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Plasticity in CMOS neuromorphic circuits

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Plasticity in CMOS neuromorphic circuits

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Content PlasticityinCMOSNeuromorphicCircuits
by
JonathanJoshi
ADissertationPresentedtothe
FACULTYOFTHEUSCGRADUATESCHOOL
UNIVERSITYOFSOUTHERNCALIFORNIA
InPartialFulfillmentofthe
RequirementsfortheDegree
DOCTOROFPHILOSOPHY
(ElectricalEngineering)
May2013
Copyright 2013 JonathanJoshi
Dedication
To my loving grandparents Jayaben and Rasiklal Joshi, my loving parents
Josephine and Rajendra Joshi, whose sacrifice and blessings have always
guidedmethroughlife.
ii
Acknowledgments
I have been very fortunate to interact and work with some of the brightest minds during
my graduate studies in the last 5 years. First and foremost, is my academic advisor
Dr. Alice C. Parker, without whose support, enthusiasm, and meaningful guidance this
thesis would not have been possible. She gave me an opportunity and a platform to
explore my talents. I have learned things from Prof. Parker that go well beyond the
regular,traditionalPh.D.advice,whichhavehelpedmetogrowbothinmyprofessional
and personal life. Besides my academic advisor, I am grateful to have interacted with
our collaborator Dr. Tansu Celikel. His guidance and expertise has taken this thesis to a
different level. I would also like to thank my committee members, Dr. Jeff Draper, Dr.
Norberto Grzywacz and Dr. Melvin Breuer. In my interactions with Dr. Parker and Dr.
Breuer, I have learnt how to ask the right research questions and answer them in a way
that makes me present my work better. I would like to thank Dr. Raghavendra and Dr.
Guptafortheirgeneralguidance.
Apartfromthevisiblecontributionscitedabove,Iwouldliketotakethisopportunity
to thank all the past and present members of the Biomimetic Real-time Cortex (BioRC)
group of which I have been a member throughout my graduate studies. In particular,
iii
I thank Dr. Ben Raskob, Dr. Adi Azar, Dr. Ko-Chung Tseng, Chih-Chieh Hsu, Yilda
Irizarry-Valle and Matthew Christian. Ben has been a close friend and a great senior
member to work with. Matt and I have had countless discussions that have led to inter-
estingwork.
I would like to thank my friends from the USC squash team of 2007 who made my
transition into the American way of life easier. I would like to thank Juan Pablo, Tyle,
Gautam, Harsh and Chuck. Playing with you guys was great. I also want to thank
membersoftheUSCcricketclubwithwhomIhaveplayed4greatyears. Iwouldliketo
thankSushil,Vignesh,TarunSandhu,TarunTyagi,Gurikbal,Gagan,Bikram,Abhishek,
SimerpreetandAnkurSaxena.
I would like to thank a few of my fellow Ph.D. and graduate students with whom
I have shared some great times and have made great friends. I would like to thank
Siddharth, Prasanjeet, Anantha, Aditya, Waleed, Anurag, Mohammed, Suvil, Sridhar
andArun. IwouldliketothankSehajitwhohasbeenagreatfriend.
I would like to thank members of Vidushak, the improv group that I was a part of
since 2009. The laughter that we gave each other was priceless and it definitely eased
the pain in life. I would like to thank Adarsh, Vikram, Kimish, Krishnakali, Sushmita,
AdityaChachad,MeghaandPankaj. Performingwithyouguysisalwaysanhonor.
I would also like to thank my past and present house mates Karthik, Sabya, Sunil,
Aditya, Snehit, Krishnakanth, Abhijit, Gourav, Amit, Aman and Jean Pierre with whom
I had a wonderful time living under the same roof during various years of my Ph.D.
iv
Through our traditional birthday parties in the backyard, the trips to Robex the next day
and then Omelette Parlor rides will be the most cherished of them all. Karthik you have
beenapillarofsupportasanolderbrotherduringdifficulttimesin2009. Ithankyoufor
beingthere.
I would like to thank Dr. Om Prakash Vyas, my mentor at K.J. Somaiya college of
engineering. He got me introduced and interested in VLSI and has supported me ever
since. Thank you sir for your presence and guidance. I would like to thank the faculty
atK.J.Somaiyacollegeof engineering. Dr. SanjaySinghThakur andMr. NitinNagori,
who stood by me when internal politics took over progress. I would like to thank Mrs.
Kundargi,Mrs. Jadhav,Mrs. Doshi,Mr. ZalteandDr. Karandikar. Iwouldliketothank
the lab staff at K.J. Somaiya college of engineering, Madame Sunanda and Mr. Natu. A
specialmentionforMr. AshokandtheregistrarofourcollegeMr. Shetty.
I have also been blessed to have some wonderful friends in my life who have seen
methroughtimesofjoyandsorrow. Inparticular,Ifeeladeepsenseofgratitudetoward
mylongtimefriendsandbrothersRajivRibeiro,RaashidKhanandKarnaFulzele,who
have helped me during times of crisis as well as celebrated with me during times of
happiness. IwouldliketothankMallikaSanyal,mylovingfriend. Iwouldliketothank
averyspecialPoornimaBalakrishnan, whohasstuckbymethroughmycrazinessasan
entrepreneurandfriend. YouhavebeenapillarofsupportandIshareaveryspecialbond
withyou.
v
TableofContents
Dedication ii
Acknowledgments iii
ListofFigures viii
Abstract xii
Chapter1: Introduction 1
1.1 ProblemMotivationandGoals . . . . . . . . . . . . . . . . . . . . . . 1
1.2 StructuralPlasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 NeuromorphicStructuralPlasticity . . . . . . . . . . . . . . . . . . . . 4
1.3.1 SynapseClaiming . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.2 RatWhiskerReceptiveField . . . . . . . . . . . . . . . . . . . 5
1.3.3 DesignMethodology . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter2: NeuromorphicCircuits-BackgroundandRelatedWork 8
2.1 Comparison of Implemented Research to State of the Art in Neuromor-
phicCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 BiologicalStructuralPlasticity . . . . . . . . . . . . . . . . . . . . . . 11
Chapter3: BiomimeticNeuralCircuitswithPlasticity 14
3.1 RelatedGeneralNeuroscience . . . . . . . . . . . . . . . . . . . . . . 14
3.2 BackgroundinNeuromorphicCircuits . . . . . . . . . . . . . . . . . . 18
3.3 ImplementationMethodology . . . . . . . . . . . . . . . . . . . . . . 20
3.4 NeuronwithPlasticExcitatorySynapses . . . . . . . . . . . . . . . . . 22
3.4.1 TheExcitatorySynapse . . . . . . . . . . . . . . . . . . . . . 23
3.4.2 TheVoltageAdderandDendriticArbor . . . . . . . . . . . . . 25
3.4.3 BiomimeticSTDPCircuit . . . . . . . . . . . . . . . . . . . . 26
3.4.4 ExperimentswithTheCorticalNeurondemonstratingSTDP . 28
3.5 NeuronswithPlasticInhibitorySynapses . . . . . . . . . . . . . . . . 31
3.5.1 TheDendriticArborIncorporatingtheInhibitorySynapse . . . 34
vi
3.5.2 ExperimentstoDemonstratetheEffectofthe
InhibitorySynapse . . . . . . . . . . . . . . . . . . . . . . . . 36
3.6 SpikingCorticalNeuronCircuit . . . . . . . . . . . . . . . . . . . . . 37
3.6.1 TheBiomimeticSpikingAxonHillockCircuit . . . . . . . . . 40
3.6.2 ExperimentswiththeCorticalNeurontoDemonstrate
SpikingProperties . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter4: GlialMicrodomaintoExhibitExcitabilityin
Networks 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 AstrocyteBiologicalBackground . . . . . . . . . . . . . . . . . . . . . 47
4.3 TheSynapseandAstrocyteCircuits . . . . . . . . . . . . . . . . . . . 49
4.4 ExperimentalNetworktoDemonstrate
Astrocyte-NeuronCommunication . . . . . . . . . . . . . . . . . . . . 52
Chapter5: ApproachtowardsNeuromorphicNetworkRestructuringusingSynapse
Claiming 57
5.1 ComparisonofApproachtoSynapticWeight-ChangeMethod . . . . . 65
Chapter 6: Neuromorphic Structural Plasticity-The Rat Whisker Receptive
Field 69
6.1 BiologicalMotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 NeuromorphicCircuitImplementingWhiskerReceptiveField . . . . . 73
6.2.1 ExpectedSimulationResults . . . . . . . . . . . . . . . . . . . 75
6.2.2 Simulationresults . . . . . . . . . . . . . . . . . . . . . . . . 76
Chapter7: ConclusionandFutureWork 83
ReferenceList 86
vii
ListofFigures
3.1 Biologicalinhibitorypost-synapticpotentials[1] . . . . . . . . . . . . 16
3.2 A system block diagram of the cortical neuron model with a pyramidal
neuroncartoon[2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Thecarboncanotubeexcitatorysynapse . . . . . . . . . . . . . . . . . 23
3.4 Thevoltageadder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 Thedendriticarborportion . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6 TheSTDPcircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.7 Change in EPSP voltage with LTP induction in synapse 1 and LTD in-
ductioninsynapse2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.8 ChangeinSTDPwindowasreceptordisablingrateschange . . . . . . 31
3.9 Thecarbonnanotubeinhibitorysynapse . . . . . . . . . . . . . . . . . 32
3.10 Thedendriticarborportion . . . . . . . . . . . . . . . . . . . . . . . . 34
3.11 Circuitdiagramoftheaxonhillockmodule[2] . . . . . . . . . . . . . 35
3.12 Firingoftheneuronwithinhibitorysynapseinactive . . . . . . . . . . 37
3.13 FiringoftheneuronwithweakandstrongIPSP . . . . . . . . . . . . . 38
3.14 Thespikingaxonhillockcircuit . . . . . . . . . . . . . . . . . . . . . 39
viii
3.15 Inputactionpotential(greentrace)andresultantincreaseindendriticpo-
tential(redtrace)leadingtocontinuousneuralspikingofhigherduration
(purpletrace)andlowerduration(bluetrace) . . . . . . . . . . . . . . 41
3.16 ChangeinspikedurationwindowwithchangeinDurationControlVoltage 42
3.17 High-frequency firing of neuron 1 leads to an output spike train from
neuron2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.18 Low-frequencyfiringofneuron1failstoproduceanoutputfromneuron2 44
4.1 Cartoonshowingastrocyticmechanismsimplemented(Credit-Ko-Chung
Tseng) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 TheBioRCexcitatorysynapsecircuit . . . . . . . . . . . . . . . . . . 50
4.3 Circuit containing several compartments of an astrocyte communicating
withmultiplesynapses . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Neuralnetworkillustratingastrocytemicrodomain . . . . . . . . . . . 52
4.5 Case1: Simulationresultsforthenetworkwithoutastrocytecircuit . . 53
4.6 Case 2: Simulation results for the network with the astrocyte circuit in-
vokingexcitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.7 Comparison of cleft voltages and PSPs in cases with and without the
astrocytecircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.1 Synapse-claimingschematic . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 CircuitusedtomodeltheFTandSTtimeconstants . . . . . . . . . . . 59
5.3 Nosynapseclaimingasbothneuronsareactive . . . . . . . . . . . . . 60
5.4 Simulationresults: Nosynapseclaimingasbothneuronsareactive . . . 61
5.5 SynapseclaimingasN2isactiveandN1lacksneuralactivity . . . . . . 62
5.6 Simulationresults:SynapseclaimingasN2isactiveandN1lacksneural
activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
ix
5.7 Networktodemonstratehardwarecostfornetworkrestructuring . . . . 65
5.8 Networktodemonstratehardwarecostforsynapticweightchangemethod 66
5.9 Cost comparison between synaptic weight change method and imple-
mentedmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1 Biologicalschematicofthesomatosensoryratsensorysignaling . . . . 70
6.2 Biological results taken from [3], showing the normalized spiking rate
fortheintra-columnarneuron(N3)fordifferentwhiskerstimulation(dark
bluewithcrossinhibition,lightbluelinewithoutcrossinhibition) . . . 71
6.3 Biologicalschematicoftheratsensorysignalingwhenonewhisker(W1)
iscut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.4 Biological results taken from [3], showing the normalized spiking rate
for the intra-columnar neuron (N3) when whisker W1 is cut : Results
show that N3 fires more spikes (light blue) due to surround whisker W2
in contrast to W1 in the previous case. This is due to the change in
topographyofthenetwork. . . . . . . . . . . . . . . . . . . . . . . . . 73
6.5 Circuitschematicoftheratsensorysignaling . . . . . . . . . . . . . . 74
6.6 CircuitschematicoftheratsensorysignalingwhenW1isgrounded(W1
isclipped) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.7 Simulation results summary: Figure (a) shows the number of spikes for
N3 (normalized) vs whisker stimulation. Light blue line indicates with-
outinhibitionanddarkbluelineindicatespresenceofinhibition. Wesee
that the number of spikes are more for principal whisker W1 and it in-
creasesinabsenceofinhibition. Figure(b)showstheeffectofgrounding
W1. We observe that N3 now fires spikes due to W2 which shows that
thenetworktopographyhaschanged . . . . . . . . . . . . . . . . . . . 77
6.8 Simulationresultsshowingwaveformsatdifferentkeypointsofthenet-
workwhenW1isnotclippedandactive,withoutanycrossinhibition . 80
6.9 Simulationresultsshowingwaveformsatdifferentkeypointsofthenet-
workwhenW1isnotclippedandactivewithcrossinhibitionpresent. . 81
x
6.10 Simulationresultsshowingwaveformsatdifferentkeypointsofthenet-
workwhenW1isclipped . . . . . . . . . . . . . . . . . . . . . . . . . 82
xi
Abstract
Athesisexploringfirst-orderin-silicomodelingofchanges(plasticity)inbiologicalneu-
ronsispresented. Inbiologicalneuralnetworksthereisanintricatefeedbackrelationship
betweenneuronsthatresultsinsynapticandstructuralplasticity,includingalterationsin
the connectivity and signaling between cells. Plasticity is widely believed to be key to
memory, learning and intelligence. For engineers trying to implement biological neu-
ral networks in silicon, changes in neural functionality and rewiring could be essential
mechanisms to examine. Modeling an electronic neural network that restructures itself
coulddemonstratelearningandmemory,andcouldleadtoabetterunderstandingofthe
wayneuralpathwaysimplementlearningandmemory. Thisthesislooksatthreeaspects
ofneuromorphicdesigninparallel: functionalcomplexity,scalabilityandplasticity.
Wehavemodeledplasticexcitatoryandinhibitorysynapseswhereinchangesinneu-
