320(146) 19;274 380(260) 24;40 400(381) In the simulation, LLBNs receive inputs from both FEF and SC, while SC receives inputs from both FEF and parietal cortex. Thus, lesioning FEF allows position data to reach the LLBNs from PP via SC, whereas lesioning SC allows position data to reach the LLBNs from PP via FEF. Following our simulated lesions, if we increase the strength of the remaining connections to LLBNs, the reduced amplitude is corrected and the target is reached on the first saccade. This suggests that the postoperative recovery involves the strengthening of these connections in the animal. The functions of SC and FEF in saccade generation overlap but are not completely redundant. The cortical control from FEF imposes attentional and possibly cognitive constraints on the saccade system. In the absence of engaged attention, monkeys were able to make express saccades with latency 70-80 ms, in contrast to the latencies on the order of 200 ms for simple saccades (Fischer and Boch 1983). The short latencies of the express saccades could be explained by the use of a trans-collicular path from superficial to deep SC (Sparks 1986). The advantage of this mechanism is that it is fast, the disadvantage is that it is not selective. The additional overhead of the cortical control provides discrimination in target selection, so that, for example, in a learned task the subject can ignore a target if necessary, as when the peripheral target is initially ignored in the memory saccade. 3 Values in 0 indicate differences in these values from the non-lesion cases 4 Two amplitudes indicate that multiple steps were needed to attain the target 65 3.4 Discussion We have developed a computer model based on physiological data from a variety of saccade related studies. The simulation demonstrates that the following assumptions can lead to a functionally correct model: a) Managing the inhibitory projection from SNr to SC allows selective cortical control of target locations for voluntary saccades to immediate and remembered targets. This control is directed by FEF via the caudate nucleus, b) Saccades can be driven by representational memory that is hosted in reciprocal connections between mediodorsal thalamus and dorsolateral prefrontal cortex that are governed by SNr. A subtle, yet significant aspect o f this memory driven saccade capability is that a state change is being driven by a representation of a stimulus, rather than by the stimulus itself, indicating a primitive symbolic processing capability, c) The LLBNs of the brainstem saccade generator are innervated by projections from both FEF and SC whose strengths increase as a function of eccentricity from the fovea. Further, either of these projections alone can specify saccade targets in a degraded mode. The model of Guitton et al. (1990) and the scheme suggested by Pelisson et al. (1991) and Munoz et al. (1991) go beyond the fixed head paradigm to consider how the head and eye motor plants cooperate, via SC and the vestibular system, to produce coordinated gaze control, but they do not address the roles of many cortical and subcortical structure that are involved in the control of gaze. By including the interactions between cortex, basal ganglia and thalamus in our model we make explicit statements, which can be tested, about the roles of these structures in the control of saccades. In this sense the model can evolve. For example, a lesion of mediodorsal thalamus will impair memory saccades, but leave visually guided saccades intact. Experimental results can lead both to the modular replacement of structures by improved models, as well as global reorganization of the model. It is likely that our proposed cortico-thalamic mechanism for spatial memory, which ! is based on the thalamocortical mechanisms seen in the delay-response function (Fuster I I 66 and Alexander 1973), operates in cooperation with the cortico-cortical interactions between FEF, PS and PP (Goldman-Rakic 1987, Fuster 1989). As the delay-response performance is not compromised by lesions of PP (Goldman-Rakic 1987), we suggest an experiment in the next chapter to determine if the spatial memory related areas of PP are required for double-step memory saccades. Indeed, the effects of cooling posterior parietal cortex on eye movements in the recent study of Quintana et al. (1989) indicate that in visual discrimination tasks with delayed choice, eye movements are slowed and their accuracy decreased. The experimental demonstration of the separation and or cooperation of these two systems continues pose a challenge to experimentalists as well as to modelers. In conclusion, we have presented a model for primate saccade generation that includes superior colliculus and brainstem as well as the additional cortical and subcortical structures that guide and modulate these structures in the control of voluntary saccades. By considering the interactions of cortex, basal ganglia and thalamus with the SC and brainstem, we introduce additional constraints that might otherwise be ignored. This evolving model should prove useful in the oculomotor community as it permits simulation and prediction within a larger system level framework than those provided by existing models. Towards this end, in the next chapter we expand on this model to consider spatial accuracy in double and colliding saccades. Then, in Chapters 5 and 6 we consider a learning mechanism in the basal ganglia that allows the acquisition of conditional behaviors. In Chapter 7 we examine the ability to generalize these behaviors, and in Chapter 8, we see how these mechanisms are affected by disease. 67 Chapter 4 Shared and Interacting Mechanisms for Double- Step and Colliding Saccades Saccadic eye movement has been extensively studied in terms of behavior and the corresponding electrophysiology, yet this system continues to elude a final functional neurobiological characterization. Transformations must be performed to update "retinal error" as eye position changes, and also to account for delays in the system so that visual and eye-position information is temporally aligned. Different paradigms suggest different mechanisms for spatial accuracy, and challenge us to reconcile their respective functions. Here we consider in detail two paradigms that introduce a discrepancy between retinal images of targets in space, and the motor commands necessary to attain those targets. We develop two partially redundant mechanisms to address the two sets of data, and recall that additional mechanisms that utilize allocentric cues may contribute to the observed behavior. Experiments are suggested that may help reconcile some questions that remain.________________________________________________________ 4.1 Introduction Single unit recording studies of PP (Andersen et al. 1990, Barash et al. 1991b), FEF (Segraves and Goldberg 1987) and SC (Sparks 1986) during visual and memory guided saccades, and stimulation of FEF (Bruce and Goldberg 1984) and SC (Robinson 1972) indicate that cells in these regions code saccades in terms of direction and amplitude (sometimes modulated by eye position), rather than head-centered spatial 68 locations. In this chapter we consider two saccade paradigms in which retinotopic coding alone is inadequate to explain spatial accuracy of the saccades. The primary controversy we address involves localization of the mechanism that allows a saccade to accurately attain its target when an intervening saccade takes the eyes away from the location at which that target was specified. The problem is that in many oculomotor structures, saccades are coded as a displacement from a given eye position, rather than as a final location. Hence that coded displacement is only valid if either: a) the saccade begins from the eye position at which the target (displacement) was specified by a retinal image, or b) the displacement code is updated to account for the intervening change in eye position. Some experimental conditions indicate that this update has already occurred at the level of the FEF (Goldberg and Bruce 1990), while other experiments demonstrate that the transformation occurs downstream from FEF (Schlag and Schlag-Rey 1990). The problem is confounded by additional mechanisms that appear to rely on allocentric cues in correctly performing this transformation (Dassonville et al. 1992). The first paradigm that we consider involves the execution of two saccades in rapid succession to the locations of two sequentially flashed targets, each of which disappears before the first saccade - the double saccade. Here, the initial retinotopic encoding of the second target does not correspond to the saccade required to fixate it, since the eye is displaced by the saccade to the first target. However, human (Hallett and Lightstone 1976) and non-human (Mays and Sparks 1980) primates can make these saccades, though the accuracy is considerably affected by differences in delay between the retinal error input and the representation of eye position. This accuracy is somewhat improved by the brain's damping of the representation of eye position that is combined with the retinal location of the second target (Dassonville et al. 1992). The accuracy can be further improved when allocentric cues become more salient (Dassonville et al. 1992), which may be an important concern in our subsequent data analysis. In the double-step paradigm (Fig 4.1), two targets are briefly flashed after the j offset of a central fixation point, and the subject must make saccades to the two target locations, in the order of presentation, as quickly and accurately as possible. The j second saccade, AB, can be produced if vector OA, the eye movement occurring after presentation of B, is subtracted from the retinal error OB. This implies a need to know 69 where the eye was when B was presented. To compensate for changes in eye position that might occur during neural transmission delay of the retinal error after B’ s presentation, the brain uses a damped eye position signal (DEPS) that approximates this delay (Dassonville et al. 1992). variable j V VE A AB = OB - OA AB = RB - RA O Figure 4.1 Double Step Saccade. To produce a correct second saccade in the double-step task, saccade vector OA can be subtracted from retinal error vector OB, yielding saccade vector AB. If B is presented during the saccade to A (e.g while the eye is in position R ), then RA can be subtracted from RB, if R is known, to yield AB. U \ _________________ StimforFV ------------------- a - ™ A FV stim AB = FV - RA AB = RB - RA | Figure 4.2 Colliding Saccade. FV is the saccade evoked by FEF stimulation while the eyes are fixed. In a collision, stimulated saccade vector FV is modified by subtraction of RA, where R is the brain's estimation of the eye position (DEPS) at the time of the fictive target flash whose activity is simulated i in FEF by electrical stimulation. i i Use of the same DEPS has been demonstrated in the second paradigm we consider, the colliding saccade. In the FEF colliding saccade (Fig 4.2), during an i ongoing movement a second saccade is induced by stimulation of the FEF (Schlag and 7 0 Schlag-Rey 1990, Dassonville et al. 1992). Stimulation that begins immediately after the the initial movement onset evokes saccades that compensate for m ost of the intervening eye displacement As the stimulation comes later after the initial movement onset, the compensation is reduced. The dependency on timing indicates that a DEPS is used in producing the compensation (Dassonville et al. 1992b). This suggests that a common shared mechanism, downstream from FEF, subtracts the eye movement, RA, that occurs after B presentation (with the eye at R) from the retinal vector RB (or FV in the collision) to generate the correct second saccade AB, and that reconstruction of RA uses a damped estimation of eye position R to account for transmission delays. In contrast to this conclusion, however, the results of such a subtraction have also been seen upstream from FEF in parietal cortex (e.g. Gnadt and Andersen 1988) and in FEF itself (Goldberg and Bruce 1990) during double-step saccades. DCEP trig [OPN RI ^ R e tin a T ' VisCx delay OMN PL LLBN, MLBN FEF EBN TN 7a/LIP DCEP - damped change in eye position 7a/LIP - oculomotor regions of parietal cx FEF - frontal eye field SCd - deep, motor layer in superior colliculus LLBN, MLBN - medium and long lead burst neurons EBN - excitatory burst neurons OPN - omni-pause neurons RI - resettable integrator TN - tonic neurons OMN,PL - oculomotor neurons, plant trig - OMN trigger from FEF and SC 0 - saccade dimension 0 - saccade velocity F igure 4.3 Shared and Cooperating Spatial Accuracy Mechanisms. Mechanism A is a Droulez-Berthoz (1991) style dynamic memory that updates motor error via an efferent velocity signal that is approximated by DCEP. Mechanism B subtracts DCEP from the retinal error in FEF, yielding an approximation of the correct second saccade vector. 71 In Fig. 4.3, we display the possible arrangement of two spatial accuracy mechanisms A and B, placed within the existing model of the oculomotor saccade system from Chapter 3, in order to address the requirements of the double and colliding saccades. M odel "A" employs only mechanism A, with the results of its transformation projecting to FEF and SC to generate correct behavior in the double saccade, and generation of the FEF activity reported by Goldberg and Bruce (1990). This model fails in the FEF collision, however, because the transformation occurs upstream from FEF. We then consider model "B," in which the transformation is only performed downstream from FEF by B, and does not influence SC (Schlag-Rey et al. 1990). This arrangement performs both colliding and double saccades, but misses some electrophysiology data. Finally we consider how these two mechanisms may cooperate. In the parallel model "AB," A's transformation influences SC but not FEF, so that the FEF signal is modified only by B, and not by A. We then compare the models' behavior and electrophysiology results and consider how a single model might explain a variety of data. 4.2 Cortical Dynamic Remapping Evidence of the remapping discussed above was found in the form of tonic quasi visual (QV) cells and phasic saccade-related cells (SR) in the intermediate layers of the superior colliculus (Mays and Sparks 1980, Sparks and Porter 1983). After the initial saccade, the QV cells that encoded the topographic metrics of the (correct) second saccade, were tonically active even though a visual stimulus did not appear in the receptive field of these cells. The SR cells were similar, but produced saccade-related bursts encoding both correct second saccades in double step trials, and also single saccades in their preferred direction. Many of these trials involved two distinct targets, rather than the "round-trip" (a phrase coined in the Schlag laboratory) double saccade in which the second saccade is a return to the original point of fixation. In addition, the trials were intermixed with controls for non-specific effects of double saccades, so the animal was not able to predict the occurrence of a given trial (Mays and Sparks 1980). This type of response has been found in the cortex as well. Gnadt and Andersen (1988) found cells in the posterior parietal cortex that appear to code for future eye movements and show QV cell behavior similar to that reported for the SC. In a double saccade task they found cells in the lateral intraparietal area (LIP) of PP that code for the second eye movement though a visual stimulus never falls in the cells’ receptive field. They propose that PP may receive corollary feedback activity of saccades, suggesting that PP has access to eye position information that could be used in generating the QV shifting activity. Colby (1991), Goldberg et al. (1990) and Barash et al. (1991b) reported on similar cells in LIP that perform this retinal to oculomotor transformation. While most QV activity is seen after the first saccade, Duhamel et al. (1991) reported on 16/36 (44%) cells in LIP that showed possible evidence of predictive QV activity - that is, prior to a saccade, the cells responded to stimuli that would be in their receptive field following that saccade. Unfortunately, the paradigm allowed for ample prediction, including repetitive blocked trials with fixed target and visual stimuli locations. Indeed, this kind of predicted response is common in repetitive paradigms, and it is not clear from this study if such a predictive mechanism would be observed in non-repetitive settings. In addition there are neurons in FEF that have response properties similar to those of QV cells (Goldberg and Bruce 1990). Coding for the second saccade in the double saccade, these cells demonstrate the right m ovem ent fie ld and the w ro n g receptive fie ld responses for the second target, characteristic of QV cells, and are referred to as right-MF/wrong-RF cells (Goldberg and Bruce 1990). Thus, under some two-target double saccade conditions, a remapping of the second target can be observed in PP, FEF and SC. Given this data, we ask if there is a single source of QV-like activity, or if it is generated intrinsically at each site. The studies of Schiller and Sandell (1983) which showed that lesion of SC or FEF leaves double saccades intact might argue that the remapping is intrinsic to these two areas, allowing them to operation in isolation. However, the use of multiple sites for remapping introduces the problem of coordination so that representations are not remapped more than the appropriate amount. In contrast to the notion of intrinsic remapping at PP, FEF, SC and possibly other sites, we consider that the structure farthest upstream - here the PP - is the source of the remapping, and via projections including those to the FEF and SC, this activity 73 is transmitted to those structures. The hypothesis that the remapping may be central rather than intrinsic is supported by recent evidence from an individual with a cortical lesion involving the frontal and parietal lobes, encompassing the right FEF and right intra-parietal sulcus (Duhamel et al. 1993). This patient made double saccades if the first saccade was ipsi-lesion, but failed to make an accurate second saccade if the first saccade was in a contra-lesion direction. These authors interpret the results in terms of an inability to register and use information related to the amplitude and direction of a saccade to the contra-lesion field. If the SC were capable of performing the required spatial remapping via intrinsic mechanisms, rather than receiving this information from cortical sources, we would expect the function to remain intact in spite of this lesion. In summary, cells have been seen in SC (Fig. 2C Sparks and Porter 1983), in LIP (Fig. 16 Barash et al. 1991b, Fig. 3B Gnadt and Andersen 1988, Fig. 5 Goldberg et al. 19901 ) and in FEF (Fig. 2D Goldberg and Bruce 1990) whose movement fields correspond to the second saccade in a double step trial. In each of these cells the activity increases after the first saccade, and remains elevated until after completion of the second movement. Based on this data, and the fact that a temporal coding of eye position information is available in that area (Gnadt and Andersen 1988, Anderson et al. 1990, Sakata, Shibutani, Kawano 1980), we suggest that efferent eye position signals produced upstream from the abducens nucleus are used to direct the QV shifting in PP, and that PP is the origin of the QV activity that is seen in SC and in FEF. This belief is strengthened by the result that compensatory saccades could be elicited by stimulation of either SC or FEF when the other area had been lesioned (Schiller and Sandell 1983). Since PP projects to both FEF and SC, it is likely involved in the QV shifting in both of these areas. This allows us to simulate a variety of experiments, and provide one explanation for the presence of QV cells in LIP and SC, and right- MF/wrong-RF cells in FEF. Using PP as the source of dynamic remapping also eliminates the need to explain why targets don't accidentally get remapped three times - in PP, then in FEF then in SC. A pparently these trials were run in blocks o f 16, which permits some predictive or anticipatory element in the unit's activity. 74 Visual input from output c) 1-D Spatial convolution masks • inhibitory Q excitatory Qj b) Rightward Shift (leftward saccade) - T T T > , opauai u S y V delay ----- ------ ----- ™ V V \m \ H |g Leftward Shift (rightward saccade' No Shift | H I (eyes stationary) . . . — — — ■ — mmrn----- 1 x-1 x x+1 Figure 4.4 Mechanism for Dynamic Remapping Using Eye Position. One dimensional case, a) PPqv cells receive inputs from their nearest neighbors via type "S" (shifting) interneurons, as well as self excitation, via type "r" (reverberatory) intemeurons. "S" neuron gates the flow of information between PPqv neurons according to the signed difference between the two damped version of the eye position signal TN. The leftmost eye position produces TN’ s lowest firing rate, and the rightmost position it’ s highest, b) A leftward saccade will generate dynamic remapping that shifts to the right. TNdelay-TN will be positive, so the S’ neuron allows activity from PPqv’ to excite PPqv. S" has the sign of its gating inputs reversed so PPqv" inhibits PPqv through s". Thus, as a mound of activation shifts from left to right, it erases the activity behind it, preventing a smearing of the activation on the map. The type r neuron gates the self activation of the PPqv cells based on its unsigned input. With no input this cell allows complete self excitation of PPqv. As the input (the unsigned difference between TN and TNdelay) increases, r reduces PPqv’ s self excitation, c) Convolution masks used to implement this shifting. When a cell is being updated, the convolution mask specifies how the neighboring cells will influence it. In a rightward saccade, the mask shown will cause a PPqv cell to be excited by its neighbor on the left, inhibited by its neighbor on the right and partially self excited - the same as performed by the S and r neurons. 75 Droulez and Berthoz (1990) implemented a model of predictive dynamic memory for motor error that takes into account intervening movements. The 2-dimensional model represents the motor error surface of SC. Changes in eye velocity, due to an eye movement, modulate the activity of cells in the two dimensional layer to produce a spatial shift in the locus of activity that corresponds to the predicted motor error for the visual target in the compensatory saccade. We employ a similar mechanism to effect compensatory shifts of activity in a motor error map. QV cells in Posterior Parietal cortex (PPqv): To date, a representation of eye velocity has not been recorded in posterior parietal cortex. In Fig. 4.4 we illustrate how two damped eye position signals can be used in a neural architecture for dynamic remapping. The difference between the two position signals is used to modulate two types of intemeurons. Type "r" neurons implement rec u rren t self-excitation of the PPqv cells when the eye position signals are equal, which is reduced when the eyes are moving. The type "S" intemeurons gate the lateral sh ift of activation between neighboring cells as a function of the difference between the two position inputs. In a leftward saccade, the difference between the delayed signal and the original signal (calculated by S') is positive (see Fig. 4.4b), so activity shifts from left to right, from PPqv' to PPqv. In our implementation of this network, the function Shift () generates a spatial convolution mask (QVMASK) from damped2 horizontal and vertical eye position components coded by the horizontal and vertical tonic neurons in the brainstem saccade generator, HTN, HTNdamp6, VTN and VTNdamp6 respectively: QVMASK = Shift(HTN, HTNdamp6, VTN,VTNdamp6)*1.23 (1) The function Shift () returns a mask with the following elements: QVMASK[x-l,y] = (HTNdamp6 - HTN)/q QVMASK[x+l,y] = (HTN - HTND AMP6)/q QVMASK[x,y-l] = (VTNdamp6 - VTN)/q QVMASK[x,y+l] = (VTN - VTNdamp6)/q QVMASK[x+l,y+l] = ((HTN - HTNdamp6) + (VTN - VTNdamp6))/r QVMASK[x-l,y-l] = ((HTNdamp6 - HTN) + (VTNdamp6 - VTN))/r QVMASK[x-l,y+l] = ((HTNdamp6 - HTN) + (VTN - VTNdamp6))/r QVMASK[x+l,y-l] = ((HTN - HTNDAMP6) + (VTNdamp6 - VTN))/r QVMASK[x,y] = [1- ( I VTNdamp6 - VTN I + I HTNdamp6 - HTN I )/q] 2 We believe that the brain approximates a delayed position signal by using a damped signal. Even in cases where a perfect delayed signal would be preferable, the brain appears to approximate the delayed signal with a damped one (Dassonville, Schlag, Schlag-Rey 1990). 