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Deficits and rehabilitation of upper-extremity multi-joint movements in individuals with chronic stroke

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Deficits and rehabilitation of upper-extremity multi-joint movements in individuals with chronic stroke

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Deficits and rehabilitation of upper-extremity multi-joint movements in
individuals with chronic stroke

by

YANNICK DARMON

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOKINESIOLOGY)

August 2023
ii

Acknowledgements
I would like to thank my parents, Robert and Claire, for supporting my decision and helping me
achieve my goals. From an early age, my father fostered in me the curiosity, the will to understand,
and the thirst for knowledge, all the necessary qualities for the pursuit of science. Also my brother
and sister, Frederic and Sophie, for constantly making me laugh and cheer me up no matter the
distance between us.
I would like to thank my committee members. Their input was essential to shape my work into its
final form. My advisor Dr. Nicolas Schweighofer, guided, supported, and motivated me throughout
the journey that was my Ph.D. From our weekly to sometimes daily meetings, I learned to think
about problems through the lens of science, which complemented my clinical view. He taught me
to be pragmatic, efficient, and dedicated these are essential qualities to become a future leader in
the field. Dr. Gerald Loeb, for generously spending multiple hours meeting with me in the lab or
in the research setting. Our discussion led me to deeply understand problems, not hesitating to
question the rationale of theory and pushing the limit of science. Dr. Carolee Winstein, your
expertise in neuro-rehabilitation was essential for this work. You helped me to constantly improve
my writing and now I will always remember that words have meaning. Dr. James Finley for
teaching me how to communicate my ideas in a clear and succinct way, and the secret of data
processing. Dr. James Gordon for helping to take a bird's eye view and appreciate the big picture
of a research question. Your guidance helped me to understand how to select significant research
questions that will impact the field.
I would like to thank our research collaborators, Dr. Emily Rosario, Niko Fullmer, Dr. Hannah
Cone, and the therapist team at Casa Colina. Without your help, this work will likely be different.
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I would like to thank some of the great people I met throughout my journey in the Ph.D. program.
Dr. Nina Bradley, who year after year taught me the intricacy of the neural pathways hidden below
the surface of the brain. Your positive approach to teaching will be forever remembered: “Students
are more motivated by chocolates than carrots”! Dr. Victor Barradas for teaching me all the secrets
behind mechanical and electrical engineering, you definitely helped me starting with the Ph.D.
program. Alec Roig with whom I spent countless hours in the lab laughing, tweaking our
experimental set-up, and learning from each other. With you, I made a wonderful and lifelong
friend. Dr. Natalia Sanchez for all the fun we had teaching neuroanatomy, and always making sure
I was surviving in the program. Sarah Bonnet and Kento Hirayama the joy and energy you brought
to the lab helped creating a wonderful workplace. Thanks to current and former CNRL members:
Gianni, Sana, Rukshana, Tanya, Lyn, Yan, Yuecheng, and Yifan, for their positive outlook, their
camaraderie, and the discussions and feedback that you provided.
I would also like to thank my friend Bozorgmehr that I met throughout the program who took me
rock climbing and surfing all over Southern California. Your patience and generosity were highly
appreciated and offered me an escape from science. Thank you to my roommate, Brian, for his
friendship and patience with my usual 10 pm dinner time. I would like to give a special thanks to
the Fuentes family William, Elina, and Pierrot for your amazing support. William convinced me
to do a 6-month internship in California that turned into a 5-year Ph.D. Finally, my girlfriend Jin,
for accepting all the long hours I spent away from her in the lab. Luckily she was able to participate
in some of the experiments we conducted. Your support was an essential piece that kept me going
through all the ups and downs of this journey.

iv

Table of Contents
Acknowledgements ......................................................................................................................... ii
List of Figures ................................................................................................................................ vi
Abstract ........................................................................................................................................ viii
Chapter 1: Introduction and background ........................................................................................ 1
Clinical significance.................................................................................................................... 1
Impairment of multi-joint movements in chronic stroke individuals ......................................... 1
Control for interaction torques in multi-joint arm movements ................................................... 2
Adaptive feedforward control of interaction torques in the central nervous system .................. 3
Possible lesions affecting the updated of the feedforward controller post-stroke ...................... 4
Deficits in the feedforward controller promote the use of feedback control strategies .............. 5
Effect of motor training post-stroke ............................................................................................ 6
Outline......................................................................................................................................... 8
Chapter 2: Reaching Kinematic in stroke survivors. .................................................................... 10
Introduction ............................................................................................................................... 10
Methods..................................................................................................................................... 12
Results ....................................................................................................................................... 20
Discussion ................................................................................................................................. 27

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Chapter 3: Anticipatory control of interaction torques in fast single-joint arm movements
in individuals with chronic stroke ................................................................................................ 31
Introduction ............................................................................................................................... 31
Material and Methods ............................................................................................................... 34
Results ....................................................................................................................................... 48
Discussion ................................................................................................................................. 53
Chapter 4: Effect of fast and accuracy motor training in arm reaching in chronic stroke ............ 59
Introduction ............................................................................................................................... 59
Methods..................................................................................................................................... 64
Results ....................................................................................................................................... 73
Assessment 1: 3-target reaching transfer task ........................................................................... 73
Discussion ................................................................................................................................. 78
Chapter 5: Conclusion................................................................................................................... 83
References ..................................................................................................................................... 87

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List of Figures
Figure 2.1: Example of hand path trajectories .............................................................................. 12
Figure 2.2: Real and simulated hand path trajectory, joint-angle acceleration profiles,
and joint interaction torque profiles .............................................................................................. 22
Figure 2.3: Simulation of deficits in control for interaction torques. ........................................... 23
Figure 2.4: mean trajectory deviation ........................................................................................... 25
Figure 2.5: Real hand-path trajectories, and joint acceleration profiles ....................................... 26
Figure 2.6: distribution of the cross-correlation between shoulder and elbow
joint-angle acceleration profile .................................................................................................... 27
Figure 2.7: Relationship between trajectory deviation and inter-joint correlation ....................... 29
Figure 3.1. Experimental set-ups .................................................................................................. 36
Figure 3.2: examples of muscle torque control at the elbow. ....................................................... 47
Figure 3.3: Examples of shoulder interaction torque control ....................................................... 50
Figure 3.4: Cross-correlation value and corresponding time lag .................................................. 51
Figure 3.5: Examples of reaching movements .............................................................................. 52
Figure 3.6: Absolute initial trajectory deviation as a function of the cross-correlation value
at the shoulder ............................................................................................................................... 52
Figure 4.1: Examples of hand path trajectory for the speed and accuracy bias
training conditions ........................................................................................................................ 64
Figure 4.2: Illustration of feedback received by the participant during training .......................... 69
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Figure 4.3: Evolution of movement time (A) and deviation from the straight line (C) ................ 75
Figure 4.4: Evolution of the linear relationship between movement time and index of
difficulty ........................................................................................................................................ 77
Figure 4.5: Slope evolution of the linear relationship between the movement time and the
index of difficulty ......................................................................................................................... 78
Figure 4.6: Evolution of the peak angular acceleration scaling to target distances. ..................... 80

viii

Abstract
Cerebrovascular Accident (CVA) is the leading cause of long-term disability, resulting in upper
extremity (UE) impairments, activity limitation, and participation restrictions. Generating fast,
smooth, and straight trajectories for multi-joint planar reaching movement requires adequate
compensation for the interaction torques that arise at both proximal and distal joints. However,
stroke survivors exhibit some deficits in the feedforward motor command, leading to a stronger
reliance on the feedback controller. The impaired feedforward controller may be accompanied by
a deficit in accounting for and controlling interaction torques that arise during multi-joint reaching
movements.
First, we investigated the control of UE multiple-joint movements during a planar reaching task.
Using a two-link arm model, our simulations revealed that the pattern of trajectory deviation
depends on the type of deficit in control for interaction torques. Contrary to previous reports in the
literature, chronic stroke individuals did not consistently exhibit deficits in the control of
interaction torques at a single joint (e.g., the elbow). However, we confirmed that the absolute
trajectory deviation is greater for the more-affected side in comparison to the less-affected side
and the dominant side of control participants.
Then, we focused on the predictive control of interaction torques during fast single-joint elbow
movements. By utilizing electromyography (EMG) and estimating torque through inverse
dynamics, we examined the feedforward motor command involved in controlling interaction
torques generated at the shoulder. Our findings indicated that the more-affected side demonstrates
a significant delay in the onset of shoulder muscle activities and a reduced ability to modulate the
anticipatory muscle activities to control for the interaction torques generated at the shoulder, in
ix

comparison to both the less-affected side and dominant side of control participants. Furthermore,
the inability to compensate for the shoulder interaction torques in the more-affected side correlated
with the absolute trajectory deviations in the early (feedforward) phase of planar reaching
movements. We argue that the trajectory deviation may be due to either a decreased ability to
compensate for interaction torques in the feedforward command or as a result of a compensatory
strategy to overcome the control of interaction torques.
Finally, we evaluated the effect of four sessions of speed or accuracy training with 520 movements
per session on the recovery of multi-joint reaching movements. When tested on a transfer reaching
test, all groups showed a significant effect of training on movement time, trajectory deviation, and
movement smoothness. However, the speed group exhibited a larger decrease in movement time
at three days and a significantly larger decrease in trajectory deviation at one month following the
intervention. When tested on a speed and accuracy test, the speed group showed a larger decrease
of the Fitts’ slope, both at three days and at one month following the intervention.
Overall, this thesis presents a comprehensive investigation of the UE motor control deficits and
potential rehabilitation strategies in multi-joint reaching movements following a stroke.

1

Chapter 1: Introduction and background
Clinical significance
Stroke is the leading cause of long-term disability, often resulting in upper extremity impairments,
activity limitation, and participation restrictions (Kwakkel et al., 2003; Tsao et al., 2022). Studies
indicate that up to 70% of chronic stroke survivors experience severe to moderate upper limb
impairment (Lawrence et al., 2001). Common deficits observed in reaching activities include
prolonged movement time, trajectory deviations, and multiple peaks in the endpoint velocity
profiles (Cirstea et al., 2003; Levin, 1996). These upper extremity (UE) impairments strongly
correlate with functional limitations in daily life activities (Kamper et al., 2002; Lang et al., 2013).
Because recent clinical trial interventions have failed to demonstrate the superiority of a particular
rehabilitation intervention compared to standard care (Krakauer et al., 2021; Lang et al., 2016;
Winstein et al., 2016), a better understanding of the origins of stroke motor impairments are
required. In particular theoretical-driven studies of the pathophysiology of stroke motor-control
impairments could be helpful in the design of successful rehabilitation interventions (Winstein &
Varghese, 2018).
Impairment of multi-joint movements in chronic stroke individuals
Daily life activities such as reaching and grasping involve the coordinated use of multiple joints
(Murphy et al., 2011; Roby-Brami et al., 2003). In neuro-typical individuals, discrete reaching
movements exhibit stereotypical kinematic patterns. The velocity profile is typically bell-shaped,
characterized by a single velocity peak, with the hand path following roughly a straight line
(McCrea & Eng, 2005; Morasso, 1981; Murphy et al., 2011). Achieving a straight trajectory
necessitates a high level of coordination of the multiple joints involved in the movement (Flanagan
2

et al., 1993). In the case of two-dimensional planar reaching movements, the amount of inter-joint
coordination varies for reaches based on target locations. Reaches into the ipsilateral space involve
primarily the elbow joint, while reaches into the contralateral space require a nearly equivalent
contribution of the shoulder and the elbow joints (Morasso, 1981). Chronic stroke individuals
typically exhibit more trajectory deviation when reaching into the contralateral space indicating a
deficit in inter-joint coordination (Levin, 1996).
Control for interaction torques in multi-joint arm movements
During multiple-joint movements, the simultaneous movement of each limb segment gives rise to
three types of highly non-linear torques: inertial, centripetal, and Coriolis torques (Hollerbach &
Flash, 1982). For example, in horizontal planar reaching movements, the inertial torques
correspond to the torques that arise from the normal acceleration during a single-joint movement
and from the acceleration of the other segment. The centripetal torques represent the torque that
arise from the square velocity of the other segment. Finally, the Coriolis torques represent the
torques that arise from the product of the velocities between the shoulder and elbow joints, present
only in the net torque equation at the shoulder. The interaction torques are defined as the sum of
the torques not due to the normal acceleration from a single joint movement.
The observed straightness of the hand trajectory in reaching movements, suggests that the central
nervous system (CNS) accounts for the intersegmental dynamics and compensates for these
torques (Hollerbach & Flash, 1982; Sainburg et al., 1999). Feedback and feedforward strategies
are used to control movements. However, it is important to note that feedback strategies cannot
effectively control trajectory deviations due to the absence of sensory feedback to modulate the
motor response for at least 50ms (Kurtzer et al., 2008; Pruszynski et al., 2008). Because of these
long delays preventing fast feedback control, the compensation for interaction torques must occur
3

in a feedforward manner (Schweighofer et al., 1998). The muscle activity involved in controlling
intersegmental dynamics both preceding and scaling to the interaction torques that arise during
multi-joint movements (Gribble & Ostry, 1999; Maeda et al., 2017) supports the notion that the
control of interaction torques is achieved via feedforward mechanisms.
Reaching in a new dynamical environment leads to significant trajectory deviations. However,
with practice, the hand path trajectory converges towards a straight path (Shadmehr & Mussa-
Ivaldi, 1994). These adaptations are believed to be mediated by neuronal adaptation in the CNS
(Li et al., 2001). Similarly, modifying the physical properties of the shoulder can modulate the
muscle activity involved in controlling the interaction torques that arise at the shoulder during a
single-joint movement (Maeda et al., 2018). Therefore, these findings suggest that the control of
interaction torques is adaptive and that the CNS uses feedforward mechanisms to control these
torques.
Adaptive feedforward control of interaction torques in the central
nervous system
The feedforward controllers are believed to be refined through practice (Kawato, 1999; Loeb,
2021). In novel dynamical environments, or after a stroke, motor commands often result in motor
errors (Franklin et al., 2012; Patton et al., 2006). These errors induce changes in subsequent motor
commands, indicating that the feedforward controllers are updated (Kawato et al., 1987; Shadmehr
& Mussa-Ivaldi, 1994). According to the theory of “feedback error learning”, largely supported
experimentally (Kawato & Gomi, 1992; Lisberger, 2009; Shidara et al., 1993), feedback
controllers simultaneously control movements and provide error signals to tune the feedforward
controllers.
4

Following cerebellar lesions, movements often exhibit poor coordination between joints,
inadequate compensation for interaction torques, and overshooting (Bastian et al., 1996). In
addition, severe cerebellar lesions have been shown to prevent the ability to adapt to new
dynamical environments (Smith & Shadmehr, 2005). This emphasizes the critical role played by
the cerebellum in the control of multi-joint movements.
It has been proposed that the feedforward controllers, responsible for generating anticipatory motor
commands, are updated through error-based learning involving the cerebellum (Ito, 1970). The
anatomy and physiology of the cerebellum, particularly the climbing fiber input, which carries
errors that modify the Purkinje cells’ input synapses (Hansel et al., 2001; Kitazawa et al., 1998),
support the idea that the cerebellum plays a role in tuning the feedforward controllers (Kawato &
Gomi, 1992; Schweighofer et al., 1998; Shadmehr & Krakauer, 2008). This process allows the
CNS to detect and correct errors between predicted and actual motor outcomes, contributing to the
refinement of feedforward control signals.
Possible lesions affecting the updated of the feedforward controller
post-stroke
Lesions resulting from a stroke in the supratentorial region (the region containing the cerebrum)
can have direct and indirect consequences and significantly impact motor control (Schulz et al.,
2017). For instance, infarct primarily in the sensory-motor cortical areas can damage the cortico-
ponto-cerebellar tract (CPCT) and cause a phenomenon known as crossed cerebellar diaschisis
(Infeld et al., 1995; Pantano et al., 1986). Cerebellar diaschisis results in the form of atrophy and
lowered neuronal activity due to a decrease in excitatory input (Gold & Lauritzen, 2002).
5