rotransmitter and receptor concentrations can be emulated to a first-order. Results show
that we can use these synapses in different combinations to demonstrate different kinds
of behavior such as spike-timing-dependant plasticity and the effect of astrocytes (glial
cells) on synaptic efficacy. We have also shown a circuit that emulates a spiking axon
hillock. Itcanbetunedusinganexternalvoltagetoproducedifferentspikingpatternsof
xii
variableduration. Adesignapproachhasbeendiscussedtowardsbuildinglargescalable
nueromorphicnetworks.
To demonstrate a plausible biological example of structural plasticity, a first-order
neuromorphic analog circuit implementation of upper layers of the rodent barrel (so-
matosensory) cortex has been implemented. We have modeled spiking behavior of so-
matosensorycorticalneuronsinlayers2-4andneuronalreceptivefieldswhilereplicating
biologicalobservationsonexperience-dependentchangesinreceptivefieldorganization,
networktopologyandsynapticconnectivityinsilico. Anatomicalandfunctionalchanges
in synaptic connectivity have been modeled using analog switching, based on change in
neural network activity. We demonstrate the effects of loss of inhibition and the loss of
sensory (whisker) inputs with our circuits, and show that the self-organizing neuromor-
phicanalogcircuit in silicoexhibitsstructuralplasticity.
Future applications of this thesis would include intelligent prosthetic devices, au-
tonomousroboticvehiclesandsystemsthatarecapableofhandlingsensordamage.
xiii
Chapter1
Introduction
1.1 ProblemMotivationandGoals
Changesinthehumancortexarebelievedtoplayanimportantroleinlearningandmem-
ory. While synaptic plasticity [Long Term Potentiation (LTP) /Long Term Depression
(LTD)]isanimportantmechanismsupportingmemoryandlearning,theadditionofnew
synaptic connections, new synapses, and incorporation of synapses recruited from other
purposesaremechanismsthatarealsobelievedtoberequired. Synaptogenesis[4][5]is
the process by which new synapses are formed. This involves the growth of a neuronal
axonthatformsanaxo-dendriticcontactwiththedendriticstructuresofanotherneuron.
Ithasbeenobservedthattheseconnectionsareformedlocally[5]demonstratestructural
plasticity in vitroand in vivo.
1
An engineering solution to the rewiring of the cortex presents many challenges. The
firstchallengebeginswithsiliconimplementationofneuralcircuits,siliconbeingasub-
stance that cannot change its structural properties over time. For a restructurable neu-
romimetic network we need new connections to be made; with a hardwired approach in
silicon; this proves virtually impossible without bulky, complicated reconfiguration cir-
cuitry. Changes in synapse numbers and usage call for new hardware to be created on
the fly, a daunting task with our current technological capabilities in silicon. Hence we
must model structural changes in a silicon neural network behaviourally by anticipating
such changes and designing in capabilities. Change in inter-neuron connection strength
with increase or decrease in the number of synapses is a plausible contributor towards
memory and change in sensory perception. The second challenge is to create a design
methodologyandalibraryofcircuitsrepresentingneuralcompartmentsthatcansupport
the rapid design and implementation of neural circuits as additional significant neural
mechanisms are understood, and can support the design of a wide variety of the cortical
neurons without extensive redesign. A consequence of the second challenge is the need
forthemethodologytohavecircuitsthatareadaptableinaplugandplayfashion,rather
thanwithablack-boxapproachtodesigningcompleteneurons.
The major goal of this thesis is to capture biological neural plasticity at a first-order,
plasticity that would include synaptic and structural plasticity. By building circuits that
haveahighlevelofbiologicalcomplexitywewishtoestablishcommunicationfeedback
with the neuroscience community in terms of potential questions that could be raised
2
with respect to important biological mechanisms. By modeling structural plasticity we
wish to apply this research to the building of future intelligent prosthetic devices. We
plantoachievethisbybuildingcircuitsthatcanrestructurethemselvesanddesigncircuit
buildingblocksthatcanbeusedinaplugandplaystyleforscalability.
Inpreparationforneuromorphiccircuitsthatexhibitstructuralplasticity,wedesigned
a library of neuromorphic components. We have modeled plastic excitatory and in-
hibitory synapses wherein changes in neurotransmitter and receptor concentrations can
be emulated to a first-order. Results show that we can use these synapses in different
combinationstodemonstratedifferentkindsofbehaviorsuchasspike-timing-dependent
plasticity and the effect of astrocytes (glial cells) on synaptic efficacy. We have also
shown a circuit that emulates a spiking axon hillock. It can be tuned using an external
voltagetoproducedifferentspikingpatternsofvariableduration. Adesignapproachhas
beendiscussedtowardsbuildinglargescalableneuromorphicnetworks.
1.2 StructuralPlasticity
Thefocusofneurallearningresearchhasbeenonactivity-dependentweightchangesbe-
tween already connected neurons. This mode of plasticity could involve changes in the
weights of existing synapses. In the case of synaptic plasticity, the storage capacity lies
in the system’s ability to increase and decrease the weights on existing connections as a
means of encoding learned information. Research has also suggested structural changes
thatleadtotheadditionorsubtractionofsynapsesbetweenpreviouslyconnectedpre-and
3
post-synapticunits[6]. Inadditiontoweightchanges,learningcouldinvolvealterations
totheconnectionnetwork,wherebypreviouslyunconnectedunitsbecomeconnectedand
viceversa. Wiringchangesrequirestructuralplasticity. Inthislearningmode,thestorage
capacity lies in the neuron’s ability to connect (form synapses) with other post-synaptic
neurons. Weight and wiring changes are not mutually exclusive (wiring plasticity can
evenbeviewedasaspecialcaseofweightplasticity),andcurrentresearchisinvestigat-
inghowneuronsandtheirsynapsesmightbeengagedinbothformsoflearning[7].
1.3 NeuromorphicStructuralPlasticity
Wehavebuiltaneuralnetworkthatcanrestructureitssynapticconnectionsautonomously.
Also the implemented network provides a platform where digital control can be added.
Therestructuringofthesesynapticconnectionsoccursondetectingchangesinneuraland
synaptic activity. We propose a method called Synapse Claiming with which restructur-
ing can be implemented in silico (term commonly used by neuroscientists to mean in
silicon, but refers generally to electronic circuits implemented in hardware). The corre-
spondencebetweenthismethodandbiologicalmechanismswillbeexplainedinChapter
5.
4
1.3.1 SynapseClaiming
With synapse claiming we incorporate a circuit in the neural network that transfers an
existing synapse between two neurons (an existing pre-synaptic and post-synaptic (tar-
get) neuron) to a new pre-synaptic neuron. As a result a new connection forms between
the new pre-synaptic neuron and the post-synaptic neuron. This circuit will first detect
thelackofneuralactivitybetweentheoldpre-synapticneuronandthetargetneuron. Ifa
timethresholdforinactivityiscrossedthenthecircuitwilllookforanincreaseinneural
activity between the new pre-synaptic neuron and the target neuron. If a second time
threshold is crossed then the circuit will transfer the synapse to this second pre-synaptic
neuron, thus forming a synaptic connection between the new pre-synaptic neuron and
the target neuron. This models the removal of existing synaptic connections when there
is lack of neural activity over time. Details of synapse claiming will be discussed in
Chapter5.
1.3.2 RatWhiskerReceptiveField
Weapplythesynapseclaimingmethodtoalargernetworkofneuronsthatmodelstherat
whisker receptive field, i.e. how whisker stimulation affects neural activity in the rat’s
cortex. Wehaveshownthatincaseswherethereisinhibitioninthenetworktheneurons
firelessspikesincomparisontowhenthereisdisinhibition. Weshowthatwhenthereis
sensory deprivation (whisker is clipped), the network changes its topography to process
thereceptivefieldofanotherwhiskerinthesensorynetwork.
5
1.3.3 DesignMethodology
To implement the system we propose a methodology for designing circuits that emulate
neuronal behavior. The basis of the design methodology is a library of circuits that
model the behavior of neural sub-components (synapses, dendrites, axon hillocks.etc)
in a tunable fashion. Our previously published work has shown samples of the design
methodology [2] [8]. Tunable behavior can be achieved by providing control knobs on
thecircuitssuchthatkeyneuralattributescanbevaried. Thisprovidesanopportunityfor
us to investigate the need for real-time tuning of neural parameters. Another advantage
of the methodology is that it makes the system components plug and play. Systems can
be expanded as new mechanisms are discovered. The plug and play methodology gives
usanincreasednumberofcombinationsintermsofemulatingdifferentneuralbehavior.
Thisbroadensthespectrumfortheimplementedsystemtoactasatestplatform.
Thekeyaspectsofthismethodologyare-
1. The building blocks are biomimetic such that they can capture the key first-order
mechanismsfortheirbiologicalcounterparts.
2. Thebuildingblocksmustbetunablesothattheycandemonstrateneuralplasticity.
3. Futuredesignscanevolveonthesebuildingblocks.
4. Evolutionary steps are designed in such a way that old and new circuits can function
asplugandplayblocks. Ourinterpretationofplugandplayistheabilitytotakedifferent
analogneuralcircuitcomponentsandconnectthemtogetherwithouttheneedofinterface
circuits.
6
Another reason for tunability is to give the ability to build other circuits that can
control voltages at these knobs (transistor gates) so that we can build more complex or
autonomous circuits. The goal of this methodology is to give future designers a capa-
bility of building networks that can evolve and are controllable to provide a family of
neurons with variable behavior without the need for circuit redesign. Potential appli-
cations could include a CAD tool for building neuromorphic hardware where building
blocks could be used to construct novel neural circuitry without redesign of the blocks.
Ourcurrentlibraryofcircuitsisincomplete;forexamplewearemissingcircuitsforgap
junctions. However with our current library we can still demonstrate a broad range of
neuralfunctioning.
As proof of concept for this methodology we take the following examples in this
thesis-
1. We have taken the synapse circuits designed and then connected more extensive cir-
cuitsthatcanperformfunctionssuchasSpike-Timing-DependentPlasticity(STDP).
2. We have taken the synapse circuits (excitatory and inhibitory), dendritic adders and
axonhillockcircuitstodemonstrateeffectofinhibition.
3. Webuiltanetworkofneuronsthatemploysacircuit,thatmimicstheglutamateinjec-
tionbyanAstrocyte(atypeofglialcells)toincreaseexcitabilityinagivennetwork.
7
Chapter2
NeuromorphicCircuits-BackgroundandRelatedWork
2.1 ComparisonofImplementedResearchtoStateofthe
ArtinNeuromorphicCircuits
Currentresearchinneuromorphicstructuralplasticityhasmainlyfocusedonneuralsys-
tems with analog neurons that are digitally controlled. Synaptic rewiring has been in-
vestigatedtowardstopographicmapformation[9]inhardware[10]. Themodelformap
formationtakesintoaccountsynapticwiringthatiscreatedprobabilisticallyandsynaptic
targets are global. That implementation employs Address Event Representation to com-
municate with some hardware overhead. Synapses and other neural circuit components
needcontrolsignalsforweightchange,whichincreasehardwareandcontroloverhead.
Systems built by the Indiveri group do implement neural networks that have synap-
tic learning based on modeled algorithms. However their implementation of network
restructuring is based on digital control to model changes in synaptic connection and
8
Address Event Represented (AER) communication for off-chip signals [11] [12]. The
implemented network will provide a platform where neurons will form new synaptic
connections autonomously without external control. The change in network structure
willbebasedonlocalneuralactivityandifneededtheplatformwillbecapableofincor-
poratingdigitalcontrolandAERbasedcommunicationsystems.
Work done by the FACETs project comprises a computer interface to program the
mixed signal neural network. The neurons used are basic and changes in synaptic plas-
ticity are made digitally [13]. This approach could prove to be expensive in terms of
hardware if the system is scaled to biological numbers. The system proposed hence
would eliminate the computer interface and the digital updating of synaptic strength.
However our system would be able to provide a programmable interface if needed. In
comparison to both the FACETs and Indiveri projects, our designs are more biomimetic
withdirectrelationshipbetweenourcircuittimeconstantsandbiologicalmechanisms.
Researchershavetakenexamplesfromtraditionalprogrammabledigitallogictocre-
ate neural circuits that can reconfigure in real time [14]. The work was based on the de-
signofatraditionalFPGAwithneuralcomponentsthathavelittlebiomimeticcomplex-
ity. Ourimplementedcircuitcomprisesofneuronsthatmimicthebiologicalcomplexity
toagreaterdepthwitheachsectionofthecircuitmimickingaparticularmechanismand
time constant. This helps us tune our circuits to demonstrate plasticity. Our previously
publishedwork[2][8][15]demonstratesafewexamples. Thedesignmethodologywill
9
allow for the individual neural components to be programmable so that the network can
betunedfordifferentapplicationsifnecessary.
WorkdoneatStanford[16][17]focusesonasystemthatreconstructsitselfinaway
whereby neural connectivity is stored in a digital SRAM memory. Information is com-
municatedtothememoryfromthenetworkusinganAERcommunicationplatformand