76 xHTNdamp6 = 6 ms s HTNdamp6 = HTN (2) tVTNdamp6 = 6 ms SVTNdamp6 = VTN (3) Here, x,y is the central element of the mask, and q and r are constants with values 100 and 160 respectively. These values were determined to ensure that the QVMASK elements vary between -1 and 1 as required for a given velocity. This QVMASK represents the function of the S and r cells in the neural network shown in Fig. 4.4. Essentially, the QV shifting performs a spatial integration of the change in position, to yield a mirror image displacement on a spatial map. By modulating the connections between neighboring cells in PPqv as a function of eye position signals, a spatial shift of activity is produced in the PPqv layer. Note that all symmetric pairs of elements in the mask have the same value with opposite signs. Positive values induce shifting, and negative values erase the "trail" behind a shift. When the velocity is zero the central element of the mask, (x,y) is 1.233, yielding convolution mask that causes no shifting. As the rightward horizontal velocity increases, the mask element to the right of center increases in value, the element left of center decreases its value, while the central element decreases by an equal amount. Convolution with this mask will cause a leftward shift of activity in PPqv, compensating for the rightward eye movement, by causing a neuron to be activated by its neighbor on the right (recall the previous discussion of convolution). In our simulations, the QV activity generated in PPqv provides input to SC for the correct generation of the saccades in the double saccade task. Application of the QV convolution mask to the parietal cortex QV cells themselves yields: tpPqv = 6 ms SPPqv = PP + QVM ASK’PPqv (4) 3 As a target is being shifted, there is some lateral spreading of its activity. The result is that at the end of shift, the resulting target activity will be reduced. A value greater than one is required to account for the reduction in a target representation's activation that occurs when shifting takes place. When the eyes are stationary, this acts as a form of spatial memory as seen in the Droulez-Berthoz model. ____________________________________________________________________________________ 77 j PPqv QVMASK QVMASK QVMASK SACCADE:DoubleSaccade F ix a tio n _ P o m t Target_A RightRF_W rongM F LAYER:FEFvis RlghtM F_W rongRF LAYERiFEFvls Hori2 o n tal_ E y e_ P o s t l : 1.00 Figure 4.5 Dynamic Spatial Remapping Simulation: Double Saccade. This figure illustrates the QV convolution mask and resultant shifting activity that is seen in posterior parietal cortex PPqv during the course of the double saccade task defined in Fig. 1C. The convolution mask is generated from temporally offset horizontal and vertical eye position components. When convolved with PPqv in eqn. 2, the QVMASK represents local cellular interactions thought to implement the QV shifting in parietal cortex. The result is that the new locus of activity that codes for a saccade has been updated by shifting in the opposite direction and magnitude of the initial saccade. A. The first frame (left) shows the configuration just following the presentation of the two stimuli, prior to the first saccade. In the second frame, during the initial 20 degree leftward saccade, the QVMASK indicates that PPqv cells are excited by their neighbors on the left, and inhibited by those on their right - generating a rightward shift. The third frame shows that following the completion of the first saccade, the updated locus of activity for the second target (now shifted 20 degrees to the right) becomes the next saccade target. B. The time-course of presentation of central fixation point and two targets is shown. In eqn. 10 we see that FEFvis receives its input from PPqv. The two traces labeled FEFvis indicate the activity of two FEF cells - one with a visual and movement field corresponding to the retinal location of the second target when it is presented (right-RF/wrong-MF) and a second cell with the visual and movement fields corresponding to the dynamically remapped retinal error of the second target (wrong-RF/right-MF. Thus, by using PPqv as input to FEFsac, we see the same responses as recorded in FEF by Goldberg and Bruce (1990) during the double saccade. The horizontal and vertical eye positions are provided by EyeH and EyeV respectively. In this instance the first target is 20 degrees left - indicated by the downward deflection of EyeH. The second target is 30 degrees up, but it must compensate for the 20 degree rightward saccade, so the compensatory movement from A to B is an oblique saccade 20 degrees right and 30 degrees up, shown in the EyeH and EyeV traces. Both the first and second saccades brought the eyes their respective targets with less than 1 degree of error. Figure 4.5 illustrates the QV convolution mask and resultant shifting activity that is seen in parietal cortex, FEF4 and in SC during the course of the double saccade task. The simulation accurately generates activation of the PPqv cells that code for the dynamically remapped second saccade. We also illustrate the activation of cells receiving PPqv input in FEF that represent the right-MF/wrong-RF and wrong- MF/right-RF cells discussed by Goldberg & Bruce (1990). We see here how dynamically updating a motor error map by shifting activity profiles in the opposite direction of the saccade yields the functional equivalent of a spatiotopic map embodied in motor error coordinates. The dynamically remapped spatial information contributes to the second saccade via multiple routes: 1) PPqv to SCqv, 2) PPqv to FEFsac to SCsac and 3) PPqv to FEFsac to LLBNs. This helps explain Mays and Sparks (1980) 4 A s we make explicit shortly, we believe that a majority o f the FEF saccade related cells receive input from PPqv. 79 and Goldberg and Bruce (1990) found that correct performance of this task was "a natural behavior if the monkey was already well trained to follow single-step displacements" (Goldberg and Bruce 1990 p. 492)5. Discrete or Continuous Remapping? Recall the response characteristic of the QV dynamic remapping: shifting a target to a new location will yield activity with the right movement field and wrong receptive field. In the double saccade paradigm, Goldberg and Bruce (1990) reported that a significant majority of all movement, visuomovement and visually responsive cells they record from displayed the right-MF/wrong-RF with respect to the second saccade. Goldberg and Bruce (1990) suggest the dimensions of the second saccade are obtained by vector subtraction of the dimensions of the first saccade (encoded by post-saccadic cells) from the vector described by the retinal location of the target (encoded in visual cells). This mechanism is discrete - subtracting one entire saccade from another. The neural circuit for this mechanism would require long distance connections between all neurons in FEF involved in this vector manipulation. This is in contrast with the local connections required in the continuous mechanism we suggest, which produces the same net vector subtraction, but does it continuously, in small pieces that are mediated by local connections alone. The findings of Schlag, Schlag-Rey and Dassonville (1990), that saccades can be aimed at the location of targets flashed during pursuit argues for a continuous, rather than a discrete mechanism. The most compelling evidence that the mechanism is continuous are the error results in Dassonville et al. (1990) which indicate that a damped eye position signal, rather than an accurate post- saccadic activity, is used to produce the remapping. In Fig. 4.6 we illustrate how the continuous effect of this damped position signal can be seen in the double saccade. The QV shifting acts as a spatial integrator of the velocity signal. If the second target is presented late, near the first saccade onset, by the time it reaches PPqv, some of the velocity signal has already been missed, and the shifting is less than required, producing an error in the direction of the first saccade. 5We must be aware of a distinction in double saccades: Case 1: the second target is the fixation point, i.e. the sequence is F - A - F, versus Case 2: the second target is not the fixation point, i.e.. the sequence is F - A - B. The case 1 double saccade is a natural behavior, whereas the case 2 double saccade is difficult for the animal and takes additional training (Schlag, personal communication.) 80 DoubleFamiiy:A E ye_ P o sitio n EyeH LAYERiEyeH wym ln:-10.00 wymax:50.00 ts:0.36 t0:0.00 EyeV LAYER:EyeV wymin:-'! 0.00 wymax:50.00 ts:0.3G t0;0,00 t1;0.50 E J Figure 4.6 Damped Signal Effect: In this family of curves we see that the second saccade may undershoot the target if presented near the first saccade onset. In order to improve the spatial resolution in this investigation, we modified the 9x9 format to 19x19 for all subsequent simulations. In Fig 4.6, the first target is 40° right, and the second 30° up, so the final horizontal component should be zero. In the window labeled EyeH, the horizontal eye position traces for different trials are presented such that the rightward extent of each line indicates the second targets' relative presentation time with respect to the first saccade. For targets presented well before or well after the first saccade, the accuracy of the second saccade is good, whereas for those inbetween, there is an undershoot, or error in the direction of the first saccade. This is due to the fact that the entire change in position signal must be 81 used to perform the QV shifting. If the target appears late, some of the initial change in position will not effect it, and it will be undershifted. Again, this argues for continuous shifting. It is likely, however, that for the double saccades in which the second target is the original fixation point (round trips) the existence of post-saccadic cells specialized for this function (Bruce and Goldberg 1984) may bypass or supplement the continuous mechanism. Indeed, cells that code for the second movement in these retraction double saccades begin to fire almost immediately after the first saccade, whereas in the two target double saccade, the cells coding the second target respond about 100ms later (Goldberg and Bruce 1990.) In addition, the allocentric mechanism demonstrated by Dassonville et al. (1992) also appears to bypass or supplement the continuous shifting mechanism. 4.3 Brainstem Dynamic Remapping The second type of experiment that we consider is the colliding saccade (Schlag and Schlag-Rey 1990), in which an electrically stimulated saccade collides with an ongoing saccade (Fig. 4.2). In previous stimulation studies, it was shown that fixed vector eye movements (fixed amplitude and direction, independent of initial eye position) were evoked by stimulation of FEF, SC and thalamic (rostral IMLc) sites. However, when these structures are stimulated during ongoing movements the elicited saccades are different from the fixed vector movements as depicted in Fig 4.7. Depending on which structure is stimulated, the brain compensates for different components of the ongoing movement. With deep SC, no compensation is seen - the fixed vector simply interrupts the ongoing movement which then continues to the original target. Stimulation of superficial SC (SCsup) produces compensation for the movement occurring between the time of stimulation and the collision (Schlag-Rey et al. 1989). With FEF stimulation, the system appears to approximate the reference position at which a retinal stimulation by a visual target would have led to the activity that is electrically induced in I the experiment, i.e. the putative transmission delay is compensated for. The targeting ; saccade (to the spatial location of the fictive stimulated target) is then made with respect to this approximation of the previous eye position (Dassonville, Schlag, Schlag-Rey I 1990). 82_ _ In the FEF collision, the error signal leaving FEF is transformed to account for the eye movement that occurred during the delay from the retinal sampling of the target to the execution of the saccade. In our current formulation, the PPqv shifter cannot produce this transformation since it is upstream from FEF. It also appears that the transformation does not occur in FEF itself, as Schlag-Rey et al. (1990) found that in the FEF collision, the SC cells corresponding to the fixed vector (and not to the evoked movement) were activated by this FEF stimulation, indicating that no compensation for the previous movement takes place between FEF and SC. FV vector retinal error AE / retinal error from time of hypothetical flash Case 1: Deep SC - no compensation, saccade = FV Case 2: Superficial SC - compensate for efferent delay saccade = FV - E Case 3: FEF, IMLc - compensate for efferent and afferent delay. saccade = FV - AE Figure 4.7 Colliding Saccades Modify Fixed Vector Saccades. (Modified from Schlag and Schlag-Rey 1990 Fig 1) FV - fixed vector saccade evoked by electrical stimulation, stim - duration of electrical stimulation applied during execution of initial saccade. E - component of initial saccade that occurs during efferent delay between stimulation and collision. A - component of initial saccade that occurs during afferent delay between (hypothetical) retinal stimulation and resulting FEF activation. Illustration of different forms of compensation dependent on stimulation site. This suggests that the transformation occurs downstream from FEF. For SCd, there is no transformation. For SCs there is a transformation for the efferent delay, and for FEF and IMLc, a compensation for both efferent and afferent delays. W e note that the E and A components of the correction are equal in direction, and vary only by a scaling factor. Thus, the different effects of SCs and FEF collisions can be quantified in terms of a scalar multiplier. I I I _________________________________________________________________________ 83 1 In the model of Fig. 4.3, we place mechanism B downstream from FEF, well situated for producing the collision effect. Recall that the outputs of FEF are still in retinal (2-d map) form. In order to modify a map with a scalar value we introduce a convolution mask, FEFshiftMask, that will produce a shift equal and opposite to that DCEP. This mask performs a temporal-spatial transformation, subtracting DCEP from the target code in FEF. DCEP is the difference between two damped versions of the tonic neuron activity that codes position, produced as follows: %tn_dl = 6 ms shtn_dl = HTN HTNdl = htn_dl (5) %tn_d2 = 20 ms shtn_d2 = HTN HTNdl = htn_d2 (6) 'Mcepjh = 40 ms s dcep_h = HTNdl - HNTd2 DCEPh = dcepjh (7) The convolution mask is then produced by: FEFShiftMask (CntrlndexX + (DCEPh ) / c , CntrIndexY+(DCEPv)/c) = 1 ShiftedFEFsac = FEFshiftMask*FEFsac (8) where CntrlndexX and CntrlndexY specify the center of the mask, and c is a constant that divides DCEP to produce the appropriately scaled indices. While we do not explicitly implement this function in a network, the model of Mazzoni et al. (1991) performs a similar combination of temporally and spatially coded position signals to yield and update position signal, and thus would provide a plausible basis for a neural implementation of our FEFShiftMask. The input to the LLBN from FEF is thus modified in Eqn. 3a: Tllbn = 40m s s Ubn = W innerTakeAll(2.67*SC + 5.4*ShiftedFEFsac) LLBN = sigmiod(llbn, 0, 950, 0,950) (9:3a) 84 SC_CoilisionFamily:B GO Eye_Position EyeH LAYER:EyeH w ym in :-10.00 wy rnax:50.00 ts:0.42 t0:0.00 FEFCollisions:B @ Eye_Position EyeH LAYER:EyeH w ym in:-10.00 wy m ax:50.00 ts:0.42 t1:0.50 Figure 4.8 Colliding Saccade Simulation: Mechanism B: Visual saccade 40° right, stimulated saccade 30° up. Above- SCd collision. Below - FEF collision. 85 Schlag and Schlag-Rey (1990) and Dassonville, Schlag and Schlag-Rey (1990) note that in FEF collisions, as the delay between the initial saccade onset and the electrical stimulus increases, the influence of the first saccade on the second one decreases exponentially. We see this in the set of curves in Fig. 4.8B The upper traces there represent the horizontal eye position during a collision. In the successive plots, the stimulation is delayed by intervals of 20-30 ms up to 160 ms, with the shortest trace for a stimulation just after saccade onset. We see that the collision effect decreases as the delay between saccade onset and stimulation increases. This supports the view that the brain maintains a damped, rather than delayed, position signal. 1 - 1 [1] E y e _ P o sitio n EyeH LAYER:EyeH wym in:-10.00 wymax:50.00 ts:0.40 I "V t0:0.00 EyeV LAYER:EyeV w ym in:-10.00 wymax:50.00 ts:0.40 t0:0.00 t1:0.75 Figure 4.9 Mechanism B - Double Saccade Simulation: First target 40° right, second target 30° up. 86 In Fig. 4.9 we see a family of double saccades produced by mechanism B, again with the visible effect of the time-course of DCEP. Recall that mechanism B, downstream from FEF, samples the DCEP when FEF is active for the second target, and combines the DCEP signal with the FEF output. If the second target is presented well before the first saccade, then by the time the FEF becomes active for the second saccade, the DCEP has registered the change in position due to the first saccade. The DCEP is then combined with the retinal error signal in FEF to produce second saccade that compensates for the first. If, however, the second target is presented late, then the by the time FEF registers the retinal error, the DCEP is diminishing, and we will see an under compensation. Targets appearing during the saccade will be have part of the compensation already in the retinal signal due to the eye movement, and partially due to DCEP and mechanism B. 4.4 Interacting Mechanisms We now recall the original controversy concerning the localization of compensation for intervening eye movements. Our mechanism A agrees in part, with the interpretation of Goldberg and Bruce (1990) that the compensation will be seen in FEF. We differ from them, by making PP, rather than FEF, the source of that transformation in our implementation of mechanism A. This cannot be the complete story, however, as mechanism A, while addressing double saccade data, fails in the FEF collision test. Based on observations from the Schlag laboratory, we introduce mechanism B, downstream from FEF, where it can address both double and collision studies, but fails to reproduce some of the QV electrophysiology. We note an additional difference between A and B. In A, during the first saccade (SI), the activity in the PPqv for the second target (T2) is shifted to account for SI. Until the activity for T2 becomes stable again after completion of SI, it does not reside in any one location long enough to evoke a saccade. This phenomenon produces the second saccade’ s latency. In mechanism B, there is no QV shifting, so as soon as the T2 code arrives in FEF it can begin to command a saccade. This can lead to execution of the S2 with a latency that is much too short. We addressed this issue by introducing a refractory period such that once active, the OPNs cannot be shut off again prior to a delay after the previous saccade has completed. If the OPNs are already silenced, however, then an incoming command can be executed, as in the colliding paradigm. We implement this by modifying the equation for the trigger cells as follows: T trig= 6 ms Strig = (FEFsac + SC)*Ksst TRIG = max(trig)*PauseRefractory (10:8a) PauseRefractory = step(DCEP, Refractory Threshold, 1, 0) (11) After a saccade, the DCEP remains non-zero during its decay. Until it is less that RefractoryThreshold (200), the trigger cells cannot be activated, thus producing the second saccade latency. In the double saccade, after the refractory period, the pause neurons are silenced, and the updated second saccade, proceeds. There are two issues here. First, the signal that contains the FEF activity updated by eye position must be maintained somewhere during this latency. In one implementation, the PP and thus FEF continue to fire during the second latency, and are combined with the eye position that was sampled at the start of activity in FEF. This predicts that in PP and FEF we will see activity related to the second saccade that is not updated, and activity downstream from FEF that is updated. The questions then remain, 1) what are the right-MF/wrong-RF cells doing in FEF (Goldberg and Bruce 1990), and 2) why isn't their activity transformed downstream by B? One interesting explanation would involve a connection back to FEF from mechanism B, in which the FEF motor error activity is combined with DCEP, and then stored back in FEF. In this sense, FEF will initially show right-RF/wrong-MF activity for the second saccade, and then after the eye position information is added, it will display wrong-RF/right-MF activity, as demonstrated by Goldberg and Bruce (1990.) This is an open issue that we continue to investigate, and discuss below. 88 MODEL DATA A B AB Sparks(l) yes no yes Schiller(2) yes no yes Andersen (3) yes no yes Schlag(4) no yes yes Goldberg(5) yes (7) (7) Dassonville(6) yes yes yes Table 4.1 Comparison of Compensation Model Configurations 1. Mays and Sparks 1980, Sparks and Porter 1983: Evidence of vector subtraction seen in SC during double and compensatory saccades. 2. Schiller and Sandell 1983: With FEF or SC lesion, saccades to visual targets compensate for intervening saccades stimulated in unlesioned area. 3. Gnadt and Andersen 1988 - vector subtraction in parietal cortex during double saccades. 4. Schlag and Schlag-Rey 1990: FEF collisions demonstrate subtraction of component RA from the stimulated saccade FV (Fig 4.2). 5. Goldberg and Bruce 1990: Cells with the right movement field and wrong receptive field (R-MF/W-RF) for the second target are seen in FEF, indicating that the subtraction of FA has already occurred there (fig. 4.1). 6 . Dassonville, Schlag and Schlag-Rey 1992: The same damped position signal is used in both double-step and colliding saccades. 7. If the output of transformation B is made available in FEF, then R-MF/W-RF cells could be seen in FEF with "B" and "AB." To comply with the observation that SC cells receive specification of FV rather than AB in FEF collisions (Fig 4.2), a non updated population of FEF cells would project to SC and an updated population to the brainstem. A single mechanism (B) can combine retinal and eye position information to yield double-step and colliding saccade behavior. Augmented with remapping mechanism, A, and the provision that FEF gets input from the non-QV cells from parietal and other visual cortical areas, model "AB" provides an explanation for R-MF/W-RF cells in parietal cortex and SC. The question still remains to explain R-MF/W-RF cells in FEF. We consider three possible explanations, that will suggest experiments in a later section. 1. The brain uses allocentric cues (e.g. spatial or temporal proximity of two targets) | in producing more accurate saccades (Dassonville et al. 1992.) R-MF/W-RF activity in j FEF may be due to allocentric mechanisms. Elimination of the R-MF/W-RF activity in FEF by using the non-allocentric (targets temporally separated rather than contiguous) double-step paradigm (Dassonville et al. 1992) would support this explanation 2. A subpopulation of FEF cells may receive output from B, and project to LLBNs but not SC. That the collision effect is seen in all FEF cells from which saccades can be stimulated (Dassonville et al. 1992b) argues against separate populations. 3. A and B may operate under different conditions - e.g. A, when double saccades are planned, and B when a target appears suddenly, during a saccade, as simulated in the collision. 4.5 Simulation Results In the previous sections we presented graphical displays of double and colliding saccade experiment simulations. Here we provide numerical data for some these and other related paradigm simulations. 4.5.1 Double Saccades Double saccades (Fig. 4.51: In the double saccade task, the motor error representation of the second target is dynamically remapped to compensate for the intervening movement. By using the PPqv layer as input to the FEFvis layer the FEF can contribute to the correct specification of both saccades in the double step task. As seen in Fig. 4.5, the model produces both types of double step related FEF cells reported by Goldberg and Bruce (1990), cells with the right receptive field but wrong movement field, and cells with the wrong receptive field and right movement field. We differ from Goldberg and Bruce in our interpretation of these cells' presence, as our model indicates that the compensation is not necessarily intrinsic to FEF. Table 4.2 provides the details of two characteristic double step saccades using mechanism A. In both cases, the first and second saccades resulted in eye position error of less than one degree. 90 Table 4.2 Double saccades Protocol: Time course DS.I DS.n 0.0 - 0.02 fixation (0, 0) ( 0, 0) 0.02 - 0.07 targetA (0, 30) (-20, 0) 0.08-0.12 targetB (30,30) ( 0,30) Sacc.A start Sacc.A end ampl ygl Sacc.B start Sacc.B..eM— amp--------- 3 £ fil DS.I .130 .190 30 500 .230 .300 30 428 DS.II .135 .185 20 400 .225 .280 36[20,30] 654 4.5.2 Compensatory and Colliding Saccades Com pensatory Saccades: In an effort to understand the role of SC in compensation for eye movements, Sparks and Mays (1983) substituted an electrically stimulated saccade for the first saccade on a double saccade task. After the brief I presentation of a target, the eyes are driven to another location by electrical stimulation. As in the double saccade, the system compensates for the first (stimulated) movement, bringing the eyes to the correct spatial location for the second target. Continuing with the same compensatory saccade paradigm, Sparks and Porter (1983) recorded from SC cells that had the correct movement field for the compensated movement, and found that 49 of the 50 cells they studied discharged before all saccades in their movement field, whether in a visual, double or compensatory saccade task. We simulate electrical stimulation of both FEF and SC, including the Schiller and Sandell (1983) experiments in which one of SC or FEF was lesioned and the other area was stimulated. We repeat eqns. 7 and 15 from Chapter 3. For FEF stimulation we set the k l parameter to 1.58 in eqn. 7, and apply electrical stimulation at 175 Hz for 40ms to various locations in FEF. For SC stimulation we set the k l parameter to 2.9 in eqn. 15, and apply electrical stimulation at 175 Hz for 40 ms to various locations in SC. The timing and movement data for these trials are summarized in table 4.3. X fef_sac = 8 ms Sfef_sac = FEFvis + 2*FEFmem - 3*FOn FEFsac = sigmoid(fef_sac, 0, 90, 0,90) + kl*ElectricalStim (7) 91 T sc = 38ms Ssc = WinnerTakeAII(4*SCsup + 1.5*SCqv + SCsac - 2*FOn) + ElectricalStim SC = sigmoid(sc, 85,99,0,500) (15) For the FEF and SC lesions, we increased the strength of the projection of the remaining area to the LLBNs. For FEF lesion recovery, the SC to LLBN connection is increased from 2.67 to 5.0. For SC lesion recovery, we increase the FEF to LLBN from 5.4 to 9.4. These changes, we believe, correspond to the post-operative adaptation of the system that is reported by Schiller and Sandell (1983). Our simulations demonstrate that for the normal and recovered lesion states, the model generates compensatory saccades that are within 1 degree of accuracy for the two movements. T able 4.3 C om pensatory saccades Protocol: stim.1 (this stimulation reduces the target error) 0.0 - 0.02 fixation 0.02 - 0.07 target (30,30) 0.07-0.11 stimulation (0,30) Protocol: stim.II (this stim increases the target error - see Fig. 14) 0.0 - 0.02 fixation 0.02 - 0.07 target (0,30) 0.07-0.11 stimulation (-20,0) StimMvmtBeein StimMvmtEnd ampl vel VisMvmtBeff VisMvmtEnd am D vel SC stim.I 0.095 0.165 30 428 0.205 0.260 30 545 SC stim.II 0.100 0.150 -20 500 0.195 0.255 36[20,30] 600 FEF stim.I 0.095 0.160 29 446 0.200 0.255 30 545 FEF stim.II 0.095 0.145 -20 500 0.190 0.245 36[20,30] 654 SC lesion, FEF stim.I 0.90 0.130 -21 525 0.200 0.260 36[20,30] 600 FEF lesion, SC Stim.1 0.90 0.130 -21 525 0.195 0.250 36[20,30] 654 C olliding Saccades: We simulated these experiments by applying simulated stimulation to FEF and SC as described above in eqns. 7 and 15. For the SC collision 92 k l = 6; for FEF collision k l = 3.27. Note that in the colliding paradigm, the electrical stimulation occurs later than in the compensatory paradigm, generating a collision rather than a preemptive saccade. For these conditionshe final position for the SC collision was (37,-2), and was (41,-2) for the FEF collision, with the original target at (40,0). In the FEF collision, almost the entire first component was compensated for by the temporal remapping of the FEF signal (that had undergone the spatio-temporal transformation) in the brainstem. Thus, the reference position was at or near the location of the eyes during the onset of the saccade. T able 4.4 Colliding Saccade: Protocol: stim.schlag 0.0 - 0.02 fixation 0.02 - 0.07 target (40,0) 0.013 - 0.17 stim ulation^,-20) TgtMvmtBegin 0.125 0.125 Collision 0.155 0.160 amplitude 15(15,0) 15(15,0) velocity 500 428 CollisionEnd 0.190 0.190 Amplitude 20(0,20) 25(-16,20) Velocity 571 853 TgtMvmtResume .245 .250 TgtMvmtEnd .290 .295 Amplitude 30(21,22) 44(40, -20) Velocity____________ 675__________ 950 4.6 Predictions and Experimental Design 1. D ouble Step M em ory Saccade: In these two experiment we ask the questions: a) Does the spatial memory mechanism we have proposed have access to the shifted representations of the PPqv layer? and b) Can this access be interrupted? 