Furthermore, a sensory-motor stroke can indirectly damage ascending cerebello-cortical fibers,
notably the dentato-thalamo-cortical tract (DTCT) (Bostan et al., 2013; Förster et al., 2014).
Therefore, significant damage to the CPCT and DTCT may impair the critical loop involved in
updating the feedforward controllers, thereby disrupting the control of interaction torques, and
limiting the modulatory effect of the cerebellum on the CNS. Failure to update the feedforward
controllers can threaten the control of intersegmental dynamics and increase trajectory deviations.
However, it is important to note that in many patients with supratentorial stroke, the cerebellum
still retains some residual activity, and still serves an important role in motor recovery (Park et al.,
2011; Várkuti et al., 2013; Wang et al., 2010). If sufficiently spared, the cortico-cerebellar system
could relearn feedforward control from large errors generated during reaching movement in
therapy.
Deficits in the feedforward controller promote the use of feedback
control strategies
Neurotypical individuals scale the magnitude of the peak velocity to the target distance indicating
a reliance on feedforward control strategies in movement execution (Gordon & Ghez, 1987;
Sainburg & Schaefer, 2004). However, chronic stroke individuals, while still maintaining some
abilities to plan the peak velocity to target distances, demonstrate diminished movement planning
compared to neuro-typical individuals (Stewart et al., 2014b, 2014a). The second phase of the
movement displays various velocity peaks and a tendency to prolong the deceleration phase
(Murphy et al., 2011; Roby-Brami et al., 2003).
Additionally, stroke survivors exhibit trajectory deviations from the straight line (Beer et al., 2000;
Kamper et al., 2002; Levin, 1996). Although mild to moderate impaired stroke individuals can still
6

roughly modulate reaching directions for different target locations, this modulation seems almost
lost for the severely impaired stroke individuals (Reinkensmeyer et al., 2002). The second phase
of the reaching movement is marked by multiple peak accelerations suggesting that stroke
survivors multiply movement adjustments to compensate for errors in planning (McCrea & Eng,
2005). These adjustments demonstrate a strong reliance on feedback to achieve the movement,
suggesting a feedback control strategy that could result from a deficit in feedforward control.
Effect of motor training post-stroke
The idea of increasing motor errors has received support both in motor learning (Sharp et al., 2011)
and in rehabilitation post-stroke (Abdollahi et al., 2014; Patton et al., 2006). In the context of gait
rehabilitation after stroke, increasing walking asymmetry with split-belt training has been shown
to restore symmetry (Reisman et al., 2007), possibly via the involvement of error-based cerebellar
plasticity (Reisman et al., 2010). Similar error-based learning could be involved in UE reaching
movements. According to the theory of feedback error learning, large errors generated by poorly
compensated interaction torques during fast multi-joint arm movements are precisely the errors
needed to readjust feedforward controllers (Schweighofer et al., 1998; Schweighofer et al., 1998).
Intensive UE training conducted over multiple sessions has been shown to improve movement
speed, smoothness, and clinical scores (Ward et al., 2019; Wolf et al., 2006). Two specific studies
suggest that short-duration and intensive speed bias training is effective at improving arm
movement performance and UE function in individuals with chronic stroke with mild to moderate
impairments (Kantak et al., 2017; Park et al., 2016).
In the study by (Park et al., 2016), participants performed two sessions of unassisted reach training
with their paretic arm, with 600 movements per session. Movements were followed by feedback
7

that continuously promoted fast movements. Training gains generalized over a large workspace,
with significant and durable (1-month) improvements in movement time and smoothness, notably
to contralateral targets. Training also durably improved Box Block test scores (23% gains at 1
month, a clinically significant improvement).
In the study by (Kantak et al., 2017), participants engaged in practice sessions for a complex motor
skill task over two consecutive days, with a total of 300 trials. The task involved maintaining the
paretic hand within a complex track displayed on a monitor, by performing a sequence of elbow
and shoulder rotations. Similar to the previous study, feedback was provided to reward fast
movements. The training led to large and durable (1-month) improvements both in the speed and
accuracy trade-off for this task and in performance on an unpracticed reaching task, with
improvements in movement velocity, smoothness, time-to-peak acceleration, and scaling of peak
acceleration to target distance.
These studies thus suggest that, in chronic stroke, intensive speed training can yield significant
improvements in arm movement performance compatible with improved feedforward control. In
this study, we will assess a novel training method that prioritizes fast movements in complex
reaching tasks to increase motor errors, which in turn would promote the update of the feedforward
controllers. It is worth noting, however, that, unlike previous methods that increase errors via
visual or mechanical perturbations, our approach involves indirectly increasing errors by requiring
fast movements. Because in the case of error augmentation experiments, movements are slow,
improvement in reaching does not necessarily require an update of the feedforward controller.
8

Outline
In this thesis, we will test to what extent stroke survivors deal with and re-learn how to control
upper-extremity multiple-joint movements. Our original mechanistic and theory-driven approach
seeks to provide valuable insights into the motor deficits following a stroke and contribute to the
field of neuro-rehabilitation.
The second chapter will focus on investigating the deficit in control in multi-joint reaching
movements. Specifically, we will analyze the pattern of trajectory deviation and how various
deficits in control for interaction torques affect the movement trajectory. To achieve this, we will
simulate several deficits in the control of interaction torques to predict the resulting trajectory
deviation.
The third chapter will investigate the predictive control of interaction torques during fast single-
joint elbow movements. By utilizing electromyography (EMG), we will examine the feedforward
motor command involved in controlling the interaction torques generated at the shoulder during
single-joint elbow movements. A comparison will be made between the kinematic and kinetic
makers of aged-matched neuro-typical individuals and the less-affected versus the more-affected
side of stroke survivors. Furthermore, we will investigate whether the inability to compensate for
the shoulder interaction torques will correlate with direction deviations in the early (feedforward)
phase of planar reaching movements.
The fourth chapter will evaluate, the effect of speed training compared to accuracy training on the
recovery of trajectory deviation, inter-joint coordination, and the restoration of the feedforward
control. By manipulating training conditions, we aim to examine how prioritizing speed over
accuracy impact the recovery of multi-joint reaching movements in chronic stroke individuals. The
9

fast movements in the speed training condition will increase motor errors, which in turn can
promote the update of the feedforward controllers.
Overall, this thesis presents a comprehensive investigation of motor control deficits and potential
recovery strategies following a stroke. The findings from this study will contribute to a better
understanding of post-stroke motor impairments and provide insights for the development of
effective rehabilitation interventions.

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Chapter 2: Reaching Kinematic in stroke survivors.
Introduction
Reaching movements in neuro-typical individuals are fast, smooth, and relatively straight. The
velocity profile of these movements typically exhibits a single velocity peak (Flash & Hogan,
1985; Morasso, 1981), and the magnitude of the peak acceleration is scaled to the target distances,
indicating a reliance on feedforward control strategies (Gordon & Ghez, 1987; Sainburg &
Schaefer, 2004). However, while maintaining some abilities to plan the peak acceleration to the
target distances, chronic stroke individuals demonstrate diminished movement planning compared
to neuro-typical individuals (Stewart et al., 2014b, 2014a). Additionally, chronic stroke individuals
exhibit trajectory deviations from the straight line (Figure 2.1), even though they can still roughly
plan the reaching directions for different target locations (Beer et al., 2000; Reinkensmeyer et al.,
2002). Reaching movements are characterized by an increase in movement duration, movement
segmentations, and trajectory deviations (Cirstea et al., 2003; Levin et al., 2016; Murphy et al.,
2011; Wagner et al., 2007a), suggesting that stroke survivors multiply movement adjustments to
compensate for errors in planning (McCrea & Eng, 2005). These deficits in UE reaching
movements are particularly observed in movements involving the coordination of multiple joints
(Beer et al., 2000; Levin, 1996).
When multiple limb segments are moved simultaneously, they generate three types of highly non-
linear interaction torques at the other joints: inertial, centripetal, and Coriolis torques (Hollerbach
& Flash, 1982). Thus, producing fast, smooth, well-coordinated, and straight-reaching movements
requires adequate compensation for these interaction torques (Flanagan et al., 1993; Hollerbach &
Flash, 1982; Lackner & Dizio, 1994; Pigeon et al., 2003; Sainburg et al., 1995). Because long
11

delays in the nervous system prevent fast feedback control, the compensation for these interaction
torques must occur in a feedforward manner (Bastian et al., 1996; Schweighofer et al., 1998). The
muscle activity involved in controlling the intersegmental dynamics both precedes and scales the
amount of interaction torques that arise during multi-joint movements (Gribble & Ostry, 1999;
Maeda et al., 2017) supporting the notion that the control of interaction torques is achieved via
feedforward mechanisms. It has been proposed that individuals post-stroke exhibit deficits in the
control of interaction torques (Beer et al., 2000; Laczko et al., 2017; Raj et al., 2020). Using planar
UE reaching movements to multiple targets performed in a frictionless environment, (Beer et al.,
2000) showed that participants with chronic stroke generated systematic deviations. Specifically,
for the more-affected side, with right side reaching movements as a reference, there was a
trajectory deviation to the right for targets at 135 and 90 degrees and a small deviation for the
target at 45 degrees (where 0 degrees is to the right, and 90 degrees straight ahead) (Beer et al.,
2000). These deviations were found to be qualitatively consistent with the deviations generated by
an inverse controller model that lacks control for interaction torques at the elbow. It is unclear if
these results could also be reproduced by an inverse controller model that lacks control for
interaction torques at the shoulder or at both the shoulder and the elbow.
Here, using a combination of arm movement experiments and simulations, we therefore re-
examine this issue of the control of interaction torques post-stoke. In simulations, we first
investigate how deficits in the control of interaction torques affect the hand path trajectory. We
then characterize the pattern of trajectory deviation in chronic stroke individuals. We hypothesize
that the more-affected side will exhibit larger deviations from the straight line compared to the
less-affected side and the dominant side of age-matched control participants. Additionally, we
12

hypothesize that the deviation will occur in the direction predicted by simulations of deficits in the
control of interaction torque.
Methods
Population
Thirty-seven chronic stroke individuals with moderate to mild impairments (17 Females, 59.58+-
2.2 years old, time since stroke 2.4+-0.58, UEMF 38.7+-2.7), as well as twelve age-matched neuro-
typical individuals (9 Females, 61+-2.9 years old), were enrolled in the study. Participants post-
stroke were included if they had: a hemorrhagic or ischemic stroke not directly affecting the
cerebellum, more than 180 days ago; no additional neurological diagnoses; any contraindication
to MRI scanning; persistent upper-extremity impairment measured by a UE-FM (Upper Extremity
Fugl-Meyer) between 21-57, and were able to slide their arm over 25cm without assistance and
with the trunk constrained within 5 seconds. Participants were excluded if they: were unable to
follow a 2-step command; exhibited signs of hemispatial neglect (more than 4% of lines left
A: More-affected
B: Less-affected C: Control
Figure 2.1: Example of hand path trajectories to three different targets located at 45, 90, and
135 deg from the starting position. Each line represents the hand path of a reaching movement
to one of the three targets. A represents the more-affected side (right), B represents the Less-
affected side (left) of a representative chronic stroke individual (FT40, UEFM = 31), and C
represents an age-matched neuro-typical individual (dominant right side).
13

uncrossed Albert’s line test)(Fullerton et al., 1986), and had severe pain or upper extremity
orthopedics disorder. Please refer to Table 4.1 for individual demographic and clinical data of the
stroke group. Participants in the age-matched control group were included if they reported no
neurological diagnoses. All participants signed informed consent for participation in this study
approved by the Internal Review Board of Casa Colina Hospital.
Planar arm reaching movements
Participants sat in an adjustable chair positioned in front of a table, and a restraining belt was used
to minimize compensatory trunk motion during reaching movements (see Figure 3.1B). The height
of the chair was adjusted to align the xiphoid process with the tabletop. Wrist movements were
restricted using a wrist brace and finger movements were constrained with a splint.
Experiment 1: Planar arm reaching movements
Participants were instructed to move their index finger from the home position to a target by sliding
their hand and lower arm on the tabletop as rapidly and accurately as possible. To reduce friction,
the upper extremity was covered with a tubular bandage. Following a familiarization session of 32
reaches, participants were instructed to perform 10 reaches to each of the 3 targets, shown in
pseudo-random order. The targets (black circle of 4 cm diameter) were located at 45°, 90°, and
135° on an arc of 20 cm radius centered on the starting position (green circle 5cm diameter),
located approximately 20 cm from the participant’s sternum (Figure 3.1 B). After a random wait
period lasting between 0.5 and 2.5 seconds, one of the targets was displayed and an auditory cue
was played signaling the start of the movement. To ensure that the participants completely stopped
at the target, the target initially turned orange once the finger entered the target area and then turned
green after 0.5s, accompanied by a pleasant sound, signaling the return to the home position. To
14

ensure that participants slid their hand and lower arm on the table, the trial started and ended only
if the finger was less than 4 cm above the tabletop.
Magnetic sensors (3D Guidance Model 800 Sensor) were placed on top of the index fingernail, the
lateral epicondyle of the elbow, the acromion, and the manubrium of the sternum. Sensor data were
recorded via the data acquisition system (3D Guidance TrackStar) programmed to sample position
at 255Hz.
Experiment 2: Fast planar arm reaching movements without visual feedback
In the first experiment, participants self-selected their movement speed to achieve a balance
between speed and accuracy. However, it is known that faster movements generate a larger amount
of interaction torques. As it was described by Woodworth (1899), removing visual feedback and
constraining movement time, thereby reduces the reliance on feedback correction and allows a
better assessment of the integrity of the feedforward controller. To investigate the effects of
interaction torques on reaching movement trajectories, we designed a second task in which
participants were required to move quickly without visual feedback.
Seventeen of the chronic stroke survivors group (4 Females, 56.9+-3.4 years old, time since stroke
1.6+-0.3, UEMF 33.25+-4) and the control group performed this task. We blocked the vision of
the hand, by placing a white cardboard horizontally 25 cm above the tabletop. The display of the
start position and target was similar to Experiment 1. Participants were instructed to go to the target
as fast as possible with the understanding that it was acceptable if they did not precisely end within
the target as long as they crossed through it. At the end of each trial, the final hand position and
target were displayed. Participants completed at least 10 reaches to each of the targets described
in Experiment 1. To ensure participants maximize their speed, we set an endpoint velocity cutoff.
The cutoff was determined based on 150% of the 80
th
percentile peak velocity of the 10 reaches
15

during experiment 1 for each target location. If the participant did not meet the velocity cutoff for
the trial, the trial was repeated, typically 5 to 10 trials were repeated.
Simulations
To study the impact of interaction torques planar reaching movement on the initial part of the
trajectories, we developed a two-link arm model controlled via feedforward control with a model
of the inverse dynamics. This model was appropriate to study reaching movements considering
that the movement from the wrist, the fingers, and the trunk were restrained during Experiments 1
and 2. In addition, we could reasonably neglect the effect of gravity as the upper extremity was
supported by the tabletop.
Generating feedforward reaching movements
The objective of the simulation was first to replicate the stereotypical hand movement observed in
planar reaching (Morasso, 1981). To compare the kinematics of the simulated movements to real
trajectories generated by our participants we calculated the average movement time and initial
shoulder and elbow joint angles for each participant. Then, we adjusted the required movement
time and initial joint angles accordingly for each participant. The desired trajectory was defined
entirely using the minimum jerk equation (Flash & Hogan, 1985), which described a straight line
from the start position to the center of the target.
Generating endpoint movement
Using the desired trajectory described above, we applied the inverse kinematic equations (1) and
(2) to calculate the desired shoulder and elbow joint angles:
16

These desired joint angles were then utilized to estimate the desired angular velocity and
acceleration at the shoulder and elbow joints. Subsequently, employing the inverse dynamic
equations (3) and (4) for a two-link arm model (Hollerbach & Flash, 1982), we calculated the
desired torque to generate the desired movement.
In the equations below, Ts and Te correspond to the net torques at the shoulder and elbow
respectively. m1 and m2, are the masses, I1 and I2 the inertia and l1 and l2 the length of the arm and
forearm, 𝜃 𝑠 and 𝜃 e represent the joint angle, 𝜃 ̇ s and 𝜃 ̇ e, represent the joint angle velocity, 𝜃 ̈ s and 𝜃 ̈ e
represent the joint angle acceleration of the shoulder and elbow, respectively.
The net torque at the shoulder Ts and elbow Te were used in the forward dynamic equation, to
estimate the new states of the system. We then used the forward kinematic equations to update the
endpoint position of the system. The equations of inverse dynamics (3) and (4) regroup several
terms: the first terms represent the inertial torques corresponding to the normal acceleration during
a single-joint movement, the second terms represent the inertial interaction torques arising from
the acceleration of the other segment, and the third terms that include the square velocity of the
𝜃 𝑠 =
𝑎𝑐𝑜𝑠 ((𝑥 2
+𝑦 2
)−(𝑙 1
2
+ 𝑙 2
2
))
2 𝑙 1
𝑙 2
(1)
𝜃 𝑒 = atan (
𝑦 𝑥 ) − atan (
𝑙 2
𝑠𝑖𝑛 (𝜃 2
)
𝑙 1
+𝑙 2
𝑐𝑜𝑠 (𝜃 2
)
) (2)
𝑇𝑠 = 𝜃 ̈ 𝑠
(𝐼 1
+ 𝐼 2
+ 𝑚 2
𝑙 1
𝑙 2
cos(𝜃 𝑒 ) +
𝑚 1
𝑙 1
2
𝑚 2
𝑙 2
2
4
+ 𝑚 2
𝑙 1
2
) + 𝜃 ̈ 𝑒
(𝐼 2
𝑚 2
𝑙 2
2
4
+
𝑚 2
𝑙 1
𝑙 2
2
+
𝑐𝑜𝑠 (𝜃 𝑒 ) ) −
𝑚 2
𝑙 1
𝑙 2

