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程序代写案例-EEEN40070

时间：2021-05-04

UCD School of Electrical and Electronic Engineering

EEEN40070 Neural Engineering

Laboratory 5

Mechanism of Deep Brain Stimulation using Dither

Injection and the Equivalent Nonlinearity

Introduction

The aim of this laboratory is to explore mechanism of Deep Brain Stimulation in GPe-STN loop

using both direct high frequency dither injection and the equivalent non-linearity. You will use

Simulink to conduct a series of simulation studies to examine the effects of Deep Brain

Stimulation on the GPe-STN network.

Report

Each of these steps should be described in your laboratory report along with a series of graphs

describing your results. Your laboratory report should contain the following sections:

1. Introduction

2. Methods

3. Results

4. Discussion

Deep Brain Stimulation (DBS)

DBS is a widely applied clinical procedure for the alleviation of pathological neural activity and

is particularly effective in suppressing symptoms of Parkinson’s disease. Parkinson’s disease

is associated with the death of dopamine producing cells in the Substantia Nigra pars

compacta (SNc), one of the areas comprising the Basal Ganglia of the brain. The mechanisms

of action of DBS remain to be fully elucidated. In the lab, we will present an application to DBS

of the concepts of dither injection and equivalent nonlinearity from the theory of nonlinear

feedback control systems. This model provides a framework for understanding the mechanism

by which an injected high frequency signal can quench undesired oscillations in closed-loop

systems of interacting neurons in the brain.

A critical feature of DBS is that the frequency of the stimulation must be sufficiently high for it

to be effective (typically >100 Hz). The clinically effective frequency range lies well-above the

frequency range of both Parkinsonian tremor (4-10 Hz) and related pathological oscillations.

These include increased beta-band (15-30 Hz) synchronization in the basal ganglia–cortex

loop, which is hypothesized to be linked to the symptoms of akinesia and bradykinesia. This

characteristic feature suggested that insight might be gained by invoking the concept of “high

frequency” dither injection used to quench “low frequency” oscillations in nonlinear feedback

control loops.

Methods

A schematic diagram of the relevant basal-ganglia topology is presented below.

GPe, STN and GPi are modelled by nonlinear sigmoidal algebraic elements, followed by linear

blocks with dynamics enshrined in Laplace transfer functions.

• G(s): The output of the G(s) blocks represents the deviation from zero of the ensemble

averaged mean field output of all the cells in each of these areas. The mean field

evolves into an almost sinusoidal oscillation, governed by second order dynamics,

superimposed on a possible nonzero shift. The simplest form of G(s) is of the form:

(1)

where k and b are constants

The transfer functions for GPe and STN are set to be identical for simplicity.

• NL (h, g): The output from each sigmoid indicates the deviation from zero of the total

synaptic current averaged over all cells in the ensemble. The sigmoid in GPe is the

arctan characteristic:

(2)

The sharpness of the arctan is set by h, the smaller h the steeper becomes the slope

at the origin, given by . The nonlinear characteristic NL,g in the STN is

taken to be of the same form, with h replaced by g.

• The gain, -1, input to STN means that it is inhibitory input.

• Assuming that the non-linear characteristic in the STN has input, where e

is the negative mean field deviation from GPe neurons and d(t) is the DBS or ‘dither’

injection. This can be replaced by an equivalent non-linearity as following:

(3)

where is the mean value of y over a dither cycle.

Exercises

1. Model Implementation

Implement the model, GPe-STN loop only shown in the schematic diagram. The

parameter values are given as following; for a mean-field

oscillation frequency of 5.5 Hz, typical frequency of the tremor in Parkinson’s disease,

g set equal to 1 and h reduced to 0.1 to represent dopamine depletion. As h decreases,

the GPe-STN loop eventually bursts into oscillation.

2. Direct high frequency stimulation (DBS) and equivalent non-linearity

Apply a biphasic 100 Hz DBS input to the STN, of amplitude equal to 5 and a pulse

width of 500 µs. Also replace the high frequency stimulation and STN function with an

equivalent non-linearity (α = 0.05, A = 5 and g = 1). Compare the results.

3. Beta-band frequency application

Calculate the value of b in the second order transfer function (1) for beta-band (15-30

Hz) and then implement exercise 1 and 2 with this new value.

Supplement Exercises

1. It is known that GPe has inhibitory synaptic input from other GPe cells and STN has

excitatory feedback from other STN cells. Include these two inputs into the model, one

at a time and both at the same time. Explore their effects to the model and discuss the

results.

2. Plot the effect of different DBS frequency on STN output in the model with 5.5 Hz

(tremor frequency) and 20 Hz (Beta frequency) with pulse widths of 100, 200 and 500

µs.