93 j 1.1 Cooperation of spatial accuracy and spatial memory mechanisms: This experiment that combines the main elements of the double and memory saccades, illustrated in Fig. 4.10. After the fixation offset, two targets are briefly presented in succession, as in the double saccade. Just before the first saccade terminates, the first target location is re-illuminated. The first saccade brings the eyes to this location, so the target is on or near the fovea when it appears. This fixation returns FOn to activation, which inhibits the second saccade. At the same time the PPqv input to FEFvis and FEFmem initiates the inhibition of SNRmem, and the activation of the memory loop between FEFmem and THmem for representation of target 2's motor error that has been shifted to account for the first saccade, as illustrated by sustained activation of the FEFmem cell that codes for this updated location in Fig. 4.10 500 ms after it is re-illuminated, the first target is again removed. This causes FOn to return to non-active resting state, freeing the SC to implement a saccade to the remembered location. A summary of the timing and results for one trial are provided in table 4.4. Chapter 3 provides a reference for tracing the activity through PPqv, to FEFmem, FEFsac, the caudate and SNr sustained memory cells, the thalamus sustained memory cells (THmem), and when FOn is deactivated after the memory phase, finally to the SC and LLBNs to generate the delayed movement to the dynamically remapped target This experiment, then generates behavioral and electrophysiological predictions that test the function of our mechanism A. The behavioral prediction is that primates will be able to perform this task. The electrophysiological prediction is that some cells in the FEF that show sustained activity in the standard memory saccade will be found, in the double step memory saccade to show the right-MF/wrong-RF properties with sustained activity for the duration of the delay in this task. Table 4.5 Predictive Experiment: Combine FEF-Thal memory with QV sh iftin g Protocol: Double Memory Saccade 0.00 - 0.20 fixation 0.02 - 0.05 target A (0,30) 0.085- 0.10 target B (30,30) 0.165- 0.665 target A - eyes are there, fixation 0.665 - target A, the new fixation, offset BeginA Latncv EndA Ampl Vel BeginB Memory EndB_Ampl___Yd. 0.125 0.105 .175 30 600 0.715 .615 0.770 33 600 94 SACCADErDoubleMemSaccade Fixation_Point I 1 _______________ Target_A n _ j 1 Target_B — — f\____________ FOn Horizontal_Eye_Pos Vertical_Eye_Pos t1:1,00 Figure 4.10 Double step memory saccade: . This task combines the spatial accuracy mechanism used in the double saccade with the spatial memory mechanism used in the memory saccade. After fixation offset, TgtA is presented for 35 ms, followed by a 35 ms delay, then TgtB is presented for 15 ms. Just as the saccade to A is completing, TgtA is reintroduced. The fovea is located at the site of TgtA, so immediate fixation begins, and the FOn cell becomes active. This leads to inhibition of SC via FOn, as well as the inhibition of SNRmem by CDmem which is receiving input from FEFmem. The removal of SNRmem inhibition on THmem allows the FEFmem - THmem loop to store the shifted representation of TgtB from PPqv. Following the offset of TgtA, the standard memory saccade takes place, i.e. the FOn inhibition of SC and FEFsac is removed, leading to the production of a saccade to the spatially accurate remapped location of TgtB. 95 1.2 Dissociation of spatial accuracy and spatial memory mechanisms: Lesion studies indicate that the integrity of the dorsolateral prefrontal cortex is required in order to make saccades to remembered locations, while lesions of posterior parietal cortex do not impair the memory capability in the related delayed-response task (see Goldman-Rakic 1987 for a review). We have postulated that a mechanism for spatial accuracy maintenance resides in PP. A lesion of PP would, according to our model, deprive the intact dorsolateral prefrontal cortex of the corrected target motor error in the double step memory saccade.. If the memory saccade is like other delay-response tasks, then a posterior parietal lesion should leave the pure memory behavior intact. Thus, we predict that with a PP lesion, in the double step memory saccade, the animal will mislocalize the second target by an amount equal to the first saccade. Note: This result is partially confirmed by Duhamel et al. (1993). A human suffering from a frontoparietal lesion performing double saccades in the Left-Right condition (taxing the lesioned hemisphere) makes the second saccade as if no shift occurred. 2. Differentiation o f A and B Via Ego- and Allocentric Coding: Dassonville et al. (1992) demonstrated that if the two double saccade targets are well separated in time, then errors in localizing the second saccade reveal the use of a damped eye position signal, and allocentric cues can reduce this error. It may be the case that the "allocentric" presentation, used by Goldberg and Bruce (1990), increases the probability of right-MF/wrong-RF cells found in FEF. Recording from one of these cells under both the ego- and allo-centric conditions will clarify this issue. 4.7 Discussion This work was initially motivated by data on double saccades and QV cells (Mays and Sparks 1980, Sparks and Mays 1983, Sparks and Porter 1983), and led to our implementation of a variation of the Dynamic Memory of Droulez and Berthoz (1990, Berthoz and Droulez 1991) for the shifting of target memory on a motor error map. For double saccades, the model (A) produces cells in parietal cortex (Anderson et al. 1990, Colby 1991, Colby and Goldberg 1990), FEF (Goldberg and Bruce 1990) and 96 I SC (Sparks and Porter 1983) that have the correct movement field and incorrect receptive field for the second saccade. These cells result naturally from the dynamic remapping of targets in the motor error map. Data on colliding saccades from the Schlag laboratory forced us to realize that mechanism A cannot tell the whole story. We then introduced mechansim B that operates downstream from FEF, and thus provides the capability to produce double and colliding saccades. By combining these mechanisms we have a model that leaves only one body of data unaccounted for in a straightforward way, the famous Goldberg and Bruce (1990) cells. We speculate that the coding of double saccade targets in allocentric coordinates may explain the presence of these cells. In addition, since A and B are redundant with respect to double saccades, it is likely that under different behavioral conditions these mechanisms can be selectively activated in an exclusive way. The "upstream" mechanism (A) is well adapted for situations in which a spatial target must be remembered during a prior movement, since this mechanism operates on the spatial memory to account for that prior movement. The "downstream" mechanism (B), however, is adapted for situations in which a spatial target overrides the current saccade, commanding a new "colliding" saccade, though we note that model B can perform double saccades. We note a curious condition with respect to the dynamical properties of PPqv. In both our model and that of Droulez and Berthoz (1990), the dynamic memory has the property that it can store information indefinitely. This is in part due to the need for the dynamic memory to strengthen activity that has been weakened during the shifting. Recalling the lesion studies reviewed by Goldman-Rakic (1987) we see that lesions of dorsolateral prefrontal cortex impair memory saccades (i.e. PP without FEF cannot support prolonged spatial memory), while the results of Schiller and Sandell's (1983) lesion studies indicate that the dynamic remapping can exist with only one of FEF or SC. This leads us to believe that the dynamic memory in PPqv is probably tuned to | allow shifting and stationary targets to persist for approximately 500ms from the time of their presentation to this area. This is enough time to support two or three quick sequential saccades, but not to support the memory saccade. From this perspective, the i FEF receives dynamic motor map input from PPqv, and in turn provides a sustained memory capability to PP. Again, based on the previous discussion of A and B, this remains an issue to investigate. t Chapter 5 Sensorimotor Convergence and Stimulus- Response Associations - Dopam ine and Corticostriatal Plasticity Until now, we have addressed saccade tasks in which the behavioral measure was one of accuracy. We now consider cognitive tasks that require a choice from multiple targets. We augment the existing model with cortical apparatus involved in object ' discrimination that will support the capability to associate visual cues with the correct saccade choice from multiple targets, based on the following three principles: i) Visual input produces patterns of activity in cortex, ii) Cortex influences the saccade system in part via cortico-striatal projections, iii) A reinforcement learning mechanism that relies on reward-related dopamine release modifies cortico-striatal synapses to link patterns of cortical activity to the correct saccade responses during trial-and-error learning. Our conditional visual discrimination model learns to associate visual cues with the corresponding saccades to one of two left-right targets. A visual cue produces patterns of neuronal activity in inferotemporal cortex (IT) which projects to the oculomotor region of the striatum. Initially random saccadic "guesses," when directed to the correct target for the current cue, result in increased synaptic strength between the cue-related IT cells and the striatal cells that participate in the correct saccade, increasing the probability that this cue will later elicit the correct saccade. We show that the model generates "inhibitory gradients" in the striatum as the substrate for spatial generalization._________________________________________________________ 5.1 Introduction - Context and Behavior The basal ganglia have traditionally been associated with initiation and parametric control of movement (see Alexander et al. 1986), and with the conditional selection of appropriate context dependent behavior (e.g. Mishkin et al. 1984, Robins et al. 1990, Reading et al. 1991). We present models of conditional behavior in which distributed patterns of cortical activity represent visual, spatial and temporal context. This cortical activity selectively interacts with striatum, yielding the execution of context dependent movements. Through learning, these patterns of cortical activity become causally linked to selection of the correct one of multiple targets for a saccadic eye movement Targets Cue lliC ue 1 I T afS ets I F ig u r e 5.1 C ue-saccade Association Task. The fixation point is a visual cue with color and shape. Each cue is assigned to one of the two targets, and the subject must learn by trial and error to make a saccade to the correct target for each cue. Timeline below. After the cue is presented the subject must fixate it. During this fixation the two targets appear. Offset of the cue is die saccade go-signal. Arrow indicates correct saccade for this cue. In the conditional visual discrimination (CVD) task, one of two saccades must be chosen based on the presentation of a fixated visual cue (Dominey et al. 1992). The visual cue provides an external source of context, specifying which of the two | responses is correct In the CVD task these patterns of activity arise through perception I of the visual cue, and are then linked, by learning, to production of the correct j saccades. The task is learned in a trial-and-error paradigm, with a correction procedure such that a given trial is repeatedly presented until the correct response is made, then the next trial is randomly selected. The paradigm is illustrated in Fig 5.1. 99 5.2 The Role of Basal Ganglia in the "Base" Model The present model extends that of Chapters 2-4 (Dominey and Arbib 1992) which thus provides the "base model" for the current study. There, the control of voluntary saccades to visual and remembered targets is modeled in terms of interactions between posterior parietal cortex, frontal eye fields, the basal ganglia (caudate and substantia nigra), superior colliculus, mediodorsal thalamus, and the saccade generator of the brainstem. Interactions include the modulation of eye movement motor error maps by topographic inhibitory projections; dynamic remapping of spatial target representations in saccade motor error maps; and sustained neural activity that embodies spatial memory. In the present section, we recall the role of the basal ganglia in the previous model, and then show how plasticity may extend and clarify that role. Briefly, reflex saccades may be elicited by the projection of the superior colliculus (SC) to the brainstem saccade generator (SG). In voluntary saccades, frontal eye fields (FEF) serve both to inhibit the reflex responsiveness of SC during fixation on a fixation point (the inhibition comes from cells called FOn in the model), and to command (via SC or directly to SG) saccades to targets based on memory or dynamic remapping of visual stimuli that are no longer visible. However, two inhibitory nuclei of the basal ganglia, caudate (CD) and substantia nigra pars reticulata (SNr), are arranged in series and provide an additional, indirect link between FEF and SC which allows FEF to selectively modulate the tonic inhibition of SNr on SC and thalamus (Chevalier et al. 1985, Boussaoud and Joseph 1985, Hikosaka and W urtz 1985) through caudate nucleus (Stanton et al. 1988a). In addition, the basal ganglia pathways provide a mechanism for the initiation of cortico-thalamic interactions via the removal of SNr inhibition on the mediodorsal thalamus (MD) (Deniau and Chevalier 1985, Ilinsky et al. 1985). The FEF has an excitatory topographical projection to caudate that preserves saccade amplitude and direction and so can trigger the selective release of SNr's inhibition on SC (Bruce and Goldberg 1984; Segraves and Goldberg 1987; Stanton et al. 1988a). To provide cortical control while a target is foveated, : foveal cells in FEF (FOn) gate activity in caudate and SC, preventing saccades while a target is fixated. 100 Posterior Parietal C x V isual o Input Caudate Thalamus (VA-M D) Figure 5.2 The Role of Basal Ganglia and Inhibitory Masks in the Base M odel (based on D om iney and A rbib 1992). Visual input arrives in PP, influencing FEF. FEF effects saccades directly via its projection to SC, and indirectly via the striato-nigro-collicular path. SNr tonically inhibits SC, forming an inhibitory mask on SC. This mask is selectively modulated by the influence of CD on SNr, releasing a restricted region of SC from SNr inhibition. Thalamus and FEF interact via reciprocal excitatory projections when SNr's inh ib itio n of T halam us is temporarily removed. Thus, CD manages saccade activity by its influence over the inhibitory SNr that in turn controls the activity of saccade-related activity in SC, thalamus and FEF. SC output produces saccades via the brainstem saccade generator (not shown.) Superior C olliculus We show how this works in the model's production of a so-called simple saccade, in which the fixation point goes off just as the target light goes on, providing the target for an immediate saccade. At fixation offset and target onset the visual information from retina, via posterior parietal cortex (PP) excites the FEF element corresponding to the location of the new target, and projects topographically to the caudate. This excitation, combined with the loss of the FOn inhibition activates the corresponding CD element, which projects an inhibitory signal to SNr, resulting in the release of SNr's inhibition of the topographically corresponding cells of SC. The topographic excitatory FEF projection to SC, combined with the release of the SNr inhibition activates the SC element that generates a motor burst signal of saccade direction and amplitude corresponding to the target location coded in FEF. The equations (3 -1 0 ) 101 implementing this core model are presented in Appendix A1. All cell arrays in the present model are 5x5, except for V4 which is 1x6 (see Fig 5.4.) "raw" target map context-dependent (learned) biases on caudate activity context-dependent disinhibition c SNr activity biases winner-take-all to determ ine w hich FEF target w ins SG D Figure 5.3 Corticostriatal Plasticity for Selective Disinhibition. In this simplified illustration of the system we model, we demonstrated that when multiple targets are represented in the FEF command to caudate and SC, the choice between these targets can be made through the influence of additional corticostriatal influences that will favor one of the targets. IT corticostriatal projections are modified by learning to bias caudate in favor of the correct one of multiple saccade targets dependent on the association or sequence context. Although we will not go into the details here, the full Dominey-Arbib model shows how working memory may be supplied by reciprocal connections between FEF and medio-dorsolateral thalamus (MD); and how posterior parietal cortex (PP) may provide the dynamic remapping of retinotopic representations when multiple saccades are made i j to remembered targets. The simulations reproduce simple, memory, and double j saccades, inter alia, to demonstrate a functionally correct model in which: j 1. Managing the inhibitory projection from SNr to SC allows selective cortical I ! control of target locations for voluntary saccades to immediate and remembered targets. This control is directed by FEF via CD. 1 iThis and subsequent Eqns can be found in Appendix 1. 102 2. Saccades can be driven by representational memory that is hosted in reciprocal connections between MD and FEF that are governed by projections to MD from SNr. A state change is thus driven by the representation of a stimulus in the absence of the stimulus itself, indicating a primitive symbolic processing capability. The key point for the present paper is the observation that "managing the inhibitory projection from SNr to SC allows selective cortical control of target locations". In the previous model, the role of CD and SNr seems functionally gratuitous (although it is necessary for a biologically plausible model that addresses the data of, e.g., Hikosaka et al. 1989), since the CD disinhibition simply mimics the combined effect of the removal of FOn inhibition and the issuance of the topographic command from FEF to SC. The thesis of this chapter is shown in Figure 5.3. The reflex and cortical FEF commands for a saccade are combined in a topographical map within the deep layers of SC, where a winner-take-all (WTA) network selects the largest peak of activity to form the saccade command to be executed by the brainstem saccade generator SC. However, this command will only be executed if FOn and SNr allow the activity in deep SC to reach a critical level. In the models considered above, FEF relayed the location of only one target to SC and so the role of CD and SNr did not seem crucial. However, in the present paper, we consider cases in which FEF relays the location of multiple targets. Our hypothesis is that context-dependent learning can modify the pattern of disinhibition applied at the caudate, thus favoring one target over the other(s). I 5.3 Formation of Visuomotor Associations j i i To address the association task, we augment the core model with a cortical structure | I * j involved in representation of visual cues, corresponding to the inferior temporal cortex | (IT), and a learning mechanism that can modify the corticostriatal projections (Fig. j 5.3,5.4.) IT corticostriatal projections form longitudinal bands that distribute ; information along the anterior-posterior extent of the striatum including target areas adjacent to and overlapping with the caudate nucleus (Selemon and Goldman-Rakic 1985), the striatal component of the oculomotor loop, allowing IT to influence saccade 103 generation. We will demonstrate how this influence will support the correct choice of multiple targets. E xternal Inputs and O utputs: Visual input to the model is provided by a 5x5 spatial array in which each element can code either a visual target or a visual cue. Such a cue is defined by its color (Red, Green or Blue value), and a coded shape (Circle, Square or Diamond). This is represented as the 6-tuple (R,G,B; C,S,D). These are graded values, allowing us to blend colors and shapes to create a variety of cues. The model will produce outputs that code eye movements by activation of an element in a 5x5 spatial map that we will consider to be an eye movement map in SC. For each trial the simulation will compare the model’ s response to the desired response and provide a reward or punishment signal as appropriate. Stim ulus R epresentation: The inferior temporal lobe, of the "what" visual system, provides a cortical area in which the properties of visual stimuli including color and shape are encoded in populations of cells with feature preferences (Desimone et al. 1984, Fuster 1990, Tanaka et al. 1991). In our model (Fig. 5.4), visual input is decomposed into form (color and shape) and position information which feed IT and PP respectively. We do not model the relevant pathways in detail. Instead, a map of target position, including the cue, is transferred directly to PP, while "form" is coded (unbiologically) as a 6-element vector in an array labeled "V4" (Eqn 11). This 6 element vector that codes shape and color is transformed by a random, unmodifiable set of synapses connecting V4 and IT (Eqn 12). A Site for Sensory Motor Association: The caudate nucleus of the striatum participates in the preparation and execution of voluntary, context dependent saccades (Hikosaka et al. 1989a,b,c), and receives projections containing external context information from the occipitotemporal pathway - including IT - and spatial movement information from posterior parietal cortex and frontal eye fields (Selemon, Goldman- Rakic 1985, Stanton et al. 1988a) (Eqn 7). In this view, caudate provides an anatomical site for the formation of context-behavior associations (Rolls and Williams 1987, Yeterian and Pandya 1991). The intact function of the striatum is necessary for j learning CVD tasks, as their learning and performance are impaired by selective striatal lesion (Reading et al. 1991). Noise Visual Input Posterior Parietal Cx * Infenor Temporal Cortex \ Randomized trials Caudate Modifiable Synapses Reward Simulation Environment Thalamus (VA-MD) ^Behavior Superior Colliculus Figure 5.4 Schematic of Association Model. The model of Chapter 3 is augmented with "V4," IT and modifiable IT-Caudate synapses, and the SNc dopamine system. Cue-related activity in IT is produced from color and shape features that are extracted from visual cue input in V4. IT influences saccade production via its projections to caudate. Random noise added to the visual input in PP breaks the symmetry between the two targets, providing a form of guessing. The noise-favored target has stronger activation in all subsequent stages and is selected as the saccade target in SC. On correct cue-guided saccades, the simulation environment provides a reward that leads to phasic release of dopamine, which contributes to strengthening of synapses between I IT cells activated by the cue, and caudate cells participating in the saccade. After training, the cue-driven activity in IT will preferentially drive the caudate cells involved in the correct saccade. This influence will overpower that of the noise in PP, and performance will increase. These investigators (Robbins et al. 1990) also demonstrated that the intact j nigrostriatal dopamine system is necessary for learning this task, as we describe below, j In the model, IT units encode features of the cue, and the IT corticostriatal path provides the caudate with access to this information. In the naive state, the connections in this non-topographic projection are randomized values between 0 and 1. By learning, these synapses are modified so that IT cells active for a given cue excite 105 caudate cells that participate in the associated saccade, inhibiting SNr (Eqn 8), allowing SC to select the correct saccade. A key role for the caudate, then, is to participate in the selection of the correct one of multiple saccade options. Regulation of Cortico-striatal Input: For a given pattern of activity in IT, and multiple targets represented in FEF, multiple caudate cells with different saccade preferences will be activated. Ideally, the caudate will use the cue-driven IT bias, established by learning as described above, to select the correct target. However, if the combined activity of IT bias and target exceeds the threshold of caudate sensitivity at more than one topographic location in CD, then the bias information from IT that would normally favor one site over another will be lost. In order to bring the caudate activity back into a range in which the IT bias can be detected, we introduce a negative feedback circuit that decreases corticostriatal excitability in this situation. B. Glutamate Striatum GABA Dopamine 3 with DA moduation without DA modulation two peaks of activity in striatum F igure 5.5 Dopamine Regulation of Corticostriatal Activity. A. DA Modulation Circuit. Excitatory inputs represented with arrows, inhibitory with blunt ends. Corticostriatal activation inhibits the SNr. Excessive