2
𝜃 ̇ 𝑒 2
𝑠𝑖𝑛 (𝜃 𝑒 ) − 𝑚 2
𝑙 1
𝑙 2
𝜃 ̇ 𝑠 𝜃 ̇ 𝑒 𝑠𝑖𝑛 (𝜃 𝑒 ) (3)
𝑇𝑒 = 𝜃 ̈ 𝑒
(𝐼 2
+
𝑚 2
𝑙 2
2
4
) + 𝜃 ̈ 𝑠
(𝐼 2
+
𝑚 2
𝑙 1
𝑙 2
2
𝑐𝑜𝑠 (𝜃 𝑒 ) +
𝑚 2
𝑙 2
2
4
) +
𝑚 2
𝑙 1
𝑙 2

2
𝜃 ̇ 𝑠 2
𝑠𝑖𝑛 (𝜃 𝑒 ) (4)
17

other segment represent the centripetal torques. Finally, the product of the velocities between the
shoulder and elbow joints, present only in the net torque equation at the shoulder (3), represent the
Coriolis torques. We refer to interaction torque as the sum of the second, third, and fourth terms.
Simulating deficit in control for interaction torque.
To simulate a decrease in control for interaction torques we used three different models: complete
loss of compensation for interaction torques at the elbow, complete loss of compensation for
interaction torque at the shoulder, and complete loss of compensation for interaction torque at both
shoulder and elbow. We did so by setting the interaction torques in the net torque equations at zero
in (3), zero in (4), and 0 in both (3) and (4) respectively.
Kinematic analyses
The kinematic analyses described below were the same for the real and simulated movements.
Joint kinematic analyses
In experimental data, angular joint angles were derived from the position sensor data. We
computed the angles for the shoulder horizontal abduction/adduction and the elbow
flexion/extension. We first determined the three following vectors: v1: representing the collar
bone, v2 representing the upper arm, and v3 representing the forearm. The shoulder angle was
calculated as the angle formed by v1 and v2, while the elbow angle was determined as the angle
formed by v3 and v4. At the shoulder, 0 deg corresponded to the upper arm aligning with the collar
bone, and a positive angle represented horizontal adduction. At the elbow, 0 deg denoted a pure
elbow extension and positive angles indicated elbow flexing. In the simulation, the joint angles
were estimated via the inverse kinematics equations (1) and (2).
18

We then estimated the first and second derivatives of the joint angles by locally fitting a parabola
with five points (Scheid, 1968) to obtain the shoulder and elbow joint angle velocity and
acceleration respectively.
Inter-joint coordination
Inter-joint coordination was calculated via a cross-correlation between the angular shoulder and
elbow acceleration at zero time lag (Murphy et al., 2011). The resulting metric ranged from -1 and
1, where –1 indicated perfect anti-phase correlation, 1 denoted perfect in-phase correlation, and 0
indicated no correlation between the two signals.
Trajectory deviation
To quantify the trajectory deviation from the straight trajectory, we identified the largest
orthogonal projection from the trajectory onto the straight line (Levin, 1996). Because the targets
were relatively large (4 cm diameter), the straight line was determined as the line between the
movement onset endpoint location and movement end, calculated relative to the 5% tangential
peak velocity. We set the counterclockwise deviation as positive. For reaches made with the left
hand, we flipped the sign to allow direct comparison between sides.
Estimation of interaction torques
The interaction torque at the shoulder and the elbow were computed using the equation of motions
(3). The interaction torques were therefore the sum of the second, third, and fourth terms. For each
participant, the length of the arms l1, and the forearms l2, were measured directly, while the mass
of the arms m1, the mass of the forearms m2, the moment of inertia of the arms I1 and the forearms
I2 were estimated via anthropometric approximation (Winter, 2009). Then, for each trial, we
summed the absolute interaction torque signal at the shoulder and the elbow and computed the
19

mean. This metric estimated the total amount of interaction torques generated during each trial at
both joints.
Statistical analyses
All the statistical analyses were conducted using the statistical toolbox in MATLAB. For
Experiment 1, we performed a mixed-effect model analysis with trajectory deviation or absolute
trajectory deviation as the dependent variable. The tested arm was treated as the independent
variable, and the participant’s ID as a random effect. To examine the effect of target location, two
additional mixed-effect models were employed, similar to the previous ones, with the addition of
an interaction term between the target location and the tested sub-group (more-affected, less-
affected side of the stroke group, and the dominant side of the control group).
Then for Experiment 2, the relationship between absolute trajectory deviation with either
interaction torques or inter-joint correlation was evaluated. Because reaches to the contralateral
target required the highest level of shoulder and elbow coordination, we only studied the effect of
inter-joint coordination on absolute trajectory deviation for the contralateral target. To study the
effect of interaction torques, we used the reaching movement performed at all target locations. For
this second set of analyses, we performed another set of mixed-effect model analyses, with
absolute trajectory deviation as a dependent variable and the inter-joint correlation. The other two
models were with trajectory deviation as a dependent variable and peak interaction torques at the
shoulder or the elbow as the independent variable. The participant’s ID and the independent
variables were treated as random effects. We perform one model for each sub-group.
20

Results
Simulations
Simulation of neuro-typical movements
In Figure 2.2, we compare the reaching movement from an actual control participant and a
simulated participant. The hand path trajectory, the shoulder and elbow angular acceleration
profiles, as well as the interaction torques generated at the shoulder and elbow are depicted for the
less-affected side of a representative participant in Figure 2.2A, and a simulated participant in
Figure 2.2B. The real hand path trajectory of this participant follows a straight line similar to the
simulated hand path trajectory. The shoulder and elbow joint acceleration profiles are anti-phase
and proportional, indicating that the two joints are equivalently rotating in opposite directions. The
simulated inter-joint correlation value was -0.99 for the central and contralateral targets and 0.04
for the ipsilateral target. Confirming that reaches to the contralateral targets are more sensitive to
a deficit in inter-joint coordination than reaches to the ipsilateral target. It is worth noting that for
the ipsilateral target, although not represented in this figure, the interaction torque is predominantly
generated at the shoulder, as opposed to the central and the contralateral targets, where a similar
amount of interaction torques are generated at both the shoulder and the elbow joints.
Simulation of deficits in control for interaction torque
Figure 2.3 represents the pattern of trajectory deviation for the three sets of simulated deficits in
control for interaction torques: at the elbow joint (Figure 2.3A), at the shoulder joint (Figure 2.3B),
and both at the shoulder and the elbow joint (Figure 2.3C). These simulated deficits in control for
interaction torques resulted in three distinct patterns of trajectory deviation. The direction of the
deviation could be either positive or negative for each target location depending on the specific
interaction torque control deficit simulated. Overall, the simulations demonstrate that a deficit in
21

control for interaction torques influences the hand path trajectory but we could not conclude that
it generates a unique pattern of trajectory deviation as suggested by (Beer et al., 2000), as multiple
deficits in control for interaction may exist.
Experimental data: Trajectory deviation
The trajectory deviation and absolute trajectory deviation for the three target locations are shown
in Figure 2.4. Regarding the ipsilateral target, more absolute trajectory deviations were generated
on the more-affected side than on the less-affected side (deviation = -0.23 cm, p< 0.001), and the
dominant side of the control participant (deviation = -0.25 cm, p< 0.05). For the central target,
more absolute trajectory deviations were generated on the more-affected side compared to both
the less-affected side (deviation = -0.62 cm, p< 0.001), and the dominant side of the control
participant (deviation = -0.95 cm, p< 0.001). Similarly, for the contralateral target, significantly
higher absolute trajectory deviations were observed on the more-affected side compared to both
the less-affected side (deviation = -0.89 cm, p< 0.001), and the dominant side of the control
participant (deviation = -1.16 cm, p< 0.001). Consistent with previous findings (Levin, 1996), we
found that on the more-affected side, the absolute trajectory deviation was higher on the
contralateral target than on the ipsilateral target (0.83 cm, p<0.001). However, no significant
differences were observed between the ipsilateral and contralateral targets on the less-affected side.
Interestingly, for the control group, the absolute trajectory deviation was the highest for the
ipsilateral target and the smallest for the contralateral target (-0.3 cm, p<0.001). This is likely
because control participants perform the ipsilateral reach as a pure single-joint elbow movement
generating a small natural curvature (Flanagan et al., 1993).

22

Figure 2.2: Real and simulated hand path trajectory, joint-angle acceleration profiles, and
joint interaction torque profiles for one trial to the central target. Panel A represents the less-
affected side, and panel B represents the associated simulated data based on the participant’s
initial joint position and anthropometric measurements. On the first row, we see the endpoint
trajectory, on the second row we see the shoulder (blue), and elbow (orange) angle acceleration
profiles, and on the third row, we see the interaction torque generated at the shoulder (blue), and
elbow (orange).
B A
23

Regarding the trajectory deviation, for the ipsilateral and central targets, all three groups showed
a biased towards the positive direction (counterclockwise deviation), but no significant differences
were observed between the more-affected and the less-affected side or the more-affected and the
dominant arm of control participants. However, for the contralateral target, the more-affected side
exhibited a significant positive bias (0.91 cm, p<0.001), and was significantly different, compared
to both the less-affected side (-1.01 cm, p<0.001) and the dominant side of the control participant
(-0.86cm, p<0.001).
Figure 2.3: Simulation of deficits in control for interaction torques. In the upper panel, the
black, copper, and yellow traces correspond to the hand path trajectories with deficits in control
for interaction torques, to the contralateral, central, and ipsilateral targets respectively. The grey
dotted line represents the ideal hand path trajectory from the starting position to the target. In the
lower panel, the associated value in trajectory deviations is depicted for the graph immediately
above. Column A represents a deficit in control for elbow interaction torques, column B
represents a deficit in control for shoulder interaction torques, and column C represents a deficit
in control for interaction torques at both the shoulder and elbow.
A
B C
24

Experimental data: Joint coordination
Different patterns of impaired trajectory
The hand path and acceleration profiles of two representative chronic stroke participants’ more-
affected sides are plotted in Figure 2.5. The hand path trajectories show significant deviation from
the straight line. Note that, to facilitate direct comparison, we flipped the left-hand reaches
trajectory along the y-axis, so all trajectories are represented as if performed by the right side. For
Participant A, we observe significant negative deviations from the straight line for the central and
contralateral targets, while Participant B displays positive deviations. However, minimal hand path
deviations are observed for the ipsilateral target. Upon visual inspection, the acceleration profile
remains somewhat correlated for Participant A, whereas Participant B is marked by a diminution
of elbow angle acceleration relative to the shoulder.
Inter-joint coordination varied importantly between targets and between groups. To investigate
inter-joint coordination further, we focused on the contralateral target which requires a high level
of coordination between the shoulder and the elbow. We analyzed the cross-correlation between
the angular acceleration at the shoulder and elbow for the contralateral target. The acceleration
profiles were less anti-phase for the more affected side compared to the less affected side (-0.07,
p<0.001) and the dominant arm of the control group (-0.12. p<0.001) (Figure 2.6).
Next, we examined the relationship between the inter-joint coordination and absolute trajectory
deviation for the contralateral target in experiment 1, Figure 2.7. We found a significant linear
relationship between inter-joint coordination and the absolute trajectory deviation for all groups.

25

Similarly, we tested the relationship between both the peak interaction torques at the shoulder or
the elbow and trajectory deviation in experiment 2. We performed a mixed effect model with
trajectory deviation as dependent variables and peak interaction torques. For each subgroup, the
models exhibited a poor effect size as indicated by an R-squared value below 0.3 both for the
shoulder and the elbow. Therefore we also performed a Pearson correlation test between the peak
interaction torques at the shoulder or the elbow and trajectory deviation but we did not find any
significant correlation for any of the groups or the covariates.
B
Figure 2.4: mean trajectory deviation
for each participant for 10 trials per
target. The red, blue, and yellow dots
represent the more- and the less-affected
sides of the stroke survivors and the
dominant side of control participants
respectively. The black lines link the
more-affected to the less-affected sides
for each stroke participant. A represents
the mean of the absolute trajectory
deviation, and B represents the mean of
the trajectory deviation.
A
26

A
Figure 2.5: Real hand-path trajectories, and joint acceleration profiles to each target for the more-
affected side of two participants (A FM-UE = 40, B FM-UE = 38). Description for A and B: On the
first row, B we see the end-point trajectory (the trajectories are flipped along the y-axis if performed
by the left side and plotted as performed by the right side); On the second row we see the shoulder
(blue), and elbow (orange) angle acceleration profiles.
B
27

Discussion
In this study, we confirmed that the absolute trajectory deviation is greater for the more-affected
side in comparison to the less-affected side and the dominant side of control participants. Contrary
to previous reports in the literature (Beer et al., 2000), the trajectory deviations in our study were
slightly biased in the positive direction (counterclockwise) for all groups and all targets. In
addition, the direction of the deviation did not consistently align with the direction predicted by a
deficit in control for interaction torques at the elbow, the shoulder, or both. Indeed, as shown in
Figure 2.4B participants exhibited trajectory deviations in both directions for all targets. As
demonstrated in our simulations various deficits in control for interaction torques may exist and
therefore generate various patterns of trajectory deviations. When investigating the control of
interaction torques for fast movements, we did not observe a significant correlation between
trajectory deviation and peak interaction torque at the shoulder or the elbow. These findings
Figure 2.6: distribution of the
cross-correlation between
shoulder and elbow joint-
angle acceleration profile for
reaches to the contralateral
target, for the more-affected
side red, the less-affected side
blue, and the dominant side of
age-matched control
participants yellow. The black
line is linking the fixed effect
for each group.
28

suggest that we cannot conclude if interaction torques affect the trajectory by simply looking at
the direction of the deviation.
Decomposition of movement as a compensatory mechanism
Our findings suggest that the more-affected side present a deficit in inter-joint coordination, which
is consistent with previous studies (Cirstea et al., 2003; Levin, 1996). We propose that the decrease
in inter-joint coordination may be a compensatory strategy employed to circumvent a lack of
feedforward control for interaction torques. Previous studies suggested that chronic stroke
individuals overcompensated for interaction torques (Raj et al., 2020) by increasing co-contraction
and therefore increasing stiffness at the joint to reduce the effect of interaction torques. This
observation could be linked to the concept of functional spasticity, which may serve as a beneficial
adaptation for movement stability (Dietz & Sinkjaer, 2007). The decomposition of movement
appears to be a strategy employed by stroke survivors to cope with the challenge to control for
interaction torques that emerge while simultaneously moving the shoulder and elbow joints. The
increase in distal joint stiffness could explain why, in some severely impaired stroke survivors, the
displacement of the Upper Extremity (UE) can be explained by the variance in shoulder motion
(Reisman & Scholz, 2003). In the literature, it has been reported that some chronic stroke
individuals develop novel reaching patterns, using new sets of joint combinations to accomplish a
task, which can sometimes lead to improved function (Cirstea & Levin, 2000; Mandon et al., 2016;
Nibras et al., 2021). This suggests that some chronic stroke individuals may not rely on predicting
and accounting for interaction torques in the planning of the motor command but rather develop
new movement strategies to address the challenge.
29

Impaired feedforward control can generate multiple patterns of trajectory deviation
In our simulations, we showed that poor control of interaction torques can largely affect the end-
point trajectory. However, the specific pattern of trajectory deviations depends on the type of
deficit in control of interaction torques. For instance, a lack of compensation of interaction torques
at both the shoulder and elbow should generate a deviation to the left for targets at 90 and 45
degrees; for no compensation at the shoulder only, there is a minimal deviation for a target at 135
degrees and again deviations to the left for targets at 90 and 45 degrees (Figure 2.3). It is unclear
why chronic stroke individuals would exhibit deficits in the control of interaction torques at only
a single joint (e.g., the elbow) consistently across the population.
Therefore, the variability in the trajectory deviation among chronic stroke individuals could be
explained by a deficit in control of interaction torques but also by novel reaching strategies
developed to circumvent their impairment. Consequently, the study of the planar-reaching
movements as developed in this chapter does not suffice to conclude that chronic stroke individuals
present a deficit in control for interaction torques.
Figure 2.7: Relationship between trajectory deviation and inter-joint correlation. On each
plot are represented individual trial max deviation and its associated inter-joint cross-
correlation for reaches to the contralateral target. Each color represents a participant, with the
10 reaching movements to that target. A, B, and C are the more- and the less-affected side of
the stroke group, and the dominant side of the control participants respectively.
A B C
30

Therefore, in the next chapter, we develop a new experiment relying on fast single-joint ballistic
movements primarily controlled via feedforward mechanisms, limiting the development of
alternative feedback control strategies. In this new experimental paradigm, we will directly assess
the anticipatory scaling of muscle activity to the interaction torques generated at the shoulder as
presented in (Gribble & Ostry, 1999). Observing a deficit in scaling for the interaction torques at
the shoulder would likely indicate a deficiency in control of interaction torques.