the memory is updated to model network reconfiguration. This does provide a simpler
platform to model reconnection between neurons; however it does not model a restruc-
turing network from a biomimetic perspective and the system needs extensive control
for digital information to be managed. Although the approach that has been employed
supports easily implementable systems it does not take into account certain key issues
such as storage space needed for local neural activity of individual neurons and its ef-
fectswhenwescaleneuronstohighernumbers. Thiswouldalsomakethestoragespace
extremelyexpensivetomanageintermsofprocessingpower. Ourimplementednetwork
contains autonomous analog circuits to detect neural activity and change connections
betweenneuronswithouttheconcernsofstoragespaceandneuralactivitycoding.
As mentioned in Chapter 1, to implement the proposed system we further propose a
designmethodologyforbiomimeticneuralsub-circuits. Themethodologywillmakethe
circuitsplugandplaysuchthatthesystemwillbescalableandadaptabletodigital,ana-
logandmixed-signalsystems. Theadaptabilityofthemethodologywillhelpusaddnew
biomimeticcapabilitiesastheyarediscovered. Apartofthedesignmethodologywould
betomakethecircuitcomponentstunable. Theapproachforusingprogrammableneural
10
componentshasbeeninvestigatedbytheLiugroup[18]usingtraditionalDigitaltoAna-
log Converters (DACs); however this approach is expensive in terms of the number of
transistorsneededifeachneuralcomponentistobeprogrammed. Ourmethodologywill
takeintoaccountthecostfactor(numberoftransistors,power)andeaseofscalabilityin
terms of number of transistors while also considering making the neurons in our system
adaptabletoprogrammableplatforms.
2.2 BiologicalStructuralPlasticity
The fundamental aspect behind the formation of a new synapse is the formation of an
axo-dendritic contact. The general belief had been that axons perform active roles,
whereas dendrites are relatively passive, probably a carryover from studies concerning
the formation of the neuromuscular junction, where the targets (muscles) are rather sta-
tionary [19]. However dendrites also extend growth cones displaying elongation and
bifurcation. Furthermore, more recent research [20] revealed that numerous synapses
formed are located on newly grown dendritic growth cones and filopodia. These obser-
vations led to the conclusion that many of the synaptogenic contacts occurring during
this period are initiated by dendritic growth. As early as 2002, Trachtenberg et al. [21]
suggested that sensory experience drives the formation and elimination of synapses and
that these changes might underlie structural plasticity. In vitro studies show that high-
frequency synaptic stimulation leading to local synaptic long-term potentiation (LTP)
has been shown to induce the extension of numerous dendritic filopodia, some of which
11
make axo-dendritic contacts to create new synapses [22] [23]. High frequency stimula-
tioninvitrocouldbeunrealisticasmanyneuronsfireatlowerfrequencies. Experiments
performed in vivo using external stimuli received from neurons rather than probe stim-
uli [6] show that previously connected neurons can form new synapses along the same
dendritic arbors due to growth of new dendritic spines, showing an increase in synaptic
strength with formation of new synapses. Paola et al. [24] suggest that structural plas-
ticity of axonal branches and boutons contributes to the remodeling of biological neural
circuits.
Synapses form by a process known as Synaptogenesis [4]. This involves the forma-
tion of an axo-dendritic contact followed by a series of events. As reviewed in [5], after
an axo-dendritic contact is formed there is activity from the axonal side that triggers the
uptakeofsynapticvesicles. Thisprocessiscalledpre-synapticdifferentiation(PRESD).
PRESD then triggers the dendritic (pos-synaptic) side to recruit receptors thus complet-
ing the synapse. This mechanism forms a part of post-synaptic differentiation (POSD).
There is speculation in the findings that say PESD triggers POSD in the formation of a
synapse. AnotherschoolofthoughtsaysthatPOSDisindependentofPESDasdendrites
are active elements as well [5]. A point to note is that in the implemented research we
haveconsideredonlythefirst-ordermechanismsmentionedaboveinPRESDandPOSD,
although there are more detailed mechanisms which do occur in PRESD and POSD [5].
Wehaveconsideredonlytheabovetwotolimitcomplexityofoutcircuits,asoursynapse
12
circuits have been modeled to include neurotransmitter and receptor concentrations in
synapses[8].
Tosummarizetheneuralmechanismsunderinvestigation: increaseinneuralactivity
causes axonal growth, increase in local synaptic efficacy leads to growth of a dendritic
spine and on formation of an axo-dendritic contact synaptogenesis occurs that involves
PRESD triggering POSD. The case where POSD is triggered independently is not con-
sidered; as this is an effect which is being investigated and can be modeled if needed.
Thefocusofourresearchistomodeltwoaspectsofstructuralplasticity. Thefirstaspect
involvestheeliminationofexistingsynapsesbetweenalreadyconnectednon-interacting
neurons. Thesecondaspectistoemulatetheformationofnewsynapsesbetweenalready
connectedneuronstoincreasesynapticconnectivity.
13
Chapter3
BiomimeticNeuralCircuitswithPlasticity
3.1 RelatedGeneralNeuroscience
The biological synapse is complex, with controllable transmitters that can decrease or
increase the excitability of the post-synaptic receptors. The activation probability of a
given synaptic junction is regulated by the amount and timing of pre-synaptic and post-
synaptic activity. Neurotransmitters must be present in sufficient amounts to develop
post-synapticpotentials(PSPs),andtheconcentrationoftransmittersreleasedcanaffect
theheightanddurationofthePSP[25]. Actionpotentialsimpingingonthesynapticcleft
can result in temporal summation of the resulting PSPs, increasing the likelihood of the
post-synapticneuroneventuallyfiring.
Synapses, vary their strengths with learning. Changes in synaptic strength are also
thoughttounderlielearningandstoringofnewmemories. Aparticularformofthislearn-
ing is spike-timing dependent plasticity (STDP) [26], [27], [28]. With STDP, a synapse
is strengthened (long-term potentiation LTP) when the pre-synaptic action potential at a
14
particular synapse preceeds the post-synaptic action potential (the output of the neuron
containing the synapse). A synapse is weakened (long-term depression LTD) when the
post-synaptic action potential preceeds the pre-synaptic action potential. Thus, neurons
modify their synaptic connections to adapt to changes in sensory input. The ability of
manyneuronstomodulatethestrengthsoftheirsynapticconnectionshasbeenshownto
depend on the relative timing of pre- and post-synaptic action potentials (APs). STDP
has become an attractive model for learning at the single-cell level [26]. The temporal
order of pre-synaptic and post-synaptic firing is a critically important aspect of STDP.
The synapse is thought to be strengthened by action potentials backpropagating along
the dendrites along with depolarization caused by a previous action potential impinging
on a synapse. The backpropagation absent the previous action potential weakens the
futuresynapticresponse.
At many synapses, the induction of spike-timing-dependent long-term potentiation
(LTP)/long-termdepression(LTD)requiresactivationoftheNMDAglutamatereceptors
(NMDARs) [27]. In some cases, LTD induction was also shown to require the activa-
tion of calcium channels. A straightforward explanation for the temporally-asymmetric
STDP is that the relative timing of glutamate binding to NMDARs and the spiking of
the post-synaptic backpropagating AP determine theCa
2+
level required for either LTP
or LTD; Prepost spiking (pre-synaptic firing first) leads to the opening of NMDARs via
depolarization-induced removal of the Mg2+ block [28], resulting in a high-levelCa
2+
influx,whereaspostprespiking(post-synapticspikingfirst)leadstoalow-levelsustained
15
Ca
2+
rise by the opening of voltage-dependentCa
2+
channels (VDCCs) and/or limited
NMDAR activation. These cellular mechanisms, among others, underlie induction of
STDP[26].
Figure3.1: Biologicalinhibitorypost-synapticpotentials[1]
Thebiologicalinhibitorysynapsehasacomplexstructure[29][1]. Inhibitorysynapses
can be shunting, effectively vetoing depolarization caused by excitatory post-synaptic
potentials, or hyperpolarizing, subtracting potential from the dendrite. The modulation
of quantity of neurotransmitters released at the pre-synaptic terminal affects the actions
of the receptors on the post-synaptic side that control ligand-gated ion channels, result-
ing in a variation in hyperpolarizing potentials across the cell membrane. The rate that
neurotransmitters are reuptaken into the pre-synaptic terminal also affects synaptic be-
havior by controlling the decrease in post-synaptic potential. Example biological IPSP
measurementsareshowninFigure3.1[1].
16
Withintheneuronsinthecortex,significantdendriticcomputationsoccurthataffect
the probability and frequency of neural firing. Action potentials arriving at the synapses
createpost-synapticpotentialsonthedendriticarborthatcombineincomplexways[30].
These computations include linear, sublinear and superlinear additions. There is grow-
ing consensus among neuroscientists that these detailed aspects of dendritic behavior
contributesignificantlytocorticalfunctioning.
Most biological neurons fire by emitting several closely-spaced spikes or a burst of
spikes when input stimulation is sufficient to cause spiking. The biological mechanism
behind a neural spike is well understood [31]. Bursts of spikes or higher-frequency
spike trains are more likely to result in relaying sensory inputs to the cortex than lower-
frequency trains [32]. For example Neurons in the visual cortex respond with varying
frequencywhenthereisadetectionofanedgeataparticularorientation[33],depending
onthecontrastoftheedge.
Spiking neurons can be classified into many types [34]. Neurons can emit single
spikes, spike trains or bursts of spikes. Many neurons are either all-or-nothing spiking
neurons or exhibit spiking frequency increase as the somatic membrane potential in-
creases. Arecentpublication[35]describesneuronsinthesomatosensorycortexthatare
classified as either Regular Spiking (RS) pyramidal or Fast Spiking (FS) interneurons.
RSneuronshaveahigherspikingratefromtheonsetofspikingandsettledowntoabase
frequency whereas FS cells have a high frequency from onset itself, and cease spiking
completelywhenthecellmembranepotentialdropsbelowacriticalthreshold.
17
3.2 BackgroundinNeuromorphicCircuits
NotableresearchinneuromorphicengineeringincludesMeadsartificialretina[36]. This
significant work originated with Mahowald and Mead [37], followed by Boahen [38],
Zaghloul and Boahen [39] and more recently Farquhar and Hasler [40]. Hynna and
Boahen report on a circuit that generates a calcium spike with attention paid to exact
replication of waveforms, and describe incorporation of the calcium spike circuit in an
entireneuroncircuit[41]. Somemixed-signalelectronicmodelsclosetobiologicalneu-
ronsincludeLiuandFrenzel’sspiketrainneuron[42]. An8-transistorexcitatoryCMOS
synapse [43] is close in scale and nature to our synapses, although they plan to use that
synapseforsummationofinputsfrommanypre-synapticsites.
Electronicinhibitorysynapsecircuitshaveprimarilyimplementedshuntingsynapses.
Eliaswasoneofthefirstresearcherstoproposeelectronicmodelsfordendriticcomputa-
tions[44]. Grattarollaetal. simulateaneuronwithinhibitorysynapsesconstructedusing
integrators and comparators [45]. An electronic neuron design with both inhibition and
excitationmodelsaburstingoscillatorwithadepressedsynapseconstructedofacurrent
mirror and amplifier, with the circuit modulating the output current of the synapse, and
the lowest potential being ground [46]. It is not clear if that synapse exhibits plasticity.
Leemodelsacentralpatterngeneratorthatemploysaninhibitorysynapse[47]usingop-
erational amplifiers and multipliers to emulate predefined equations. Shi and Horiuchi
modelbothshuntingandhyperpolarizinginhibitorysynapses[48].
18
There has been a keen interest in modeling synapses with Spike-Timing-Dependent
Plasticity (STDP). Arthur and Boahen [49] model CMOS synapses which correlate and
storethepre-postsynchronizationusinganSRAM-basedapproach. WorkdonebyTovar
[50]modelstheSTDPbasedonReichardt’scorrelationandusesthecorrelationtowards
inhibitionandexcitationofneighbouringneurons. TanakademonstratesanSTDPcircuit
based on digital gates and flip flops to store synchronization information [51]. Work by
Huo [52] shows the role of membrane threshold in their STDP synapse as a part of an
integrate and fire neuron. Similar circuitry has been reported on by Indiveri et al [53].
It differs in technology, and how biomimetic the circuits are, with less correspondence
betweencircuitstructuresandbiologicalmechanisms.
Different implementations of spiking neurons have been observed. Hynna and Boa-
hen [54] describe a silicon thalamic relay neuron that exhibits tonic firing, then bursts
with sufficient simulation. This neuron uses a spiking circuit [39] that depends on an
off-chipresetsignalfromadigitalcircuittoregenerateaspike. FarquharandHasler[40]
describeabiomimeticaxonhillockcircuit,anddemonstratechangesinspikingfrequency
when different amplitudes of current are injected into the circuit. An electronic neuron
design with both inhibition and excitation models a bursting oscillator with a depressed
synapse constructed of a current mirror and amplifier, with the circuit modulating the
output current of the synapse [46] without control over frequency or spiking duration.
These oscillators are found in central pattern generators in neural circuits. Work done