inhibition of SNr releases inhibition on SNc, allowing an increase in SNc nigrostriatal dopamine production. B. The effect of this dopamine release in striatum is to attenuate the corticostriatal activity, bringing it back into a range in which striatum can function normally. The circuit is based on the knowledge that the release of dopamine in striatum decreases the excitability of striatal cells by corticostriatal afferents (Mercuri et al. 1985, Garcia-Munoz et al. 1991, Nisenbaum and Berger 1992, Calabresi et al. 1993), and j thus attenuates corticostriatal activity, allowing striatum once again to detect the effect ; 106 I of IT's bias. In our model (Fig 5.5), suggested in part by Carlsson and Carlsson (1990), when strong cortical inputs overstimulate striatum, SNr is strongly inhibited. This inhibition of SNr leads to the ifmnhibition of SNc (Carlsson and Carlsson 1990). The resulting increase in activity of SNc DA cells leads to the increased release of DA in striatum, which attenuates the corticostriatal signal (Calabresi et al. 1993), bringing the most active cells back to the maximum input capacity of striatum, and reducing the activity of the less active surrounding striatal cells, thus increasing the signal to noise ratio (Fig 5.5B). We currently model this circuit and SNc DA function in the simplified form of Eqns 6 and 7. This allows caudate to make better use of cue-related information from IT, and assists in the learning and execution of cue-saccade associations by providing a kind of contrast enhancement between strong, competing striatal inputs, resulting in a 30-40% increase in performance (percent correct) during a training session. An Adaptive M echanism : In addition to its short-term modulatory role, the observations of reward related DA release during learning, and the impairment of learning with DA depletion suggest that dopamine plays an additional important role in long-term synaptic changes required for learning stimulus-response habits. First, Ljungberg et al. (1991) found that during learning a delayed alternation task, nigrostriatal dopamine producing cells are activated by the reward, and cues associated with the reward, and that these responses are qualitatively preserved during conditioning, postconditioning and overtraining. On error trials, a depression of activity was seen at the time when a reward would have been given (Ljungberg et al. 1991). Second, depletion of dopamine from the dorsal striatum in rodents impairs their ability to learn a cued-choice task (Robins et al. 1990) similar to our cued-saccade task. The relatively high level of NMDA receptors in striatum (Monaghan and Cotman 1985), and the observation that striatal NMDA receptor density varies inversely with striatal DA levels in PD patients (Weihmuller et al. 1992) suggests a relation between DA and learning-related corticostriatal plasticity. i It thus appears that phasic, reward related DA activity participates in long term j modification of corticostriatal synapses that link contextual sensory inputs with striatal cells involved in producing the correct behavior. Both long term- potentiation and 1 depression have been observed in the striatum, and at least long-term depression has been observed to specifically require the presence of dopamine (Calabresi et al. 1992a.) J Repetitive activation of cortical inputs produces LTD in striatal cells whose NMDA channels are inactive, and LTP in those whose NMDA channels are active, effects that can be readily observed by manipulating the Mg++ NMDA block (Calabresi et al. 1992b, Walsh and Dunia in press). We can simplify this by saying that sufficient depolarization (which removes the Mg++ block of the NMDA receptors) in striatal cells makes these cells candidates for LTP in the presence of additional cortical input, while insufficiently depolarized cells will be candidates for LTD. Recall that by reducing all striatal activity so that only the maximally active cells fire at their maximum rate, our modeled striatal regulation by DA actually pushes the less active cells into the LTD region. We now take a first step in relating these observations to a formal learning rule for our model, with the acknowledgment that the problem of assigning physiological mechanisms to the formal elements of a learning model is neither trivial nor complete. Learning Rule: We employ a reinforcement based learning rule (see Barto 1990 for review) to modify corticostriatal synaptic strength based on correct/incorrect behavior. The learning rule produces incremental changes in synaptic connections between IT (source) and caudate (target) neurons. Correct responses strengthen synapses between IT and caudate cells that were active during the response, while errors weaken active synapses. These changes will tend to produce IT driven caudate activity that increasingly favors correct behavior, and disfavors incorrect behavior, since IT cells specific for a given cue will become more strongly connected to caudate cells active in the associated saccade, and more weakly connected to other caudate cells. W e also implement a form of competition so that for a given source cell, increases in its synaptic influence on some target cells will be compensated for by small decreases in its synaptic influence on other target cells. These increases and decreases correspond roughly to the LTP and LTD described above. The most active synapses are strengthened (LTP) and via normalization, the less active synapses are weakened (LTD). The learning-related updating is performed by: wij(t+l) := wjj(t) + (DA_Modulation*RewardContingency - 1)* Cl*Fj * Fj (1) : Ew..(t) j y w (t+l) :=w (t+l) * i J J £w ..(t+l) j y (2) 108 where the denotes assignment rather than equality. Here, wjj is the strength of the synapse connecting IT cell i to caudate cell j. These w’ s make up the elements of IT_CD_Synapses in Eqn 7, and are modified after each simulated saccade. Eqn 6 sets DA_Modulation as a function of its role in the SNc feedback loop. In Eqn 1, based on the arrival or denial of expected reward, we simulate SNc reward related modulation by the term RewardContingency which is 1.5 for correct trials, and .5 for incorrect trials, and 1 when no reward or punishment is applied, corresponding to the increases and decreases in SNc activity for reward and error trials, respectively (Schultz et al. 1993). Fi and Fj are the firing rates of the IT and caudate cells, respectively. The term (DA_Modulation * RewardContingency -1) will be positive on rewarded trials and negative on error trials. C l is a constant that specifies the learning rate, and is set to 2.5e-5 . A form of competition is provided by a weight normalization procedure that conserves the total synaptic Weight that each IT cell can distribute to its striatal synapses (Eqn. 2). Consider that after learning has occurred, one synapse from cell i to cell j was increased. In the normalization, the total synaptic weight from cell i is conserved, so the result of this increase is a small decrease in all other synapses from i. Similarly, when a weight is decreased due to an incorrect response, the other synapses from i are increased. Via this normalization process, the postsynaptic cells compete for influence from presynaptic cells, producing cue discrimination. After each saccade, the simulator applies Eqns 1 and 2 with the appropriate value for RewardContingency. Especially in the case of rewarded trials, Eqns 1 and 2 approximate how LTP may occur in the most active post-synaptic cells (via Eqn 1), and LTD in the others (via normalization of Eqn 2). While captured here in the same equations, it may be that learning on error trials also involves other structures including the nucleus accumbens (Robbins et al. 1990, Reading et al. 1991) and we consider this in the discussion. In summary, the interaction of DA's feedback and plasticity roles is captured in Eqn. s 1, 2 and 6. During initial learning, Eqn 6 will set DA_Modulation to 1, since the corticostriatal inputs are initially weak. In Eqn 1, based on RewardContingency, synapses active in saccade generation will be strengthened or weakened for correct and incorrect saccades, respectively. When synapses are strengthened for saccade related cells on correct trials, the surrounding synapses are weakened by the normalization of 109 Eqn 2. After significant learning, strong IT corticostriatal inputs may be above striatal threshold for more than one target, even though this input is biased toward the correct target. Eqn 6 reduces DA_Modulation so that the maximum IT-striatal input is just equal to the striatal threshold, increasing the signal to noise ratio so that the correct bias is now perceived in striatum, leading to the correct choice. In addition, by reducing DA_Modulation, the synaptic change for this well learned cue is reduced (but still positive) in Eqn. 1, helping to prevent overlearning. 5.4 Model performance and single unit activity We now describe the evolution of behavior from an initial naive state to a final trained state for our model of visuomotor association learning, and compare the behavior and single unit activity of the model with those of primates performing related tasks. Recall from Fig. 5.4 that the site of adaptation is in the IT cortico-striatal synapses, so that representation of cues in IT can influence saccade generation. In the naive state, these connections are initialized to random values on the interval (0,1), so a given cue has no large a priori preference for any saccade. A trial is initiated by the onset of the central fixation point (FP). Once the model initiates fixation, the FP is replaced by a colored shape (cue). The "form vector" is projected by "V4" to IT with synapses fixed at random values on the interval (-.5, .5.) These non-modifiable positive and negative weights produce cells in IT that are sensitive to individual color and shape features, as well as to their various conjunctions and disjunctions. The IT activity projects to caudate via the modifiable synapses. j After a delay, the two peripheral targets appear, leading to the activation of PP, ! which in turn signals to FEF and then to caudate. Each element of PP receives its | topographic spatial input, to which is added a "noise pattern" which contributes 30% of ! the total PP activity, and provides a "symmetry breaking" function - a form of guessing I between the two targets during initial learning.2 During the period of cue and target overlap, the combined activity of FEF and IT produces "preparatory" activity in the caudate, leading to its inhibition of SNr, which in turn disinhibits thalamic nuclei that project back to FEF (Eqn 10). Reverberatory excitation between disinhibited thalamic and FEF cells, combined with the lateral inhibition in caudate, tends to amplify slight differences in corticostriatal inputs, favoring the stronger and reducing the weaker. This is similar to the reverberatory FEF-thalamic interactions that maintain spatial memory in Dominey and Arbib (1992), but in the present case, the reverberatory activity contributes both to selection and memory functions as we will see below. At the go signal (offset of the cue), inhibitory fixation-related cells in FEF are deactivated, allowing SC to respond to inputs from FEF and SNr. In the naive state, the cue-driven IT activity projects with randomized strength to caudate, while the effects of noise in PP are seen in caudate and downstream, and drive the winner take all (WTA) mechanism in SC resulting in a saccadic "guess". After a correct "guess" the IT-caudate synapses between cue and saccade related cells are strengthened, increasing the probability that the cue, when repeated, will drive the correct caudate cells (Eqns 1 and 2). Incorrect trials result in a reduction of the active corticostriatal synapses. After significant learning, the IT influence on caudate dominates that of noise, and the performance approaches 100%. We trained the model on four sets of cue-target associations using two fixed targets. Two cues were associated with the left, and two with the right target. We examined the task-related activity of caudate cells during initial training, intermediate and overtrained epochs. Recall that in the model, CD receives input from FEF, so that even in the naive state, caudate cells have saccade related activity with a spatial preference. As training proceeds, cue-related activity in IT becomes increasingly associated with activation of the correct saccade-related cells in CD. In Fig. 5.6 we display the changes in IT-striatal synapses and the corresponding changes in cue-driven striatal activity that results from learning. The upper panel of Fig 5.6 shows the : activity produced by a "go right" cue in IT; the initial (naive) synaptic weights between i i i 2 (a) The signal to noise ratio is .7. (b) cf. the symmetry breaking in the Fagg- Arbib (1992) model. IT and caudate, and the corresponding influence produced in caudate and SNr by that cue. Before training the cue-driven caudate activity is low and homogeneous. ' l IT.Achvily IT _ C D _ S y n a p se s CD_iT„ S y n a p se s a Activity S N r_ ln h ib ito ry ..M a s k _ o n _ S C m a m ■ m ■ a • ■ !T _ ln ? lu e rK e _ O n _ C a u d a te ■ ■ ■ ■ ■ B E B BBB ■ ■ a ■ a BBBBB ■ a ■ ■ ■ ■B BBB ■ ■ a ■ ■ BB ■ H B ■ ■ a ■ a BBBB f l A ctivity lT _ C D _ S y n a p sa s C D .IT ^S y n ap sesS A ctlv lty IT _ 1 n N u e n c e _ O n _ C a u d a te P F $ N rIln liib ito ry _ M astc._ o r> _ sC ■ u a o w aaoHoaaDaaaaaanaaa ■□Dap D a a a o u a a a a a a a a a B a a a □■■□Djaaajaaaaaaaaaaaaaaa ■□■■D B M p g B i i s i f l i B n a o i i aaaoaaaQauaaaBDasagaaaaaB 9!!!9 ■■□■□□BBBaaoSoaaBoa 3 g 3 3 3 d S 3 3 3 S S 3 S S 3 S 8 S S S S S 3 S □ D aaaaB O aB H B o aaaaaaaaaaao 8 S 2 8 9 ..B 8 0 B a B O B n ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■BBDoaafia aaaaaaaaaB B aaaa aaaaaaaaaaaa0 B a * B 3 O B B o a a a ■aaao a a aa aaa aaa aa aasa aaB ■aagf BaBBoaaaaasaaaaaasa ■ aaB saB aa■ oaaD D aiB D aisaaa ■■ aaB D aaajB eaaaaoaaaiaiaa □ sa ao jo aa ao aa aa aaa iaiflB a a ■DaaDooaaaaBaaaaaaaaiuaBU ■BBBBaaaa BaaoaooaaBBaaaa ■■■□■.■•■■aBaaBBBaaaaaaoB 10:0 11:4 JQ:Q J1:4 lma> Figure 5.6 Changes in caudate response due to learning. Above. Cue- related activity in IT, caudate and SNr before learning the cue-saccade association. Below. After learning the IT_Caudate_Synapses are modified, and the same cue now produces activation of caudate and inhibition of SNr appropriate for the associated saccade. Fig 5.6 lower panel, shows the change in synaptic weights and the corresponding I change in caudate and SNr activity elicited by the same cue after training to 95% | performance for two (left and right) cues. Note that via training, the weights are now J redistributed into the two columns corresponding to learned association between two ( cues and the left and right targets. The "go right" cue produces an increased activation 112 of cells related to rightward saccades, and a small decrease, due to our normalization model of LTD, in other cells. This cue also produces some activity for the left saccade target because its representation in IT overlaps partially with that of the "go left" cue. Thus we see how, through learning, cortical activity driven by a cue produces an inhibitory mask in SNr that guides the connect saccade choice. During the intermediate stages of training, before this transition between noise- driven vs. cue driven saccades occurs, we see that activation of caudate cells during the cued period accurately predicts the direction of the upcoming saccade, independent of the cue. Figure 5.7 illustrates a cell with leftward saccade preference in different phases of training. In the first row, the cell is shown with well learned cues for left and right saccades. In the second and third rows during the intermediate phases of training when mistakes were still being made, we see that activation of this cell during the cued period predicts saccade direction independent of the cue, or the correctness of the saccade. Note on the second row, the differences in activity of the cell during the cue-only period on these two trials. When noise favors the leftward saccade, a stronger response is seen both during the cue and cue with targets periods. When noise favors a rightward saccade, the influence of the cue is much less apparent, indicating how at this stage of learning, noise is more influential than cue-related activity. Once the IT-caudate learning dominates the influence of noise, errors are greatly or completely reduced, and activation of these cells predicts correct cue-guided saccades, dependent both on the cue and the correct saccade. A noteworthy property of these cells is that equivalent cues (i.e. having different color and shape, but associated with the same saccade) produce similar activation in their associated saccade-related caudate cells. This can be seen for the four correct (arrow and shaded target match) cue-guided saccades in Fig 5.7. Task acquisition rate, and the final performance rate are functions of the reward and penalty signal strengths, and the signal to noise ratio. In each window of Fig 5.7 the upper trace is the cell activity, and the lower traces indicate the periods where the cue and targets appear (refer to fig 5.1 for task paradigm timing.) All traces are from a cell that has preference for leftward saccades. Left column: responses to cued leftward saccades. In the first row and second rows, the cues are associated with a leftward saccade. The cell discharges with the cues, and increasingly with the targets through the saccade. This demonstrates the task related i activity, and the equivalence of two cues associated with the same saccade. J 113 I Figure 5.7 Simulated saccade preparation cell. Arrow indicates direction of j saccade, dark square indicates correct direction. See Text. i ■ ;- i • ! ' 114 In the bottom row, an incorrect saccade is made to the left with a cue that is associated with a rightward saccade. The cell still discharges for its preferred direction. In the right column, rightward saccades are made both in correct and in incorrect situations, and in neither case is there significant activity. C om parison of m odel and data: Our preliminary data from a cue-guided saccade experiment in rhesus macaque monkeys (Dominey and Joseph, in preparation) indicate that task-related caudate cells may encode combinations of cue and saccade properties, as suggested by the model. A typical cell is shown in Fig 5.8. Like the simulated cell in Fig 5.7, for intermediate stage learning this cell responds during the cue-target overlap, and predicts saccade direction, independent of the cue, whereas for well learned cues it predicts cue and saccade direction. The two cues in the top row were well-learned and the only errors were fixation related. On the second and third rows, we see correct and error trials for cues that were being learned. As in the model, for this intermediate learning, the cell predicts saccade direction, independent of cue. Interestingly, in both model and animal, the activity increases near the onset of the cue, well before the saccade itself. In the model, this early response is produced by combined cue-related activity from IT, and the noise/target-related activity in FEF in PP. Competition in striatum via inhibitory axon collaterals, along with the FEF thalamic interactions, tends to increase the activity in the area favored by noise or learning, decreasing the activity related to the disfavored target, thus producing the effect of presaccade direction prediction. We recorded 60 task-related cells from the head of the caudate nucleus while a trained primate performed this task in which a head-fixed primate learned to associate centrally-fixated visual cues with saccades to one of two peripheral targets (choice). A temporal delay between cue onset and saccade go-signal allowed dissociation of cue- and saccade-related activities. Following a delay after a correct saccade, the cue re- j appeared at the correct peripheral location (peripheral cue) where the animal was I fixating, and the reward was given. The animal was also studied in a saccade-with-gap i i I task in which onset of a single peripheral target indicated the direction of the saccade . i j (no choice). Purely cue-related responses (linked only to a cue, independent of the subsequent correct or incorrect orientation) were observed in 4 (7%) cells. Sustained peri-cue activity that reliably predicting saccade direction, (oculomotor set - see Figs 5.6, 5.7) I _______________________________________________________________________________________ l m J was seen in 16 cells (27%). Different cues associated with the same saccade evoked similar activity in all of 7 oculomotor set cells tested (cue equivalence). Peri-saccadic activity was recorded in 34 cells, with 17 (28%) of them spatially selective. 13 of these 17 cells displayed sustained discharge until the reward. Of the 17 non-spatially selective cells, 15 showed sustained discharge until the reward. The spatially selective and non-selective sustained discharge suggests expectation of peripheral cue and reward, respectively. Six cells (10%) showed peri-saccade inhibition. Approximately 40% of task-related cells appeared to distinguish cue-guided (choice) from visually guided (no choice) saccades, and further analysis will be performed to clarify this distinction. The small number of purely cue-related cells might suggest that caudate does not participate directly in this task. However, we suggest a different inteipretation of this data in terms of our neural-network model that learns this task. The model employs a mechanism for S-R habit learning in which synapses conveying cortical cue-related activity impinge on striatal saccade-related cells. Prior to learning, cue-related activity in caudate is weak and distributed. With learning, corticostriatal synapses are modified so a given cue produces activity in the associated saccade-related caudate cells. Thus, cue-related activity is rarely seen independent of saccade-related activity, consistent with the small number of cue-related cells we recorded. The model also predicted oculomotor set cells that display cue equivalence, as we found in the animal. Thus, these data support our model for corticostriatal plasticity in habit formation, and are consistent with the emerging view that striatum participates in the construction and execution of S-R habits. Hikosaka et al. (1983c) note that a common characteristic of caudate cells is their predictive or anticipatory activity. We see this in Fig 5.8, where, before the cue onset (denoted by the first "2"), the cell begins to fire as if anticipating the cue, and continues to fire if it is a preferred cue, while stopping if not. This anticipatory activity appears to { demonstrates a temporal (as opposed to visuo-spatial) association capability that may j represent preparation for, or expectation of a future event, and poses a challenge for ( future modeling. MILLISECONDS , 4 0 — □ D 2 5 “ ! - 5 8 8 MILLISECONDS 2 5 “ | MILLISECONDS MILLISECONDS Figure 5.8 Saccade preparation cell. Same notation and arrangement as in Fig 5.7. Symbols on time scale: 3: peripheral target onset, 1: Fixation onset, 2: cue onset, 2: cue offset and go signal, 4: reward. In the left column, for both correct and incorrect saccades to the left, this cell becomes active with or before the cue, throughout the saccade. On the right, for correct or incorrect saccades to the right, the response is mostly absent. This cell predicts leftward saccades, independent of the cue. Cue FEF C a u d a te SNr T h a l a m u s SuperiorColliculus Figure 5.9 Cue-guided memory saccade. During fixation, q well-learned cue is briefly presented, then replaced by a neutral fixation point. At offset of the fp, the two targets appear, and the subject must saccade to the correct target. The brief cue presentation activates the topographic region of caudate corresponding to the learned saccade. This in turn inhibits SNr, releasing SNr inhibition on Thalamus. Background cortical activity now excites Thalamus, and the reciprocal interaction between FEF and Thalamus amplifies this activity, seen as a rise in FEF and Thalamus traces. After removal of the cue, this activity remains, in a form of spatial memory that is activated by central cue. At the go signal, this memory effect of sustained reduction of SNr activity at the topographic location for die correct saccade, leads to collicular activation for that saccade. Prediction 1: In a related set of experiments on remembered saccades, Hikosaka et al. (1989) demonstrated sustained activity during the delay period of a memory saccade task in caudate cells that had spatial preferences for the remembered saccade locations. This activity was elicited both in cases where the target was presented transiently before the memory period, as well as in cases where the saccades alternated between two left-right targets so that the next saccade direction could be predicted from the previous saccade. In this second case, cells with spatially selective movement/memory fields were activated without a visual stimulus falling in that field. In Fig 5.9, we show the results of a modified version of this memory saccade task in which the cue itself (rather than a target flash or the previous saccade) informs the correct saccade. The cue is presented phasically during fixation, activating the reverberatory thalamocortical circuit via striatonigral disinhibition. A "spatial memory" evoked by a central cue, rather than the target, is stored in this circuit until the go signal occurs and the saccade is executed without the target being presented. In this case, we predict that for well-learned cues, saccade related caudate cells will be driven by the central cue, and continue to fire after the cue is removed, through the go signal until the correct saccade, without a target stimulus falling in the cells' receptive field. It has been noted that many responses in basal ganglia neurons to external stimuli are not primarily sensory, but instead are related to the movement associated with that stimulus (Schultz 1989). In a CVD go-nogo task roughly one third of caudate cells responded to the trigger stimulus, and one-quarter of these responding cells were activated only in the go trials. When the go-nogo meaning of the stimuli were reversed, the majority of these differentially responding neurons also reversed their stimulus preference, indicating that the neuronal response was related to the behavior itself, and not to the stimulus that triggered that behavior (Rolls et al. 1983). In our own modeled reversal experiments the same is true. In reversal, a behavior that was previously rewarded is now punished. As the initially strong IT-caudate synapses are weakened during the reversal, there is a perseverance until the original behavior is sufficiently weakened so that noise can again contribute to guessing. The new behavioral association is gradually formed, first via guess and then via increased effects of learning the new association, yielding finally a cue-guided response for the opposite saccade direction. 