31

Chapter 3: Anticipatory control of interaction torques in fast
single-joint arm movements in individuals with chronic
stroke
Introduction
Approximately 65% of individuals post-stroke experience long-term limitations in upper extremity
functions (Lum et al., 2009). Notably, limitations in goal-directed reaching movements are often
prominent and strongly correlate with patients’ impairment levels (Kamper et al., 2002; van
Dokkum et al., 2014). Reaching movements post-stroke are often characterized by trajectory
deviations, segmented movements, prolonged movement time, and poor inter-joint coordination
(Hammond et al., 1988; Levin, 1996; Levin et al., 2016; Murphy et al., 2011; Reinkensmeyer et
al., 2002).
The control of multi-joint movement is challenging due to the simultaneous rotation of each limb
segment generating three types of highly non-linear interaction torques at the other joints: inertial,
centripetal, and Coriolis torques (Hollerbach & Flash, 1982). Consequently, producing fast,
smooth, and straight-reaching movements requires adequate compensation for these interaction
torques (Beer et al., 2000; Lackner & Dizio, 1994; Pigeon et al., 2003; Sainburg et al., 1995). As
fast feedback control is hindered by long delays in the nervous system, the compensation for these
interaction torques must occur in a feedforward and predictive manner (Schweighofer et al., 1998).
The feedforward controllers are believed to be refined through practice with the involvement of
cerebellar processes (Kawato, 1999; Shadmehr & Krakauer, 2008). Severe cerebellar damage may
32

induce deficits in the control of interaction torques (Bastian et al., 1996), and prevent the ability to
adapt to a new arm dynamics environment (Smith & Shadmehr, 2005).
It has been proposed that individuals post-stroke exhibit deficits in the control of interaction
torques (Beer et al., 2000; Laczko et al., 2017; Raj et al., 2020). Using planar two-dimension arm
movements to multiple targets performed in a frictionless environment, (Beer et al., 2000) showed
that participants with chronic stroke generated systematic deviations in horizontal reaching
movements. Specifically, for the more-affected side arm movements, with right side reaches as a
reference, there was a trajectory deviation to the right for targets at 135 and 90 degrees and minimal
deviation for the target at 45 degrees (where 0 degrees is to the right, and 90 degrees straight ahead)
(Beer et al., 2000). These deviations were found to be qualitatively consistent with the deviations
generated by an inverse controller model that lacks control for interaction torques at the elbow.
However, in similar simulations presented in the second chapter, we demonstrated that inverse
controller models that either lack control for interaction torques the shoulder only or at both the
shoulder and elbow, exhibit patterns of deviations inconsistent with these results. For instance, a
lack of compensation of interaction torques at both the shoulder and elbow should generate a
deviation to the left for targets at 90 and 45 degrees; for no compensation at the shoulder only,
there is a minimal deviation for a target at 135 degrees and again deviations to the left for targets
at 90 and 45 degrees (Figure 2.4). It is unclear why chronic stroke individuals would exhibit
deficits in the control of interaction torques at only a single joint (e.g., the elbow) consistently
across the population. Thus, these simulations point to the need for a re-examination of the deficits
in the control for interaction torques post-stroke.
While Beer et al. (Beer et al., 2000) qualitatively matched the reaching deviations to simulation
results at the group level, this study aims to directly estimate the degree of compensation for
33

shoulder interaction torques resulting from fast elbow movements. Additionally, we investigate
how such control deficits are associated with reaching movement deviations in both the more and
less-affected sides in participants post-stroke as well as in the dominant arm of age-matched
control participants. For this purpose, we extended the methods proposed by (Gribble & Ostry,
1999), who demonstrated that muscle activity at the shoulder both precedes and scales with the
interaction torques generated at the shoulder in single-joint elbow movement (Gribble & Ostry,
1999; Maeda et al., 2018).
We included chronic stroke individuals with mild to moderate impairments and we excluded
participants with lesions directly affecting the cerebellum. However, we presume that the stroke
will indirectly affect cerebellar function because it will affect the cortico-ponto-cerebellar tracts,
as well as cerebello-thalamo-cortical tract, the main cerebellar input and out outputs (Infeld et al.,
1995b; Pantano et al., 1986). Therefore, our first hypothesis posits that compared to the less-
affected side and the dominant side of an age-matched control group, the more-affected side of
chronic stroke individuals will demonstrate reduced predictive control of interaction torques at the
shoulder during fast single-joint elbow movements. Our second hypothesis suggests that the
inability to compensate for the interaction torques generated at the shoulder will correlate with
trajectory deviation in the early (feedforward) phase of planar reaching movements.
To test our first hypothesis, we conducted Experiment 1, involving fast single-joint elbow flexions
and extensions using a specially designed apparatus that constrained the movements to elbow
rotations. We computed the cross-correlation between the interaction torque at the shoulder
estimated from inverse dynamics and the compensatory torque at the shoulder derived from surface
EMG activity of two shoulder muscles involved in horizontal shoulder movements, the pectoralis
for flexion and the posterior deltoid for extension. For each trial, we obtained the maximal cross-
34

correlation value and its associated lag value. Following the findings of (Gribble & Ostry, 1999),
and considering the predictive nature of interaction torque, we expect maximal correlation at a
negative lag (i.e., the torque generated by shoulder muscle activity is leading the torque estimated
from elbow kinematics).
However, because of electro-mechanical delay, the muscle activation detected by EMGs occurs in
advance of the movement. Thus, to confirm the predictive nature of shoulder muscle activity, we
also computed the cross-correlation between the net torque signal at the elbow and the EMG-
estimated torque at the elbow using the kinematic data and elbow muscles’ EMG activity. If the
shoulder EMG activity is indeed predictive, the lag at the shoulder cross-correlation should exhibit
a larger negative shift than the lag at the elbow. Considering that we recorded EMG activity from
five elbow muscles (biceps, brachialis, brachioradialis, triceps lateral head, and triceps long head),
we initially estimated the contributions of these muscles to elbow torque by developing an EMG
to torque model at the elbow via linear regression, following the methods in (Osu et al., 2002). To
estimate the parameters of this model, and then the lag at the elbow, we first conducted Experiment
2, in which we recorded EMGs in these five muscles in an isometric elbow flexion and extensions
using the same apparatus. Lastly, in Experiment 3, we evaluated performance during reaching
movements, by instructing participants to slide their hand reaching on a low-friction tabletop. To
focus on deviations attributable to feedforward control, we analyzed the deviation occurring at 150
msec into the movements ( Franklin et al., 2008; Thoroughman & Shadmehr, 1999).
Material and Methods
Study design
Chronic stroke Individuals with mild to moderate impairment as well as an aged-matched group
control participated in the study. During the first visit, we screened the participants to determine
35

their eligibility based on specific inclusion and exclusion criteria. On the second and third visit,
we tested the less affected and the more-affected side, respectively. During either the second or
third visit, an MRI scan was conducted to confirm that the participants did not have direct
cerebellar lesions due to stroke. For the control group participants, we tested the dominant arm in
a single visit. Each testing visit consisted of three experiments. In Experiment 1, participants
performed fast elbow flexions and extensions. Experiment 2 involved isometric elbow flexions
and extensions. Finally, in Experiment 3, participants performed planar reaching movements by
sliding their hand on a tabletop.
Participants
A total of thirty-five chronic stroke individuals with moderate to mild impairments (16 Females,
59.73+-2.3 years old, time since stroke 2.5+-0.6, UEMF 44+-2.1 ), as well as twelve age-matched
neurotypical control individuals (9 Females, 61+-2.9 years old) were enrolled in the study.
Participants post-stroke were included if they had: a hemorrhagic or ischemic stroke not directly
affecting the cerebellum, more than 180 days ago; no additional neurological diagnoses; any
contraindication to MRI scanning; persistent upper-extremity impairment measured by a UE-FM
(Upper Extremity Fugl-Meyer) between 21-57, and were able to slide their arm over 25cm without
assistance and with the trunk constrained within 5 seconds. Participants were excluded if they:
could not follow a 2-step command; had signs of hemispatial neglect (more than 4% of lines left
uncrossed Albert’s line test)(Fullerton et al., 1986), and had severe pain or upper extremity
orthopedics disorder. See Table 3.1 for individual demographic and clinical data in the stroke
group. Participants in the age-matched control group were included if they reported no
neurological diagnoses. All participants signed an informed consent for participation in this study
approved by the Internal Review Board of Casa Colina Hospital.
36

Experiment 1: Fast elbow movements
Participants sat in a wheelchair with their trunk constrained by a 4-points seat belt. They were
positioned as close as possible to a specially designed arm apparatus, which restrains arm
movement to allow elbow flexion and extension only (Figure 3.1A). The participant held a handle
and placed their forearm (secured via Velcro straps) in a brace in a neutral pronation/supination
position. The position of the handle was adjusted so that the axis of rotation of the handle was in
line with the center of rotation of the elbow (under the medial epicondyle). The apparatus height
was adjusted so the hand was approximately 5cm below the acromion and the width such that the
arm was approximately at 60° of horizontal shoulder adduction (0° corresponds to the upper arm
in the coronal plane). To measure angular position, a potentiometer (6639S-1-102, Bourns Inc.)
was attached to the axis of rotation. Additionally, a monitor was positioned in front of the
participant to display the virtual environment.

Figure 3.1. Experimental set-ups. A Set-up used for fast elbow movements of Experiment 1
and the isometric elbow movements of Experiment 2. A, the virtual environment was shown on
a monitor in front of the participants. B, set-up for planar reaching movements in Experiment 3.
Targets were directly displayed on the tabletop via an overhead projector.
A B
37

Participants were instructed to generate fast and accurate elbow flexion or extension movements
of 30, 50, or 70° amplitudes. A 10 cm line, representing their forearm, was displayed on the screen
and rotated as participant move their forearm. The involved moving the forearm between a green
circle representing the start position, and a white circle representing the target. However, once the
forearm left the start position, the white line disappeared. The starting positions for extension were
respectively 115, 125, and 135° of elbow flexion, and for flexion 75, 65, and 55° of elbow flexion
(0° corresponds to the arm fully extended). The sizes of the targets were increased as the
amplitudes increased (diameter = 3.4, 5.8, 8 cm). To ensure fast movements, and therefore generate
large interaction torques at the shoulder, we used a two-phase approach. In the first phase,
participants completed 10 flexions and extensions for each of the three amplitudes (60 trials) with
the instructions to move as fast and accurately as possible. If the participants reached the target
and the forearm stayed in the target for 0.2s, the target turned yellow and the movement time was
displayed; if the participants did not reach the target (or did not stay for 0.2 sec in the target), a
small red disk showed the final position and “outside the target” was displayed. Then, in the second
phase, participants were instructed to perform fast movements with times shorter than
predetermined thresholds. These time thresholds corresponded to the 20th percentile of the
movement times for the 10 flexion or extension blocks in the first phase. If movements were too
fast we set a time cutoff at 0.1s, 0.12s, and 0.15 for the small, medium, and large amplitude. The
movement time was computed based on the duration it took for the line representing the forearm
to travel between the start position and the target. Participants completed a minimum of 10 flexions
and extensions for each of the three amplitude (60 trials) but each trial could be repeated up to four
times if it was not successful. The same feedback as in the first phase was provided, except that if
the target was reached with a movement time above the time threshold, the target turned orange
38

and “too slow” with the actual movement time was displayed. We analyzed data for all movements
(including “too slow” movements).
We recorded surface EMG activity, with active bipolar electrodes (Biometrics Ltd, Newport, UK),
from seven different muscles: two shoulder muscles: Pectoralis (Pec; flexor), Posterior Deltoid
(PD: extensor); two bi-articular muscles: Biceps Brachii (BI; flexor), Triceps Brachii long head
(TLg; extensor); and three elbow muscles: Brachioradialis (BD; flexor) and Brachialis (BR;
flexor), and Triceps Brachii lateral head (TLt; extensor). The EMG signals were sampled at 1 kHz
using the Biometrics DataLog system. Then position, force, and EMG were digitized at 2 kHz
using a USB analog-to-digital converter (USB-6259; National Instruments).
Experiment 2: Isometric elbow task
The same elbow apparatus as in Experiment 1 was used for this experiment, except that the handle
was locked with pins at 45°, 65°, and 85° of elbow flexion. A one-axis force cell was mounted at
the base of the handle and calibrated to measure the elbow torque.
The participants were instructed to move a cursor (red disk, 1.25 cm diameter) from a starting
position (green circle) to a target (white circle). The targets were placed so that participants needed
to achieve three levels of torque corresponding to 10, 25, and 40 % of MVF (maximum voluntary
force; see below) in both flexion and extension. There were five trials for each level of force for
three arm postures in both flexion and extension (total 90 trials), plus 12 MVF trials. After placing
the cursor in the green circle by applying no elbow force, a goal target appeared, indicating the
start of force production. After the cursor moved to, and then remained in the target for 0.5 sec,
the target became orange, and “Hold” was displayed for 0.75 sec. The target then became yellow,
indicating a return to the starting position, and “Success” was displayed. Because it was more
difficult to hold the cursor in the target for higher force levels, we increased the size of the targets
39

from 3.6 cm, 4.7cm, and 6cm for the three force levels. The motion of the cursor followed a mass-
spring-damper, with the stiffness of the spring proportional to the MVF so that the displacement
of the cursor to the targets was equivalent between participants (see (Barradas et al., 2020) for
details).
For each arm posture, we first presented an MVF block consisting of two maximum voluntary
isometric elbow flexions and two extensions lasting 5 sec during which the experimenter motivated
the participants to generate maximal elbow torque. The MVF was set as the 5sec average force for
the best of the two trials in each flexion and extension. Surface EMG was recorded from the seven
arm muscles, as described in Experiment 1.
Experiment 3: Planar arm reaching movements
For this experiment, participants sat in an adjustable chair facing a table, and a restraining belt
minimized compensatory trunk motion during reaching movements (see Figure 3.1B). The height
of the chair was adjusted so the xiphoid process was aligned with the tabletop. Wrist movements
were restrained via a wrist brace and finger movements with a splint.
Participants were instructed to move their index finger from the home position to a target by sliding
their hand and lower arm on the tabletop as rapidly and accurately as possible. To limit friction,
the upper extremity was covered with a tubular bandage. Following a familiarization session of 32
reaches, participants were instructed to perform 10 reaches to each of the three targets, shown in
pseudo-random orders. The targets (black circle of 4 cm diameter) were located at 45°, 90°, and
135° on an arc of 20 cm radius centered on the starting position (green circle 5cm diameter),
located approximately 20 cm from the participant’s sternum (Figure 3.1). After a random wait
period lasting between 0.5 and 2.5 seconds, one of the targets was displayed and an auditory cue
signaled the start of the movement. To ensure that the participants completely stopped at the target,
40

it first turned orange once the finger entered the target area, and after 0.5s, it turned green together
with a pleasant sound, signaling the return to the home position. To ensure that participants slid
their hand and lower arm on the table, the trial started and ended only if the finger was less than 4
cm above the tabletop.
Magnetic sensors (3D Guidance Model 800 Sensor) were placed on top of the index fingernail, the
lateral epicondyle of the elbow, the acromion, and the manubrium of the sternum. However, for
the purpose of the current study, only data from index fingers are presented. Sensor data were
recorded via the data acquisition system (3D Guidance TrackStar) programmed to sample position
at 255Hz.
Data processing and analyses
All data processing, analyses, and experiments were performed using MATLAB.
Estimation of interaction torques at the shoulder from kinematic data in Experiment 1.
Angular rotation data from the potentiometer were low-pass filtered twice (8Hz, 6
th
order filter
Butterworth) and then derived to obtain angular velocity and acceleration (using a time step of 0.5
msec and by locally fitting a parabola with five points (Scheid, 1968). The beginning of the
movement was set as the time at which the angular velocity first exceeded 5% peak velocity and
end of the movement as the time at which it fell below the 5% peak velocity.
To compute the interaction torque at the shoulder we used the equation of motions (Gribble &
Ostry, 1999; Hollerbach & Flash, 1982). Since we assumed that the shoulder angular velocity was
zero, a reasonable assumption since the shoulder rotation was constrained by the belt and the axis
of rotation under the elbow, the Coriolis torques was considered negligible. The interaction torques
are therefore the sum of the inertial interaction and centripetal torques:
41

