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.






























































































































































































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