by Indiveri [55] presents a firing circuit similar to our spiking axon hillock circuit [56]
19
intermsoftherefractoryperiodcontrolbutlackscontrolovervariationsintotalspiking
duration.
3.3 ImplementationMethodology
A synthetic cortex containing trillions of synapses could be constructed using nanode-
vices. CarbonnanotubesthatcanbehaveasmetallicwiresaswellasFETsareapromis-
ingtechnology. Carbonnanotubesareextremelysmall(afewnm. indiameter). Current
flow is largely ballistic (comparable to the flow of electrons in free space), capacitances
are in attofarads, and rise and fall times in picoseconds. Channel resistance is primarily
due to the quantum resistance at the junction between the nanotubes and metallic con-
nections,relatedtothedifferencesinelectronenergylevels. Thiscreatesachallengefor
biomimeticneuralcircuitdesignsinceresistancecannotbeadjustedeasily. Currentflow
between drain and source is typically controlled by using series and parallel nanotubes,
although small adjustments can be made by varying nanotube length. Appropriate in-
terfaces could be used to convert to/from biological signal levels and delays. Finally,
carboninducesminimumimmunesystemreactionsinlivingtissue,makingcarbonnan-
otubeprostheticdevicesdesirable[57].
Our basic cortical neuron, shown in Figure 3.2 in [2], consists of four types of sub-
modules: the basic excitatory and inhibitory synapses ( [58], [15]) the STDP synapses,
the simplified dendritic arbor [15] and the axon hillock [2]. Circuit models for the den-
dritesandaxonarenotprovidedhere. Thecircuitsdescribedintheforthcomingsections
20
Figure 3.2: A system block diagram of the cortical neuron model with a pyramidal neu-
roncartoon[2]
havebeensimulatedusingcarbonnanotubeSPICEmodels[59]. Totestforfunctionality
we have simulated all the circuits described in this proposal in TSMC 180nm CMOS
technology using SPECTRE. The implemented work is completed in CMOS, as model
accuracies, lack of a mature technology and simulation times limit us from simulating
largenetworksusingcarbonnanotubeSPICEmodels.
Inatypicalbiologicalneuron,potentialsrangefromaround-75mVto+40mVwith
actionpotentialspeakingaround+40mV.Sincethecarbonnanotubeneuronisdesigned
21
to operate with Vdd around 0.9 V as the peak action potential voltage, and with 0.0 V
(Ground) as the resting potential, the post-synaptic potentials were scaled accordingly,
with 0.0 V circuit potential corresponding to -75 mV biological potential and 0.9 V
circuitpotentialcorrespondingto40mVbiologicalpotential. Wescaledthedelayswith
about 1 ms in the biological neuron scaling to about 10 ps in the nanotube neuron [60].
For CMOS we modeled the APs to about 1.8 V in peak and 10 ns in durations. The
EPSPsweremodeledtobeabout200mVinamplitudeand60nsofaverageduration.
3.4 NeuronwithPlasticExcitatorySynapses
Thissectiondescribesacarbonnanotubecircuitimplementationofabiomimeticsynapse
withSTDP,asapartofatypicalcorticalneuron. TheSTDPcircuitdetectsthetimingof
the backpropagating action potential relative to the pre-synaptic action potential. Based
ontherelativetimingofthetwoevents,LTPorLTDisinducedinthesynapse. TheSTDP
circuit has control knobs corresponding to timings of biological mechanisms. Experi-
ments on the neuron show that when the backpropagating AP succeeds the pre-synaptic
AP,LTPisinduced,otherwiseLTDisinduced. LTPandLTDaretestedontwoidentical
synapsesofthesameneuronandexperimentsshowthatanexamplesynapseundergoing
LTP contributes to neural firing whereas the example synapse undergoing LTD fails to
contributeadequately,andtheneurondoesnotfire. Resultsalsoshowtheabilitytocon-
trol the acceptable duration of the timing window between the backpropagating AP and
thepre-synapticAP.Theresultsshownareforasinglespike(phasic)neuron.
22
We have used two basic synapses [15] and two STDP synapses so that we can high-
lighttheinductionofLTPorLTDineachsynapse,demonstratingtheeffectofSTDPon
neuralfiring.
Figure3.3: Thecarboncanotubeexcitatorysynapse
3.4.1 TheExcitatorySynapse
The work here is based on a biomimetic depolarizing excitatory synapse [29], with cor-
respondencebetweenbiologicalmechanismsandcircuitstructures. Thissynapsecircuit
evolved from an earlier synapse [15] based on this synapse [2]. This circuit models
23
cellpotentialsandneurotransmitterconcentrationswithvoltages,withacorrespondence
betweencircuitelementsandbiologicalmechanisms.
Partsoftheexcitatorysynapsecircuit(Figure3.3)exhibitbiomimeticbehaviorcorre-
spondingtobiologicalmechanisms. Theactionpotentialimpingesontwosectionsofthe
synapse, namely the neurotransmitter (pre-synaptic) section and a mechanism (delay 1)
that delays the neurotransmitter reuptake. The pull-up transistor in the neurotransmitter
section controls the neurotransmitter concentration in the synaptic cleft (the voltage at
the synaptic cleft node) while the pull-down transistor models the reuptake mechanism
that controls the drop in neurotransmitter concentration in the cleft. The reuptake delay
is controlled by the rise time of the delay circuit, by varying the length of its PMOS
transistor to indirectly control the falling RC time constant of the neurotransmitter con-
centration. The neurotransmitter release causes ion channels to open; depolarization is
modeled by the pull-up transistor in the receptor section tied to Vdd. The fall of the
EPSP is modeled by the pull-down in the same section. The time delay between the
positivepeakoftheEPSPanditsfalltogroundismodeledbyasecondtunabledelaycir-
cuit (delay 2). Variation in neurotransmitter concentration in the synaptic cleft causes a
changeintheEPSPpeakamplitude,directlyalteringthesynapsestrength. Thereuptake
mechanism inputs R and spread control the spread of the EPSP, which modulates the
temporal summation of the synapse EPSPs when successive action potentials impinge
on a synapse or multiple synapses are stimulated at close intervals. The voltage across
the gate labeled Neurotransmitter conc controls the neurotransmitter release while the
24
voltage across the gate Receptor conc controls the receptor activation. Varying these
twovoltagescontrolstheEPSPamplitudeandprovidesawaytoaddcircuitsthatexhibit
plasticity.
3.4.2 TheVoltageAdderandDendriticArbor
Theaddercircuit[61]isshowninFigure3.4. Ourresultslaterinthechapterhaveshown
theuseofthisaddertodemonstratedendritic-likecomputationswithsub-thresholdexci-
tatoryandinhibitoryvoltages.
Figure3.4: Thevoltageadder
A block diagram of the dendritic arbor portion is shown in Figure 3.5. There are
foursynapses(twobasicandtwoSTDPbased)inthearbor,eachonaseparatedendritic
branch. Ouraxonhillockcircuitisdescribedin[2]. OurbasicneuronoperateswithVdd
25
Figure3.5: Thedendriticarborportion
around 0.9V as the action potential voltage, and with 0.0V as the resting potential. We
scaled the delays with 1 ms in the biological neuron scaling to 10 ps in the nanotube
neuron [60]. The post-synaptic potential at the dendritic trunk is approximately 10% of
theactionpotentialandthedurationisabout6timesaslongastheactionpotential.
3.4.3 BiomimeticSTDPCircuit
TheSTDPcircuitasshowninFigure3.6isdividedintofivesections. TheNMDARecep-
torActivationSectionandtheMagnesiumBlockRemovalSectionareresponsibleforco-
incidencedetectionwhenthepre-synapticactionpotential(inputAP)precedesthepost-
synapticactionpotential(backpropagatingAP)toinduceLTP.The NMDA Deactivation
SectionandtheCalciumChannelSectionareresponsibleforcoincidencedetectionwhen
26
Figure3.6: TheSTDPcircuit
theinputAPsucceedsthebackpropagatingAPtoinduceLTD.Thepre-synapticAP(in-
put AP) impinges on the NMDA Receptor Activation section (transistor X2) to disable
the LTD mechanismby raising the potential ofpointA and grounding the potentialat B
(X21)throughthecurrentmirrorintheNMDAReceptor(NMDAR)ActivationSection.
The raised potential at A also contributes to removing the magnesium block by turning
on X8 in the Magnesium Block Removal Section. The backpropagated AP impinges on
27
X9 completing the magnesium block removal by pulling down point C through the in-
verting current mirror in the Block Removal section. The output of point C controls the
pull-upoftheCa
2+
Levelthatcontrolsthereceptorconcentration,thesignallabeledRe-
ceptor concinthesynapsedescribedinFigure3.3toinduceLTP.Thevoltageacrossthe
gate of X5 (Receptor Disabling) controls the duration of the time window for which the
synapse has the receptors activated for LTP induction (discussed in experiments). The
X11 gate voltage (Magnesium Block Removal Delay) controls the rise time for the re-
ceptor control voltage. However when the backpropagated AP precedes the input AP it
deactivates the NMDAR by turning on X26 in the NMDA Deactivation Section causing
the rise in potential at B which pulls the A potential to ground (X6) and turns on X19.
The post-pre spiking on the calcium channel section (X19 and X20) raises the potential
at point D, pulling down the receptor conc control voltage to induce LTD. The voltage
across gate of X24 (NMDA Deactivation) controls the timing of the window for which
thesynapsehasthereceptorsdeactivatedforLTDinduction. Thevoltageacrossthegate
of X17 (Voltage DependentCa
2+
Channel Control) controls the fall time for the final
receptorcontrolvoltage.
3.4.4 ExperimentswithTheCorticalNeurondemonstratingSTDP
WeperformedCarbonNanotubeSPICEsimulationexperimentstodemonstratesynaptic
plasticity. The neuron was tested with action potentials input to each synapse, and the
output of the neuron measured. As shown in Figure 3.7 , Action Potential 1 (dotted
28
trace) impinges on synapse 1 at 40ps resulting in EPSP 1 (dotted trace). The sum of
EPSP 1, and the EPSPs of synapse 3 and 4 (EPSPs kept constant at 80mv) crosses the
thresholdoftheneuroncausingittofireanoutputAP(darktrace)at70psasshown. This
outputAPactsasthebackpropagatingAPforbothsynapses1and2. ActionPotential2
(dark trace) impinges on synapse 2 at 100ps resulting in EPSP 2 (dark trace). Synapse
1depolarizedbeforethebackpropagatingAPresultinginLTPbeinginducedinsynapse
1asshownbytheincreaseinthemagnitudeofEPSP1at125psand180psrespectively.
Ontheotherhand,Synapse2undergoesLTDasshownbythedecreaseinthemagnitude
of EPSP 2 at 200ps as a result of the pre-synaptic AP at 100 ps arriving too late to
contribute to STDP. We tested the effects of synaptic changes on neural firing and, as
shownat180ps,theEPSPatsynapse1individuallyfacilitatesneuralfiringwhenadded
tothefixedEPSPsforsynapses3and4,whereasat250ps,theloweredEPSPatsynapse
2 is too weak to cause an output spike. Figure 3.8 shows the effect of changing the
receptordeactivationvoltageontheSTDPtimingwindowforLTP.WedefinetheSTDP
window as the time gap between the input action potential and backpropagating action
potential in which LTP or LTD can be induced. As the receptor deactivation voltage
increases the STDP window reduces, thus the time difference needed to induce LTP or
LTD between the input AP and the backpropagating AP would be smaller. Changes in
NMDA Deactivation for the LTD timing window is the same as shown in Figure 3.8.
Thechangesin Magnesium Block Removal Delayand Voltage DependentCa
2+
Control
affectthefrequencyatwhichthebackpropagatingAPinducesLTPorLTD.Experiments
29
involving the relationship between spiking frequency and plasticity are the subject of a
futurepublication.
Figure3.7: ChangeinEPSPvoltagewithLTPinductioninsynapse1andLTDinduction
insynapse2
30
Figure3.8: ChangeinSTDPwindowasreceptordisablingrateschange
3.5 NeuronswithPlasticInhibitorySynapses
Ourbasicmodelforacorticalneurontodemonstrateinhibitorysynapses,showninFig-
ure3.2,consistsofthreetypesofsub-modules: theexcitatory([58],[15])andinhibitory
synapses,thedendriticarbor[15]andtheaxonhillock.
The work presented here is based on the biomimetic behavior of a hyperpolarizing
inhibitory synapse circuit designed to be compact, with correspondence between bio-
logical mechanisms and circuit structures. This synapse circuit evolved from an earlier
excitatory synapse [15]. Synapse behavior is controlled by voltages on the gates of the
transistors, acting as control knobs. The neurotransmitter concentration and the spread
31
of the IPSP (delay of return to resting potential) can be varied by controlling the neuro-
transmitterreleaseandreuptakerates. Thesynapsealsoexhibitstemporalsummationof
the IPSPs when action potentials impinge on the synapse at close intervals. This circuit
modelscellpotentialsandneurotransmitterconcentrationswithvoltages,alongwiththe
correspondencebetweencircuitelementsandbiologicalmechanisms.
Figure3.9: Thecarbonnanotubeinhibitorysynapse
Figure 3.9 presents the inhibitory synapse circuit that displays plasticity. The design
is segmented into parts that facilitate biomimetic behavior corresponding to biological
32
mechanisms. The action potential impinges on two sections of the synapse as shown,
namely the neurotransmitter section and a mechanism (delay 1) that delays the reuptake
of neurotransmitters. The pull-up transistor in the Neurotransmitter section controls the
actualneurotransmitterconcentrationinthesynapticcleft,modeledbythevoltageatthe
synaptic cleft node, whereas the pull-down transistor models the reuptake mechanism
that controls the drop in neurotransmitter concentration in the cleft. The chronological
occurrence of reuptake is controlled by the rise time of the delay circuit, by varying
the length of its PMOS transistor to indirectly control the falling RC time constant of
the neurotransmitter concentration. The neurotransmitter release cause one or more ion
channels to open; hyperpolarization is modeled by the pull-down transistor in the ion
channel section tied to negative potential (Vss). The ion flow responsible for the rise of
theIPSPtotherestingpotentialismodeledbythepull-uptogroundinthesamesection.
ThetimedelaybetweenthenegativepeakoftheIPSPanditsriseuptogroundpotential
ismodeledbyaseconddelaycircuit(delay2)thatistunabletovarythesynapseproper-