𝜽 𝐞 , 𝜽 ̇ 𝐞 , 𝜽 ̈ 𝐞
represent angular position, velocity, and acceleration at the elbow, respectively. 𝑰 𝟐 is
the moment of inertia of the forearm, 𝒍 𝟏 and 𝒍 𝟐 are the lengths of upper arm and lower arm, and
𝒎 𝟐 is the mass of the lower arm. 𝒍 𝟏 and 𝒍 𝟐 were measured directly for each participant, while the
𝒎 𝟐 and 𝑰 𝟐 of the lower arm were estimated via anthropometric estimation (Winter, 2009). We
then computed TSNORM, the normalized interaction torque at the shoulder, by dividing TS by the
99th percentile value of the absolute value of TS across all trials. Finally, to reproduce (and extend
to older adults and post-stroke) the results (Gribble & Ostry, 1999), we also recorded the peak
interaction torque defined as the maximal absolute value of the first peak of interaction torque for
each trial.
Estimation of net torques at the elbow from kinematic data in Experiment 1.
Because the lower arm was supported and the shoulder was assumed fixed, the net joint torque
equation at the elbow simplified to a single inertial term:
Estimation of torques at the shoulder from EMG data in Experiment 1.
In this paradigm, we were specifically interested in how shoulder EMG activity was modulated
relative to the interaction torque signal estimated at the shoulder. Assuming that rectified surface
EMG signals are proportional to isometric muscle tension (Osu et al., 2002; Shin et al., 2009; Zhou
& Rymer, 2004), the joint torque can be expressed as the difference between the flexion torque
exerted by flexor muscles and the extension torque exerted by extensor muscles. In horizontal
TS = 𝜽 ̈ 𝒆
( 𝑰 𝟐 +
𝒎 𝟐 𝒍 𝟐 𝟐 𝟒 +
𝒎 𝟐 𝒍 𝟏 𝒍 𝟐 𝟐 + 𝒄𝒐𝒔 (𝜽 𝐞 ) ) −
𝒎 𝟐 𝒍 𝟏 𝒍 𝟐
𝟐 𝜽 ̇ 𝐞 𝟐
𝒔𝒊𝒏 (𝜽 𝐞 ) (1)
TE = 𝜽 ̈ 𝒆
( 𝑰 𝟐 +
𝒎 𝟐 𝒍 𝟐 𝟐 𝟒 ) (2)
42

movements at the shoulder, the Posterior Deltoid (PD) and the Pectoralis (PEC) extend and flex
the upper arm, respectively. We first filtered the EMG signals (band-pass filtered 25-350Hz, via
6
th
order filter Butterworth). We then low-pass filtered (8Hz, 6
th
order filter Butterworth) the full-
wave rectified signal. To model the activation dynamics, the EMG activity was then transform into
muscle activation following the procedure described in (Lan, 2002). At the shoulder, the joint were
assumed to work in an isometric condition, therefore, the muscle tension corresponded to the
muscle activation. However, for the estimation of the elbow torque, muscle activation was
transform into muscle tension after approximation of the force-velocity factor transformation
similar to (Lan, 2002).
Torque values were assigned to be negative in extension and positive in flexion. We, therefore,
estimated the EMG estimated joint torque as:
Here, 𝑇𝑆
𝐸𝑀𝐺 denote the shoulder joint torque. The parameters 𝑐 𝑃𝐸𝐶 and 𝑐 𝑃𝐷
are positive and
correspond to the conversion factor from the muscle tension to muscle force (Osu et al., 2002).
𝑢 𝑃𝐸𝐶 and 𝑢 𝑃𝐷
are positive and denotes the motor commands to the PEC and PD respectively.
𝑢 𝑃𝐸𝐶 and 𝑢 𝑃𝐷
were taken as the EMG data during the movement normalized by the average EMG
across all movements. The coefficients 𝑐 𝑃𝐸 𝐶 and 𝑐 𝑃𝐷
were arbitrarily set to 1, thus assuming equal
and opposite effects of the PEC and the PD (Kuechle et al., 1997; Landin et al., 2017, 2018).
Overall, control participants generated more acceleration and therefore more torques than
participants post-stroke, and the less-affected side of stroke participants generated more torques
than the more-affected side. To ensure similar ranges of kinematic-estimated interaction torques
at the shoulder, we matched peak interaction torque data between the less and the more-affected
𝑇𝑆
𝐸𝑀𝐺 = 𝑐 𝑃𝐸𝐶 𝑢 𝑃𝐸𝐶 − 𝑐 𝑃𝐷
𝑢 𝑃𝐷
(3)
43

side via a one-to-one matching procedure without replacement. For each flexion or extension of
the more-affected side, we searched for a movement with the less-affected side (selected pseudo-
randomly), for which the difference in the peak interaction torque movement was less than a caliper
of 2Nm. Once two trials were matched, they were not available for further matches. We repeated
the process until there were no further matches possible. If less than 10 trials remained after the
matching procedure the participant was removed from the analysis. As a result one participant was
removed from the analysis.
Estimation of elbow torques at the shoulder from EMG data in Experiment 2 and 1.
Here, we assumed a model akin to that of equation 3, but with five muscles acting on the elbow as
in (Osu et al., 2002). Flexor muscles BI, BR, and BD and extensor muscles TLt and TLg. Using
the same convention and assumption as above:
Since we recorded isometric torque measurements at the elbow in Experiment 2, the c coefficients
were found via regression of the normalized filtered torques and EMG data (as above) with the
constraints that all coefficients be positive (using the function lsqlin in Matlab). We then used this
model to estimate the elbow muscle torques during the fast movements by “plugging” the
(normalized) muscle activity recorded in Experiment 1. We refer the reader to (Osu et al., 2002)
for the rationale and the validity of this approach.
Assessing feedforward motor performance in Experiment 3.
Position data from the magnetic sensor were low-pass filtered (8Hz, 6th order dual-pass
Butterworth). The beginning and end of each movement were determined based on the 5% peak
tangential velocity cutoff (Sainburg & Schaefer, 2004). The initial trajectory deviation was
𝑇𝐸
𝐸𝑀𝐺 = 𝑐 𝐵𝐼
𝑢 𝐵𝐼
+ 𝑐 𝐵𝑅
𝑢 𝐵𝑅
+ 𝑐 𝐵𝐶
𝑢 𝐵𝐷
− 𝑐 𝑇𝐿𝑡 𝑢 𝑇𝐿𝑡 − 𝑐 𝑇𝐿𝑔 𝑢 𝑇𝐿𝑔 (4)
44

calculated as the difference between the initial and final reach direction. To quantify feedforward
motor control in reaching movements, we defined the initial direction as the vector defined by the
starting position and at 150ms after the start of the movement. The final reach direction was
defined as the vector between the starting position and the final position at the end of the
movement. It is important to note that reach directions were not computed from the target centers
due to their large size (4cm diameter) relative to the movement distance (20cm). Counterclockwise
deviations were set as positive, however, we flipped the sign of the deviation for left side reaches
to allow direct comparison between the left and right side reaches. Outliers with absolute reaching
deviations exceeding 50 deg, were excluded from the analysis as they were indicative of planning
errors, where participants initially reached to the wrong target but corrected their movement. A
total of 19 movements representing 1.02% of the total number of trials were removed via this
procedure.
Estimation of predictive control via correlation between the sum (area under the curve) of
shoulder muscle activity and peak interaction torques.
To test our hypothesis that the muscle torque generated at the shoulder by the pectoralis and
posterior deltoid muscles compensate for interaction torques generated by fast elbow movements
in Experiment 1, we first reproduced in control participants (albeit in an older cohort), and then
extended in post-stroke participants, the methods developed by (Gribble & Ostry, 1999). Briefly,
we correlated the peak positive interaction torque at the shoulder obtained via Equation 1 with the
z-score of the EMG area of the posterior deltoid during elbow extension. We set the onset and
offset of the EMG burst at 100 msec around the movement onset similar to previous studies
(Gribble et al., 2003; Thoroughman & Shadmehr, 1999). The EMG area corresponded to the sum
of the EMG envelope from the burst onset to the offset. The EMG area was then normalized to a
45

z-score by taking the mean and standard deviations of the EMGs in all extension trials on each
side.
Estimation of predictive control via cross-correlation between estimated muscle torques and
interaction torques.
The method developed by (Gribble & Ostry, 1999) above, is adequate for movements in young
neurotypical adults in which 1) EMG bursts are well-defined with a clear reciprocal modulation of
agonist and antagonist muscle activity (Brown & Cooke, 1981), 2) movement velocity profile are
marked by a single peak (Morasso, 1981) and therefore are marked by two distinct peaks in the
interaction torque profile. However, post-stroke the EMG bursts are often less clearly defined,
have reduced amplitudes(absolute value), may be prolonged, and show high variability from one
movement to another (Fagioli et al., 1988; Gemperline et al., 1995; Chae et al., 2002; Wagner et
al., 2007b). In addition, the method developed by (Gribble & Ostry, 1999) considers the
contribution of one muscle controlling for interaction torque in relation only to the peak interaction
torque in either single joint shoulder or elbow flexion. Yet, interaction torques comprise both
positive and negative components, with agonist and antagonist muscles being activated at different
times during the movement to compensate for these two components. Hence, a method that
accounts for the dynamic modulation of muscle activity across the entire movement is preferable
to a method that captures a snapshot of the peak interaction torque.
To address these limitations, we employed a novel approach based on the whole movement
kinematics and EMG signals. We computed the cross-correlation between the muscle
torque -TSEMG (equation 3) and the kinematic-estimated torque TSNORM (from equation 1). A cross-
correlation of 1 would indicate that the kinematic-estimated torque generated at the shoulder is
perfectly compensated. Because we were interested in feedforward, predictive, control of
46

interaction torque, we searched for the maximal (normalized) cross-correlation value with lags
of -TSEMG from -200ms to 50 ms lag relative to TSNORM. Thus, for each trial, we obtained a
normalized cross-correlation value and its associated lag value.
Because of electro-mechanical delay, the muscle activity detected by the EMG always precedes
the movement. Thus, to verify that the shoulder muscle activity is indeed predictive, we also
computed the cross-correlation between the EMG estimated torque at the elbow TEEMG (equation
4) and the net torque signal at the elbow TE (equation 2) using the EMG and kinematic data of
Experiment 1 and the model derived from Experiment 2. If the shoulder EMG activity is indeed
predictive, the lag at the shoulder cross-correlation should exhibit a larger negative shift than the
elbow lag.
Statistical analyses.
We conducted statistical analyses using the MATLAB statistical toolbox. To examine the
relationship between the shoulder muscle activity and peak interaction torque we performed three
mixed-effect models for each sub-group: the more-affected and less-affected side of the stroke
group, and the dominant side of the control group. The dependent variable was the z-score of the
PD EMG area while the independent variable was the peak interaction torque in extension. The
participant’s ID and the independent variables were treated as random effects.
For the analysis of cross-correlation values and lags, our focus was on group differences.
Therefore, the dependent variable was either the cross-correlation value or the lags, and the
independent variable was the subgroup ID. In addition, the participant’s ID was treated as random
effects. We compared the subgroups pairwise: the more and less-affected sides, the more-affected
side and the control group, and finally the less-affected side and the control group. The same
47

methodology was applied to both shoulder and elbow analyses, resulting in a total of 12 mixed-
effect models.
Next, we examined whether the ability to control for interaction torque at the shoulder correlated
with the absolute initial trajectory deviation in planar reaching movements. For this purpose, we
performed a linear regression analysis with the median absolute initial trajectory deviation as the
dependent variable, and the median cross-correlation values as the independent variable.
Figure 3.2: examples of muscle torque control at the elbow. The top row shows the
(filtered and rectified) EMG activation at the elbow during a single joint elbow extension
of 75 deg for a representative trial of a control participant (C) and representative trials of a
participant post-stroke for the less (B) and more affected (A) sides. On the second row are
represented the estimated normalized EMG torque (purple) and the normalized torque
estimated via inverse dynamics at the shoulder (black).
A C B
48

Results
Experiment 1: control for single joint interaction torque
Figure 3.2 illustrates representative examples of net torque control (TENORM) and the estimated
EMG net torque (TEEMG) at the elbow. Figure 3.3 displays representative examples of interaction
torque at the shoulder (TSNORM) calculated using equation 1 and the negative muscle torques
TSEMG computed via equation 3. It is apparent from the control and less-affected side trials that
TSEMG appear to be modulated according to the interaction torque but precedes it. However, this
modulation is less distinct for the more-affected side.
These observations are confirmed at the population levels after comparing the cross-correlation
values for all trials between groups (Figure 3.4). First, the cross-correlation value for the more-
affected side (estimate = 0.28) was significantly lower compared to the less-affected side (estimate
= 0.47, p<0.001), and the control (estimate = 0.47, p<0.001). Secondly, the time lag exhibited
significantly smaller negative shift on the more-affected side (estimate = -0.03 s) than on the less-
affected side (estimate = - 0.08 s, p<0.001), and the control (estimate = - 0.06 s, p<0.001). This
demonstrates a significantly reduced predictive compensation for interaction torque on the more-
affected side. The less-affected side did not show any differences compared to the control
participant for the cross-correlation value. However, the lags on the less-affected side were
significantly smaller compared to the control (p > 0.001).
To verify that TSEMG is truly predictive, it is important to compare the lag relatively to the lag
observed in the activation of the prime movers (elbow muscles activity). In contrast to the shoulder,
the cross-correlation between the elbow EMG activity and the elbow muscle torque (Figure 3.4)
show minimal differences between the more (estimate = 0.65) and the less-affected side (estimate
= 0.58, p<0.05). Regarding the time lag at the elbow, we did not observe differences between the
49

more-affected side (estimate = -0.05 s) and the less-affected side (estimate = -0.046 s, p>0.05).
However, the time lag at the elbow was significantly smaller for the control (estimate = -0.033 s,
p<0.01). These results suggest that the EMG activity at the shoulder of the more-affected side
completely lost its predictive activation relative to the EMG activity at the elbow. We looked at
the correlation of the EMG area of the PD with the peak interaction torque generated at the
shoulder for all. Consistent with previous studies (Gribble & Ostry, 1999), our findings confirmed
that in control participants, the shoulder muscle activity was significantly scaled with the amount
of interaction torque generated at the shoulder (fixed effect = 5.0, p < 0.001). A similar relationship
was obtained with the less-affected side, (fixed effect = 4.2, p < 0.001) and on the more-affected
side (fixed effect = 3, p < 0.001) of the chronic stroke individuals. We note that there were no
significant differences in peak interaction torque between the more and the less-affected sides as
we matched the peak interaction torque value in each side to get a comparable data set.
50

Figure 3.3: Examples of shoulder interaction torque control. The top row shows the
(filtered and rectified) EMG activation at the shoulder during a single joint elbow extension
of 75 deg for a representative trial of a control participant (C) and representative trials of a
participant post-stroke for the less (B) and more affected (A) sides. Red: activation of the
Posterior deltoid PEC; blue: (negative) activation of the Pectoralis PD. On the second row
are represented the estimated normalized EMG torque (purple) and the normalized
interaction torque estimated via inverse dynamics at the shoulder (black).
A B C
51