119 5.5 Discussion We have developed minimal extensions of our previous model of saccade generation (Dominey and Arbib 1992) that solves the CVD task. In doing so, we have demonstrated that for this task, correct performance can be achieved by a mechanism that involves adaptive interaction between cortex and striatum. Stable patterns of activity are established in cortex, arising from sensory input related to the cue. These patterns of activity in cortex influence the oculomotor saccade circuit via adaptive cortico-striatal projections. A reward-based learning mechanism modifies cortico striatal synapses to link these patterns of cortical activity to the correct saccade responses during trail-and-error learning, and is motivated by studies of LTP and LTD in striatum. Learning proceeds on a trial and error basis, where initial "guesses" are provided by low levels of random activity that are injected into the network in order to break the "symmetry" between choices. Dopamine Function: In our models, we suggest two roles for dopamine in the striatum, consistent with the view that neuromodulation in basal ganglia operates on multiple time scales (Graybiel 1990). In the model, DA participates in an adaptive mechanism for inducing long-term (LTP and LTD) changes in corticostriatal synapses during behavioral conditioning. This is based on the observations of LTP and LTD in the striatum (Calabresi et al. 1992b), and the modulatory role of dopamine there (Mercuri et al. 1985.) These synaptic changes construct causal associations between cortical patterns of activity, representing behavioral contexts, and the correct saccades for those contexts. It is known that loss of striatal DA impairs learning of CVD tasks similar to ours (Robins et al. 1990), and may disrupt the normal function of NMDA receptors involved in corticostriatal plasticity (Weilhmuller et al. 1992). Ljungberg et al. (1992) have found that during learning of simple tasks, nigrostriatal dopamine producing cells are activated by the reward, and cues associated with the reward, and that these responses diminish after the behavior is overleamed. During performance of a more complex delayed alternation task, however, the same investigators (Ljungberg et al. 1991) found that responses in DA cells to trigger and reward were qualitatively preserved in conditioning, postconditioning and overtraining. These selective responses to salient stimuli only during learning of a simple task suggest that DA i neurons participate in behavioral adaptation, and are no longer required once a behavior 120 becomes a habit. Indeed, for our CVD task, once the associations are learned, we can reduce the reinforcement value to zero and still maintain correct performance, whereas the well trained sequence model continues to rely on learning, and drops 27% in performance without it. The second function of striatal DA in our models is to modulate cortical inputs to the striatum, ensuring that these inputs remain in a range to which striatum is sensitive, as suggested by observation that dopamine decreases striatal excitability (Mercuri et al. 1985.) This agrees with the view that DA increases the signal to noise ratio in a population of cells, as suggested by Servan-Schreiber et al. (1990). Insufficient DA leaves striatum insensitive to the relative strengths of cortical inputs. This insensitivity will impair learning and recall of learned associations, as seen in the striatal DA depletion studies of Robins et al. (1990). In constructing this regulatory circuit, we suggest, as do Carlsson and Carlsson (1990), that the striatal input to the SNc dopamine producing cells undergoes a sign change, either via an intrinsic GABA neuron, or via influence from SNr. The functional result is a negative feedback control on corticostriatal activity, ensuring that striatum is not saturated by cortical inputs. In addition, by its down-regulation of striatal activity, this circuit will attenuate thalamocortical activity, thus bringing cortex itself back into a nominal range of activation. We have made a first effort at modeling the multiple time-scale effects of DA, and future research should address these mechanisms in detail. These two mechanisms cooperate in a useful way. By pushing striatal activity down so that only the most active cells fire at maximum rate, dopamine sets up the conditions for LTP in the most active cells and LTD in the others. This is captured in our learning and normalization rules, where corticostriatal synapses for caudate cells participating in the correct saccade (most active) are strengthened (LTP), and then by normalization, all other synapses are weakened (LTD). Learning. Forgetting and Strategy: So far we have concentrated on the effects of reward-related changes, though the absence of reward on error trials likely also | contributes to learning. While we only model "forgetting" as a negative value for the reinforcement signal, we note that depletion of dopamine from nucleus accumbens septi impairs reversal of associations in CVD tasks (Robins et al. 1990), suggesting its role in unlearning or reversal. In tests of temporal order and conditional associative ■ learning, PD patients were impaired only when learning by trial-and-error was required i _______________________________________________ 121 j (Vriezen and Moscovitch 1990), but not when corrections were provided on error trials. Indicating that the reinforcement pathway is intact, while the punishment pathway is not. We can observe this effect by setting our penalty signal to zero, after which both CVD and sequence learning are significantly impaired. Perseveration of unrewarded behavior was seen to increase in animals with dopamine depletion in the nucleus accumbens, while they were not impaired in the standard task (Robbins et al. 1990.) In the correction procedure used in training, the same trial was repeated until performed correctly, thus the "lose shift" strategy, if learned would allow these animals to learn the task while only producing synaptic change on rewarded trials. It would be interesting to see if learning is modified for the NAS animals when trials are presented randomly rather than in the correction procedure. Generation of Diversity: Associating input patterns with output patterns is facilitated if the input patterns do not have significant overlap, and can thus be easily distinguished. IT in this model ensures that visual cues are represented by patterns of activity that are sufficiently non-overlapping to be associated uniquely with the correct saccade. By using mixed excitatory and inhibitory connections from V4 to IT we get IT cells that detect features, conjunctions and disjunctions of features, and the general property that the degree of similarity or dissimilarity in cues is reflected in the corresponding IT activity. In the next chapter we will see how a related organization of prefrontal cortex can lead to generation of diversity there. Related Models and Data: The model of Fagg and Arbib (1992) learns stimulus- response mappings using reinforcement to form feature detectors that activate voting units that become associated, again by reinforcement, with the correct response. In our models, the PFC and IT cells are hardwired feature detectors whose votes are determined by reinforcement of corticostriatal synapses. Dehaene and Changeux have modeled prefrontal cortical function in solving delayed-response tasks (1989), the Wisconsin Card Sorting Test (WCST) (1991). In these models, reinforcement is used to stabilize correct performance and de-stabilize incorrect performance, and to modify "rule coding" activity as a form of search for correct state. An important aspect of these tasks, is the need to rapidly respond to a change in reinforcement schedule. This constraint is addressed by coding "rules of behavior" as patterns of activity, capable of rapid change, rather than as slowly adapting synaptic weights. The trade-off for this rapid rule changing capability is a 122 limitation on the number of available rules that are built into the system as pre representations. Mitz et al. (1991) studied cortical premotor (PM) cortical activity as primates learned to associate visual cues with motor responses. These PM cells with a preference for a given response were activated by different cues associated with that response, and (less intensely) when that same response was made in error. Often, however, the PM cells were not activated during initial correct responses, indicating a segregation of cue and premotor related inputs. If we compare PM to FEF, then we can suggest that the PM activity may result from parietal input, as well as from caudate controlled thalamic input that increases as a cue becomes well learned. The fact that PM activity sometimes was missing during initial correct responses suggests that this cortical area is less strictly motor-related than the FEF. An Alternate View and Final Prediction: We have taken a specific, refutable position on a mechanism for sensorimotor associations that is implemented by synaptic changes between cortical inputs to striatal cells that participate in motor loops. An alternative mechanism could involve synaptic changes between cortico-cortical sensory inputs from sensory to motor-related cortices, possibly facilitated by striatal activity. These two mechanisms may be resolved by examination of unit activity in the caudate during the learning of a complex SR habit. If the caudate only participates transiently, by facilitating cortico-cortical learning, then a transitory change will be observed in caudate cells during learning. If corticostriatal synapses are permanently changed in SR formation, then a permanent change will be seen in the caudate cells, as predicted by our model. 123 ; Chapter 6 Internal State Transitions and Sequential Behavior - Connected Associations Here we extend the ideas developed in Chapter 5 to produce a model of sequence learning. We consider a behavioral sequence as a concatenation of associations in which current state and current input become associated with both the next response and the next internal state. We develop this concept to form a model that reproduces primate behavior and single unit activity in prefrontal cortex during an oculomotor sequencing task. Our sequence reproduction model learns, when presented with temporal sequences of spatial targets, to reproduce the corresponding sequence of saccades. At any point in the execution of a saccade sequence, the current pattern of activity in prefrontal cortex (PFC), combined with visual input and the motor efferent copy of the previous saccade, produces a new pattern of activity in PFC. Like IT, PFC also projects to the oculomotor region of the striatum. Correct guesses for the next saccade in the sequence result in strengthening of cortico-striatal synapses between active PFC cells and striatal cells involved in the correct saccade. The sequence is thus reproduced as a concatenation of associations. We compare the results of this model with data previously obtained in the monkey and discuss the nature of cortical representations of spatio-temporal information.___________________________________ 6.1 Introduction - Connected Contexts and Sequences In the sequence reproduction task (Barone and Joseph 1989), three targets must be j I sequentially chosen in the order of their initial presentation. During execution of the 124 sequence, the internal state encoding those targets that have been visited so far provides an internal source of context that guides the next movement We will demonstrate that this task, like the association task of Chapter 6 can be reduced to forming causal associations between patterns of cortical activity and the correct saccade choice. In the sequence task (Fig 6.1), the first target provided during sequence presentation creates a pattern of activity in prefrontal cortex, based on the visual-related inputs to that area. The second target modifies this pattern, yielding a new pattern that is again modified by the third target. This final pattern should then be able to elicit the first saccade on presentation of the "go" signal, via the association learning mechanism of Chapter 5. After this saccade, the state is modified again by the resulting new visual input and the saccade motor efferent. This new pattern is set to elicit the second saccade, and so on. In summary (cf. Arbib 1969), training produces an approximation to finite automaton behavior in which current state and current input determine both the next response and the next internal state, illustrated in Fig 6.IB. In both tasks, the subject must chose the correct one of multiple targets, and that choice is driven by context - in one case provided by a cue and in the other case provided by visual input and stored state of previous actions. 6.2 Sequence Learning The previous model learned static inputioutput mappings. In the sequence task the mappings learned are of time varying rather than static elements. In order to address this temporal processing, we augment the model with a cortical structure involved in representation of spatial and temporal features, corresponding to prefrontal cortex (PFC) including the superior arcuate area and caudal part of the principal sulcus (Barone and Joseph 1989), along with its corticostriatal projections, and a learning mechanism that can modify these connections (Fig. 6.2). Like those of IT, the PFC corticostriatal projections form longitudinal bands that include target areas adjacent to and overlapping with the caudate nucleus (Selemon Goldman-Rakic 1985), the striatal : i ] component of the oculomotor loop. In the model this is reflected by overlapping the ] PFC and FEF projections in the caudate. In this section we will identify information j processing requirements for the sequence task, and then present our implementation I I i based on known biological constraints. In the following section we will present | I I ________________________________________________________________________ 125 1 simulation results and provide a more detailed discussion of the structure and function of the model, and comparison with primate data for similar tasks. f Tl ^ Target /Previous Motor f New D Input State Output 'State MFP T2 Ta / _ / Sa Ta + Tb / Sa _ / Sb FP 1 ........... 1 Ta+Tb+Tc / Sb / Sc t i i ---------- 1 n T2 i ------ i n n Ta+Tb +Tc / Sc Ma / Sd T3 r - i r - i n r L Tb +Tc / Sd Mb / Se Eve----------------- r - 't Tc / Se Me / Sf f e J_ _ _ _ : _ _ 1 3 _ _ _ _ _ _ t i n n n n to n i~i n n T3 r-i r-i n r-i F ig u re 6.1 Sequence Task and Connected Contexts. A. Sequence reproduction task (modified form Barone and Joseph 1989). The three targets are up (1), right (2) and left (3) of the fp. The sequences are of three targets with no repetition, yielding 6 possible sequences. While a central point (FP) is fixated, three fixed targets are presented in a sequence. The fixation point is removed and the targets that have not yet been visited are illuminated three times in succession to form three go-signals. The subject must saccade to the targets in the order they were presented, triggered by the go-signals. Tonic and phasic versions shown, see text. B. Stimulus-Response Table illustrating contexts connected by internal state transitions. Time flows from top to bottom, as the state transitions in the sequence reproduction task are traversed. External and inputs and outputs: As in the association model, the visual input is | provided by a 5x5 spatial array. As illustrated in Fig. 6.1 A, the input consists of a J fixation point and a sequence of three visual targets. After a delay, the model must j reproduce the target sequence as a sequence of saccades to the targets in the order they j j were presented. Each saccade moves the "eye" so that the retina is centered on the j saccade target (Eqn 3). For each trial the simulation will compare the model's response to the desired response and provide a reward or punishment signal as appropriate, triggering the application of Eqns 1 and 2 for the modification of PFC to caudate synapses. Visual Input Noise EEF Posterior Parietal C x/ Prefrontal Cortex Randomized trials Caudate Modifiable Synapses Reward .SNr Simulation Environment SNc Thalamus (VA-MD) Behavior Superior Colliculus Figure 6.2 Schematic of Sequencing Model. Caudate saccade-related cells are influenced again by topographic projections from FEF, and also by modifiable, non-topographic projections from PFC. PFC combines visual, saccade efferent copy, and self input in order to generate a time varying sequence of internal states for each presaccade period in the sequence reproduction task. These states or patterns of activity become associated with caudate activity for the correct saccade by learning, just as the IT patterns did in the association model. Again, noise in PP provides initial guessing which is dominated after learning modifies PFC-to-Caudate synapses. 127 Processing requirem ents: We consider sequence reproduction in terms of transitions between successive states, such that in each state the correct next saccade is known, and its execution leads to a transition to the next state. The ability to learn to recognize and then reproduce a sensorimotor sequence requires the following: a) After the ordered presentation of the targets, the model must be in a state to produce a saccade to the first target, b) After the nlh saccade, the model must enter a state in which it will produce the (n+l)1 * 1 saccade, and so on. As illustrated in Fig. 6.1 A, in this sequence task, the central point is fixated while the three peripheral targets are illuminated in some order. This activity pattern can then be associated with the first saccade of the sequence. Execution of this saccade results in a new visual input, since the eyes move to the first target. Modification of the previous internal state by the combination of the new visual input and a "copy" of the previous saccade produces a new pattern of activity that should be sufficient to specify the next move, and so on. The sequencing problem requires a site that receives a) visual input from the "where” system, b) a form of motor efferent copy of saccade outputs, and finally c) some form of self-input for maintaining state information through time. Internal Representation of Temporal Events: The dorsolateral prefrontal cortex provides a likely anatomical site for representation of context from internal and external sources in this sequencing task. Visuospatial activity from PP provides the spatial "where" input to PFC (Goldman-Rakic 1987), satisfying (a). Thalamic inputs to PFC provide a form of simple spatial memory, as seen in the FEFmem cells of our original model (Dominey and Arbib 1992), and the real FEF (Bruce and Goldberg 1984) during memory saccades. Post-saccadic activity corresponding to the previous saccade(s), as seen in the FEF (Bruce and Goldberg 1984) is provided to PFC via a thalamic relay of SC activity, SC_POST, (Eqn 15), satisfying (b). The final input to the PFC (Eqn 13) j i is a damped self input (Eqn 14) with randomized projections varying between -.6 and ! I .4, satisfying (c). This allows for complex recurrent memory loops, and also for the j 1 i j inhibitory interactions that will produce order selectivity. Via the learning and j normalization rules (Eqns 1 and 2) that apply reward or punishment after each saccade, | the patterns of PFC activity that precede each saccade influence caudate (Eqn 7) so that I each pattern activates the correct saccade related cells. This leads to inhibition of the SNr (Eqn 8), and disinhibition of SC (Eqn 9) for production of the correct saccade. PFC.. la y e r P F C _ C D _ S y n a p se s s s s e s s s ^ i C D _ lA T _ U y e r »P8S'a a B S a B a 8 8 S S 5 S I S S S S a B aaaS S S y S S S S S S S aad flaD D iE iB BBBflBflBB_lBIB BIB IBIII P F C _ C D _ S y n a p se s Figure 6.3 Activity differences in Sequences RUL and RLU. Snapshots of PFC and caudate activity after the first saccade to R in the sequences RUL and RLU. In both cases the model must select from the remaining two targets. Though the first saccades were identical, the patterns of cortical activity in PFC are different in these two sequences. These patterns are transformed to caudate activity via the PFC_CD_Synapses. In Caudate, we see that for sequence RUL, above, the upper target is favored, while in RLU, below, the left target is favored. 129 Cortical Diversity: This PFC architecture was chosen specifically so that at each point in the execution of each of the sequences, there will be a unique pattern of activity in PFC. Consider the two sequences RLU and RUL. Though the first saccade is the same in both sequences, the resulting patterns of cortical activity must be different if they are to be reliably associated with correct second saccades appropriate for these two different sequences. Due to the order preservation provided by the mixed excitatory and inhibitory PFC inputs, and the recurrent connections in PFC, perception of these two sequences produces different patterns in PFC which remain different even after identical saccades to R, and identical visual input resulting from this saccade. Fig 6.3 illustrates the PFC and caudate activity after the saccades to R in these two sequences. Note the different patterns of PFC activity, and the resulting preference in CD for the L and U targets, respectively, produced by these divergent patterns. Since the model, in both sequences, has just made a saccade to the right target, the visual inputs are now shifted to the left on retina, and in CD_LAT_Layer in this figure. The associative learning model presented above has demonstrated that a unique pattern of activity (generated by a visual cue) can be associated with the correct one of two targets via cortico-striatal trial-and-error learning. In the current simulation, the model learns to associate PFC activity patterns (generated by the context of the sequence) with the correct one of three targets, again via cortico-striatal trial-and-error learning. 6.3 Model performance and single unit activity: Barone and Joseph (1989) recorded prefrontal cortex neurons in monkeys trained to observe and reproduce sequences of three lighted push buttons arranged respectively above, to the left, and to the right of a central lighted fixation point In the first phase of each trial, the three targets were turned on in random order; in the second phase, the animal had to saccade to and press each target in the order of their illumination, cued by full illumination of the targets that remained to be pressed three successive times, as illustrated in our Fig 6.1. Three hundred and two cells were recorded from the superior arcuate area and caudal part of the principal sulcus, and were classified as Visual tonic (VT), fixation, context, saccade related and visual phasic cells. VT cells (35/302-11.5%) showed sustained activation during fixation of the central fixation point (FP) following onset of _____________________ 130 j one of the three targets, and were spatially selective, similar to the sustained activity of real (Barone and Joseph 1989b, Funahashi and Goldman-Rakic 1990) and simulated (Dominey and Arbib 1992) FEF cells during memory saccades. Unlike these cells, the VT cells also had a preference for the temporal order in which their spatially preferred target appeared. Fourteen VT cells were selective for the first target in the sequence, 10 cells were active for the first or second targets in the sequence, 8 were active just for the second target, and three cells were active for the second or third target. In one group of VT cells, the saccade to the target reset the cell to its pre-trial firing rate, whereas a second group of VT cells were not reset with the targeting saccade. Context cells made up the largest class of task-related units (116/302 = 38.5%). They were activated during the fixation of a given target in the sequence execution phase, contingent on which other targets had been, or were going to be pressed. 