Basal GangliaBasal Ganglia

• Involved in the control of movement

• Dysfunction associated with Parkinson’s and Huntington’s disease

• Site of surgical procedures -- Deep Brain Stimulation (DBS)

BASAL GANGLIA

STN

Deep Brain Stimulation (DBS)

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Parkinson’s disease associated with:

Loss of dopamine:

Parkinson’s disease associated with

changes in firing patterns.

Some neurons within basal ganglia exhibit:

• Increased synchronization

• Increased bursting activity

Why should these changes in firing patterns lead to the motor symptoms seen in PD?

cortex

basalganglia thalamus

Inhibitory synapses

Strong pathological output patterns ofBG inhibit motor activity.

MODELING STUDY • Construct model GPe/STN network.

Plenz & Kitai showed that a GPe/STN network can display synchronous activity.

• Can the network generate both synchronous, tremor-like rhythms and irregular, uncorrelated activity?

• Mechanism underlying DBS?

Striatum

STN GPi

GPe Cortex

Thalamus

inh

exc

Based on Experiments (Bevan and Wilson)

MODEL STN NEURON

CMV’ = – IL – INa – IK – IT – IAHP – ICa + IAPP IL = gL(V – VL) IK = gKn4(V – VK) INa = gNam

3(V)h(V – VNa) IT = gTa∞3( )V r(V – VCa)

ICa = gCa s∞2( )V ( V – VCa) IAHP = gAHP[ ]/(1+[ ]Ca Ca)( V – VK)

X’ = (X∞(V) – X)/ X(V) X = ,n ,h r [Ca]’ = ( – ICa – IT – kCa[Ca])

Firing Properties of STN Cells

Experiment Model

Firing Properties of STN/GPE Neurons

Post Inhibitory Rebound Firing Profiles

STN GPE

STRIATUM

STN / GPe NETWORK

Can this network exhibit both irregular and correlated activity (same architecture, different parameters) ?

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Irregular firing Clustering

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When does the network exhibit irregular or correlated activity?

I

GPe STN inhibition

Input tostriatum

Irregularfiring

Clustering

• 10 STN & GPe cells• Sparse, structured coupling

PCA

Consider a Periodically Forced GPe Cell:

Outline of Analysis:

• Fast/Slow Analysis of GPe Cell

• Phase-Response Curve for GPe Cell

• Construct a 1-D Map

Analysis of Irregular Firing

STN

GPe

MODEL GPe NEURON

We consider Ca as a slow variable.

CMV’ = – IL – INa – IK – IT – IAHP – ICa + IAPP IL = gL(V – VL) IK = gKn4(V – VK) INa = gNam

3(V)h(V – VNa) IT = gTa∞3( )V r(V – VCa)

ICa = gCa s∞2( )V ( V – VCa) IAHP = gAHP[ ]/(1+[ ]Ca Ca)( V – VK)

X’ = (X∞(V) – X)/ X(V) X = ,n ,h r [Ca]’ = ( – ICa – IT – kCa[Ca])

GPe bifurcation diagram

Stable fixed ptsunstable fixed pts

stable periodic orbits Saddle-node of limit cycles

Hopf

bifurcation

Dynamics Reduce to a Single Equation for the Slow Variable

Good Approximation:

Ca’ =

- S cell silent

A cell active

VGPe

Ca

A one-dimensional map

Linear Approximation of Map

TGPe > TSTN

π(t) =t + TGPe - TSTN TSTN - TGPe < t ≤ TSTN -TS

(λs/λA)(TSTN - t) TSTN - TS < t ≤ TSTN

TGPe = period of an isolated,bursting, GPe cell.

TSTN = interval between STNspikes

TS = GPe silent phaseTA = GPe active phase

TSTNTSTN-TS

TGPe - TSTN

TA

π(t)Slope -S / A

Slope 1

Tent map predicts:

λS < λA : number of spikes per burst is nearly constant

λS > λA : number of spikes per burst may vary chaotically

Numerically Computed MapTGPe > TSTN TGPe < TSTN

Poincare Section

Remark: This analysis does a very good job in predicting when irregular activity arises in larger networks.

STN

Mechanisms Underlying DBS Mysterious

Poorly understood:

• Which neurons DBS acts on.

• How DBS effects different parts of neurons.

• How DBS depends on geometry of neurons.

• Whether DBS is excitatory or inhibitory.

That is, does DBS increase or decrease output from stimulated structure?

Evidence That DBS is Inhibitory:

• Clinical effects similar to ablative surgery

• There is increased BG activity during PD

Evidence That DBS is Excitatory:

• Recent experimental data (Vitek et al.)

Question: How can one explain improvement of PD symptoms if DBS increases GPi output activity?

Parkinson

Normal

DBS

Basal Ganglia

How Does Input From BG Effect Thalamic Ability to Relay Excitatory Input?

Thalamus

???

ExcitatoryInput

Irregular (Normal) Activity

Basal ganglia Thalamus

STN GPi TC

DBS exc. input

DBS off

Basal ganglia Thalamus

PD: DBS off

PD: DBS on

DBS on

ThalamusBasal ganglia

DBS off

Basal ganglia Thalamus

PD: DBS on off

Data-driven computational study

We now consider signal obtained from single-unitGPi recordings from:

• control (normal) monkeys• parkinsonian (MPTP) monkeys without DBS• parkinsonian monkeys under sub-therapeutic STN-DBS• parkinsonian monkeys under therapeutic STN-DBS

Inhibitory signal si

GPi spike time

TC voltage

Excitatory signal

V (

mV

)V

(m

V)

V (

mV

)V

(m

V)

A

B

C

D

time (msec)

PD without DBS

sub-therapeutic DBS

therapeutic DBS

control

periodicinput

Poissoninput

ESTEST

err

or

ind

ex

err

or

ind

ex

EST = elevated spiking time of GPi signal

Normal PD w/o DBS sub-DBS therapeutic DBS

#bad + #misses #exc. inputs

error index =

small: low firing ratemedium: burstinglarge: high tonic firing

Collaborators

Charles WilsonJonathan RubinYixin GuoCameron McIntyreJerold VitekJanet BestChoongseok Park