学霸联盟

EEEN40070 Neural Engineering

Laboratory 5

Mechanism of Deep Brain Stimulation using Dither

Injection and the Equivalent Nonlinearity

Introduction

The aim of this laboratory is to explore mechanism of Deep Brain Stimulation in GPe-STN loop

using both direct high frequency dither injection and the equivalent non-linearity. You will use

Simulink to conduct a series of simulation studies to examine the effects of Deep Brain

Stimulation on the GPe-STN network.

Report

Each of these steps should be described in your laboratory report along with a series of graphs

describing your results. Your laboratory report should contain the following sections:

1. Introduction

2. Methods

3. Results

4. Discussion

Deep Brain Stimulation (DBS)

DBS is a widely applied clinical procedure for the alleviation of pathological neural activity and

is particularly effective in suppressing symptoms of Parkinson’s disease. Parkinson’s disease

is associated with the death of dopamine producing cells in the Substantia Nigra pars

compacta (SNc), one of the areas comprising the Basal Ganglia of the brain. The mechanisms

of action of DBS remain to be fully elucidated. In the lab, we will present an application to DBS

of the concepts of dither injection and equivalent nonlinearity from the theory of nonlinear

feedback control systems. This model provides a framework for understanding the mechanism

by which an injected high frequency signal can quench undesired oscillations in closed-loop

systems of interacting neurons in the brain.

A critical feature of DBS is that the frequency of the stimulation must be sufficiently high for it

to be effective (typically >100 Hz). The clinically effective frequency range lies well-above the

frequency range of both Parkinsonian tremor (4-10 Hz) and related pathological oscillations.

These include increased beta-band (15-30 Hz) synchronization in the basal ganglia–cortex

loop, which is hypothesized to be linked to the symptoms of akinesia and bradykinesia. This

characteristic feature suggested that insight might be gained by invoking the concept of “high

frequency” dither injection used to quench “low frequency” oscillations in nonlinear feedback

control loops.

Methods

A schematic diagram of the relevant basal-ganglia topology is presented below.

GPe, STN and GPi are modelled by nonlinear sigmoidal algebraic elements, followed by linear

blocks with dynamics enshrined in Laplace transfer functions.

• G(s): The output of the G(s) blocks represents the deviation from zero of the ensemble

averaged mean field output of all the cells in each of these areas. The mean field

evolves into an almost sinusoidal oscillation, governed by second order dynamics,

superimposed on a possible nonzero shift. The simplest form of G(s) is of the form:

(1)

where k and b are constants

The transfer functions for GPe and STN are set to be identical for simplicity.

• NL (h, g): The output from each sigmoid indicates the deviation from zero of the total

synaptic current averaged over all cells in the ensemble. The sigmoid in GPe is the

arctan characteristic:

(2)

The sharpness of the arctan is set by h, the smaller h the steeper becomes the slope

at the origin, given by . The nonlinear characteristic NL,g in the STN is

taken to be of the same form, with h replaced by g.

• The gain, -1, input to STN means that it is inhibitory input.

• Assuming that the non-linear characteristic in the STN has input, where e

is the negative mean field deviation from GPe neurons and d(t) is the DBS or ‘dither’

injection. This can be replaced by an equivalent non-linearity as following:

(3)

where is the mean value of y over a dither cycle.

Exercises

1. Model Implementation

Implement the model, GPe-STN loop only shown in the schematic diagram. The

parameter values are given as following; for a mean-field

oscillation frequency of 5.5 Hz, typical frequency of the tremor in Parkinson’s disease,

g set equal to 1 and h reduced to 0.1 to represent dopamine depletion. As h decreases,

the GPe-STN loop eventually bursts into oscillation.

2. Direct high frequency stimulation (DBS) and equivalent non-linearity

Apply a biphasic 100 Hz DBS input to the STN, of amplitude equal to 5 and a pulse

width of 500 µs. Also replace the high frequency stimulation and STN function with an

equivalent non-linearity (α = 0.05, A = 5 and g = 1). Compare the results.

3. Beta-band frequency application

Calculate the value of b in the second order transfer function (1) for beta-band (15-30

Hz) and then implement exercise 1 and 2 with this new value.

Supplement Exercises

1. It is known that GPe has inhibitory synaptic input from other GPe cells and STN has

excitatory feedback from other STN cells. Include these two inputs into the model, one

at a time and both at the same time. Explore their effects to the model and discuss the

results.

2. Plot the effect of different DBS frequency on STN output in the model with 5.5 Hz

(tremor frequency) and 20 Hz (Beta frequency) with pulse widths of 100, 200 and 500

µs.

学霸联盟