Figure 3.4: Cross-correlation value and corresponding time lag for the more-affected side
(red), less-affected side (blue), and control dominant side (yellow). On the top panel, we see
the cross-correlation value between -TSEMG and TS at the shoulder (Left) and TEEMG and TE at
the elbow (Right). On the lower panel is displayed the associated cross-correlation at the
shoulder (Left) and the elbow (Right). At the shoulder, the cross-correlation value is
significantly smaller on the more-affected side compared to both the less-affected side and the
control. The time lags at the shoulder show 3 different distributions. For the control, the time
lags distribution is centered at -90ms, for the less-affected side the distribution is centered at -
120ms while the more-affected side distribution was centered at -50ms. At the Elbow, no
significant differences were observed for the cross-correlation value. For the lag distribution,
all the distributions are centered at -50ms. (*) p<0.05, (**) p<0.01, (***) p<0.001
Shoulder Elbow
52

Experiment 3: Multi-joint planar reaching movements
Deficit in control for interaction torque predicts errors in planar reaching movements
We then tested if the ability to control for interaction torque at the shoulder correlated with absolute
initial trajectory deviations in planar reaching movements. We found a significant linear
correlation between the median absolute initial trajectory deviations across the central and
Figure 3.5: Examples of reaching movements for more-affected side, A, less-
affected side, B, and control participants, C.
A
B C
Figure 3.6: Absolute initial trajectory deviation as a function of the cross-correlation
value at the shoulder. The y-axis represents the initial direction error during the multi-joint
planar reaching movements. The x-axis represents the cross-correlation value obtained
during the single-joint elbow movement. Each data point represents a single participant. We
observed a significant effect of the cross-correlation value on error angles for the more
affected side but not for the less affected side. (*) p<0.05, (**) p<0.01, (***) p<0.001
A B C
53

contralateral targets and the cross-correlation value obtained in experiment 2 for the more-affected
side (slope = -9.69, p<0.05). We did not find a significant relationship on the less-affected side or
for the control group Figure 3.6.
Discussion
Here, we tested whether the more-affected side of chronic stroke individuals maintains the
predictive control of interaction torques during fast single-joint elbow movements. Our findings
indicate that the more-affected side demonstrates a reduced predictive ability to properly modulate
the anticipatory muscle activities to control for the interaction torques generated at the shoulder,
in comparison to both the less-affected side of chronic stroke individuals and control participants.
The more-affected side exhibits a significant delay in the onset of shoulder muscle activities as
suggested by the time lag differences observed in the cross-correlation analysis when compared to
the less-affected side and the control participants. Interestingly, the less-affected side demonstrates
a more predictive pattern of muscle activation compared to control participants. Furthermore, we
tested whether a reduced ability to modulate anticipatory muscle activities was linked to trajectory
deviations. For the more-affected side, we discovered a correlation between the absolute trajectory
deviation in planar reaching and the cross-correlation value at the shoulder.
It is important to highlight that the observed correlation specifically applies to the absolute initial
trajectory deviation. It can be speculated that individuals who do not exhibit signs of compensation
for interaction torque may demonstrate two potential movement patterns. Some individuals may
opt to decompose their movements, resulting in positive deviations for contralateral targets (if
increased stiffness at the elbow). On the other hand, the simulations conducted in Chapter 2, show
that moving without compensating for interaction torques, and without such decomposition, can
lead to either positive or negative deviations. Moreover, the magnitude of these deviations is
54

expected to be greater in cases where there are greater deficits in compensation for interaction
torques. Thus, overall, we expect a greater deviation in absolute value for individuals with less
ability to compensate for interaction torques, either as a direct consequence of the movement or as
a result of compensation.
Motor commands can be generated by feedback control, feedforward control, or a combination of
both (Ghez et al., 1990; Polit & Bizzi, 1979; Schweighofer, et al., 1998; Vercher et al., 2003).
Feedback control, however, is limited by long delays, resulting in poor compensation of interaction
torques during fast arm movements

(Kurtzer et al., 2008; Schweighofer, et al., 1998). In contrast,
feedforward control is not affected by loop delays and operates quickly. In novel dynamical
environments, or following CNS lesions, motor commands are followed by motor errors
(Shadmehr & Mussa-Ivaldi, 1994; Smith & Shadmehr, 2005). These errors induce changes in
subsequent motor commands, promoting the update of the feedforward controllers via cerebellar
processes (Kawato et al., 1987; Shadmehr & Mussa-Ivaldi, 1994; Wolpert et al., 1995). Not
surprisingly, it was observed that severe cerebellar lesions can disrupt the control of interaction
torques and the adaptation to new dynamical environments (Bastian et al., 1996; Martin et al.,
1996; Smith & Shadmehr, 2005).
Previous findings have demonstrated a link between the disruption of cerebellar inputs by a stroke
and motor recovery (Guder et al., 2020; Schulz et al., 2017; Soulard et al., 2020). Disruption of
the descending cortico-ponto-cerebellar tract (CPCT) by a stroke can lead to “cerebellar
diaschisis” contralateral to the lesion (Kim et al., 2005; Pantano et al., 1986), in the form of atrophy
and lowered neuronal activity (Fan et al., 2013; Gold & Lauritzen, 2002). In addition, a stroke can
also damage ascending cerebello-cortical fibers, notably the dentato-thalamo-cortical tract
(DTCT), which projects contralaterally (Bostan et al., 2013; Förster et al., 2014). Therefore,
55

cortico-cerebellar deficit after a stroke can impair the critical loop involved in updating the
feedforward controllers, therefore disrupting the control for interaction torques. Nonetheless, in
most patients with supratentorial stroke, the cerebellum shows at least some residual activity and
serves as an important node in the motor network for recovery (Park et al., 2011; Várkuti et al.,
2013; Wang et al., 2010). If the cortico-cerebellar is sufficiently spared, it could contribute to
relearning the feedforward control from large errors (Patton et al., 2006).
Proprioception plays a crucial role in the control of movements. The disruption of peripheral
sensory inputs can significantly impair the control of interaction torques in multi-joint movements
(Sainburg et al., 1993, 1995). Similarly, central proprioception deficits following a stroke can
significantly impair UE motor function and performance (Meyer et al., 2014; Vidoni & Boyd,
2009). Central proprioception deficit has also been linked to deficits in motor learning but does
not seem to interfere with learned skills performance (Pavlides et al., 1993; Vidoni et al., 2010).
Previous findings have established a link between changes in excitability in the sensory cortex and
the excitability of the primary motor cortex (Hamdy et al., 1998).
Rapid feedback correction is believed to be mediated through transcortical pathways involving the
primary sensory cortex and the primary motor cortex. (Cheney & Fetz, 1984; Evarts & Tanji, 1976;
Scott et al., 2015). Therefore, deficits in proprioception integration can impair feedback control.
However, the update of the feedforward controller is believed to involve the use of the motor
command from the feedback controller (Kawato, 1999; Wolpert et al., 1995). Consequently,
limitations in accessing and integrating proprioceptive information could also prevent the update
of the feedforward controller (Rizzolatti & Luppino, 2001; Shadmehr & Krakauer, 2008). While
we excluded chronic stroke individuals with severe central proprioception deficits from our cohort,
it is important to note that some participants presented limited lesions in the somatosensory cortex.
56

Therefore, we should not rule out central proprioception deficits as an alternative explanation for
deficits in controlling interaction torques.
An important characteristic of interaction torques control is the timing of muscle activity, where
the muscles involved in stabilizing the adjacent limb segments precede the activity of the prime
mover muscles (Gribble & Ostry, 1999). In our study, we found that this temporal relationship was
disrupted, yet not in the same direction, for both the more and the less-affected sides. The early
onset of muscle activity involved in stabilizing the shoulder is comparable to the anticipatory
muscle onset involved in postural adjustment (Cordo & Nashner, 1982). Previous studies have
demonstrated that stroke individuals exhibit delayed activation of trunk activation while lifting
their arms (Dickstein et al., 2004; McCombe Waller et al., 2016; Pereira et al., 2014). The precise
pathway involved in anticipatory postural responses is not fully understood but likely involves the
interplay of corticospinal pathways, cerebellar structures, and brainstem nuclei (Thach, 1998).
The reticular formation, which received inputs from both the cerebellum and the cortex, appears
to be a potential structure that can explain the differences in timing. The cortico-reticular
projections have been studied in stroke individuals, revealing an increase in contralesional
reticulospinal tract integrity (Karbasforoushan et al., 2019; Soulard et al., 2020). The excitatory
brainstem projections to the lower motor neurons are mediated by monoamine transmitters,
strongly influencing the excitability of the pool of motor neurons and promoting self-sustained
firing (Heckman et al., 2005). Therefore, self-sustained firing, generated by persistent inward
current from dysregulated brainstem nuclei projections tract (Li et al., 2019) could explain changes
in the excitability state of the pool of lower motor neurons and variation in the timing of muscle
activation. However, the evidence for such a mechanism in chronic stroke individuals remains
inconsistent (Burke et al., 2013; McPherson et al., 2008; Mottram et al., 2009).
57

In addition, following a stroke, chronic disuse reduced voluntary muscle recruitment and relative
immobilization leads to important plastic rearrangement at the musculoskeletal level (Gracies,
2005). These structural changes in the muscles involve a switch of Myosin heavy chain (MHC)
muscle fibers composition. Typically, older adults have a higher proportion of slow-twitch fibers
(MHC type I), which are resistant to fatigue (Hafer-Macko et al., 2008). However, following a
stroke, decreased physical activity results in a reduction in muscle cross-sectional area and an
increase in the proportion of fast-twitch fibers (MHC type IIx) (De Deyne et al., 2004; Frontera et
al., 1997; Ryan et al., 2000). According to the size principles, the change in the muscle fiber
composition could influence the pattern of motor unit recruitment observed in muscles on the
more-affected side (Frontera et al., 1997; Hu et al., 2015), thus impacting the muscle fibers
contraction time (Fuglevand et al., 1999).
Finally, we note that because our movements were constrained at the elbow joint, a potential deficit
in control of interaction torques at the shoulder did not affect the movement outcome. However,
in natural movements that are not constrained to pure elbow rotation, the muscles should
consistently compensate for interaction torques at the shoulder, which can influence the overall
movement. From an efficiency standpoint, these “unnecessary” muscle activations may be sub-
optimal. Previous research has demonstrated that it takes approximately 1000 constrained elbow
movements for this activation to dampen (Maeda et al., 2018). This suggests that the CNS
compensates for torques that would be present in daily activities, indicating that our experimental
design captures an accurate representation of the feedforward motor command.
Because supratentorial stroke lead to weakness and poor motor control, patients rely on slow and
variable feedback control to complete movements. Reaching movements in particular are often
slow, curved, not smooth, and variable (Cirstea et al., 2003; Kamper et al., 2002; McCrea & Eng,
58

2005). Coordinated arm movements to contralateral targets are in particular difficult, possibly
because of a reduced ability to account for interaction torques (Beer et al., 2000, 2004; Levin,
1996). In the following study, we investigate the effect of fast movement reaching in retraining
the feedforward controller and the control of interaction torques.

59

Chapter 4: Effect of fast and accuracy motor training in arm
reaching in chronic stroke
Introduction
Approximately 30% of chronic stroke individuals are unable to move their upper arm, and around
40% show limited recovery, restricting their arm usage to simple daily life activities like holding
a bag or stabilizing an object (Álvarez et al., 2017; Lum et al., 2009). Arm-reaching movements
are particularly affected by stroke and strongly correlate with patients’ overall impairment levels
(Kamper et al., 2002; van Dokkum et al., 2014).
Despite the prevalence of Upper Extremity (UE) limitations in chronic stroke individuals, the
specific training parameters required for effective rehabilitation of UE function are unknown. In
particular, multiple recent Randomized Clinical Trials (RCTs) targeting UE functional capability
have failed to demonstrate the superiority of particular rehabilitation interventions over standard
care (Krakauer et al., 2021; Lang et al., 2016; Rodgers et al., 2019; Winstein et al., 2016). A
potential reason for the lack of significant differences between these novel interventions and
standard care could be that movements were performed at an insufficient speed.
Speed training holds promise for retraining Upper Extremity (UE) movements in chronic stroke
individuals. This is particularly relevant considering that stroke survivors often rely on slow and
variable feedback mechanisms to execute movements and exhibit deficits in movement planning
compared to neuro-typical individuals (McCrea & Eng, 2005; Stewart et al., 2014a, 2014b). As a
result, their reaching movements are characterized by reduced speed, trajectory deviations,
prolonged deceleration phase, and multiple peaks in the velocity profiles (Murphy et al., 2011;
60

Roby-Brami et al., 2003). Coordinated UE reaching movements to contralateral targets are in
particular difficult, potentially due to reduced ability to account for interaction torques (Beer et al.,
2000; Levin, 1996). Indeed, faster movement generates a higher amount of interaction torques,
and accumulating evidence suggests that some chronic stroke individuals present deficits in
controlling these torques (Beer et al., 2000; Laczko et al., 2017; Raj et al., 2020). However,
producing fast, smooth, and straight-reaching movements requires adequate compensation for
these interaction torques generated (Beer et al., 2000; Lackner & Dizio, 1994; Pigeon et al., 2003;
Sainburg et al., 1999). As fast feedback control is hindered by long delays in the nervous system,
the compensation for these interaction torques must occur in a feedforward and predictive manner
(Schweighofer et al., 1998).
Therefore, learning to move fast and accurately requires re-calibrating the feedforward controller.
In novel environments, or following CNS lesions, motor commands are followed by motor errors.
These errors induce changes in subsequent motor commands, indicating that the CNS updates the
feedforward controller (Kawato et al., 1987; Shadmehr & Mussa-Ivaldi, 1994; Wolpert et al.,
1995). According to the theory of “feedback error learning”, the feedback controller
simultaneously controls movements and provides error signals to re-calibrate the feedforward
controller (Kawato et al., 1987; Kitazawa et al., 1998; Shidara et al., 1993). Fast movements
generate large feedback errors, generating large error signals, therefore, promoting the
improvement of the feedforward controller. In contrast, slow accurate movements generate small
errors and have little effect in improving the feedforward controller. Because relearning lost motor
functions in chronic stroke parallels motor learning in neuro-typical participants (Kitago &
Krakauer, 2013), this theory predicts that fast movements training is most effective in restoring
feedforward control of UE movements post-stroke.
61

Two studies with chronic stroke participants have suggested that indeed, speed training is effective
at improving arm movement performance and UE function in individuals with chronic stroke and
mild to moderate impairments (Kantak et al., 2017; Park et al., 2016). In Park et al. (2016) (Park
et al., 2016), participants performed two sessions of unassisted reach training with their paretic
arm, with 600 movements per session. Movements were followed by feedback that continuously
promoted fast movements. Training gains generalized over a large workspace, with significant and
durable (one-month) improvements in movement time and smoothness, notably to contralateral
targets. Training also durably improved Box and Block test scores (23% gains one month
following the intervention). In Kantak et al. (2017) (Kantak et al., 2017), participants practiced a
complex motor skill task over two consecutive days, with a total of 300 trials. The task consisted
of keeping the paretic hand within a track, by performing a sequence of elbow and shoulder
rotations. Here also, fast movements were rewarded by feedback. Training led to large and durable
(one-month) improvements both in the speed and accuracy trade-off for this task and in
performance on an unpracticed reaching task, with improvements in velocity, smoothness, time-
to-peak acceleration, and scaling of peak acceleration to target distance. These studies thus suggest
that, in chronic stroke, intensive speed training can lead to large improvements in UE movement
performance compatible with improved feedforward UE control.
Despite showing promising results, these two studies did not include a control group. It is therefore
unclear whether the improvements were truly due to the fast movements during training or to the
relatively large dose of movements. Thus, an RCT with two groups that receive the same dose of
training, one in a fast speed condition, and the other in a slow speed condition, is needed. Here,
using training tracks similar to that in the Kantak et al study (Kantak et al., 2017), we perform such
a RCT. We compared the change in reaching performance before and after four sessions of training
62

scheduled within a week, in two conditions: a speed bias condition and an accuracy bias condition,
in which we only manipulated the track width.
We hypothesized that following the speed bias training intervention, participants will generate
faster and straighter movements on an unpracticed reaching transfer test. In addition, we
hypothesized that, on a speed and accuracy generalization test, it will take less time to reach targets
with larger difficulty indices. Finally, we hypothesized that speed training will lead to improved
feedforward control in fast single-joint movements, as shown by an improvement in the scaling of
the first peak of acceleration as a function of target distances. The amplitude of the first peak of
acceleration occurring early in the movement has been shown to reflect feedforward control
strategies (Gordon & Ghez, 1987; Sainburg & Schaefer, 2004).
63