96 of these cells were spatially selective, in that they had a preference for spatial location of the target. These cells seem to reflect the state of execution of the sequence and could be considered to provide a state-transition function for the system. For all 6 of the possible sequences of three elements, the first trigger is fp offset, and the lighting at full strength of all targets. This ambiguous trigger must be augmented with some internal information to resolve the ambiguity. Recall that 68.5% of the VT cells showed sustained activity only when the target in their visual field was first in the sequence. The pairing of these "rank 1" VT cells activity with the ambiguous trigger is now a unique trigger. Consider first the sequence 12 (where 1,2 and 3 represent the upper, right and left lights). On presentation of 1, a subpopulation of the VT cells with the appropriate spatial receptive field becomes active. We will refer to this subpopulation as VT1. On presentation of 2, the combination of the activity in VT1, combined with stimulus 2 will activate subpopulation VT2. Now, t when the trigger is presented, the animal will have an ensemble of activity in the VT i i cells, which when combined with the ambiguous trigger, will produce a unique j combination of internal and external activity. The point is that cortex is organized so j that presenting the different sequences produces different patterns of cortical activity. | During the learning required to execute this new two-item sequence, following the j presentation of the two targets and then the first "trigger," the animal will at some point I guess the correct first target, 1, get rewarded1, strengthening the association between the response to target 1 and the cortical pattern of activity or "motor set" produced by observing sequence 12. The new internal state, including activity of context cells that respond after the saccade to 1, resulting from the new visual input and saccade efferent copy, forms a new "motor set" which will be associated, through learning, with target 2. Thus, it appears that temporal structure is encoded in terms of transitions between internal representations of context. In the training of the animals, all 6 two-item sequences were learned first, before moving to three-item sequences. This suggests that a three-item sequence might be learned as a combination of a two-item sequence and a third element. Indeed, in Barone and Joseph's (1989) report, cells were found that were activated for a target only when it came first, either in a two-item or three-item sequence. C om parison of M odel and D ata: The model training progresses gradually, based on the shaping used in primate training, moving progressively from sequences of one, two and then three items. In a typical run of our simulation of the sequence learning task, the model attained over 95% correct performance after exposure to approximately 800 trials of the 6 three item sequences. After the learning had taken place, we plotted the responses of the 25 PFC cells during all six sequences, and analyzed them according to the criteria defined by Barone and Joseph (1989.) In Fig 6.4, we see a typical VT cell from our simulation, above, and a typical VT cell from Barone and Joseph (1989), below. For the simulated cell, the 6 traces show the activity of this cell in the six sequences, and the last trace shows the timing of the task. The three small increments on this line indicate when the first, second and third targets are presented. Near the end of the presentation of the third target presentation, the fixation point is removed, providing the go signal, indicated by the higher increment. The drop-off of this increment indicates completion of the first saccade. For the next two saccades, the high signal indicates presentation of the remaining targets, and the drop-off indicates the completion of the saccade. The simulated cell l 1 If the animal makes a wrong move at any point in the sequence, then the trial is terminated. Thus we can consider that when he makes a correct move and the trial is not terminated, this will be a form of "internal reward" which will - in the model - lead to reinforcement of the correct move, even thought the actual juice reward has not yet been received. 132 responds to the left target when it appears first, as seen in the first two traces which are for sequences 312 and 321. S E Q . 3 2 I S E Q .2 3 1 S E Q .1 3 2 S E Q .2 1 3 T r ia L P r o g r e s s Figure 6.4 Comparison of Simulated and Real Visual-Tonic Cells. Typical VT cell (Barone and Joseph 1989) in the lower traces. Vertical arrows indicate target presentations; vertical bar indicates offset of fixation point, small triangles indicates saccades. Cell responds to the upper target (1) in sequences where it appears first, and in other sequences after saccades that precede saccades to the upper target. Simulated cell shows the same behavior for the right target (3). a) First 6 traces show the activity of this cell in the six sequences, and the last trace shows the timing of the task. This cell has a tonic response to the left target (3) when it appears first - in the sequences 312 and 321. In addition in the sequences 231, 132 and 123 this cell is activated after saccades that precede saccades to 3, similar to the activity related to 1 for the displayed actual PFC cell. 133 s £ 0 7 T 2 T S E Q .1 3 2 ___________________ J~ ~ \ S £ Q _ 2 1 3 S £ Q _ 3 1 2 ■ 5 f o T 5 5 T SEQ„~321 T r ia l_ P r o g r e s s R . P F C - C P 3 1 6 3 123 132 , . ^ 4 m , T - - * ■ I - T . T, , 213 312 23 I 32 1 - Figure 6.5 Comparison of Simulated and Real Context Cells. Context cells respond after saccades to a particular target, dependent on which targets have already been - or remain to be - chosen. The lower traces display a context cell from Barone and Joseph (1989). This cell is activated after die saccade to 1 in the sequences 123 and 132, and in no other sequences. The upper traces display the response of a simulated PFC cell during execution of the six sequences. Like the real PFC cell, this simulated cell is active after saccades to 1 only when it is the first saccade in the sequence. 134 , In the remaining sequences, the cell is also activated after saccades that precede saccades to the left. This same combination of activity is seen in a primate VT c e ll, which responds to the upward target when it appears first, and after saccades that precede saccades to that target. Fig 6.5 compares typical context cells from the model and Barone and Joseph (1989). Both the animal and model cells start firing after the saccade to 1 and stop firing after the saccade to 2 or 3 in the sequences 123 and 132. Figure 6.6A presents the population of 25 PFC cells during the execution of all six sequences. Table 6.1 Number and classification of prefrontal cortex cells (Barone and Joseph 1989) (Simulation-Tonic) (cells from Fig 15A) N % N % Visual tonic 35 12 6 2 9 1,3,4,6,8,13 Fixation 65 21 - - Context 116 38 9 43 2,7,9,12,14, 17,22,23,25 Saccade-related 33 11 - - Movement-related 9 3 - - Signal-related 24 8 3 14 5,11,20 Others 20 7 3 14 10,15, 24 Table 6.1 compares the distribution of simulated cell types, from Fig. 6.6A, with those found in primates (Barone and Joseph 1989). Qualitatively, our percentage of context cells compares well with those in the monkey, and while we see a larger percentage of VT cells than in the monkey, in both the model and monkey there are less VT than context cells. Recall from Eqn. 13, that the modeled PFC is constructed to i receive spatial input from PP, a damped self input, post-saccadic input, and a form of spatial memory indirectly from thalamus, satisfying the minimum information requirements we defined previously. Regarding our lack of saccade-, fixation-, and j arm movement-related cells, it is likely that the real PFC receives other inputs in , addition to the minimal set we defined for this task. Indeed, in the animal task, there is j a reaching movement associated with each target while our simulated task involves only saccades. Barone and Joseph conclude that the activation of spatially selective fixation j neurons only intervenes during preparation for visually guided reaching, based on their own results and those of Suzuki and Azuma (1977) indicating that visually guided reaching was required for activation of the fixation cells. The absence of a visually guided reaching component to our sequential saccade task may remove the need for these and movement-related cells and justify their absence in our population. Effects of target presentation format: In the 1989 paper, Barone and Joseph presented the stimuli in a "tonic - removal" format, in which once a target came on in the sequence presentation phase it remained on until after the first saccade was completed. In the sequence reproduction phase, once a target had been visited, it was removed from subsequent go signals. This format raises two questions concerning unit activity and performance. First, is the visual-tonic effect directly related to the tonic presentation of the targets, or would it still be seen if they were phasically presented? Second, the tonic-removal format is easier since for the second and third saccades, there are only two and one target respectively to choose from. What would happen to performance if all three targets were lighted for the three go signals? We trained the model using the "phasic -nonremoval" paradigm illustrated in the lower part of Fig 6.1 A. In this case each target is presented phasically, and the three go signals use all three targets, rather than just the targets that have not yet been visited. The model performed nearly as well, consistently above 85% for the 6 sequences. Figure 6.6 compares PFC activity in the two paradigms. While the performance of the model in both cases is quite good, the unit response characteristics in the "phasic - nonremoval" are less obvious than in the "tonic - removal." These differences in activation are likely due primarily to the change to phasic presentation of the targets which removes a source of tonic input. It is noteworthy that, although the temporal structure of these PFC cells is less obvious and the task is more difficult, the model performs well. If we consider, however, the population rather than single unit activity at the time of each saccade, we can see that while the individual cells do not all have nicely stereotyped behavior, as a population j the form unique patterns for the different saccades. Fig 16 shows for the 18 saccades j made during the execution of 6 sequences, the patterns of activity in cortex at the time of each saccade. We can see that, while there is some overlap in these patterns, each one is different enough from all the others so that it can reliably be associated, via PFC- IT plastic synapses, with its corresponding saccade. I P f C _ U n i t s j n o :_ _ f t rmziTTnt i ’ ^Izr-Pn I r ,-•. n . r4" ^ — L _ _ J .. _ f c A _Iiin A f L ~ TZJTTj F tirnzrr f t — « -n ......... f t — n ....-Z______ f t i PFC_U nH s t\ tl -TT_rYL 5 u c n K -/“ L , r~ \_ j— l z^fku lin . E > i £ jh zznn: U H UHuI - j r l Figure 6.6 Comparison of Tonic and Phasic paradigms on PFC activity. Time traces for 25 PFC cells during execution of the Tonic paradigm above, and Phasic sequence paradigm above. In the tonic paradigm, cell 10 is the VT cell from figure 6.4, and cell 7 is the context cell from figure 6.5. Most of these cells show either context or VT behavior, some with mixing of both, and a few with non specific or no task-related activity. In the Phasic paradigm, below, there is more complexity in the time course of activity, with many cells not falling neatly into the categories defined by Barone and Joseph. 137 P atterns at saccades - Tonic J P F C _ P a tte r n _ is t_ '> a c c a d e s 1 1 ■ ■ ■ ■ ■ ■ ■ ■ ■ fl B fl B ■ fl ■ a B ■ ■ ■ B ■ ■ ■ I I ■ B ■ ■ ■ 1 fl fl s ■ B ■ fl PFC _ P a t t e r n _ 2 n d .S a c c a d e s ■ ■ ■ ■ I B i _i — 1 ■ ■ I B “ 1 J fl - ■ ■ ■ . ■ ■ |_ fl fl ■ I • j _i L _ i ■ ■ ■ ■ B Tfc". . P a t t e r n _ 3 r d _ S a c c a d e s ■ ■ ML ■ r r ■ r r r □ ■ 1 ■ E L 1 ■ j r i _ B ■ r L r r i ■ L r r r ■ r - H B - — — - ■ ■ ■ a fl i ■ I ■ I 1 ■ ■ ■ ■ B fl ■ ■ ■ B I P attern s a t saccades • Phasic | PFC_Paccern_ isc.Saccaoes ■ I IBr■ I I I ■ N I ... — — — — — — B f l f l f l ■ __ — f l f l — - - ■ B B ■ f l ■ B ~ ■ P ■ ■ - JL ■ I ■ B c E ■ • f lr n l a PFC._Pattero_2mJ_Saccades f l I ■ ■ rr a ■ R ■ __j a ■! ■ ■ i ■ f l J ■ ■ 1 ■ a f l __j ■ ■ □ J ■ ■ ■ 1 i 1 1 ‘pTc! . Pattern_3rd_Saccades fl - - a - - B fl ■ - f l - - - f l I m - - f l - - ... - - - — ■ - - f l f l ■ - — I I - - I - ■ I ■ ■ _ ■ ■ i i ■ ■ ■ I ■ I ■ ■ ___ Figure 6.7 PFC activity before each saccade. This figure shows for the 18 separate saccades made during the six sequences in the tonic (above) and phasic (below) paradigms, the pattern of activity in PFC at the time each saccade was made. The three 6x25 arrays represent for the 1st, 2d and 3rd saccade in the six sequences. In the first 6x25 array, each row represents the activity of the 25 PFC cells at the time of the first saccade for the six sequences. The 2nd and 3rd arrays show PFC activity before the 2nd and 3rd saccades respectively for each of the 6 sequences. The task of the learning mechanism is to correctly "recognize" these different patterns and associate them with the correct saccades. These patterns are distinct enough so that the model can correctly perform both paradigms above the levels of 85% correct as seen in well trained primates. 138 6.4 Discussion Many recurrent models (e.g. Jordan 1990, Elman 1990) use network output as part of the next input to generate sequences. These models learn by computing an error measure from the network output and the desired output and adjusting connections strengths to minimize this error. Our approach differs in that is based on a global reinforcement/penalty signal. This approach has been applied to the control of dynamical systems (see Barto 1990), and to learning sensorimotor and coordinate transformations (Fagg and Arbib 1992, Mazzoni et al. 1991). Dehaene et al. (1987) developed a model of sequence learning and reproduction in which pre-represented sequence detectors are selected to accommodate the sensory sequence input using a local Hebbian rule. Our PFC also pre-represents sequences via the existence of excitatory and inhibitory connection from sensory and self inputs, so that patterns of activity PFC encode sequential states, and subsequently become associated with production of the correct saccades. Wang and Arbib (1990) note that the selection model of Dehaene et al. (1987) relies on pre-representations which would have to be immense to learn arbitrary non-trivial sequences. They address this problem in a model of sequence recognition and reproduction based on short term memory (see our Eqn. 13) and establishing sequence-sensitivity by learning rather than by selecting existing pre-representations. In PFC, the coded "features" are related to position, temporal order, and previous saccade activity. Again by using combined inhibitory and excitatory input from visual, saccade-related and self input sources, PFC cells detect these individual "features", as well as their conjunctions and disjunctions. By allowing the output of the network to influence its state, we produce a sequence of connected states that can be used to store and reproduce behavioral sequences. It is likely that intrinsic cortical plasticity plays a role in these primate tasks, but by allowing the required information "features" relevant to the sequencing task to combine in our PFC via fix ed connections, the resulting : cellular activity is surprisingly similar to that in the primate PFC, and provides the 139 required representational diversity for learning the task. Future modeling work should address the benefits of cortico-cortical plasticity, as well as short term plasticity functions that would support the rapid encoding and reproduction of arbitrary sequences. Chapter 7 G eneralization of A ssociative and Spatial Relations In the previous two chapters we examined behaviors that are learned and executed in specific, fixed contexts. Here, we consider the extension, or generalization, of these behaviors to new contexts. In spatial generalization, or generalization on responses, a task is learned and performed with the targets presented in different locations such that the relative, rather than absolute positions of the targets are of interest For example, in the CVD task, instead of learning that cue R is associated with a saccade to a fixed target 10° right of the cue, one must now learn that cue R is associated with a saccade to the rightmost of a pair of targets, even if that happens to be 10° to the left. In a second form of generalization, generalization on stimuli, the meaning of well learned cues can be transferred or generalized to similar but new cues. For example, one can come to learn that all red cues are associated with a rightward saccade, and perform correctly on new red cues. We demonstrate that the CVD and sequencing models, when properly trained1, are capable of learning the generalized tasks, including performance with novel target configurations. We will consider the computational requirements levied by generalization, and show that the CVD and sequence model architectures are sufficient to satisfy these requirements____________________________ 1 Proper training involves not only the examples, but also the order in which they are presented as we describe below. __________________________________________________________________________________________________:_______________________________________________________________________________ H i ; 7.1 Introduction: Generalization Requires a Structured Environment While the ability to learn specific S-R associations and spatiotemporal sequences provides survival utility, the ability to generalize learned behaviors in order to behave effectively in new situations begins to approach what we think of as intelligent behavior. Indeed, generalization, abstraction, and the formation of analogies involve the capability to extract the salient components of a context and apply them in another context. The association (CVD) and sequencing tasks provide a rich environment for the investigation of different forms of generalization. In order to more carefully address this topic, we introduce a distinction concerning two different forms of generalization. Generalization on stimuli involves similar, familiar stimuli becoming associated with the same response, and the subsequent capability to produce the same response to new stimuli that is similar in the same dimension. For example, consider that multiple associations of the form <red object, right saccade> have been learned. When a new stimuli - red rectangle - is presented, then the association <red rectangle, right saccade> is produced as a generalization, where the stimuli are related in the dimension of color. In this case the generalization can be considered in terms of a rule "if red, go right." It is clear that this kind of learning is heavily dependent on the structure of the environment. In the case of our models, the environment is defined by the set of S-R pairs to be learned, and the order in which the pairs are presented during training. In order for generalization to occur, there must be some structure in the environment, corresponding for example to the rule "if red, go right." In this sense, we can consider that generalization is the process of extracting structure from the environment Generalization on response, or spatial generalization, involves the extension of a j given response to a set of related responses. Specifically, we will study the association ! task using S-R pairs in which the cues are unchanged, but the saccade targets are displaced from their standard locations (symmetrically left and right of the cue) so that they remain their relative left and right orientation, but change orientation with respect to the central cue. Thus the responses for a given cue are made in terms of relative locations, e.g. "leftmost," or "rightmost," rather than in terms of absolute spatial 142 locations. Again, this type of generalization can be described in terms of a rule, e.g. "if red, go rightmost," and again, it requires the existence of structure in the environment. Both types of generalization can be considered in terms of category formation or classification, and can be show to increase the effective storage capacity (number of learned S-R pairs) of the network by exploiting regularities in the environment 7.2 Generalization on Stimuli In the association task, the model learns to classify the cues as being related to left- or right-ward saccades. In doing so, it can extract and exploit structure in the environment. As defined above, for this task, the environment is a set of S-R pairs to be learned. Consider the following three different environments. In the first environment, there is no statistical correlation between color or shape (the two stimulus features we encode) and a given response (left or right saccade). That is, there is no structure or predictability in the environment. Each S-R pair is learned separately, and by definition, no generalization can occur. In the second environment, while all of the stimuli vary in shape, half of them are red, and all of these red stimuli are paired with the same response, a rightward saccade. The remaining stimuli are any color but red, and are paired with a leftward saccade. If we train the model on a subset of these pairs, with an equal number of "red" and "non- red" pairs it will generalize to the rest of them. That is, it will perform correctly on new pairs. In the model, IT cells that have a preference for red will become linked, via increasing synaptic strength, with caudate cells that have rightward saccade preferences. Later, a new red cue will activate these caudate cells, and the model will produce a rightward saccade, even though it has never seen this particular cue. Likewise, IT cells preferring non-red colors will become strongly linked to the leftward ! saccade-related cells, and new non-red cues will drive leftward saccades. | The second environment is structured, and the model can extract that structure. In { doing so, it represents the rule "red-right, non-red-left" in the form of synaptic ! connections between IT and caudate cells. We see, then, that our model architecture is j i ________________________________________________________________________ 143 j sufficient for allowing generalization on stimuli. Our model IT is constructed so that similar cues will produce similar patterns of activity. Thus, by construction, our model will produce generalization on stimuli. In the discussion we will address the possibility of making more formal statements about the relation between neural architectures, and the set of possible structures that can be mastered by these architectures. In particular we will consider structured environments in which the structure is dynamic, i.e. where the rule that describes the structure can change. In the second environment, the rule "red-right" specifies a consistency of the environment. We consider a third environment which is inconsistent. In an extreme case, such an environment could contain S-R pairs that use the same stimuli paired with different responses, thus requiring a reversal in order to correctly respond to the two S- R pairs. In this kind of example, generalization on stimuli is detrimental. In the discussion we will consider tasks like the Wisconsin Card Sorting Test, which are explicitly inconsistent in this way, and possible architectures for coping with inconsistent environments. E nvironm ent E lf random) E2f structured) E3fanti-structured) Trials to Criterion 58 58 58 % Correct on Gen Probe 6 2 .... 91 11 T able 7.1 Generalization on Stimuli for Structured and Unstructured Environments. In table 7.1 we show that a red circle - left, and green triangle - right can be mastered in 58 trials. E l then uses two new pairs that are not related to the first two, and we see 62 percent correct on a probe of 20 trials. In E2, the new cues share the j colors of the previous cues, and differ only slightly in shape, thus there is strong j generalization. In E3, the pairs are nearly reversals of the initial pairs, and thus the ; generalization impairs performance.2 2Preliminary simulation values. 144 7.3 Generalization on Response: Formation of a Spatial Gradient In Chapter 5 we demonstrated, using our association model, how a cue-driven pattern of neural activity in inferotemporal cortex (IT) can become associated with a saccade to the correct one of two fixed spatial targets. We are now concerned with learning the more general sensory-motor association that will allow the same cue to guide the choice of the rightmost of any two targets, as illustrated in Fig 7.1, without ad-hoc modification of the model to accommodate this requirement. Thus, the same cue-related IT activity would modulate SNr so as to select the leftmost of any two targets, even if these two targets are arranged a novel configuration. We investigated the learning of spatial generalizations with the model, using multiple target configurations with well known cues. For a given row of five positions, there are 10 different left-right configurations for two targets. Using two of the well learned cues - one each for left and right, we first trained the model using 6 of the ten target configurations as a training set, and then tested its ability to perform on the remaining 4 target configurations. As a control experiment, in a second simulation we trained the model on a single configuration of targets for the same number of trials as in the training set above, and then tested it on the remaining configurations. We determined that the model exposed to the training set performs better on the 4 test configurations than does the control, and that the performance differential is also dependent on the order used in presenting the training set. A l S m Tl □ Targets C □ V c u e T3 □ S3FP T2 □ v ) / FP 1 Cue 1 J _ _ _ _ _ _ _ 3 _______ TI n n n n I Targets 1 T2 n n n n Eye S T3 _ _ _ _ _C Ln n n Figure 7.1 Spatial Generalization Tasks. Based on the standard association and task, with the target locations varied. In the lower panels, the targets have changed absolute locations, but still maintain their relative positions. (A) Two peaks n n plus local peak of disinhibition yields a A _ from which winner-take-all selects the corresponding target (B) Two peaks ii n _ plus gradient of disinhibition from which winner-take-all selects the rightmost target Figure 7.2 Spatial Gradient Implements Spatial Generalization. In solving the spatial-generalization problem, by applying a gradient of disinhibition prior to a winner take all process: for two targets of equal strength, the given gradient ensures that the rightmost target wins. The gradient itself, then, implements the concept of "rightmost." A. Association for fixed target. B. Spatial gradient for Generalized cue-target association. 