ties. Variation in neurotransmitter concentration in the synaptic cleft causes a change in
theIPSPnegativepeakamplitudethusdirectlyalteringthesynapsestrength[1]. Alsothe
reuptakemechanismRandspreadinputcontrolthespreadoftheIPSP,whichmodulates
the temporal summation of the synapse output when multiple successive action poten-
tials impinge on the synapse or multiple synapses are stimulated at close intervals. The
voltage across the gate labeled neurotransmitter conc controls the current that models
the neurotransmitter release while the voltage across the gate R controls the reuptake.
33
Varying these two voltages controls the IPSP amplitude and the spread of the IPSP re-
spectively.
Figure3.10: Thedendriticarborportion
3.5.1 TheDendriticArborIncorporatingtheInhibitorySynapse
The adder circuit [61] is shown in Figure 3.4 . A block diagram of the dendritic arbor
portionisshowninFigure3.10.
There are four synapses (three excitatory and one inhibitory) in the arbor, each on
a separate dendritic branch. Our axon hillock circuit is shown in Figure 3.11 [2]. In a
biologicalneuron,theaxonhillockhasthehighestdensityofsodiumchannels,resulting
inthelowestthreshold(-55mV)comparedtoelsewhereintheneurontoinitiateanaction
potential. Ifthesummationofpost-synapticpotentials(PSPs)reachesathresholdvalue,
the axon hillock circuit will generate a spike. This circuit behaves in a similar fashion
to a self-resetting CMOS circuit, receiving a rising edge and producing a pulse whose
widthiscontrolledbythegatedelayoftheinvertershowninFigure3.11. Tomimicafast
34
Figure3.11: Circuitdiagramoftheaxonhillockmodule[2]
risingphase(duetotherapidincreaseofthesodiumchannelconductance)andaslower
fallingphase(duetotheslowerincreaseofthepotassiumchannels’conductances)ofan
action potential, we adjusted the pull-up and pull-down strength of transistors X8 and
X7. Alltheothertransistorsweretunedtomodelthetimecourses(timeconstants)inthe
dynamicmechanismsofthevoltage-gatedionchannels.
In our basic biological neuron, potentials range from around -75mV to +40mV with
action potentials peaking around +40mV. Since the carbon nanotube neuron is designed
to operate with Vdd around 0.9V as the peak action potential voltage, and with 0.0V
35
(Ground) as the resting potential, the post-synaptic potentials were scaled accordingly,
with0.0Vcircuitpotentialcorrespondingto-75mVbiologicalpotentialand0.9Vcircuit
potential corresponding to 40mV biological potential. Likewise, we scaled the delays
with about 1 ms in the biological neuron scaling to about 10 ps in the nanotube neuron
[60]. The post-synaptic potential appearing at the dendritic trunk is approximately 14%
of the action potential and the duration is about 6 times as long as the action potential,
similartobiologicalEPSPsdescribedintheliterature.
3.5.2 ExperimentstoDemonstratetheEffectofthe
InhibitorySynapse
WeperformedseveralSPICEsimulationexperiments. Theneuronwastestedwithaction
potentials input to each synapse, and the output of the neuron measured. The input ac-
tion potential (the red trace) is applied to each synapse module and the generated action
potential(thebluetrace)iscapturedattheaxon-hillocknode. Firstwetestedtheneuron
with an inactive inhibitory synapse (Figure 3.12). Second, we show that when the in-
hibitory synapse is strengthened, it prevents the neuron from firing since the summation
ofPSPsisbelowthethresholdtoinitiateaspikeattheaxonhillock(Figure3.13). Third,
again shown in Figure 3.13, we repeated the previous experiment with the strength of
the inhibitory synapse set to a low value using the neurotransmitter concentration knob,
showingtheneuronfiringinspiteofthesmallIPSPgenerated.
36
Figure3.12: Firingoftheneuronwithinhibitorysynapseinactive
3.6 SpikingCorticalNeuronCircuit
Our spiking cortical neuron [56] consists of four types of sub-modules: the basic ex-
citatory synapses [58], the simplified dendritic arbor [15] and a spiking axon hillock
circuit [2]. Circuit models for the dendrites are not provided here. We have used four
synapses [15] and tuned the threshold of the axon hillock so that it spikes when all four
synapsesexhibitatypicalEPSP.
37
Figure3.13: FiringoftheneuronwithweakandstrongIPSP
The synapse implemented in the neuron is a biomimetic depolarizing excitatory
synapsecircuitasshowninFigure3.3. Thiscircuitmodelscellpotentialsandneurotrans-
mitterconcentrationswithvoltages,withacorrespondencebetweencircuitelementsand
biologicalmechanisms.
The adder circuit in the simplified dendritic arbor [61] (Figure 3.4) has been shown
previously[15]. Thedendriticarborportionusedfortestingwaspublishedearlier[15].
38
Figure3.14: Thespikingaxonhillockcircuit
39
There are four excitatory synapses in the arbor, each on a separate dendritic branch.
Previous work [58] has shown that the synapses used in our neuron have the capability
oftemporalsummation.
3.6.1 TheBiomimeticSpikingAxonHillockCircuit
As shown in Figure 3.14, if the summation of post-synaptic dendritic potentials (PSPs)
connected to the gate of transistor X2 reaches a threshold value, the Gated Ion Chan-
nel section raises its potential at point A indicating the opening of a voltage-gated ion
channel. The raised potential at A is inverted to turn on PMOS X7 and the axon hillock
circuit will initiate spiking. To mimic a fast-rising phase (due to the rapid increase of
the sodium channel conductance) and a slower falling phase (due to the slower increase
of the potassium channel conductances) of an action potential, we adjusted the pull-up
andpull-downstrengthsoftransistorsX7,X8andX9. Inverters1and2inthePotassium
Delayweretunedtomodelthetimecourses(timeconstants)inthedynamicmechanisms
of the voltage-gated ion channels. The Sodium Ion Delay Section controls the delay for
whichthesodiumchannelconductanceremainsdeactivatedbyturningofftransistorX8.
The voltage across the gate of transistor X15 (refractory period control) controls the
spiking refractory period and hence spiking frequency. The voltage across the gate of
transistorX4(SpikingDurationControl)intheGatedIonChannelSectioncontrolshow
fastthevoltageatpointAwilldecayandhencecontrolstheoveralldurationofspiking.
40
The post-synaptic potential appearing at the dendritic trunk is approximately 14%
of the action potential and the duration is about 6 times as long as the action potential,
similartobiologicalEPSPsdescribedintheliterature.
Figure 3.15: Input action potential (green trace) and resultant increase in dendritic po-
tential (red trace) leading to continuous neural spiking of higher duration (purple trace)
andlowerduration(bluetrace)
3.6.2 ExperimentswiththeCorticalNeurontoDemonstrate
SpikingProperties
The neuron was tested with action potentials input to each synapse, and the output of
the neuron measured. As shown in Figure 3.15 the input APs 1 and 2 (green trace,
superimposed)causethedendriticpotential(redtrace)toriseandcausetheaxonhillock
41
Figure3.16: ChangeinspikedurationwindowwithchangeinDurationControlVoltage
toproducespikes(purpleandbluetraces). AsweobserveinFigure3.15,byvaryingthe
Spiking Duration Control voltage, the spiking duration in the upper trace (purple trace)
can be adjusted longer than the spiking duration in the lower trace (blue trace). Figure
3.16showsthevariationinthespikingdurationwithchangeinSpikingDurationControl
voltage.
We tuned the axon hillock to different refractory periods and hence different firing
frequenciesbyvaryingthecontrolvoltage Refractory Period Control. Theactionpoten-
tialsgeneratedbythetestneuron(Neuron1)weresenttothesynapsesofasimilarsecond
neuron (Neuron 2) and the output of Neuron 2 was observed. In Figure 3.17, when the
outputrefractoryperiodisadjustedto30ps(refractoryperiodcontrol=0.3V)(redtrace)
then there is temporal summation on the synapses (purple trace) of Neuron 2 to further
42
Figure3.17: High-frequencyfiringofneuron1leadstoanoutputspiketrainfromneuron
2
causethedendriticvoltageofNeuron2totemporallysum(bluetrace). Thiscausesneu-
ron 2 to produce an output train of action potentials (orange). On the other hand, as
shown in Figure 3.18, when the output refractory period is adjusted to 50 ps (refractory
periodcontrol=0.6V)(redtrace)thereisnotemporalsummationonthesynapses(purple
trace) of Neuron 2 hence there is no temporal summation of the dendritic voltage (blue
trace)whichinturnfailstoexciteneuron2toproduceatrainofactionpotentials(orange
traceat.048mV).
43
Figure3.18: Low-frequencyfiringofneuron1failstoproduceanoutputfromneuron2
44
Chapter4
GlialMicrodomaintoExhibitExcitabilityin
Networks
4.1 Introduction
Neuroscientistshavefoundevidencethatglialcellscontributetoneuralprocessing. While
glial cells were known to provide nutritional support for neurons, their roles are much
broader. Direct and diffuse communication between neurons and between glial cells
(in particular astrocytes) and neurons influences not only neural behavior [62] [63], but
alsoneuralcircuitstructure. Astrocytesareinvolvedincomplexsignalingwithneurons.
Theyrespondtoneurotransmitters,detecttheflowofionsinandoutofneighboringneu-
rons,andreleasegliotransmittersandionsthatcanaffectneuralbehavior. Thissignaling,
involvingbothpositiveandnegativefeedback,iscomplexandnotfullyunderstood.
We have chosen to model a single mechanism that captures the signaling between
astrocytes and neurons in the rat hypothalamus and cortex by means of the transmitter
45
glutamate. In particular, we show a neural-glial neuromorphic system that demonstrates
the role of astrocytes in facilitating neural firing when neighboring neurons in the same
microdomain(neuronsspannedbyeachastrocyte)areactive.
Figure 4.1: Cartoon showing astrocytic mechanisms implemented (Credit-Ko-Chung
Tseng)
Ourspecificfocushereistoconstructneuromorphiccircuitsthatemulatetherelease
of glutamate by astrocytes and show that it increases excitability in neurons located in
the microdomain. We also emulate the uptake of glutamate by astrocytes from nearby
neuronsthatsubsequentlycausescalciumconcentrationstoincreaseandspread,trigger-
ing the astrocyte glutamate release. Although the effects we show are first-order, they
are a step towards demonstrating neuronal-astrocyte communication. Figure 4.1 shows
aschematiccartoonthatdemonstratesthemechanismsthatweemulateusingourneural
circuitsinCMOS.Thecartoonshowstwosynapsesaspartofanastrocyticmicrodomain.
Weshowthesequenceofeventstoexplainhowournetworkbehaves. Increaseinsynap-
tic activity releases glutamate into the synaptic cleft (1). Some of the glutamate in the
46
cleftistakenupbytheastrocyte(2)tocauseelevationofCa
2+
concentrations(3). These
Ca
2+
elevationscauseglutamatetobereleasedbytheastrocyteatthepost-synapticsite
of Synapse 1 and at other post-synaptic sites (e.g. Synapse 2) in the microdomain (4).
ThisincreasesthePSPatSynapse2thusincreasingtheprobabilityoffiring.
Recentadvancesinneuromorphicengineeringhavefocusedmainlyonneuralmech-
anismssuchasSTDP[49][64],synapticrewiring[10][17]andneuralspiking[55][40].
There has been a focus on emulating biological neural networks based on these mecha-
nisms to demonstrate learning. Mathematical models for neuronal-astrocyte interaction
have been developed [65]. While some form of neuromorphic circuits has been investi-
gated for about half a century, we have not been able to identify any such circuits that
model glial-neuronal interactions and circuit modeling of astrocyte-neuronal communi-
cation has not been reported in the literature. We believe that our crude circuits are the
first attempt at this difficult modeling. We build on our library of neurons that contain
dendritic processing and dendritic plasticity [66], STDP [8], and other biomimetic fea-
tures.
4.2 AstrocyteBiologicalBackground
Astrocyte-neuronal signaling is observed to be a complex bidirectional communication
[67][68][69]. Withoneastrocytebeingconnectedtoover100,000synapses[67],astro-
cytes are capable of monitoring wide-ranging neuronal communication. The respective
47
regions of coverage of these astrocytes are called microdomains [67]. The most widely-
acceptedastrocyticmechanismisthemonitoringofglutamatereleasedbysynapses. The
glutamate released by synapses and uptaken by the astrocyte causes calcium (Ca
2+
)
wavesthatspreadacrosstheastrocyte. Thesewavesleadtoreleaseofglutamateatother
synaptic locations in the microdomain. Current research [67] [69] discusses the possi-
ble case where glutamate released by the astrocyte increases neural excitability due to
increaseofglutamateatthesesynapticlocations.
ThelocationwhereastrocytescommunicatewithsynapsesiscalledaTripartiteSynapse
[68] [67], a complex location with many chemical processes. Neural activity at the
synapse leads to release of glutamate which is taken up by the astrocyte. Local in-
crease in glutamate leads to increase inCa
2+
concentration that causes the astrocyte to
release a group of chemicals called Gliotransmitters [69], including Glutamate, Adno-
sine Triphosphate (ATP) and D-serine. Glutamate and D-serine are believed to play an
excitatory role at the synapse whereas ATP plays a regulating role. Glutamate release
can increase the synapse’s excitability, leading to a higher post-synaptic potential (PSP)
when action potentials (AP) impinge on it. This can cause the neuron to fire with fewer
EPSPsfromstimulatedsynapsescombininginthedendriticarbor.
Intracellular astrocyte Ca
2+
waves and oscillations have been reported, with com-
munication between astrocytes thought to occur via gap junctions [62]. Non-linearity
in the intracellular astrocyteCa
2+
processing has been reported (e.g. [70]), suggesting
48
a neuromorphic circuit implementation of intracellularCa
2+
processing in the cytosol
mightbecomplex.
4.3 TheSynapseandAstrocyteCircuits
OurpreviouslypublishedresearchhasshownneuronalcircuitswithSTDP[8]andspik-
ing[56]. Oursimulatedsynapsecircuits[8][2]havebeendesignedwithfocusonemulat-
ing neurotransmitter release, neurotransmitter concentration, neurotransmitter reuptake,