ID Sex Age
More -
Affected
Side
Time since
stroke
UE FM
score
ARAT
score
Group
1 F 52 R 2.86 47 51 S
2 M 62 L 0.9 50 54 A
3 F 46 L 0.51 50 53 S
4 F 69.1 R 1.64 55 55 A
5 M 60.4 L 0.63 53 55 S
7 M 48.4 R 1.32 27 32 S
8 M 56.6 L 2.63 48 52 S
9 F 39.6 L 2.63 45 36 A
10 M 71.2 L 3.04 53 55 A
11 F 81.3 L 2.54 48 55 A
12 M 54.5 R 0.7 36 28 A
14 F 48.2 L 0.98 28 4 S
15 F 61.9 R 0.82 29 6 A
16 F 49.3 R 9.12 34 21 S
17 M 79.1 L 0.82 55 55 S
18 F 82.3 L 3.84 52 55 A
19 F 54.1 L 2.43 57 54 A
20 F 69.1 L 1.76 55 55 S
21 F 59.1 R 4.03 26 17 S
22 M 78.7 R 21.03 40 41 A
23 M 62.5 R 2.26 44 26 A
24 F 67.5 L 0.93 41 44 S
26 F 51.7 L 2.45 49 49 A
27 M 47.1 R 0.5 36 16 S
29 M 83.5 R 0.53 44 44 S
30 M 62.9 R 1.11 37 40 A
31 F 79.5 R 3.69 30 16 S
33 M 55.4 R 0.73 38 16 S
35 M 67.8 L 1.14 46 41 A
36 M 69.1 L 4 40 40 A
37 F 39.9 L 3.29 52 48 S
38 M 56.9 L 0.93 45 51 A
39 M 47.3 R 0.65 49 47 S
40 M 34.4 R 1.12 31 16 S
41 M 66 R 0.74 32 45 A
42 M 35.1 R 0.52 44 48 S

mean +
SE
16
females
20
males
59.7 +/-
2.25
18 Right
18 Left
2.5 +/- 0.6
42.94 +/-
1.52
39.47 +/-
2.65
17
Accuracy
19 Speed
Table 4.1: Participant clinical and demographic information
Abbreviation: F: Female, M: Male, SE: Standard error, S: Speed group, A: Accuracy group
64

In addition, we expect the speed
bias training group to show larger
improvements in the speed and
accuracy tradeoff. That is, on a
Fitts like task, we expect
participants in this group to show
a higher decrease in the slope of
the linear relationship between
the movement time and the index
of difficulty.
Methods
Population
We included a total of thirty-six
chronic stroke individuals (16
Females, 59.7+-2.25 years old,
time since stroke 2.5+-0.6,
UEMF 44+-2.1) suffering from
mild to moderate impairments
(Table 1). To be included in the
study, stroke participants had to
meet the following criteria: had a
hemorrhagic or ischemic stroke
that did not directly affect the cerebellum more than 180 days ago, had no additional neurological
A
Figure 4.1: Examples of hand path trajectory for the
speed and accuracy bias training conditions. The blue
line represents the endpoint trajectory (first trial) for a
representative participant in the Speed group (panel A,
participant 3), and for a representative participant in the
Accuracy group (Panel B Participant 36).
B
65

diagnoses, had no contraindication to MRI scanning, had mild to moderate upper-extremity
impairments, as measured by the Upper Extremity Fugl-Meyer (UE-FM) scale, ranging from 21-
57, and they were able to slide their arm over a 25cm distance without assistance with trunk
constrained within 5 seconds. Participants were excluded if they were unable to follow a 2-step
command, had signs of hemispatial neglect, which was measured by more than 4% of lines left
uncrossed during the Albert's line test, or had severe pain or an upper-extremity orthopedic
disorder. All participants provided informed consent for participation in the study, which was
approved by the Internal Review Board of Casa Colina Hospital.
Study Design
Participants visited the laboratory nine times over a period of six weeks. The initial visit involved
assessing the participants to determine their eligibility based on inclusion and exclusion criteria.
We performed baseline assessments on the less-affected side during the second visit and the more-
affected side during the third visit. An MRI scan was conducted during either the second or third
visit to confirm that the participants did not have cerebellar lesions directly resulting from the
stroke. Following the baseline assessment, participants underwent four training sessions within
the next 10 days. Subsequently, three days, and one month after the end of the training protocol,
participants came back for a third and fourth testing visit.
Each testing visit consisted of three assessments, where participants performed two-dimensional
planar reaching movements in Assessments 1 and 2, and fast single-joint elbow flexions and
extensions, in Assessment 3. During the training days, participants performed Assessment 1 and
the training intervention.
66

To improve the comparison between the groups, participants were randomly assigned to one of
the groups based on age, sex, time since stroke, stroke lesion side, and more-affected side
movement time from Assessment 1.
Behavioral assessments
For the training, the 3-target transfer task (Assessment 1), and the speed and accuracy task
(Assessment 2), participants sat in an adjustable chair in front of a table with a restraining belt to
minimize compensatory trunk motion during reaching movements (Figure 3.1B). The height of
the chair was adjusted to align the tabletop to the xiphoid process. Wrist movements were
restrained via a wrist brace and finger movements with a splint. Magnetic sensors (3D Guidance
Model 800 Sensor) were placed on top of the index fingernail, the lateral epicondyle of the elbow,
the acromion, and the manubrium of the sternum. Sensor data were recorded via the data
acquisition system (3D Guidance TrackStar) programmed to sample position at 255Hz.
Assessment 1: 3-target reaching transfer task
Participants were instructed to move their index finger from the home position to a target by sliding
their hand and lower arm on the tabletop as rapidly and accurately as possible. To reduce friction,
the upper extremity was covered with a tubular bandage. Following a familiarization session of 32
reaches, participants were instructed to perform 10 reaches to each of the 3 targets, shown in
pseudo-random order. The targets (black circle of 4 cm diameter) were located at 45°, 90°, and
135° on an arc of 20 cm radius centered on the starting position (green circle 5cm diameter),
located approximately 20 cm from the participant’s sternum (Figure 3.1 B). After a random wait
period lasting between 0.5 and 2.5 seconds, one of the targets was displayed and an auditory cue
was played signaling the start of the movement. To ensure that the participants completely stopped
at the target, the target initially turned orange once the finger entered the target area and then turned
67

green after 0.5s, accompanied by a pleasant sound, signaling the return to the home position. To
ensure that participants slid their hand and lower arm on the table, the trial started and ended only
if the finger was less than 4 cm above the tabletop.
Assessment 2: speed and accuracy trade-off task
Using the same experimental setup, participants were presented with a new set of targets located
at 90°from the start position. These targets were placed at three different distances: 10, 20, and
25cm, Additionally, two different target sizes were used diameters of 4 and 8cm (McCrea & Eng,
2005). Participants were instructed to reach as rapidly and as accurately as possible six times to
each of the targets presented in a pseudo-random order.
Assessment 3: fast single-joint transfer task
Thirty-two participants participated in this portion of the experiment (due to technical difficulties).
Participants sat in a wheelchair with their trunks constrained by a 4-point seat belt and placed as
close as possible to a specially designed arm apparatus that constrain arm movement to allow only
elbow flexion/extension (Figure 3.1A). The participant held a handle and placed their forearm
(secured via Velcro straps) in a brace in a neutral pronation/supination position. The position of
the handle was adjusted so that the axis of rotation of the handle was in line with the center of
rotation of the elbow (under the medial epicondyle). The apparatus height was adjusted so the hand
was approximately 5cm below the acromion and the width such that the arm was approximately
at 60° of horizontal shoulder adduction (0° corresponds to the upper arm in the coronal plane). A
potentiometer (6639S-1-102, Bourns Inc.) attached to the axis of rotation measured angular
position. A monitor was positioned in front of the participant. At each trial, the participants were
instructed to generate fast and accurate elbow flexion or extension movements of 30, 50, or 70°
amplitudes by rotating a 10 cm line displayed on the screen between a green circle representing
68

the start position, and a white circle representing a target. The starting positions for extension were
respectively 115, 125, and 135° of elbow flexion, and for flexion 75, 65, and 55° of elbow flexion
(0° corresponds to the arm fully extended). The sizes of the targets were increased as the
amplitudes increased (diameter = 3.4, 5.8, 8 cm). To ensure fast movements, and therefore large
interaction torques at the shoulder, we used a two-phase approach. In the first phase, participants
completed 10 flexions and extensions for each of the three amplitudes (60 trials) with the
instructions to move as fast and accurately as possible. If the participants reached the target and
the cursor stayed in the target for 0.2s, the target turned yellow and the movement time was
displayed; if the participants did not reach the target (or did not stay for 0.2 sec in the target), a
small red disk showed the final position and “outside the target” was displayed. Then, in the second
phase, the participants were instructed to perform fast movements with times smaller than a
threshold, determined as the 20th percentile of the movement times for the 10 flexion or extension
blocks in the first phase. If movements were too fast (therefore too difficult for the participants to
reach the time cutoff), we set a time cutoff at 0.1s, 0.12s, and 0.15 for the small, medium, and large
amplitude (the movement time was computed by the time the line representing the arm left the
home position and the first time it reached and stayed in the target). Participants completed a
minimum of 10 flexions and extensions for each of the three amplitude (60 trials) but were
instructed that movements would be repeated up to four times each if they were too slow or outside
the target. The same feedback as in the first phase was provided, except that if the target was
reached with a movement time above the time threshold, the target turned orange, and “too slow”
with the actual movement time was displayed. We analyzed data only from the second block
(including “too slow” movements).
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Training protocol
For the training intervention, participants remained in the same setup as in Assessments 1 and 2
except that we only kept the magnetic sensor attached to the fingernail. Participants were required
to move the index finger through a complex track that was 5cm in width (Kantak et al., 2017). In
the accuracy bias group, the width of the track was reduced to one-quarter of the original width.
Participants navigated through a total of eight different complex tracks (four original tracks flipped
along the y-axis) Figure 4.1. Each training session consisted of eight blocks where one track was
repeated for 65 trials, for a total of 520 trials per day. The blocks were presented in a pseudo-
random order each day. On the first day, participants began the training following a practice block
of 20 trials, which included all eight possible tracks presented in a pseudo-random order.
Participants were instructed to slide their hand and lower arm on the tabletop, moving their index
finger from the start position to the finish box as rapidly and accurately as possible. The start and
the finish boxes were represented by a square with a 5cm width. To minimize friction, the upper
extremity was covered with a tubular bandage. The length of the tracks was adjusted to correspond
to 85% of the more-affected active arm reach.
After a random wait period lasting between 0.5 and 2.5 seconds, one of the tracks was displayed
and an auditory cue was played signaling the start of the movement. To ensure that the participants
Figure 4.2: Illustration of feedback received by the participant during training. If the
trial was successful, the selection of the visuo-auditory feedback was based on the trial
performance compared the percentiles of the performance on the last 20 successful trials.
Great!
Orange text, 3 points
3 reward sounds
Excellent!
Green text, 4 points
4 reward sounds
80
th
percentile 60
th
percentile 40
th
percentile 20
th
percentile
Very Good !
Yellow text, 2 points
2 reward sounds
Almost, hang in there
0 point
0 reward sound
Good job
Black text,1 point
1 reward sound
70

completely stopped at the target, an auditory cue sound was played only after they stayed 0.5
seconds in the finish box. After each trial, various feedback was provided on the table, and then
the starting square appeared, signaling the return to the home position.
Feedback
After each trial, the trajectory of the finger was projected on top of the track (Figure 4.1). In
addition, the real-time trace of the trajectory was displayed for the accuracy bias group.
Participants received feedback based on their performance, which included five visuo-auditory
feedback (Figure 4.2). For the speed bias group, performance was based on the movement time,
while for the accuracy bias group, it was based on the percentage of samples within the boundary
of the track (in-track percentage). Movement time was computed from the moment the finger left
the starting square until it first reached the finish square and completely stopped. The in-track
percentage was determined by dividing the total number of samples within the track by the total
number of samples during the trial, with the negative in-track percentage used for comparison.
After each trial, except the familiarization period, the feedback was provided based on a
comparison of trial performance with the last 20 successfully completed trials. For example, if the
performance was better than the 20th percentile performance of the last 20 trials, participants
received 4 points, accompanied by four rewarding coin sounds, and with a message “Excellent!”
in green (detailed in Figure 4.2). The points were added to the total score of the session displayed
on the screen. To prevent any group from solely prioritizing speed or accuracy, a trial was
considered successful if it was completed within 10sec and with more than 85% in-track
percentage (applicable to the speed bias group only). If a participant failed to meet this criteria a
message indicating to stay within the boundary of the track was displayed. If a participant failed 5
times in a row, the experimenter reminded the participant to follow the instructions.
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Both groups were instructed to go as fast and as accurately as possible. However, the speed bias
group was informed that their score was based on the movement time, while the accuracy bias
group’s score was based on the ability to stay within the boundary of the track.
Clinical assessment
Certified and experienced therapists with 1 year or more of experience measured the UE-FM and
ARAT. The UE-FM was assessed during the screening visit, and the ARAT was assessed during
the second visit.
Data processing and analyses
All data processing, analyses, and experiments were performed using MATLAB.
Assessment 1: 3-target reaching transfer task
Movement time
Movement time was calculated between the time at which the tangential velocity first exceeded
5% peak velocity and the end of the movement as the time at which it fell below the 5% peak
velocity.
Trajectory deviation
The maximum deviation from the straight trajectory was calculated by finding the largest
orthogonal projection from the straight line onto the trajectory (Levin, 1996). Because the targets
were large, the straight line corresponded to the line between the endpoint location at movement
onset and movement end, calculated relative to the 5% tangential peak velocity (Park et al., 2016).
Movement smoothness
The movement smoothness was assessed by calculating the number of peaks in the tangential
velocity profiles (Park et al., 2016). The MATLAB function (findpeaks) was used between the
start and the end of the moment to calculate the number of peaks.
72

Assessment 2: speed and accuracy trade-off task
Fitts’ law (Fitts, 1954) describes the speed and accuracy trade-off of repeated movements as a
linear relationship between movement time and the log ratio of the movement distance and
movement error tolerance:
For the purpose of this study, we defined MT as the movement time, a as the intercept, b as the
slope, D as the distance from the start position, and W as the diameter of the target (McCrea &
Eng, 2005). The ratio of the distance over the width is also called the index of difficulty. For this
experiment we were interested in the final adjustments, the movement time was calculated between
the time the participant left the start position and the time the participant reach the target (McCrea
& Eng, 2005).
Assessment 3: fast single-joint transfer task
Angular rotation data from the potentiometer were low-pass filtered twice (8Hz, 6th order filter
Butterworth) and then derived to obtain angular velocity and acceleration. The beginning of the
movement was defined as the time when the angular velocity first exceeded 5% peak velocity
while the end of the movement was determined as the time when it fell below the 5% peak velocity.
The time-to-peak velocity corresponded to the duration between the movement onset and the time
of the first absolute peak velocity (Sainburg & Schaefer, 2004). The peak acceleration value
represented the maximum absolute peak acceleration occurring between the movement onset and
the peak velocity.
Statistical analyses
We conducted several mixed-effect models to examine the impact of training on various variables
of interest. We were interested in the effect of training on, movement time, absolute trajectory
𝑀𝑇 = 𝑎 + 𝑏 𝑙𝑜𝑔 2
(
2𝐷 𝑊 ) (1)