146 A ■ 1 i B F ig u re 7.3 Neural Im plementation of Spatial Gradient. A. Before generalization learning. B. After generalization learning In Fig 7.3B we display the activity in caudate and SNr during presentation of a ! rightward cue after generalization learning. Note that the activity in caudate forms a "spatial gradient" that is monotonically increasing as we move from left to right. In SNr we see the mirror image - activity increasing from right to left. Thus, instead of forming an inhibitory mask that allows activity at only a restricted site (as in Fig 7.3A) j ! the generalized learning yields a mask that selects the leftmost of two targets in any j rs ^.Activity g§ ■ a ■ B a H • m a 1 ■ ■ ■ B ■ i Hi IT _A ctlvlty T T _C D _S ynap50S B O B O D D S iaaJlllllllliH B II SS!Sg«SSBSBH!!5B C D „IT„Synapses& A ctlvity IT_ Inti i» 0 n c e _ O n _ ( !;a iJ date D TI ■ ■ ■ ■ ■ B ■ ■ B ■ ■ * ■ B ■ ■ ■ ■ ■ ■ ■ ■ ■ f t 10:0 i t * j0:0 J1:4 lma> S N r_ ln h tb ito ry _ M a s k _ o n _ S C B ■ ■ ■ f l ■ I ■ B B B f l ■ B ■ B T T .C D .S y n a p s e s CD _IT _Synapses& A ctivfty IT_lntluence_On_Caudata ■ * a a ■ ■ ■ ■ a ■ ■ a ■ S N r_ ln hiblV ory~ M asl< _on_$C location on the trained row. A more conceptual depiction of the gradient for spatial generalization is shown in figure 7.2. The continuous shape of this gradient results from the simple statistical properties of the distribution of rewards for each target location. Consider a cue to be associated with saccades to the rightmost target In our set of 10 target pairs, as a target farther to the absolute right, the number of target pairs in which it is rightmost increases. Thus, over many trails, more rewards will be received at more rightward positions so that these positions will receive more influence from cue, thus forming a cue driven gradient of activity in caudate that is strongest at the right and diminishes to the left It is known that in randomized presentation of training data leads to a greater generalization capability than does blocking of trials (e.g. Lee et al. 1985). We observe this in simulation runs where blocked trials tend to produce humps in the middle of the gradient, leading to subsequent errors, whereas a random distribution of target configurations tends to preserve the monotonic nature of the gradient While we will not present the details here, we also observe presenting the trials such that the gradient is built up at the rightward extreme and gradually extend to the left produces a smooth gradient in a minimal number of training examples and minimal number of errors. Prediction: In a related study of target selection based on relative position, Niki (1974) used a left-right delayed alternation task, with multiple target configurations. Recording single prefrontal cortex units, he found one population of cells that was selective for relative target position during movement preparation, and another population selective for absolute target position that was active during movement execution. Our model predicts that, once the gradient is learned, cells near the favored side of the gradient will predict relative direction of the forthcoming movement, as soon as the cue is present, whereas cells at the locations specific for the actual saccades will i J predict the actual saccade direction following the target presentation, prior to and during the saccade. I 148 7.4 Generalization on Stimuli and Responses in Sequence Learning We now consider the task of generalization of sequence reproduction to different target locations. Given 3 fixed targets arranged in a triangle with vertices "up," "left," and "right," of a central fixation point, there exist six possible sequences of these targets that have no repetition. In a trial, the targets are lighted in a given order, then the subject must press the targets in the same order. Again, by using the generalization metaphor, we can train the model to perform a spatial generalization version of this task, where the three targets are displaced such that the fixed positions are changed, but the relations (left, middle, right) are preserved. Unlike the spatial generalization in the CVD task, where the cue remains the same but the targets are moved, in this case, the targets themselves form part of the "cues" that produce patterns of activity in PFC. In CVD with displaced targets we generalize over the outputs, whereas in sequence reproduction with displaced targets we generalize over the inputs and outputs3. To test generalization, we compare performance on a new sequence after training with random presentations of a training set of sequences. We generated a new set of sequences by shifting the upper target to the right, as in Fig 7.1. Starting with a naive state, we first trained the model to 90% correct on the standard sequences and five of the six new sequences. Then the remaining sequence was tested. Performance on these sequences was compared to a control case in which the model was not trained only on an equal number of the standard sequences. The pretrained model had a 51% performance advantage over the control model. As in the association task, performance was improved when practice on non-standard examples preceded the testing. While the current model has learned a small set of stereotyped sequences, the spatial generalization may provide the basis for the more generalized capability to learn ; sequences "on the fly”. It is worth noting that in general neither the monkeys, nor the I model learned the general concept of sequencing, but rather had to be trained for each j I I | sequence. j ^For CVD, generalization over inputs is tested by presenting a cue that is similar in its features to a well known cue. Since similar cues produce similar activation o f IT, they will also produce I similar activation in caudate. 149 7.5 Structure-Function Relations: Architectures and Generalization. A given system architecture is designed specifically to address a given problem or class of problems, thus it makes sense to ask the reverse question - given some architecture, what classes of problems can it address? Here we re-examine the S-R architecture to see why it can perform generalization on stimuli as well as on responses, without any additional modifications. In the S-R model, visual input produces patterns of activity in IT cortex. Each stimulus is defined by a 6 element vector, specifying the value for red, green, blue, circle, square, diamond. We adopt the convention that the total "color mass" is 10. Thus a cue can have pure color with a value of 10 for one of red, green blue and 0 for the other two, or a distribution of color. We adopt a similar convention for the shapes, with a "shape mass" of 10 that can be distributed across the three shape features. The cues produce patterns of activity in IT that arise from activity in feature-selective cells in V4 which project to FT. For a given feature, the color red for example, any cue with that feature will activate the corresponding element in V4, which in turn activates its own target units in IT. While the total pattern of activity in IT will vary for different red cues due to their different shapes, there will be a common subpattem related to the color red. Thus, in the IT cortex where the features of visual cues are represented, similar cues will produce similar patterns of activity. This is an architectural "feature" based on the existence of feature selective elements in V4 that project to IT. These patterns of activity in IT influence the saccade system via cortico-striatal projections. Cells in IT project to saccade related cells in caudate, allowing cue-related activity to influence saccade target selection. If the model is exposed to an environment in which all red cues are associated with rightward saccades, then the IT units that respond to the feature red for different cues will all become more strongly connected to the rightward saccade-related cells in caudate. The combination of the model's \ j property that similar cues produce similar IT patterns, and that these patterns produce I saccade-related activity in caudate yields an architecture that implicitly solves the generalization on stimuli problem. I Similarly, the creation of the spatial gradient and its corresponding ability to ! implement generalization on spatial responses is based on the S-R model architecture, _______________________________________________________________________________________1 5 0 j and the structure of the environment. The representation of motor space in caudate is continuous/topographic (i.e. neighboring caudate cells represent saccades of similar dimensions). Thus, any spatial relation that can be described in terms of a continuous, two dimensional surface (e.g. a plane) can be learned by this model. While we concentrated on relations like "leftmost" or "rightmost" that are described by planes, relations such as "farthest from center" or "closest to center" could also be learned. Here the spatial gradient would be similar to a parabolic function f(x) = ax2, where a is positive (x=0 is a minimum) or negative (x=0 is a maximum), respectively. 7.6 Discussion: From Habits to The Wisconsin Card Sort Generalization is a small step towards intelligent behavior from pure S-R learning. A larger step involves the selection of the correct generalization, dependent on the j behavioral context. This kind of capability is tested clinically in the Wisconsin Card Sorting Test, in which the subject must generalize in three different dimensions - color, shape and number, and must then select the correct one of these three dimensions. The task involves sorting cards by color, shape, or number. The complex element of the task is that, unannounced, the sorting rule changes, and the subject must realize it has changed, search through the remaining rules, and stick with the correct one until it changes. In its current form, our S-R model is inadequate for this task. It may learn that red cues correspond to leftward saccade, and square cues to rightward saccades, but for objects that are composites of conflicting learned generalizations, e.g. a red square, the model is not capable of attending separately or conditionally to only one at a time of the two dimensions. j We know that both in IT (Fuster 1990) and in caudate (Hikosaka et al. 1989a), | during the performance of behavioral tasks that require discrimination of stimulus j features such as color, shape or location, evoked responses to visual stimuli are greatly j j diminished if not completely eliminated when these stimuli lose their behavioral j significance. These "on-line" changes in reactivity to a stimuli are perhaps more I associated with selective attentional processes, rather than changes in the perceptual ! j salience of the stimuli. In the WCST, when the sorting dimension changes, we might expect to see these same kinds of selective changes in feature specific neurons as the significance of the associated features changes in the task. We propose that such a mechanism may underlie the WCST-class of conditional behavior. This will allow the existing, learned habit mechanisms to continue to operate, unchanged. Their recruitment is controlled upstream in the sensory cortices that drive them. By modulating the sensory responses, the features of the environment are thus selectively channeled to the habit, S-R mechanisms. The question then remains, how, where and why are the sensory modulations implemented? Since our model currently "perceives" two stimulus dimensions - color and form, we could implement attentional neurons that would selectively allow either one, or the other or both of these channels to transmit information on to IT an thus to the associative habit memory. In doing so a deeper issue would thus be overlooked. That issue relates to the question - what are the minimal architectural features that would allow for the cognitive development of something like rule encoding? We assume that attention represents the allocation of a finite processing resource. By filtering the input, this process can then operate on just the relevant information that passes through the filter. In the WCST there would be filters that allow only color, form and number information, respectively to pass on to the behavioral decision apparatus. From this perspective, then, the WCST or more general cases of this class of task can be solved with the following apparatus: 1) An associative S-R mechanism as we have described and modeled. 2) An attention mechanism that allows selective perception of single feature dimensions (i.e. color, shape etc.), and 3) A "win-stay, loose-shift" mechanism for the management of attention. Changeux and Dehaene model "rule coding" neurons that competitively select between sensitivity to the different sensory "sorting" dimensions. An interesting variation between their model and the one we propose here is related to attention and perception. In the Dehaene and Changeux model, all of the stimulus features are perceived and memorized (for use in reasoning in case of an error). The internal sensory information is gated to output intention clusters by rule coding neurons. This seems to predict that in IT, cells selective for color would continue to be active even if number was the current sorting dimension. In contrast our model (which admittedly does not use the auto-evaluation that requires memory of all the stimulus features) predicts that sensory responses will only be seen for the current sorting dimension. 152 Chapter 8 Dissociable Models of Early and Late Onset Huntington's Disease Saccadic eye movement dysfunctions often precede other HD clinical symptoms, and these deficits differ depending on the age of onset. Currently, the specific brain pathology of these early dysfunctions is not well known. However, the dissociable deficits associated with early (HD<30) and late (HD>30) onset HD suggest differences in their underlying pathologies. In this study, parameters of a physiologically based computer model of the intact saccadic eye movement system are altered to produce possible HD lesions corresponding to the early and late onset pathologies, and the associated oculomotor deficits. While different lesions or combinations of lesions (each representing a different model of HD) can produce similar motor dysfunctions in some tasks, they appear to be dissociable in others. Our modeling indicates that HD<30 emphasizes basal ganglia dysfunction, while HD>30 emphasizes cortical dysfunction, and we suggest a novel paradigm by which to further dissociate these two HD models clinically._______________ 8.1 Introduction i A large percentage of mild Huntington’s patients display oculomotor dysfunctions j (Beenen et al. 1986), including multiple deficits in saccadic eye movements (Lasker et al. 1987, 1988). Oculomotor functions in subjects at risk for HD (offspring of HD 153 | patients) are often affected before the onset of clinical symptoms (Beenen et al. 1986). HD morphology includes atrophy of the caudate head, putamen, globus pallidus and frontal lobe with dilatation of the lateral ventricles. In addition, in the HD substantia nigra, a decrease of about 40% in neuronal number, and a shrinkage and loss of both pigmented and non-pigmented neurons has been reported (Oyanagi et al. 1989). Many regions affected by HD including frontal cortex, caudate and substantia nigra participate in the oculomotor saccade system, as reviewed in Chapter 3 and in Dominey and Arbib 1992. It is of some interest that the specific oculomotor deficits in HD related to latency, accuracy and velocity are dependent on the age of HD onset, while problems with distractibility are largely independent of onset age (Lasker et al. 1987,1988). W e will first review HD saccade deficits with respect to age of onset, and then look at the corresponding saccade-related functions of brain regions affected in HD whose degradation could account for these deficits. By modification of parameters in our computer simulation of the oculomotor system (Chapters 2 ,3 and 4, and Dominey and Arbib 1992), we will produce dissociable cortical and basal ganglia lesions that lead to distractibility. We then observe the accompanying changes in latency, velocity and accuracy in order to assign these parametric HD lesions to the different age onset categories. Finally, based on these simulated HD lesions, we will suggest a new psychophysical experiment to differentiate between these different HD models, and to assess their plausibility. 8.2 Saccade Deficits in HD HD saccade deficits can be characterized in terms of: a) initiation defects b) distractibility (Lasker et al. 1987), c) slowing and d) dysmetria (Lasker et al. 1988). To explain these deficits we first review three standard saccade tasks employed by these investigators. In each, the subject is asked to fixate (stare at) a central light source (the fixation point), and later to make a saccade to the location of a second light source in the periphery (the target). In each task the "go-signal" to make the saccade is the offset of the fixation point accompanied by a short (100 ms) auditory beep. In the i I _______________________ 154 I novel stimulus task (NS) the go signal occurs simultaneously as the target appears. In the continuous stimulus (CS) task, the target is presented while the fixation point is still visible and they overlap for 1 to 1.8 seconds before the go signal. The remembered stimulus (RS) task is identical to the CS except that after the target is illuminated for 1.5 seconds, it is extinguished, and then 1 to 2 seconds later the go signal occurs. With this brief task review we proceed to a review of HD deficits in these tasks. Initiation: For patients and controls, the saccade latencies are lower for NS than for CS and RS, but the patients have a significantly longer latency than controls for the CS and RS. This increased latency is seen primarily the patients with HD onset after 30 years of age (HD>30.) Patients with onset of disease before 30 years of age (HD<30) had latencies that were not significantly different from those of the control group. Distractibility: In the CS task, all HD patients have a increased tendency to incorrectly make a saccade to the target when it appears, rather than continuing to fixate the fixation point (29.9 ±18.8% distractibility for HD patients, vs. 6.4 ±4% for controls). Similar distractibility is seen in the RS task (33.0 ±23.4% distractibility for HD patients, vs. 5.9 ±8.0% for controls). The patients are distracted by the onset of the target and make a saccade before the go signal. Behaviorally, this is a reflexive response to a change in the environment, and the correct performance of the CS and RS tasks requires active suppression of this reflexive movement Slowing: In all three tasks, the HD<30 patients had significantly reduced velocities, while the HD>30 patients had normal velocities. As in the latency results, this seems to indicate that different mechanisms are affected according to age of onset Dvsmetria: The saccade amplitude for the NS and CS saccades was normal for all HD patients (with a non significant hypometria in the CS task for HD<30 patients). In i the remembered saccade (RS) again we see a distinction in performance with respect to age of onset. The HD<30 made hypometric RS saccades, and the HD>30 made hypermetric RS saccades. Another way to summarize these data is with respect to age of onset. For the HD<30 group, the main deficits are velocity reduction in all cases, and a hypometria in j the remembered saccades. The HD>30 group shows increased latency in the CS and j RS saccades, with hypermetric remembered saccades. Again, these differences j indicate that different brain regions are affected in mild HD, dependent on age of onset. 155 Common to both age onset groups, however, is the distractibility in the CS and RS tasks. While the different brain disorders produce different velocity and latency effects in the two groups, they appear to produce the same distractibility effect. Our goal will be first to develop two separate models for distractibility that will produce the differential velocity and latency effects associated with the two age-onset groups, and then to suggest an additional experiment to test these models. Latency D istractibility Velocity Accuracy HD>30 HD<30 fbothl HD>30 HD<30 HD>30 HD<30 N S * * NA * deer * * C S incr * 30% * deer * * RS incr * 33% * deer hvpermet hvpomet Table 8.1 Summary of HD saccade deficits. (* means not significantly different from comparison group.) From Lasker et al, 1987, 1988. 8.3 Implicated Brain Regions W e now review the cortical and subcortical dysfunctions that might account for distractibility in order to and suggest two distinct pathology models that could produce distractibility. The superior colliculus (SC) is a major component in the generation of saccades, with activation of a given location in the SC "motor map" producing a saccade of corresponding amplitude and direction (Robinson 1982, Sparks 1986). The substantia nigra pars reticulata (SNr) exerts a tonic inhibition on SC which is phasically blocked during voluntary saccades by the inhibitory effects of the caudate on SNr (Chevalier et al. 1985, Hikosaka and Wurtz 1983, Hikosaka et al. 1989). Injection of the GABA agonist muscimol into the SNr inhibits the normal tonic inhibition of SNr on j SC, producing irrepressible saccades, i.e. distraction, contralateral to the injection j (Hikosaka and Wurtz 1985). This indicates that the tonic activity of SNr plays a role in 156 suppressing unwanted, distracted saccades by inhibiting SC. The atrophy of SNr described by (Oyanagi et al. 1989) could contribute to this kind of distractibility. We now consider distractibility mechanism of cortical origin. It has been shown that cells in the rostral pole of SC display tonic activity during fixation (Munoz and W urtz 1992). When these cells were inhibited with muscimol, the monkeys' distractibility increased from 2% pre-injection to 56% post injection (Munoz and Wurtz 1992). The distractibility in HD may also be due to a similar perturbation of fixation- related cells in rostral SC. A possible source of this activity in the rostral SC (as opposed to the fixation related inhibition of caudal SC via SNr) is the FEF which is known to contain cells that are active during fixation (Segraves and Goldberg 1987). We note that when Munoz and Wurtz inhibited the rostral SC fixation cells, many of the unwanted "distraction" saccades were initiated < 100 ms after the target onset, and thus fall into the range of express saccades (Fischer and Boch 1983), implying a link between distractibility and express saccades. By introducing a gap of 200 ms between the fixation point offset and target onset in the CS task, Fischer and Boch (1983) found that saccade latencies could be greatly reduced (hence "express" saccades), indicating that there is an active mechanism of fixation that must be disengaged before making a saccade. Data from Schiller et al. (1987) suggest that after unilateral FEF lesion, there is an increase in the proportion of contralateral express saccades. The fixation related activity in FEF may contribute to the rostral fixation cells in SC whose inactivity allows distractibility and express saccades; and the FEF lesion may remove a source of activation of these SC fixation cells. | 8.4 Parametric Analysis of Simulated Lesions and HD i Based on these data, we now consider two distinct (subcortical vs. cortical) candidate explanations (that may be combined in some HD patients) for the distractibility seen in the two HD age-of-onset groups. First, a reduction in the strength of the inhibitory nigro-collicular pathway that would allow inputs to SC to generate unwanted saccades, even though a target is still being fixated, similar to the effects of muscimol in the SNr. Second, a reduction of the activity of cortical fixation related cells that would remove a command for maintained fixation both from SC, and possibly also from the saccade-related cells in FEF. We will now examine the corresponding parameters of a model of the intact oculomotor saccade system (Chapters 2, 3 and 4, and Dominey and Arbib 1992), whose manipulation can produce these two distinct models of distractibility. We will then examine the effects of these parameter manipulations (i.e. the models of distractibility) on saccade latency, velocity and accuracy, in order to correlate these models with the corresponding age-of-onset group data. In this way we will produce two models that cannot be distinguished in terms of distractibility, but that potentially can be distinguished by their differences in latency, velocity and accuracy. In our model of the more subcortical dysfunction responsible for HD distractibility, we consider the atrophy of both caudate and SNr of the basal ganglia. In this model, the SNr will have an overall reduction in its tonic activity, and will also be rendered | highly insensitive to any remaining influence from caudate. This is accomplished by | the modification of two parameters in the model. The first, SNRJVIAX1 , corresponds to the maximum firing rate of the inhibitory nigrotectal cells. This value will be reduced by 80% from 100, to 20. The second parameter, CD_MAX, corresponds to the maximum firing rate of the inhibitory striatonigral cells, and will be reduced by 80& from 50 to 10. The net result of such a dysfunction will be twofold: First, the reduction in SNr tonic activity will leave the colliculus more vulnerable to respond to distracting stimuli, hence this dysfunction provides a mechanism for increased distractibility. In addition, the small remaining activity in SNr is insensitive to caudate inhibition, and thus will contribute excessive collicular inhibition in the generation of correct saccades, providing an explanation for the overall decrease in velocity observed j in the HD<30 patients, similar to the possible model suggested by Lasker et al. (1988) j l for the velocity reduction in HD<30 patients. Our model for the more cortical distractibility dysfunction involves a reduction of activity in FEF. We produce this frontal lesion by manipulation of two parameters. I FON_MAX represents the maximum firing rate of fixation-related cells in FEF, and is l The parameters SNR_MAX, CD_M AX, FON_MAX and FEF_SAC_MAX correspond to the i upper limits on the non-linear threshold functions that transform membrane potential to firing j rate for each of these cell types. 158 reduced from 90 to 50. FEF_SAC_MAX represents the maximum firing rate of saccade related cells in FEF, and is reduced from 90 to 60. In addition, the time constant for these cells was increased from 8 ms to 16 ms. The reduced activity in FEF i fixation related (FOn) cells will yield a situation in which visual fixation no longer provides an inhibitory influence on FEF saccade related cells, nor on the saccade related cells downstream in basal ganglia and colliculus. In addition, the reduction in FEF saccade-related activity will increase the time required for downstream structures to attain sufficient activation for saccade initiation, thus increasing saccade latency. In the simulation of reduced activity in SNr, during fixation the FEF saccade (FEFsac) contribution is suppressed by the FEF fixation cells (FOn). The SC is driven i only by the projection from parietal cortex, and the brainstem saccade bursting neurons are driven only by SC. We assume that the FEF fixation cells' influence on the rostral SC is not strong enough to prevent saccades without the help of SNr's additional inhibition (Hikosaka and Wurtz 1985). The resulting distracted saccades have a smaller amplitude, and in fact require a corrective saccade to attain the target. In addition the saccades have reduced velocity. We recall that reduced velocity is most prominent in the HD<30 group, suggesting that this group may be more influenced by a basal ganglia degradation than by cortical degradation. In the HD<30 distraction saccades, we suggest that dysfunction of the SNr inhibition on SC allows unwanted saccades to occur in response to other (non-FEF) inputs to SC. Latency V elocity N H2 HI N H2 H I NS 140 190 140 525 440 420 C S 130 230 130 525 525 420 RS 200 280 220 316 316 244 Table 8.2 Saccade metrics for normal and HD lesion models. Times are given in milliseconds. H I and H2 correspond to the HD<30 and HD>30 models, respectively. Note the italicized values. Latencies for H2 are greater that those for normals (N), particularly in CS and RS, as in Table 8.1. Velocities for H I are reduced for all tasks. 