and transmitter-receptor interaction. Because of both the compartmentalized construc-
tionofourneuromorphiccircuitsandalsotheabilitytocontrolneuralparametersdirectly
bymeansofspecificcontrolvoltages,insertingadditionalmechanismscanbeperformed
withoutextensivecircuitredesign. Thishelpsusemulateastrocyticbehaviorincircuitsin
a compartmental approach, such that astrocytic calciumCa
2+
release causing glutamate
releasecanbeinsertedeasilyintotheneurotransmittersectionofoursynapses.
Figure 4.2 shows an excitatory synapse circuit modified from the current synapse
circuit as discussed in Chapter 3 [8]. The circuit is divided into neurotransmitter (pre-
synaptic)andreceptor(post-synaptic)sectionsasshown. Thevoltageatthenodelabelled
synapticcleftrepresentstheneurotransmitterconcentrationinthesynapticcleft. Amod-
ification has been made to the output of the neurotransmitter section, where an analog
voltage adder [61] is connected, such that the cleft voltage is added to the neurotrans-
mitter voltage contributed by the astrocyte circuit. AstroCa
2+
is the control signal that
causesthesynapticclefttobeoffsetbyavoltageV
astro glut
. Thismodelstheamountof
49
Figure4.2: TheBioRCexcitatorysynapsecircuit
glutamategliotransmitterthatisinjectedintothecleftbytheastrocyte. Theoperationof
thesynapsecircuitwasdescribedinfurtherdetailinChapter3.
Figure 4.3 shows several compartments of an astrocyte circuit. It is a distributed re-
sistive(passtransistor)networkthattakesinputsfromthevoltagesrepresentingsynaptic
cleft neurotransmitter concentrations of different synapse circuits. The neurotransmitter
voltage from each synapse is fed into a non-inverting active delay circuit whose output
voltagerepresentingreleasedneurotransmittersissummed[61]withdelayedneurotrans-
mittervoltagesfromothersynapses. Thismodelsthetimetakenbytheastrocytetotake
50
Figure4.3: Circuitcontainingseveralcompartmentsofanastrocytecommunicatingwith
multiplesynapses
up neurotransmitters and generateCa
2+
. The rise in potential at the resistive network
(AstroCa
2+
)modelstheincreaseandspreadincalciumacrosstheastrocyte. Theoutputs
of the astrocyte compartments control transistors in each synapse such that the synapse
adds an offset voltage to the synaptic neurotransmitter concentration voltage to emulate
theincreaseinneurotransmittersinthesynapseduetotheastrocyte’sreleaseofglutamate
causedbyintracellularcalciumincrease. Previouslypublishedwork[15]hasshownthat
the adders used are capable of non-linear computations and they are used with the aim
51
of summing the calcium released nonlinearly. This work is under progress and will be
reportedlater.
4.4 ExperimentalNetworktoDemonstrate
Astrocyte-NeuronCommunication
Figure4.4: Neuralnetworkillustratingastrocytemicrodomain
Figure4.4showsanetworkofsiliconneurons[8][56]alongwithanastrocytespan-
ning the neurons to create a microdomain . The goal is to test whether synaptic activity
52
in one region of the network increases excitability at another. We set the firing thresh-
olds for the neurons in such a way that the neurons fire when there is enough dendritic
potential (about equal to the sum of the EPSPs of the three synapses). Hence, as shown
in Figure 4.4, neuron 4 (N4) will fire as it is connected to three synapses whereas neu-
ron 5 (N5) will not fire, as it has only two synaptic inputs. Neurons 1, 2 and 3 are
input neurons to the network and will be given an action potential stimulus to fire. To
demonstrate change in excitability we focus on the neurotransmitter (cleft) voltage and
theEPSPgeneratedbysynapse5.
Figure4.5: Case1: Simulationresultsforthenetworkwithoutastrocytecircuit
53
Figure4.6: Case2: Simulationresultsforthenetworkwiththeastrocytecircuitinvoking
excitability
54
Circuit simulations were conducted using TSMC 18 CMOS technology in SPEC-
TRE. We first show that without astrocytic communication provided to the network,
synapses4and5donotproducesufficientneurotransmitterrelease(representedbycleft
voltages),resultingininadequateEPSPs,sothatneuron5doesnotfire. Asshownbythe
waveformsinFigure4.5,neuronsN1andN2,whenstimulated,generateactionpotentials
(black trace). This causes neuron N4 to fire due to sufficient dendritic potential (green
trace). When Synapses 4 and 5 at Neuron 5 are excited by neurons N1 and N3, their
cleft voltages (pink trace) representing neurotransmitter concentrations are insufficient
(comparisoninFigure4.7)togeneratesufficientEPSPs(Figure4.7)tomakeneuronN5
fire(lightbluetrace,0volts).
We then connect the astrocyte circuit and execute the same set of simulations. As
shown by the waveforms in Figure 4.6, when synapses 1,2 and 3 are excited by N1 and
N2(blacktrace)thecleftvoltagegeneratedatthesynapses(bluetrace)causestheastro-
cyte circuit to generate a delayed voltage (AstroCa
2+
1, red trace). As theCa
2+
signal
propagates across the resistive network (AstroCa
2+
+5, green trace) it causes the cleft
voltage at synapse 5 to rise by an offset set by V
astro glut
, which in our experiments is
200 mV (pink trace) in Figure 4.7. When neuron N3 excites synapse 5 the cleft voltage
(pink trace) rises high enough to generate a voltage greater than in case 1 (comparison
showninFigure4.7). Thiscausesneuron5tofire(lightbluetrace). Thuswehaveimple-
mentedinsiliconastrocyticmonitoringofsynapticactivitythatcanincreaseexcitability
ofneuronscloseby. Thisisafirst-ordereffectandmorecomplexmechanismsareunder
55
Figure4.7: ComparisonofcleftvoltagesandPSPsincaseswithandwithouttheastrocyte
circuit
investigation. Circuitry exhibiting the inhibitory effects of astrocytes and the signaling
byothergliotransmittersisasubjectoffutureresearch.
56
Chapter5
ApproachtowardsNeuromorphicNetwork
RestructuringusingSynapseClaiming
Structural plasticity, in the form of network restructuring, is thought to be important
to learning. To model structural plasticity described in Section 2.2 using a neuromor-
phic circuit, we have introduced a method called Synapse Claiming, a circuit technique
for network restructuring. Our first step towards structural plasticity is to claim inac-
tive synapse structures autonomously and use them where activity warrants increased
synapses in parallel with existing synapses. Our circuits monitor synapses for activity
and when there is no activity for a long time (scaled down to order of nanoseconds) and
theadjacentsynapseisactive,thesynapseisclaimedtostrengthentheactivesynapse.
Figure 5.1 shows the detailed circuit schematic of a section of the network where
a pre-synaptic neuron with increased activity can claim the synapse of a pre-synaptic
neuron that has no neural activity. The switches shown are modeled using transmission
57
Figure5.1: Synapse-claimingschematic
gates. The switches emulate the creation and elimination of different synaptic connec-
tions. These switches are controlled using different time constants ST (slower time con-
stant) and FT (fast time constant). These time constants emulate different mechanisms
behind the formation and elimination of a synapse. Some electrical connections (FT to
STandSTtoFT)havebeenmadetomodeltheiractionsassystemtimeconstantswith-
outmodelingtheunderlyingmechanismsthatarecomplexandnotwellunderstood. The
58
synapseshavebeensplitintopreandpostsynapticsections[8]toemulatesynaptogene-
sisasdiscussedinSection2.2. Theneuroncircuitsinsynapseclaimingincludeaspiking
axonhillock,anexcitatorysynapseandaninhibitorysynapse,asdescribedinChapter3.
Figure5.2: CircuitusedtomodeltheFTandSTtimeconstants
TheFTandSTcircuitsarebasicfour-transistorintegratorcircuitsasshowninFigure
5.2 that are sized to provide required fast and slow time constants. The input to each
circuit is a train of spikes from a neuron and the output for control signals FT and ST is
arising(sloworfast)potentialwhichfallsataratecontrolledby Vbias.
Figure 5.3 shows the situation when both neurons N1 and N2 are active (black cir-
cle 1). N1 and N2 firing activate mechanisms FT1 and FT2 respectively (black circle
2). Active FT1 and FT2 control signals complete the neural connections to N3 (black
circle 3) through synapses 1 and 2. FT1 and FT2 inactivate ST1 and ST2 (black circle
4) to prevent them from closing neural connections (black circle 5) by grounding their
outputs. Thisemulatesthesituationwhenneuronsareactivelyfiring;theyhavesynapses
connectedanddonotlosethem.
59
Figure5.3: Nosynapseclaimingasbothneuronsareactive
We simulated this case using Cadence SPECTRE (TSMC 18 technology) and the
results are presented in Figure 5.4. Simulation results for this case are presented in two
halves,leftandright. Theresultsareexplainedwiththefollowingsequenceofevents:
1. Both neurons N1 and N2 (red and light pink traces), are active causing their fast
timeconstantcontrolsignals(FT1andFT2)togohigh(leftorangeandrightbluetraces).
2. AsFT1andFT2gohigh,theslowandfasttimeconstantcontrolsignals(ST1andST2)
aregrounded(disabled)(leftpurpleandrightredtraces).
60
Figure5.4: Simulationresults: Nosynapseclaimingasbothneuronsareactive
3. As a result synapse 1 and synapse 2 are excited by their respective neurons (brown
andrightpurpletraces)andneuronN3firesasshown(left/rightdarkpinktrace).
Figure 5.5 demonstrates the case when the network restructures its connectivity due
to change in neural activity. Neuron N2 has increased neural activity (black circle 1)
whileNeuronN1lacksneuralactivity(blackcircle2). N2firingactivatesFT2andST2.
FT2 deactivates ST1 so that N1 cannot form a new connection with synapse 2 (black
61
Figure5.5: SynapseclaimingasN2isactiveandN1lacksneuralactivity
circle 3). FT2 completes the connection with N3 via synapse 2 (black circle 4). With
increased neural activity from N2, ST2, being a slow rising control begins to make a
newconnectionfromN2tosynapse1,whichwasleftunclaimedbylackofactivityfrom
N1. This models the growth of an axon due to increased neural activity as described in
Section2.2(blackcircle5). ST2deactivatesFT1sothattheconnectionbetweenN1and
N3iseliminated(blackcircle6). WiththeconnectionformedbetweenN2andsynapse1,
ST2willactivatethepre-synapticsideofthenewlyconnectedsynapse1(blackcircle7)
emulatingtheeffectofPRESD(Pre-synapticdifferentiation)(Section2.2). PRESDwill
62
enable the receptor side of synapse 1 to emulate POSD (Post-synaptic differentiation)
as described in Section 2.2. With continuous activity the post synaptic connection is
completed (black circle 8) and so is the connection between synapse 1 and N3 (black
circle 9). This emulates the growth of a dendritic spine with increase in local synaptic
activity(Section2.2). AsaresultNeuron2isconnectedtoN3throughtwosynapsesthus
strengtheningitsneuralpathway. AlsotheconnectionbetweenN1andN3isfunctionally
eliminatedbyswitchingcontrolledbyST2,thusalteringtheconnectivityofthenetwork.
Thus,byreusinghardware,weareabletochangenetworkproperties.
We simulated this case using Cadence SPECTRE and the results are presented in
Figure5.6. Theresultsareexplainedwiththefollowingsequenceofevents:
1. We made neuron N1 active for a short period of time (left red trace, 0-500 ns) as
comparedtoneuronN2(rightlightpinktrace)whichiscontinuouslyactive.
2. Asobservedinthefigure,aslongasN1isactive,FT1isactive(leftorangetrace)and
ST2isgrounded(rightredtrace). ThispreventsN2fromclaimingsynapse1.
3. When N1 is inactive ( after 500ns), synapse 1 stops outputting EPSPs (500ns to
900ns).
4. During that interval as N2 is still active and due to lack of grounding from FT1, ST2
is able to slowly rise (right red trace) and then ground FT1. This indicates a loss of
connectionbetweensynapse1andN1.
6. With ST2 rising, the switch between N2 and synapse 1 is closed thus indicating the
formation of a new connection between N2 and synapse 1. This is demonstrated with
63
Figure 5.6: Simulation results:Synapse claiming as N2 is active and N1 lacks neural
activity
synapse 1 outputting EPSPs after the interval (left brown trace, 900ns) and neuron N3
firing(left/rightdarkpinktrace,900ns).
Hence,synapse1isclaimedbyneuronN2. Weplantousethiscircuitinanexamplethat
discusses the modeling of structural changes in the rat whisker receptive field (Chapter
6).
64
5.1 ComparisonofApproachtoSynapticWeight-Change
Method
In this section we would like to compare the implemented method to the traditional
approachofchangingindividualsynapticweightswithoutrestructuringorreusinghard-
ware. The comparison will be made in terms of transistor count to highlight the cost
involvedinbothapproaches.
Figure5.7: Networktodemonstratehardwarecostfornetworkrestructuring
Intheapproachimplementedwetakeunusedsynapsestostrengthentheactivepath-
wayssuchthateachstrengthenedpathwaywouldhavetwosynapseswitheachonehav-
ing one STDP circuit. To implement a network using only synaptic weight change and
65
Figure5.8: Networktodemonstratehardwarecostforsynapticweightchangemethod
with similar neural functionality we would require each pathway to have two synapses
as shown in Figure 5.8. Each pathway that is strengthened must contribute a potential
equal to two synapses and hence two synapses need to be hardwired or a synapse with
great dynamic rangemust be used. We only consider the possibility of having an extra
synapse for each pre-post connection. With each synapse we need to include an STDP
circuit, hence each synapse cost equals 40 transistors, 13 (synapse circuit) + 27 (STDP
circuit). As shown in Figure 5.8, there is control circuitry needed to increase (change)
the synaptic weights of the synapses in the active path and decrease the weights in the
inactive path. With each synapse thereis an extra dendritic element, the adders (Section
66
3.4.2 ) needed which also contributes to the cost. Figure 5.7 shows the network for the
implementedmethodofrestructuringwithfocusonneuralcircuitelementsneeded.
Figure 5.9: Cost comparison between synaptic weight change method and implemented
method
Assuming the cost incurred by each axon element is common to both, to compare
