MODELING THE PARKINSONIAN TREMOR

AND ITS TREATMENT Supervisor : Dr Towhidkhah

Designed by Yashar Sarbaz

Amirkabir University of Technology

TITLES

1. INTRODUCTION OF PARKINSON’S DISEASE (PD)

2. SIMPLE MODELING3. COMPLETING THE MODEL4. MODELING THE TREATMENTS

1.Intoduction of PD

1-1. Origin of PD (Basal ganglia)

1-2. Parts of Basal ganglia (BG)

1-3. PD & it’s symptoms

1-1.Origion of PD (BG)

1-2.Parts of BG

1-3.PD & it’s symptoms

Reason of PD:Loss of nerve cells in substantia nigra

pars compacta

Low level of Dopamine in patient’s brain

Changing activity of other blocks

1-3.PD and it’s symptoms

Symptoms of PD: HypokinesiaAkinesia: lack of slowness of

spontaneous and associative movement Rigidity: increased tone on passive

manipulation of joints Tremor:rhythmic,involuntary,oscillatorymovement around 4-6 Hz

Clinical Data Recording

Velocity laser recording of rest tremor

2.Simple modeling

2-1.Information about connections of Basal ganglia

2-2.Information about each block of Basal ganglia

2-3.Presenting mathematical model

2-1.Connection of BG The number of input and output of

each block The type of each input to block

(Inhibitory and excitatory effect ) The strength changes of

connections in patient and healthy cases

A gain corresponding to Dopamine changes

2-2.Each block of BG There are not detailed information

about function of each block The major criteria for separating

the different parts of BG are their anatomical and structural appearance and the kind of neurotransmitters

Each block contain large value of neurons

Behavior of single neuron Membrane resistance Membrane capacitance longitudinal resistance

2-3.Mathematical model

Changing activity of blocks

Healthy Patient

Changes of strengths of connections

Block diagram of model

Relations of each blocks

)(240

10)()),(sgn()(:)(1 sSogs

sAtAtSNcosG

)()30(

10)(

)(30

1)(:)(

2

12

sSNcoss

sSo

sSNcos

sSosG

)(10

501)(

10

101)(:)( 113 sSTNo

sgsSo

sgsGPosG

Relations of each blocks

)(40

1)(

)(40

1.)(:)(

2

14

sGPos

gsSTNo

sGPos

gsSTNosG

)(10

200)(

10

2001)(:)( 225 sSo

sgsSTNo

sgsOUTsG

Model response for illness case ( g=10 )

Model response for treated case ( g=1 )

Sample of clinical Data

Comparing power spectra of clinical Data and model response

Clinical Data Model Response

3.Completing the model

3-1.Synaptic transmission 3-2.Noise sources in synaptic

transmission of healthy persons 3-3.Noise sources in synaptic

transmission of patients 3-4.Completing the model

3-1.Synaptic transmission

Step1

Step2

3-1.Synaptic transmission

Step3&4

3-1.Synaptic transmission

step5

3-1.Synaptic transmission

step6

3-2.Noise sources in synaptic transmission of healthy persons

Calsium amount in cell Voltage gated channels Diffusion of neurotransmitters Ligand gated channels

3-3.Noise sources in synaptic transmission of patients

Lower of uptake Up regulation Diffusion of neurotransmitters

3-4.Completing the model

Replacing with

Considering normal physiological Tremor:

)(tnagg g

50

50)(

s

sGlp

)())(1()()( snsGgbsOUTsOUTo lp

Comparing results with clinical data

g2rof record Model responsewith a=0.2

Comparing results with clinical data

S15rof record Model responsewith a=0.2&b=0.2

Changing activity of blocks

4.MODELING THE TREATMENTS

4-1.Kinds of PD treatments

4-2.Modeling drug effect

4-3.Modeling DBS effect

4-4.Prediction based on the model

4-1.Kinds of Treatments

1-1. Medical treatment

1-2. Deep Brain Stimulation

Medical Treatment

Levodopa Drug

L-depernil Drug

DBS

Target of Stimulation GPi: The Globus Pallidus Internal

STN:The Subthalamic Nucleus

Vim: The Ventro-Intermediate nucleus Thlamus

4-2.Modeling drug effect

Pharmacodynamics

Pharmacokinetics

Pharmacodynamics

Input is Levodopa drug

Output is plasma level of drug

Model and clinical data

Relation of Pharmacodynamics

)1)(1()(

21 sTsT

kesG

Ts

2461.06073.0

05473.01418

2

1

TT

Tk

Pharmacokinetics

input is plasma level of drug

Output is g parameter of main model

Pharmacokinetics parts

A nonlinear system (Saturation element)

A first order system

Scaling part

Response signal of Parmacodynamics part

Response signal of Pharmacokinetics part

Simple model response to drug prescription

Complete model response to drug prescription

4-3.Modeling DBS effect

Characteristics of the common DBS signal:

1. Frequency greater than 100 2. Pulse width about 90 3. Amplitude of stimulation voltage

nearly 3 v

sec

DBS characteristic for different subjects

Clinical data of subjects when DBS switch to on

Clinical data of subjects when DBS switch to off

Relation of DBS

ctezz

)( 01

c

c

c

t

tn

tn

n

e

eezz

1

)1(0

)()( 0 tzgtg

ctezz

)( 12

Relation of DBS

1

ctez

c

c

t

tt

e

egtg

1

)1()( 0

0ggg c

,

0g

cteg

11

Variation of Parameter of g in DBS

05.0ct076.0ct sec sec

Response of the simple model

05.0ct076.0ct sec sec

Response of the complete model

05.0ct076.0ct sec sec

4-4.Prediction based on the model

4-4-1.Offering a new medical treatment

4-4-2.Optimization of the levodopa usage

Problems of Levodopa usage

4-4-1.Offering a new medical treatment

Including GABA effect

Model response with different g & k=1

g=10 g=1

Model response with g=10 & k=0.1

Model response with g=5 & k=0.1

4-4-2.Optimization of the levodopa usage

T

cbTF ),(

)(89.40)( )2461.0(2715.18)2461.0(6466.1 tt eety

)(89.401500 )2461.0(2715.18)2461.0(6466.1 TT ee

250024

T

Optimization problem

2461.0

121 T

xx

2121 ),( xbxaxxF

0)(89.401500 )/2715.18()/6466.1(1

22 xx eex

025.615242500 221 xxx

Answer of optimization

7977.2613.58 21 xx

hourTmg 6035.0613.58