159 j In the simulation of dysfunction of the cortical fixation cells (FOn), we see that the FEF saccade cells (FEFsac) participate as if there were no fixated target since they are no longer inhibited by the FEF fixation-on (FOn) cells. The result is that these saccades have normal amplitude and velocity. This suggests that the HD>30 dysfunction may include a more prominent cortical dysfunction related to fixation and attention. In the HD>30 model, the dysfunction of cortical fixation-related cells produces a situation in which the distraction saccades operate as if the fixated target were not there. That is, the target is fixated, but the inhibitory cortical influence of this fixation is absent, with everything else normal, including the disinhibition of SC by FEF via caudate and SNr. However, by also weakening the FEF saccade related output, and increasing its time constant, we can produce a cortical explanation for the increase in latency as shown in table 8.2. In order to produce a simulation sessions that include correct and incorrect (distraction) trials, we assume that the visual input saliency includes a stochastic component. On some trials, then, the internal representation of stimulus intensity will be greater, and thus more likely to produce a distraction. In doing so we make some simplifications that, for this level of analysis, should not corrupt our results. For the HD models, we determined the changes required in a minimal set of parameters (related to subcortical and cortical dysfunction, respectively) that would yield the transition from correct (no distraction) to incorrect (distraction) behavior in the CS and RS paradigms. Using these parameter settings, we obtained results for the distraction saccades. Then, by moving these parameters less than 10% back towards the "intact" direction, we take our latency, velocity and accuracy measures for the resulting correct (non-distracted) saccades. 8.5 Clinical Dissociation of Two HD Models A clinical dissociation, in addition to the latency and velocity differences, between these two cortical vs. basal ganglia dysfunction models of distractibility might be made by using a behavioral paradigm that differentially taxes cortical and basal ganglia j 160 function. We have developed a potential paradigm, in the form of a variation of the CS task that requires a choice between two targets, as described in Chapter 5. Recall that in this task, the fixation point is a colored geometrical shape, and there are two, rather than one, peripheral targets arranged symmetrically 20° to the left and right of the cue. Each cue is arbitrarily paired by the experimenter with one of the two targets, and at the go signal, the subject must saccade to the "correct" one of the targets. The subject must learn by trial and error whether a new cue signals left or right saccades. As described in Chapter 5, cortical signals related to the informing cue provide an input to the basal ganglia that acts to reduce the SNr inhibition on the side of SC that favors a saccade to the correct target. Hence, the intact Cd/SNr circuit is required for this task. In the HD>30 simulation, the impaired cortical fixation mechanism still leads to some distractibility, but the more intact cortex/Cd/SNr circuit still selectively disinhibits only the correct side of the colliculus (contralateral to the target) so both the distracted and non-distracted saccades are to the correct target. In the HD<30 simulation, because of the loss of the intact cortex/Cd/SNr disinhibition the SC is no longer selectively disinhibited as a result of the informing cue. Instead it is uniformly disinhibited, and there is a corresponding increased tendency to make the wrong saccade at chance level. We propose that this task separates the two age onset groups, based on two proposed models of their respective brain dysfunctions. 8.6 Discussion In this study, we have concentrated on brain mechanisms for saccade distractibility seen in mild HD. Based on a model of the intact oculomotor system and data on the gross morphology of HD, we have performed different lesion studies to produce two different lesion models of saccade distractibility similar to that seen in HD: first, lesion of the frontal cortex, including dysfunction of the fixation-related cells that appear to contribute to fixation related activity in rostral colliculus; and second, a lesion of the caudate/SNr complex that normally provides tonic inhibition of SC. The reduced saccade velocity we see in the simulated basal ganglia lesion model suggests that the HD<30 group may have a disorder of this nature, and that the increased latencies in the [ 161 | 1 cortical lesion model suggest that the HD>30 group may have a more cortical disorder. W e failed to reproduce the accuracy deficits associated with HD>30 in the RS paradigm. In order to develop a psychophysical experiment that could be used on patients to test this assignment of lesion models to the different age-onset groups, we turned to an extension of our oculomotor simulation that includes the ability to choose between left and right saccade targets based on a cue provided as the fixation point. In the model of the intact system, the cue related information influences the oculomotor system via corticostriatal projections. In the HD<30 model, these corticostriatal connections no longer provide a cortical influence on SC, and the model performs the left-right distinction only at chance level. The HD>30 model has the corticostriatal system more intact, and performs near normal levels. Thus, we propose this task or one like it to help further dissociate the brain mechanisms behind early and late onset HD. There are many assumptions that have gone into this study, and it is likely that a number of them may be misguided. As these models become more responsive to clinical data, their predictive and clinical strength will increase. It is likely that the predictions we make here concerning the dissociability of early and late onset mechanisms by the choice saccade test will differ from the observed results. It is more likely, however, that there will be at least some difference between the two groups on this or related tasks that will provide more insight into the disease. The limitations of this kind of study derive from incorrect assumption about the functional anatomy both of the intact and diseased systems. The strength is that it makes these assumptions explicit in a computer model, and uses the model to generate very specific questions and predictions. Whether the predictions are correct is not of primary importance, because correct or not, the testing of these predictions will increase the knowledge and contribute to more accurate models of the disease. 162 Chapter 9 Conclusion and Prospectus While we can look back at some significant results described over the last chapters, we can observe that there remain a number of unanswered questions. This is by no means a discouraging result. On the contrary, as scientific inquiry proceeds, there are always answers in the wake, and questions in the bow-wave. In this chapter we review the contributions of this thesis, and consider future work to answer some of the questions that developed along the way.__________________________________________________ 9.1 Summary of Results, Lessons Learned In Chapter 2 we motivated and developed a brainstem saccade generator in which saccade amplitude is specified by the location of activity on a motor error map, and saccade velocity by its firing rate. This resolves a problem with the Scudder model (1988) of which ours is an extension, and provides a basis upon which we build in the subsequent chapters. In Chapter 3 we brought together a large body of data concerning how the cortex and basal ganglia cooperate to provide voluntary control over the saccade generator. This represents an original contribution in that for the first time, these data were assembled into a descriptive and predictive model. Chapter 4 is an ambitious effort to reconcile one of the major outstanding controversies in the j oculomotor field. Data from two research teams (Goldberg and Bruce 1990, Schlag j and Schlag-Rey 1990) indicate that a transformation required for spatial accuracy in double saccades occurs both up- and downstream from FEF. This produces the ! I apparent conflict that in some cases the transformation will occur two times, yielding an ! _____________________________________________________________________ 163 | inaccurate movement. By developing and comparing multiple models to explain apparently conflicting data, we were able to state specific experimental predictions that can now be tested in order to narrow down the field of possible models. In particular, one of the configurations we presented allows a potential resolution of both data sets by considering that these transformations are redundant and non-interfering. Chapter 5 uses the oculomotor system as a behavioral platform upon which we build the capability to perform conditional visual discrimination (CVD). A novel learning mechanism is introduced that is based on both the electrophysiology and biochemistry of the reward-related nigrostriatal dopamine system. This chapter provides the basis for a new line of research in the operation of the frontostriatal system in the learning and execution of visuo-motor associations. In doing so, it provides a concrete step from motor control to cognition. Specific roles are assigned to cortex, striatum and the nigrostriatal dopamine system in the learning and execution of CVD tasks. Chapter 6 shows that this system is easily extendible to address the learning and performance of visuo-motor sequences. Two promising aspects of the corticostriatal plasticity modeling approach are that, indeed, the same principles used in the CVD model successfully apply to the rather different task of sequence reproduction, and that in both cases, not only external behavior, but also single unit activity matches well with experimental data. Chapter 7 continues with these models, addressing issues concerning the ability to generalize previous behavior in order to perform in new situations. While a small step in this direction, this work begins to approach simple mechanisms of intelligent behavior where intelligence is defined as the ability to apply existing knowledge to new situations. Chapter 8 considers two forms of Huntington's disease that emphasize subcortical and cortical degeneration, respectively, and uses the CVD task to discriminate between these two disease models. 9.2 Extensions and Prospects for Future Research In developing these models, we have made some explicit assumptions about how the brain is organized. The next step is to test these assumptions. In the pure oculomotor 164 domain, much work remains. The first set of experiments to consider are those that tease apart the relations between mechanisms A and B of Chapter 4. One approach will be to compare the movement fields of single units in FEF and LLBNs with the second saccade in the double step paradigm. Here care must be taken to distinguish between the "egocentric" and "allocentric" versions of the double step task, in order to determine if, indeed, the allocentric presentation favors the cortical transformation described by Goldberg and Bruce (1990), with the non-allocentric version taxing the downstream transformation identified by Schlag and Schlag-Rey (1990.) Experiments of this type, that can pinpoint where in the system the transformation takes place, will help us to reject, keep or modify our existing explanatory models. In addition, some of the ideas on spatial accuracy in the oculomotor system will likely have interesting applications to the skeletomotor system. The model of corticostriatal plasticity opens a large field for investigation. At the neurochemical level, we have suggested that dopamine plays a dual role in the striatum. The first role is in a regulatory circuit that maintains corticostriatal inputs in a range where striatum is maximally sensitive. While this is based on existing data concerning dopamine's reduction of corticostriatal excitability, the complete circuit by which over stimulation of striatum activates nigral dopamine cells has not yet been clearly demonstrated. The second role involves dopamine's participation in corticostriatal plasticity required in CVD learning. As discussed in chapter 5, both LTP and LTD have been demonstrated in striatal slice preparations. Future experiments can more specifically address the formation of associative memory traces in striatum in which two simultaneous inputs sufficiently depolarize a striatal target cell, allowing LTP such that later, a single input can then drive the cell. From a single unit recording perspective, we have made predictions concerning striatal function in generalization. From a behavioral perspective, our oculomotor CVD paradigm is easily and progressively extensible to tasks that will allow us to test not only CVD learning, but attention set formation, use and switching, similar to that seen in the Wisconsin Card j Sorting Test, and may be a valuable tool for classification of neurological disorders as ' l i ' discussed in chapter 8. This work has also opened the door for extensions of the current models and experiments. In particular, we have just started to tap into the workings of the j frontostriatal system. The basal ganglia not only respond to environmental event, but [ | I ! ________________________________________________________________________ 165 1 they also predict them (Hikosaka et al. 1989). Understanding this capability will provide an exciting new direction of research. The sequence learning model of Chapter 6 uses the frontostriatal system not only for specification of motor output, but also as a mechanisms by which internal state information is relayed through thalamus back to cortex. In doing so, it begins to extend the "segregated loops” view of basal ganglia function (Alexander et al. 1986). The spatial memory loop in Chapter 3, that starts in FEF and traverses caudate, substantia nigra, ventral anterior and mediodorsal thalamus back to FEF, illustrates this kind of segregated functional loop. This view of segregated function is supported by observations that striatal lesions often produce the same behavioral deficits seen in lesions of their cortical afferents (reviewed in Rolls and W illiams 1987). However, the consideration of frontal lobe dysfunction in Parkinson's disease suggests a complimentary view that striatal function is not entirely explained in terms of relaying cortical inputs along topographically segregated loops (Taylor et al. 1986), but also in terms of relaying a variety of state information to the prefrontal cortex. The possibility of combining neurological studies with modeling, and the electrophysiology of Chapter 5 represents a strong alliance of three areas of neuroscience, and promises an interesting future. This is just the beginning. i I 166 Appendices Appendix A: Brainstem Saecade-Generator Model Specification T retina = 6 ms ^retina = Eyemove(VisInput, 0r, 0jj) a SACCADEMASK RETINA = retina (la ) MN = 2.75*0 + 0.90*0+ 154 (2a) T Ubn = 40ms s l l b n = WinnerTakeAll(2.67*SC + 5.4*FEFsac) LLBN = s ig m o id (llb n , 0,950,0, 950) (3a) Tmlbn = 8 ms S m lb n = LLBN* Kstt MLBN = s ig m o id (m lb n , 0,1500,0,950) (4 a) X ^ = 6ms S8 = step(MLBN, 120, 0, 120)*Kgtt A = max(8) - 3*OPN (5a) 167 T ebn - 6 ms s ebn = MatrixToScalar (MLBN) - k*OPN EBN = ramp(ebn, 120,0,120) T opn = 6ms sopn = -kl*R I + A + 0.5*TR1G) OPN = step(opn, k2,300,0) %ig= 6 ms S trig = (FEFsac + SC)*Ksst TRIG = m a x (trig ) sri = RI + k*EBN - OPN RI =ramp(ri, 0, 0, 0) s tn = TN + k*(REBN - LEBN) TN = tn %vn = 6ms smn = EBN + TN Appendix A l: Cortico-Subcortical Saccade Model Specification T retina = 6 ms ^retina = Eyemove(VisInput, 0r, 0u ) a SACCADEMASK RETINA = retina (1) T VisPath = (5x6) ms s VisPath = RETINA (2) xpp =8 ms Spp= VisPath PP = pp (3) T fon = 6 ms Sfon = project_scalar_to_matrix ( PP[X_Center,Y_Center] ) FOn = sigmoid(fon,0,50,0,90) (4) T fef_vis = 6 ms s fef. .vis = PPqv FEFvis = sigmoid(fef_vis, 0, 90, 0, 90) (5) xfef_mem = 8 ms Sfgf mem = THmem + FEFvis - .2* FOn FEFmem = sigmoid(fef_mem,0,90, 0,90) (6) Tfef_sac = 8 ms SfefLsac = FEFvis + 2*FEFmem - 3*FOn FEFsac = sigmoid(fef_sac, 0, 90, 0,90) + kl*ElectricalStim (7) xcd_sac = 8 ms ®cd_ .sac = FEFsac CDsac = sigmoid(cd_sac,0,50, 0,60) T cd_mem = 10 ms Scd_ mem = FEFmem CDmem = sigmoid(cd_mem, 50,90,0,60) xsnr_sac = 20 ms ^snr_sac = 50 - CDsac SNRsac = sigmoid(snr_sac, 0,50,0, 100) xsnr_mem = 40 ms ^snr_mem = 50 - CDmem SNRmem = sigmoid(snr_mem, 0,50, 0,100) xsc_sup = 8 ms Ssc_sup = RETINA - 2*FQn SCsup = sigmoid(70,90,0,90) T sc_qv = 10 ms Ssc_qv = PPqv SCqv - sigmoid(sc_qv, 0,90,0,100) xsc_sac = 10 ms ^sc_sac = FEFsac - l.l*SNRsac SCsac = sigmoid(sc_sac, 0, 80, 0,80) xsc = 38 ms ^sc = WinnerTakeAll(4*SCsup + 1.5*SCqv + SCsac - 2*FOn) + ElectricalStim SC = sigmoid(sc, 85,99,0,500) xth_mem = 6 ms ^th_mem = FEFmem - SNRmem - 4* SC_Delay THmem = sigmoid(th_mem,0,45,0,10) (16) Here we provide the additional equations for the spatial accuracy mechansims of Chapter 4: QVMASK = Shift(HTN, HTNdamp6, VTN,VTNdamp6)*l .23 (1) The function Shift () returns a mask with the following elements: QVMASK[x-l,y] = (HTNdamp6 - HTN)/q QVMASK[x+ l,y] = (HTN - HTNDAMP6)/q QVMASK[x,y-l] = (VTNdamp6 - VTN)/q QVMASK[x,y+1] = (VTN - VTNdamp6)/q QVMASK[x+l,y+l] = ((HTN - HTNdamp6) + (VTN - VTNdamp6))/r QVMASK[x-l,y-l] = ((HTNdamp6 - HTN) + (VTNdamp6 - VTN))/r QVMASK[x-l,y+l] = ((HTNdamp6 - HTN) + (VTN - VTNdamp6))/r QVMASK[x+l,y-l] = ((HTN - HTNDAMP6) + (VTNdamp6 - VTN))/r QVMASK[x,y] = [1- ( I VTNdamp6 - VTN I + I HTNdamp6 - HTN I )/q] xHTNdamp6 = 6 ms s HTNdamp6 = HTN (2) xVTNdamp6 - 6 ms SVTNdamp6 = VTN (3) IpPqv = 6 ms SPPqv = PP + QVMASK*PPqv (4) xhtn_dl = 6 ms s htn_dl = HTN i HTNdl = htn_dl (5) I 171 xhtn_d2 = 20 ms s htn_d2 = HTN HTNdl = htn_d2 (6) xdcep_h = 40 ms s dcep_h = HTNdl - HNTd2 DCEPh = dcep_h FEFShiftMask (CntrlndexX + (DCEPh ) / c, CntrIndexY+(DCEPv)/c) = 1 ShiftedFEFsac = FEFshiftMask*FEFsac The input to the LLBN from FEF is thus modified in Eqn. 3a: TUbn = 40 ms SIIbn = W innerTakeAll(2.67*SC + 5.4*ShiftedFEFsac) LLBN = sigmiod(llbn, 0, 950, 0, 950) xtrig= 6 ms ^trig = (FEFsac + SC)*Ksst TRIG = max(trig)*PauseRefractory PauseRefractory = step(DCEP, Refractory Threshold, 1, 0) (7) (8) i (9:3a) (10:8a) (11) i i i 172 1 Appendix B: Association and Sequence Model Specification We first present the components of the base model [equations (1) to (10)], common to both the association and sequence models, and then present the model specific additions. The learning-related updating is performed in two steps, expressed as: The learning-related updating is performed by: w|j(t+l) := wjj(t) + (DA_Modulation*RewardContingency - 1)* Cl*Fj * Fj (1) 51 w..(t) j y w.. (t+1) := w.. (t+1) * J J E w..(t+l) j y (2) where the ":=" denotes assignment rather than equality. Here, wy is the strength of the synapse connecting IT cell i to caudate cell j. These w's make up the elements of IT_CD_Synapses in Eqn 7, and are modified after each simulated saccade. Eqn 6 sets DA_Modulation as a function of its role in the SNc feedback loop. In Eqn 1, based on the arrival or denial of expected reward, we simulate SNc reward related modulation by the term RewardContingency which is 1.5 for correct trials, and .5 for incorrect trials, j and 1 when no reward or punishment is applied, corresponding to the increases and j decreases in SNc activity for reward and error trials, respectively (Schultz et al. 1993). j Fi and Fj are the firing rates of the IT and caudate cells, respectively. The term j (DA_Modulation * RewardContingency -1) will be positive on rewarded trials and negative on error trials. C l is a constant that specifies the learning rate, and is set to 2.5e*5. A form of competition is provided by a weight normalization procedure that 1 7 3 _ J conserves the total synaptic weight that each IT cell can distribute to its striatal synapses (Eqn. 2). After a saccade, a fixed target in space is shifted on the retinal an amount equal and opposite to the saccade. The convolution mask EyePosition accounts for this by shifting the visual input to retina equal and opposite to the displacement of the eye from its zero position. retina = EyePosition * Visual_Input (3) Posterior parietal cortex gets this retinal input, and random activity from the Noise layer. Values from retina are 0 for no target and 70 for a target. Individual values in the Noise layer vary on a given trial between 0 and 15. "Fovea on" cells receive input from the central element of PP. T pp = 0.01 Spp = retina + Noise PP = sigmoid(pp, 0,85,0,110) FOn = PP(2,2) (4) FEF is influenced by PP and Thai, and gets an inhibitory influence during fixation (i.e. when the central element of PP is active), preventing distractibility during fixation. In our 5x5 arrays indexed from 0 to 4 this is indicated by PP(2,2). xfef = 0.01 Sfef = 0.4 * PP + 0.8 * Thai - 0.6 * FOn FEF = sigmoid(fef, 0,100, 0,100) (5) DA_Modulation represents our implementation of the dopamine normalization of cortical inputs. In the base model of Dominey and Arbib 1992, this modulation is not present, i.e. it is effectively set to 1. Normally the term DA_Modulation is 1, but when the maximum inputs to caudate, cd.max(), is above a threshold of caudate sensitivity, DA_Modulation is increased, corresponding to the increased activity of nigrostriatal DA producing cells, and the associated release of DA in striatum. This simulates the ________________________ 174 reduction in corticostriatal excitation due to increased striatal dopamine levels, evoked by disinhibition of dopamine producing cells in substantia nigra pars compacta. This reduction of the effect of cortical activity on striatum brings it back to the normal range of operation for caudate. In both the association and sequence models, this "contrast enhancement" increases the effect of the IT bias and aids in learning. DA_Modulation = cd.max() /CD_Upper_Threshold if cd.max() > CD_Upper_Threshold; 1 otherwise. (6) In the association model, caudate receives input from both IT, via the modifiable IT_CD_Synapses, and FEF, and produces lateral inhibition via the 5x5 InhibitoryCollaterals mask that is 0 at center, and -0.2 at all others locations. In the sequencing model, inputs from PFC to CD are via the modifiable synapses in PFC_CD_Synapses. In both models, after each saccade the modifiable synapses are subjected to the learning rule described in Eqn.s 1 and 2. Competition between input signals is implemented in part by a 5x5 convolution mask that produces lateral inhibition, InhibitoryCollaterals, with 1 in the central element, and -0.2 in all other locations. For the association model we have: Scd = DAJModulation * (0.1(IT*IT_CD_Synapses) + 0.4 * FEF + CD * InhibitoryCollaterals) and for the sequence model: Scd = DA_Modulation * (0. l(PFC*PFC_CD_Synapses) + 0.4 * FEF + CD * InhibitoryCollaterals) and for both: ted = 0.01 CD = sigmoid(cd, 0,100,0,75) (7) Here the IT_CD_Synapses and PFC_CD_Synapses are modifiable weight masks and are updated according to the reinforcement learning rule described in Eqns 1 and 2. 175 Substantia nigra is then driven by caudate: 'Tsnr = 0-01 Ssnr = 75 - CD SNr = sigmoid(snr, 0,75,0,100,) (8) The superior colliculus is then driven by FEF to the extent that it is disinhibited by caudate’ s inhibition of SNr: The SC is also inhibited by cortical fixation related activity. A Winner Take All function (Didday 1970, 1976) in SC is used to select the maximal activity for saccade generation. Tgc = 0 .0 1 Ssc = winner_take_alI(FEF - SNr - 0.6 * FOn) SC = sigmoid(sc, 30,110,0,100) (9) The thalamus has a reciprocal excitatory interaction with FEF, and also with PFC in the sequencing model. This provides the sustained thalamocortical activity responsible for a form of spatial memory in sequence and association performance, and a m echanism that in conjunction with the lateral inhibition in caudate (InhibitoryCollaterals of Eqn 7) amplifies the stronger IT influences. T thal = 0.01 Sthal = PFC + FEF - SNr THAL = sigmoid(thal, 0, 75, 100,0) (10) Equations related to IT and PFC: Here we introduce the IT and PFC cortical areas that augment the function of the base model to accommodate the association and sequence tasks. V4 simply represents the 6 elements of the FeatureVector that encode the shape and color of the cue. The FeatureVector is extracted from the central element of the retina, i.e. the cue that is being fixated. Ty4 = 0.01 Sv4 = 4 * FeatureVector V4 = sigmoid(v4,0,40, 0,40) (11) 176 V4_rr_Synapses is a 6x25 matrix of connection weights varying between -.5 and +.5, that multiplied by V4 yields the input to IT The resulting IT cells encode features, and conjunctions and disjunctions of features due to the mixed excitatory and inhibitory connections. Tft = 0.01 Sit = V4 * V4_IT_Syriapses IT = sigmoid(it, 0,40,0, 60) (12) In PFC, inputs related to visual targets, post-saccadic activation, and damped recurrent activity combine to produce activity that changes both as visual targets appear, and as saccades are made and the visual scene shifts as a result of these saccades. PFC_PFC, SC_PFC, PPJPFC are connection matrices with synaptic strengths that vary between -.6 and .4; -.5 and .5; and -.5 and .5 respectively, while the projection from THAL is topographic. Tpfc = .01 Spfc = 2.0(PP * PP_PFC) + 1.5(Damped_PFC * PFC_PFC) + 5(SC_POST * SC_PFC) + 4TH AL PFC = sigmoid(pfc, 0,100, 0,100) (13) Damped_PFC gets topographic input from PFC. Its 25 cells are split into groups of five that have five different time constants [represented as (0.1 0.6 1.1 1.6 2.1) in Eqn 14]. This diversity in temporal sensitivity helps to accommodate the phasic and tonic target presentation paradigms which produce brief and prolonged input, respectively, and thus place different requirements on the temporal sensitivity of PFC. 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