the total cost of the two methods we can do a simple comparison. Assuming that the
control circuitry in both cases incurs the same cost we can do a comparison for the cost
incurred by the synapses, dendrites and switches. As shown in Table 5.9 the method of
using synaptic weight change will cost more. To maintain symmetry we increase the
numberofsynapsesintheactivepathbyafactorof2tocheckforincreaseincost. After
observingresultsfromTable5.9wecangeneralizethecostasfollows:
67
Assuming that the transistor count of each synapse is S, with dendrite cost being D,
control cost being C and switching cost SW (cost of transmission gates = 2 transistors),
wecanarriveatacostfunctionintermsoftransistorcountforbothmethodswhereNis
thenumberofsynapses.
Method A : Transistor count for network restructuring method = (N)S + (N-1)D +
2(N)SW+C
MethodB:Transistorcountforsynapseweightchangemethod=(2N)S+(2N-1)D+C
Thus transistor count in Method B is greater than that of Method A by an amount =
(N)S+N(D)-4(N).
Henceifwedousedifferentsynapseordendritecircuitswecanarriveatacostesti-
mateforthenetworktopologyimplementedforbothmethods. Basedonourcomparison,
synapse claiming appears to be more economical than synapse strengthening alone for
neuralnetworkrestructuringandotherstructuralplasticityapplications.
68
Chapter6
NeuromorphicStructuralPlasticity-TheRatWhisker
ReceptiveField
6.1 BiologicalMotivation
Thesomatosensorycorticalnetworkintherathasbeenthefocusofrecentneuroscience
research [71] [72] [3]. Research has been conducted on the pathways that connect from
the vibrissae (whiskers) to the sensory cortex. It is well documented that there is feed-
forward excitation (additive effect) in the pathways within a column of a particular vib-
rissa and cross-columnar inhibition (subtractive effect) between two vibrissae columns.
Particular focus has been on brain plasticity with sensory deprivation (a whisker be-
ing cut), that leads to certain changes in the topography of the network [72] [3]. This
is caused due to reduced cross-columnar inhibition from the deprived column (whose
whisker is cut) that leads to increased excitation in the non-deprived column (whose
whisker is not cut). This increased excitation causes the neuron in the non-deprived
69
column to start forming synapses with the neighboring columns, thus changing the to-
pographyofthenetwork.
Figure6.1: Biologicalschematicofthesomatosensoryratsensorysignaling
Let us use a simple schematic to explain the signaling. As we see in Figure 6.1,
neurons N1 and N2 represent a cluster of L4 (layer 4) neurons in the rat somatosensory
cortex. Neurons N3 and N4 form a cluster of L2 (layer 2) neurons. N1 is receiving
sensory excitatory inputs from both intra-columnar (W1) and cross-columnar whiskers
(W2), with the excitatory synaptic weights distributed in a ratio of 3:1 (3 for W1). An
inversesignalingmechanismexistsforN2,withN2receivinginputsfromW2andW1in
70
a ratio (3 for W2) similar to N1. Neurons N1-N2 and N3-N4 form inhibitory pathways
on each other through inhibitory interneurons N5, N6, N7 and N8. N1 and N2 feed into
L2(Layer2)neuronsN3andN4thoughexcitatorypathways.
Figure 6.2: Biological results taken from [3], showing the normalized spiking rate for
the intra-columnar neuron (N3) for different whisker stimulation (dark blue with cross
inhibition,lightbluelinewithoutcrossinhibition)
Let us consider W1 to be the principal whisker (PW) and W2 to be the surrounding
whisker(SW).WhenW1andW2areexcitedthefiringpatternonN3isobservedtobeas
shown in Figure 6.2 [3], where cases of with and without cross inhibition are presented.
As we see there is more activity when there is no inhibition across the neurons. W1 and
71
W2maptocorticalcolumnsthatcontainmanyneurons,hencethecurvesarecontinuous
torepresentbehavioraswemovefromwhiskerW1toW2.
Figure 6.3: Biological schematic of the rat sensory signaling when one whisker (W1) is
cut
When W1 is cut, then there is reduced inhibition from N1 onto N2 through N5 that
causesN2tostartformingcross-columnarsynapseswithN3,thusleadingtoachangein
the network topology and thus receptive field of W2 (Figure 6.3). Biological results for
thiscasearepresentedinFigure6.4.
72
Figure6.4: Biologicalresultstakenfrom[3],showingthenormalizedspikingrateforthe
intra-columnar neuron (N3) when whisker W1 is cut : Results show that N3 fires more
spikes (light blue) due to surround whisker W2 in contrast to W1 in the previous case.
Thisisduetothechangeintopographyofthenetwork.
6.2 NeuromorphicCircuitImplementingWhiskerReceptive
Field
To model the biological behavior described in Section 6.1 using a neuromorphic circuit,
we consider a network of in-silico neurons that are built from the library of circuits
describedinChapter3andthesynapse-claimingcircuitdescribedinChapter5.
73
Figure6.5: Circuitschematicoftheratsensorysignaling
The schematic shown in Figure 6.5 is similar to the one described in Section 6.1
with the inclusion of the synapse-claiming circuits. Neurons with spiking axon hillock,
dendriticsummationsandsynapses(excitatoryandinhibitory)weredescribedinChapter
3. The FT and ST mechanisms are described in Chapter 5 for synapse claiming model
theintra-columnarandcross-columnar(dottedline)excitatoryprojectionsinourwhisker
receptive field example. The cross-columnar inhibition is modeled using the inhibitory
synapsesdescribedinChapter3.
74
6.2.1 ExpectedSimulationResults
AsobservedinSection6.1,neuronN3mustfirealargernumberofspikeswhenaninput
isgiventoW1comparedtowhenaninputisgiventoW2. Thereisanincreaseinnumber
ofspikesifcross-columnarinhibitionisremovedbetweenN1andN3.
Figure 6.6: Circuit schematic of the rat sensory signaling when W1 is grounded (W1 is
clipped)
Figure6.6showsthesecondcasewhenthewhiskerW1isnotgivenanyinputs(signi-
fyingsensorydeprivation)andwhiskerW2isgivenanexcitatoryinput,expectedresults
aredescribedwiththefollowingsequenceofevents:
75
1. NeuronN2inhibitsN1.
2. Due to no inhibition from N1, N2 fires more spikes that causes the synapse claiming
mechanismtoactivate.
3. The cross columnar projection (ST2 as described in Chapter 5) causes neuron N2 to
claimsynapseSy5thusformingacross-columnarpathwaybetweenN3andN4.
4. As a result neuron N3 outputs a larger number of spikes, thus showing a change in
topographyofthenetworkandchangeinreceptivefieldofwhiskerW2.
6.2.2 Simulationresults
The circuit shown in Figure 6.5 was simulated using Cadence SPECTRE. Figure 6.7
shows the summary of our simulation results. Figure 6.7 (a) shows the scenario when
whisker W1 is intact and Figure 6.7 (b) shows the final effect on the network when W1
isclipped. WeobservethatthebehaviorofournetworkasshowninFigure6.7issimilar
tothebiologicalbehaviordescribedinFigures6.2and6.4.
WefirstlookatthecasewhereW1wasnotclippedandtherewasnocrossinhibition
present between N1-N2 and N3-N4. We achieve this by removing the connection from
N1toN5,N2toN6,N3toN7andN4toN8. ThusthereisnopossibilityofneuronsN1
andN2inhibitingeachotherandsamegoesforN3andN4
As shown in Figure 6.8, the effect of no cross inhibition across neurons N1-N2 and
N3-N4isshown. Theresultsareexplainedwiththefollowingsequenceofevents
76
Figure 6.7: Simulation results summary: Figure (a) shows the number of spikes for
N3(normalized)vswhiskerstimulation. Lightbluelineindicateswithoutinhibitionand
darkbluelineindicatespresenceofinhibition. Weseethatthenumberofspikesaremore
for principal whisker W1 and it increases in absence of inhibition. Figure (b) shows the
effect of grounding W1. We observe that N3 now fires spikes due to W2 which shows
thatthenetworktopographyhaschanged
1. W1 and W2 are both active (black trace) that cause neurons N1 (blue trace) and
N2(graytrace)tofire.
2. Due to lack of inhibition from N2 to N1, the interneuron N6 will not fire (red trace,
0V) and as a result the inhibitory synapse does not output inhibitory potentials (IPSPs)
ontoN2(orangetrace,0V).
3. ThedendriticpotentialontoN1(lightgreentrace)causesN1tofirespikes(bluetrace)
asshown.
77
4. A similar form of signaling carries forward onto N3 and N4 causing N3 to spike
(purpleanddarkgreentraces).
We now look at the case where W1 was not clipped and there was cross inhibition
present. ResultsareshowninFigure6.9.
As shown in Figure 6.9, the effect of cross inhibition across neurons N1-N2 and
N3-N4isevident. Theresultsareexplainedwiththefollowingsequenceofevents:
1. W1 and W2 are both active (black trace) that cause neurons N1 (blue trace) and
N2(graytrace)tofire.
2. As seen N2 causes the interneuron N6 to fire (red trace) and as a result the inhibitory
synapseoutputsinhibitorypotentials(IPSPs)ontoN1(orangetrace).
3. This inhibits the dendritic potential onto N1 (light green trace) and causes N1 to fire
lessspikes(bluetrace)incomparisontothepreviouscasepresentedinFigure6.8.
4. A similar form of signaling carries forward onto N3 and N4 causing N3 to fire less
spikes compared to the previous case as shown in Figure 6.8 (purple and dark green
traces).
WenowgroundtheoutputofwhiskerW1. ThismodelstheclippingofwhiskerW1.
ResultsofthiscasearepresentedinFigure6.10.
Theresultsareexplainedwiththefollowingsequenceofevents:
1. When W2 is activated it excites N1 for a small period due to a small weighted
synapse. ThiscausesN1andN3tofireasfewspikes(bluetraceandgreentrace).
2. DuetolackofconstantinhibitionfromN1,N2firesmorespikes(graytrace).
78
3. As explained in Chapter 5, FT1 (which is activated by N1) stays active for a short
periodafterwhichST2(activatedbyN2)slowlyrises(darkbluetrace)toclaimSy5.
4. As seen in the output of N3 (green trace) there is a time interval in which there is
no activity (150ns to 750ns). After this interval N3 starts to fire spikes due to a new
connectionbeingformedwithN2.
5. ThisshowsthechangeinnetworktopographyandreceptivefieldforwhiskerW2.
Wehaveusedindividualneuronstomodelcorticallayersandtheseresultsshowthat
ourcircuitimplementationissimilarinbehaviortothebiologicalschematicpresentedin
Section6.1.
79
Figure6.8: Simulationresultsshowingwaveformsatdifferentkeypointsofthenetwork
whenW1isnotclippedandactive,withoutanycrossinhibition
80
Figure6.9: Simulationresultsshowingwaveformsatdifferentkeypointsofthenetwork
whenW1isnotclippedandactivewithcrossinhibitionpresent
81
Figure6.10: Simulationresultsshowingwaveformsatdifferentkeypointsofthenetwork
whenW1isclipped
82
Chapter7
ConclusionandFutureWork
Thisthesisdescribesresearchmodelingplasticityinneuromorphiccircuits. WithCMOS
being a rigid technology, novel circuit designs and techniques are required to build neu-
romorphic circuits and networks that can change connections autonomously. The tech-
nique, Synapse Claiming, used in this thesis is one of the many possible methods to do
so. It does have the advantage of saving local control overhead; however, it’s limit in
terms of global scaling still needs to be examined. The comparisons presented in Chap-
ter 5 take into account transistor count as a measure of complexity. We have not taken
into account transistor sizing and wiring; both play a role in estimating hardware cost.
Futureworkwouldincludetakingintoaccountthetransistorsizingandwiring.
As a part of Synapse Claiming we took into account the addition of new synaptic
connections in comparison to a synaptic weight-change method that we concluded cost
more in terms of transistors. In the synaptic weight-change method, we said that we
wouldneedmoresynapsestoincreasetheoverallconnectionstrengthbetweenneurons;
hence more hardware is required. Another possible way for the synaptic weight change
83
methodtoreduceitscostisbyincreasingthedynamicrangeofthesynapse. Thismethod
wouldprovetobegoodifwedonotchangethesynapsecircuitdesignandcharacteristics.
Thisaspectstillneedstoinvestigated.
We explored, in Chapter 4, a circuit that models astrocyte-neuron communication.
The modeling presented was a first step towards modeling astrocyte-neuron communi-
cation. The modeling presented is first-order and one of the many synaptic mechanisms
that exist in biology. The design methodology presented has led to the design of most
of the complex networks presented in this thesis. The library of circuits is still incom-
pletewithmoreneuralcircuitsneeded,suchasgap-junctionsandpathwaysthatemulate
two-waycommunication.
Anaturalextensionofthisthesiswouldbetobuildanetworkthatcontainsanetwork
offloatingsynapsesthatareusedontheflyasthenetworktopographychanges. Asimilar
approachcouldbeappliedtobuildingscientificmodelingtestbedswhereneuroscientists
couldsimulatetheirnetworks.
CMOS is not the best technology for modeling plasticity due to its physical rigidity,
but it is the best short-term solution. The future of modeling plasticity electronically
would lie in materials that are both electrically and physically changeable. The path is
beinglaidwithnanotechnology(nanotubesandgraphene)anditcouldbemoreinterest-
ingwithadvancedmaterialssuchassyntheticDNA.
84
This dissertation has shown methods for creating synaptic and structural plasticity,
for creating neurons with a variety of spiking patterns, for a modular approach to neu-
romorphiccircuits,andforincorporatingastrocytesintotheneuralcomputations. While
certain methods have been previously shown in the literature, our integration into a uni-
fiedapproachforneuromorphicdesignisnovelandpowerful. Inparticular,autonomous
structural plasticity and incorporation of astrocytes are novel. This dissertation is a be-
ginning. Itisuncleartomanyneuromorphicresearchershowdetailedanddeeptheneural
modelingmustbetoproduceneuronsthatcollectivelyexhibitintelligence. Whatisclear
isthatneuroscienceresearchresultsareemergingalmostdaily,andsomeoftheseresults
highlightmechanismsthatmustbeincorporatedinthefutureforidealneuralbehaviorto
emerge. The research results here are a start at providing circuits useful for prosthetics,
robotics,andneuroscienceexperimentation.
85
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Abstract (if available)