73

deviation, movement smoothness in Assessment 1, the linear relationship between movement time
and index of difficulty (Fitts’ slope) in Assessment 2, and peak acceleration scaling to target
distances in Assessment 3.
In separate models, movement time, absolute trajectory deviation, and inter-joint correlation were
the dependent variables. Each model included the testing day and the group as covariates, along
with an interaction term between the latter two. The participants’ ID was treated as a random effect.
Each model included the testing day and the group as covariates, along with their interaction. The
participants’ ID was treated as a random effect for the intercept in all models. We estimated the
Fitts’s slope for each participant on each testing day via a mixed effect model of the movement
time as a function of the index of difficulty of the target, with participants’ ID as a random effect
for the slope and the intercept in all models.
Results
Assessment 1: 3-target reaching transfer task
At baseline, there were no significant differences between the two groups for the MT (p>0.1), and
absolute trajectory deviation (p>0.2). Overall, both groups show a decrease in MT three days
(-0.18 sec, p<0.001) and one month (-0.054 sec, p<0.001) following the intervention (Figure
4.3A). However, the speed bias training intervention resulted in a significantly greater reduction
in MT (-0.15 sec, p<0.001), compared to the accuracy bias training intervention at three days but
no significant differences were present at one month following the intervention.
Similarly, both groups displayed a significant reduction in absolute trajectory deviation three days
(-0.31 cm, p<0.001) and one month (-0.43 cm, p<0.001) following the intervention (Figure 4.3B).
At one month following the intervention, there was a larger reduction in trajectory deviation
74

observed for the speed bias intervention compared to the accuracy bias intervention (-0.24 cm,
p<0.05).
Both groups showed improvement in movement smoothness, as indicated by a decrease in the
number of peaks at three days (-0.47, p<0.001), and one month (-0.27, p<0.001) following the
intervention. However, no significant differences between the two groups were observed in terms
of movement smoothness.
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Figure 4.3: Evolution of movement time (A) and deviation from the straight line (C) for
reaches to target located at 45, 90, and 135 deg for the two types of intervention. Each bar
corresponds to the group mean for one target. The background color represents either the
baseline (red), 3 days post (purple), or 1 month (green) following intervention. C and D
represent the change between baselines. (*) p<0.05, (**) p<0.01, (***) p<0.001
A
C D
B
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Assessment 2: speed and accuracy trade-off task
For both groups, the index of difficulty had a significant effect on movement time, indicating that
greater difficulty levels resulted in longer movement times. However, at baseline, we did not
observe any differences between the two groups (Figure 4.4A). In the speed bias training group,
we observed a significant decrease in the slope of the relationship between the index of difficulty
and movement time at both three days (-0.1, p<0.001) and one month following the intervention
(-0.07, p<0.001) (Figure 4.5A). Additionally, we observed a significant difference between the
speed and the accuracy bias interventions at three days following intervention (-0.07, p<0.05)
(Figure 4.5B). However, this difference was not significant at one month following the
intervention.
Assessment 3: fast single-joint task
Both groups demonstrated a significant effect of target distances on peak acceleration, indicating
that the scaling of the peak acceleration varied based on the distance to the target. Note, that at
baseline the accuracy bias group exhibited a significantly higher scaling of the peak acceleration
to target distances compared to the speed bias group (271, p<0.01) (Figure 4.6A). For both group,
there were no significant changes in peak acceleration scaling to the target distance at three days
or one month following intervention (Figure 4.6B). However, we observed a significant effect of
the speed bias intervention compared to the accuracy bias intervention at three days following
intervention (278, p<0.05) and at one month following intervention (304, p<0.05) (Figure 4.6C).
77

Figure 4.4: Evolution of the linear relationship between movement time and index of
difficulty for each group for experiment 2. On each graph is plotted the fixed effect (black),
the individual effect for each participant (one color), and its associated individual trials. We
also indicated the R squared of the model and the p-value of the fixed effect. On the first column
is plotted the speed bias training group and on the second column the accuracy bias training
group. On the first row is the relationship at baseline (A), three days following intervention
(B), and one month after the intervention (C).
B: 3 days
A: Baseline
C: 1 month
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Discussion
The primary findings of this study are that four sessions of speed or accuracy training with 520
movements per sessionled to significantly different effects on movement outcomes. When tested
on a 3-target generalization reaching test, participants in both groups showed significant
improvements in movement time, movement smoothness, and trajectory straightness, as measured
by deviation from the straight line. However, the speed group showed a significantly larger
decrease in movement time at the three-day post-test and a significantly larger decrease in
trajectory deviation one month following the intervention. When tested on the speed and accuracy
Figure 4.5: Slope evolution of the linear relationship between the movement time and the
index of difficulty for experiment 2. On the graph B, we plotted the change in slope relative
to baseline. (*) p<0.05, (**) p<0.01, (***), p<0.001
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tests with 3 targets distance and 2 diameters, speed training was shown to improve the speed-
accuracy tradeoff, as suggested by a larger decrease of the Fitt’s slope, both at three days and one
month following the intervention.
Taken together, these results suggest that speed bias training improves the skill of reaching in
chronic stroke individuals with mild to moderate impairments. This improvement is consistent
with a shift towards an increased reliance on feedforward control over feedback control. Feedback
and feedforward strategies are used to control reaching movements (Polit & Bizzi, 1979; Vercher
et al., 2003). Following a stroke, reaching movements are marked by multiple peaks in the velocity
profiles and an extended movement deceleration phase (Murphy et al., 2011; Roby-Brami et al.,
2003) suggesting a stronger reliance on feedback controllers (Trombly, 1992). In our study, where
precise reaching adjustments were required in reaching movements, movement time reflected the
quality of both the feedforward command and the subsequent feedback corrections (Fitts, 1954;
Meyer et al., 1988). It has been proposed that an increase in Fitt’s slope can be interpreted as a
shift from feedforward to feedback control strategies at a reduced level of the index of difficulty
(McCrea & Eng, 2005).
Furthermore, simulations in Chapter 2 demonstrated that a reduced deviation from the straight line
indicates a feedforward command that better accounts for the intersegmental dynamics. Therefore,
the significant decrease in trajectory deviation observed in the speed group at one month also
suggests an improvement in the feedforward controller.
80

Figure 4.6: Evolution of the peak angular acceleration scaling to target distances. Peak
angular acceleration at the elbow to the (A) for reaches to target located 35, 55, and 75 deg of
elbow excursion for the two types of intervention (experiment 3). Each bar correspond to the group
mean for one target. The background color represent either the baseline (red), 3days post (purple) or
1month (green) following intervention. B represents the evolution of the slope between peak angular
acceleration to the target distance, C represents the change in slope following intervention relative to
baseline. (*) p <0.05, (**) p <0.01, (***), p < 0.001
A
B
C
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We note, however, that we only found limited evidence that speed training improved the peak
acceleration scaling to the target distance in a fast elbow movements transfer task: there was a
between-group difference but no significant within-group changes. These results may be due to
the large difference in baseline scaling of acceleration between the two groups, with an already
large modulation for the accuracy group at baseline. In addition, since the fast single-joint transfer
task requires multiple fast elbow movements (see Chapter 3) motor training probably occurred
during the assessment at baseline, diminishing the differential effect of training. Finally, there may
be large individual differences in who benefits from speed training.
Thus, future studies are needed to understand which patient post-stroke can benefit the most from
speed training. The recovery of the UE following a stroke is influenced by various factors including
the lesion load, lesion location (Shelton & Reding, 2001; Zhu et al., 2010), and proprioception
deficits (Meyer et al., 2014; Vidoni & Boyd, 2009). Notably, lesions affecting the cortico-spinal
tract have been strongly associated with motor impairments (Bigourdan et al., 2016; Feng et al.,
2015; Stinear et al., 2007). Furthermore, the cortico-cerebellar tract has been implicated in motor
recovery as well (Guder et al., 2020; Schulz et al., 2017). It is worth mentioning that in many
patients with supratentorial stroke, the cerebellum may retain residual activity, playing a
significant role in motor recovery (Park et al., 2011; Várkuti et al., 2013; Wang et al., 2010).
However, if the corticospinal and cortico-cerebellar tracts were not sufficiently spared, or the
proprioception deficits were too important, these deficits may have prevented participants to
retrain their feedforward controllers.
Although our results show improvements in arm reaching performance due to speed training, it is
possible that even higher speeds would be even more effective. During training, participants
received constant feedback from their hands and index finger sliding over the track. Although the
82

exact location of the cursor was not displayed, this constant feedback may have limited the
promotion of feedforward controllers during the training. It is possible that removing visual
feedback by hiding the hand could have been beneficial. This would have increased both speed
and errors (Woodworth, 1899), which are essential components for promoting the learning of the
feedforward controller, including control for interaction torques.
In conclusion, our study shows that not all repetitions are equal in rehabilitation. Our results
suggest that slow movements are not as effective in improving arm performance. In contrast, the
same dose of movements, but performed at high speed, improves movement time and the speed
and accuracy trade-off, a signature of improvement in reaching skills. This study has the potential
for a high impact on upper-extremity stroke rehabilitation, as therapists should encourage their
patients to move as fast as possible, even at the detriment of high accuracy. This strategy can easily
be implemented in a therapy setting and appears to be an ideal approach for enhancing upper-
extremity rehabilitation without incurring additional costs.

83

Chapter 5: Conclusion
Following a sensory-motor stroke the control of the movement is severely impacted and the
underlying causes are numerous and complex. In this thesis, our focus was on investigating the
impact of interaction torques on UE multi-joint reaching movements in chronic stroke individuals.
In Chapter 2, our findings confirmed that chronic stroke individuals exhibited significant trajectory
deviations. However, these deviations did not consistently align with the direction predicted by a
deficit in control for interaction torques at the elbow as suggested in previous literature (Beer et
al., 2000). As our simulation demonstrated, deficits in control of interaction torques can give rise
to deviations in multiple directions. The simulation supports the idea that a deficit in control for
interaction torques has a significant effect on the trajectory, however, it cannot predict the
deviation into specific directions.
The inter-joint correlation analysis revealed that trajectory deviation towards the contralateral
target could also be attributed to a deficit in inter-joint coordination, which is consistent with
previous findings in the literature (Cirstea et al., 2003; Levin, 1996). The reduction in inter-joint
coordination may serve as a compensatory strategy to overcome the lack of feedforward control
for interaction torques. It has been suggested that chronic stroke individuals may exhibit
overcompensation for interaction torques (Raj et al., 2020) by increasing co-contraction and
stiffness, thereby minimizing the effect of interaction torques. Thus, movement decomposition
observed in chronic stroke individuals may represent a strategy to compensate for the inability to
effectively control interaction torques while simultaneously coordinating movements at the
shoulder and elbow joints. It leads to the idea that some chronic stroke individuals may not
84

adequately account for the control of interaction torques in their feedforward commands leading
to the development of alternative movement strategies.
In Chapter 3, we investigated the predictive control of interaction torques during fast single-joint
elbow movements. Our findings revealed that the more-affected side exhibited a diminished ability
to modulate the anticipatory muscle activities to properly control the interaction torques generated
at the shoulder compared to the less-affected side and control participants. This reduced predictive
ability to modulate anticipatory muscle activities was associated with initial trajectory deviations
observed on the more-affected side. These results suggested that the feedforward motor command
for controlling the intersegmental dynamics is impaired in chronic stroke individuals.
Consequently, chronic stroke individuals exhibit slow movement strategies relying on feedback
leading to curved, not smooth, and variable trajectories (Cirstea et al., 2003; Kamper et al., 2002;
McCrea & Eng, 2005).
It is believed that the feedforward controllers are updated through error-based learning through
cerebellum processes (Kawato et al., 1987; Shadmehr & Mussa-Ivaldi, 1994; Wolpert et al., 1995).
However, a stroke can affect the cerebellar inputs and outputs (CPCT and DTCT) (Bostan et al.,
2013; Fan et al., 2013; Förster et al., 2014; Gold & Lauritzen, 2002; Kim et al., 2005; Pantano et
al., 1986). Therefore, the link between the ability to modulate the anticipatory muscle activities
properly and the integrity of the cortico-cerebellar tracts should be explored in future studies.
Finally, in Chapter 4, we aimed to evaluate the impact of speed bias training compared to accuracy
bias training on the recovery of trajectory deviation, inter-joint coordination, and the restoration
of the feedforward control.
85

The main findings of this study were that different types of intervention had a significantly
different effect on movement outcomes. Specifically, only the speed bias training group
demonstrated a decrease in movement time at three days and a sustained decrease in absolute
trajectory deviation at one month following the intervention. Additionally, the Fitt’s slope which
has been proposed to reflect the use and quality of the feedforward controller, showed
improvement only in the speed bias training group at both three days and one month following
intervention. This suggests that the speed bias training intervention was more effective in
retraining the feedforward controller, enhancing the ability to anticipate and execute movements
accurately. Taken together, these results highlight the differential effects of speed training or
accuracy training on movement outcomes, with speed bias training showing superior results in
terms of trajectory deviation, feedforward control, and reliance on feedforward controller.
Overall, however, the gains shown in the speed group were relatively modest. It is possible that
the speed bias training group was not generating movements at a sufficient speed to effectively
train the control of interaction torques. Also, equally possible is that there is a large between-
subject variability in the re-learning of the feedforward control, for instance, due to deficits in
proprioception. To address these limitations, future experiments should consider reexamining the
speed bias training paradigm. One potential approach could involve implementing faster ballistic
movements with only knowledge of results, which would constrain stroke survivors to rely solely
on feedforward controllers to perform the task. This modified paradigm could provide a more
accurate assessment of the effectiveness of speed bias training in enhancing the control of
interaction torques.
Importantly, this relatively simple paradigm could be easily implemented in a therapy setting and
potentially boost stroke recovery: the therapist should emphasize fast movements during
86

rehabilitation even at the expense of accuracy. This speed bias training paradigm thus appears to
be an ideal method to promote UE rehabilitation without incurring additional costs.

87

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Abstract (if available)

Abstract Cerebrovascular Accident (CVA) is the leading cause of long-term disability, resulting in upper extremity (UE) impairments, activity limitation, and participation restrictions. Generating fast, smooth, and straight trajectories for multi-joint planar reaching movement requires adequate compensation for the interaction torques that arise at both proximal and distal joints. However, stroke survivors exhibit some deficits in the feedforward motor command, leading to a stronger reliance on the feedback controller. The impaired feedforward controller may be accompanied by a deficit in accounting for and controlling interaction torques that arise during multi-joint reaching movements.
First, we investigated the control of UE multiple-joint movements during a planar reaching task. Using a two-link arm model, our simulations revealed that the pattern of trajectory deviation depends on the type of deficit in control for interaction torques. Contrary to previous reports in the literature, chronic stroke individuals did not consistently exhibit deficits in the control of interaction torques at a single joint (e.g., the elbow). However, we confirmed that the absolute trajectory deviation is greater for the more-affected side in comparison to the less-affected side and the dominant side of control participants.
Then, we focused on the predictive control of interaction torques during fast single-joint elbow movements. By utilizing electromyography (EMG) and estimating torque through inverse dynamics, we examined the feedforward motor command involved in controlling interaction torques generated at the shoulder. Our findings indicated that the more-affected side demonstrates a significant delay in the onset of shoulder muscle activities and a reduced ability to modulate the anticipatory muscle activities to control for the interaction torques generated at the shoulder, in comparison to both the less-affected side and dominant side of control participants. Furthermore, the inability to compensate for the shoulder interaction torques in the more-affected side correlated with the absolute trajectory deviations in the early (feedforward) phase of planar reaching movements. We argue that the trajectory deviation may be due to either a decreased ability to compensate for interaction torques in the feedforward command or as a result of a compensatory strategy to overcome the control of interaction torques.
Finally, we evaluated the effect of four sessions of speed or accuracy training with 520 movements per session on the recovery of multi-joint reaching movements. When tested on a transfer reaching test, all groups showed a significant effect of training on movement time, trajectory deviation, and movement smoothness. However, the speed group exhibited a larger decrease in movement time at three days and a significantly larger decrease in trajectory deviation at one month following the intervention. When tested on a speed and accuracy test, the speed group showed a larger decrease of the Fitts’ slope, both at three days and at one month following the intervention.
Overall, this thesis presents a comprehensive investigation of the UE motor control deficits and potential rehabilitation strategies in multi-joint reaching movements following a stroke.

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Asset Metadata

Creator Darmon, Yannick (author)

Core Title Deficits and rehabilitation of upper-extremity multi-joint movements in individuals with chronic stroke

School School of Dentistry

Degree Doctor of Philosophy

Degree Program Biokinesiology

Degree Conferral Date 2023-08

Publication Date 01/20/2024

Defense Date 06/08/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag feedback control,feedforward control,intersegmental dynamics,motor learning,neuroplasticity,OAI-PMH Harvest,stroke,upper extremity

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Schweighofer, Nicolas (committee chair), Finley, James (committee member), Gordon, James (committee member), Loeb, Gerald (committee member), Winstein, Carolee (committee member)

Creator Email darmon@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113282086

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Legacy Identifier etd-DarmonYann-12126

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Format theses (aat)

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