Abstract A thesis exploring first-order in-silico modeling of changes (plasticity) in biological neurons is presented. In biological neural networks there is an intricate feedback relationship between neurons that results in synaptic and structural plasticity, including alterations in the connectivity and signaling between cells. Plasticity is widely believed to be key to memory, learning and intelligence. For engineers trying to implement biological neural networks in silicon, changes in neural functionality and rewiring could be essential mechanisms to examine. Modeling an electronic neural network that restructures itself could demonstrate learning and memory, and could lead to a better understanding of the way neural pathways implement learning and memory. This thesis looks at three aspects of neuromorphic design in parallel: functional complexity, scalability and plasticity. ❧ We have modeled plastic excitatory and inhibitory synapses wherein changes in neurotransmitter and receptor concentrations can be emulated to a first-order. Results show that we can use these synapses in different combinations to demonstrate different kinds of behavior such as spike-timing-dependant plasticity and the effect of astrocytes (glial cells) on synaptic efficacy. We have also shown a circuit that emulates a spiking axon hillock. It can be tuned using an external voltage to produce different spiking patterns of variable duration. A design approach has been discussed towards building large scalable nueromorphic networks. ❧ To demonstrate a plausible biological example of structural plasticity, a first-order neuromorphic analog circuit implementation of upper layers of the rodent barrel (somatosensory) cortex has been implemented. We have modeled spiking behavior of somatosensory cortical neurons in layers 2-4 and neuronal receptive fields while replicating biological observations on experience-dependent changes in receptive field organization, network topology and synaptic connectivity in silico. Anatomical and functional changes in synaptic connectivity have been modeled using analog switching, based on change in neural network activity. We demonstrate the effects of loss of inhibition and the loss of sensory (whisker) inputs with our circuits, and show that the self-organizing neuromorphic analog circuit in silico exhibits structural plasticity. ❧ Future applications of this thesis would include intelligent prosthetic devices, autonomous robotic vehicles and systems that are capable of handling sensor damage.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Joshi, Jonathan R. (author)

Core Title Plasticity in CMOS neuromorphic circuits

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 02/08/2013

Defense Date 05/02/2012

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

Tag circuits,CMOS,neuromorphic,OAI-PMH Harvest,plasticity,structural

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Parker, Alice C. (committee chair), Breuer, Melvin A. (committee member), Celikel, Tansu (committee member)

Creator Email jonjoshi@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-219476

Unique identifier UC11292863

Identifier usctheses-c3-219476 (legacy record id)

Legacy Identifier etd-JoshiJonat-1433.pdf

Dmrecord 219476

Document Type Dissertation

Rights Joshi, Jonathan R.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA