AN EFFICIENT STOCHASTIC BASED MODEL

FOR SIMULATING MICROELECTRODE RECORDINGS

OF THE DEEP BRAIN

Modelling and Analysis

K. J. Weegink

, J. J. Varghese

, P. A. Bellette

, T. Coyne

, P. A. Silburn

and P. A. Meehan

School of Mechanical and Mining Engineering, Faculty of Engineering, The University of Queensland,

4072, St Lucia, Australia

St. Andrew’s War Memorial Hospital, Brisbane, Australia

Center for Clinical Research, The University of Queensland, 4029, Herston, Australia

Keywords: Deep brain signals, Micro-electrode recordings, Point Process model.

Abstract: We have developed a computationally efficient stochastic model for simulating microelectrode recordings,

including electronic noise and neuronal noise from the local field of 3000 neurons. From this we have

shown that for a neuron network model spiking with a stationary Weibull distribution the power spectrum

can change from exhibiting periodic behaviour to non-stationary behaviour as the distribution shape is

changed. It is shown that the windowed power spectrum of the model follows an analytical result prediction

in the range of 100-5000 Hz. The analysis of the simulation is compared to the analysis of real patient

interoperative sub-thalamic nucleus microelectrode recordings. The model runs approximately 200 times

faster compared to existing models that can reproduce power spectral behaviour. The results indicate that a

spectrogram of the real patient recordings can exhibit non-stationary behaviour that can be re-created using

this efficient model in real time.

1 INTRODUCTION

For the treatment of progressed movement disorders,

such as Parkinson’s disease (PD), deep brain

stimulation (DBS) may be used. This treatment

involves locating a target deep brain structure, such

as the sub-thalamic nucleus (STN), inserting an

electrode to within 1 mm accuracy, and then

applying a pulsed electric field to the area. One of

the tools used to locate the correct nucleus structure

is a microelectrode recording (MER). MERs are

performed by insterting a recording electrode, with a

Figure 1: The micro-electrode recordings (MER) are acquired by inserting an electrode into a deep brain structure. The

electrical activity of the neurons surrounding the electrode can couple to it producing a voltage time series.

J. Weegink K., Varghese J., Bellette P., Coyne T., Silburn P. and Meehan P..

AN EFFICIENT STOCHASTIC BASED MODEL FOR SIMULATING MICROELECTRODE RECORDINGS OF THE DEEP BRAIN - Modelling and

Analysis.

DOI: 10.5220/0003782400760084

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 76-84

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

diameter around 50 um, into the nucleus structure

(figure 1) located via MRI and CT scans.

To confirm the correct location of the implanted

DBS electrodes, patients are awake to perform

neurological tests. This gives an opportunity to

monitor the candidate nucleus, for stimulation, while

the patients perform tasks. Recent work has shown

that with the correct measure, correlations between

MER recordings and patient response to symantic

tests has been demonstrated (P. A. Meehan &

Bellette, 2009; Paul A. Meehan et al., 2011;

Varghese et al., 2011).

Currently there has also been work on

developing a bi-directional brain-machine interface

for DBS treatment (Rouse et al., 2011). To further

develop these research paths appropriate methods

for efficient real time simulations to estimate neural

network behaviour are required. For instance

developing a metric that can characterise the

underlying neural behaviour from a MER, a better

understanding of the process in DBS could be made.

Current MER models only consider the

behaviour of the closest neuron and reduce the

further neurons to a local field noise (Santaniello,

Fiengo, Glielmo, & Catapano, 2008). For feedback

control of DBS the behaviour of the neural network

needs to be modelled, as it has been shown that

analysis of the closest neuron to the electrode is

insufficient (Rouse, et al., 2011). Using the current

non-linear neuron models of DBS (Rubin & Terman,

2004) for this type of feedback controller would be

too computationally intensive, for this reason models

that can take into account a large number of neurons

and display markers of pathalogical states efficiently

are needed.

In this paper we develop numerical probabilistic

models, using a point process (PP) in order to create

a much more computationally efficient model of

networked neurons. Each neuron is coupled to the

electrode, using a non-homogenous model for the

extracellular medium, via a filter function derived

from a conductance based model for the STN

extacellular current during an action potential (AP).

We use the model to compare with real patient

MERs and an analytical model using frequency

based analysis. This type of numerical model could

potentially be used in a clinical setting as part of a

feedback controller for DBS, alleviating the clinical

load of optimizing the device settings.

2 METHODS

There are several aspects to modelling and analysing

deep brain signals. The system is a complicated

system with many levels of dynamics required to

create a MER. Section 2.1 contains the procedure

used to acquire patient MERs. The factors that

contribute to modelling a MER; modelling the

behaviour of a single neuron, the network behaviour,

the neuron electrode interaction and the electrical

equipment processing the signal are detailed in the

section 2.2. A simple analytical model is presented

in 2.3 for comparison to the numerical model and to

provide more insight into how the statistical

distribution influences the expected power spectrum.

The methods of the comparative analysis are then

summarized in 2.4.

2.1 Experimental Procedure - Patient

MER Acquisition

MERs are acquired from participants with idiopathic

PD who were considered suitable for the

implantation of bilateral permanent stimulators in

the STN. Fused MRI and stereotactic CT images and

direct visualisation of FLAIR (Fluid-attenuated

inversion recovery) MRI images displayed by

Stealthstation (Medtronic Inc., Minneapolis, MN)

were used to target the STN.

During surgery characteristic STN firing patterns

were used to confirm the STN location by the

neurologist and neurosurgeon. More details of the

surgical procedure are reported in Coyne et al.

(Coyne et al., 2006).

MERs were acquired with a Tungsten

microTargeting

electrode (model mTDWAR, FHC,

Bowdoinham, ME) with a tip diameter of less than

50µm and impedance of approximately 0.5 MΩ (±

30%) at 1 kHz. MERs were filtered (500-5000 Hz)

and recorded at a sampling rate of 24 kHz from

LeadPoint™ (Medtronic Inc., Minneapolis, MN).

2.2 Numerical Modelling

of Micro-Electrode Recordings

A MER is created by the activity of the neurons

around the recording electrode. The neurons

generate currents and hence electric fields that

propagate through the different structures of the

brain tissue, which can attenuate and filter the signal

(Garonzik, Ohara, Hua, & Lenz, 2004). Finally the

field incident on the electrode is processed by the

electrical equipment to produce the recording.

Models of MERs have been developed that

consider single unit recordings, made from a

stochastic single neuron with random noise

(Santaniello, et al., 2008) and local field potentials

AN EFFICIENT STOCHASTIC BASED MODEL FOR SIMULATING MICROELECTRODE RECORDINGS OF THE

DEEP BRAIN - Modelling and Analysis

(LFP) created using the spike trains of

simultaneously recorded in-vivo cells (Bedard &

Destexhe, 2009). However neither of these models

allow for real time simulations with dynamically

altering network behaviour.

To effectively model a MER which would allow

real time simulations, there are several different

stages that need to be taken into consideration. The

four separate areas we are to model are the

behaviour of the neural network, the electrical

dynamics of individual neurons, the coupling of the

electric fields from a neuron to the electrode and the

processing of the signal by the electronics.

2.2.1 Neural Networks

For a MER a large number of neurons in the

structure surrounding the electrode contribute to the

signal. Dynamic models of neurons and neural

networks are common for simulating brain

structures(Feng, Shea-Brown, Greenwald, Kosut, &

Rabitz, 2007; Izhikevich, 2007a, 2007b; Rubin &

Terman, 2004; Terman, Rubin, Yew, & Wilson,

2002). These types of models, using synaptic

connections between neurons with dynamical neuron

models, can be very computationally intensive

(Long & Fang, 2010). To reduce the computational

burden of modelling individual neurons with

synaptic connections, the firing times of each neuron

can be characterized by a stochastic variable. This

variable is produced from a probability distribution

that depends upon the behaviour of the network.

This type of model is a point process (Perkel,

Gerstein, & Moore, 1967a, 1967b).

For single neurons the spiking statistics are often

modelled by a Poisson distribution of inter spike

interval (ISI) times. The participants for the deep

brain MER recordings are undergoing treatment for

a pathological state that is treated by altering STN

function. This could imply abnormal function of the

STN where the firing is not best described by a

Poisson distribution in ISIs.

A probability distribution that can give the

common types of behaviour found in neurons, such

as bursting, Poisson and periodic behaviour, is the

Weibull distribution (Li, 2011; McKeegan, 2002;

Perkel, et al., 1967a, 1967b). This type of

distribution can reduce to a Poisson distribution if

the shape parameter is equal to one, takes the form

of a Rayleigh distribution if the shape parameter is

larger than two and burst fire behaviour is produced

as it goes below one.

The point process simulation is performed using

MATLAB 7.12.0 (R2011a) on a PC with a quad

core 1.73GHz processor and 8.0 GB of RAM. A

spatial distribution of 3000 neurons is randomly

generated, shown in figure 2, that follows the radial

density of neurons (

(



)

) given in equation (1)

using a spatial neuron density of =10









(



)

=4



.

(1)

Figure 2: The radial distribution of neurons used for

simulations. The volume of tissue for the simulation

depends on the number of neurons simulated.

All simulations are performed over a three

second period. Time series of Dirac pulses are

created for each neuron by drawing interval times

for spike occurrences from a probability distribution.

Weibull distributions are used to generate the ISIs

given by



(



)

=

































>



0 ≤



(2)

 is the scale parameter that controls the rate and is

set to 10 Hz. The shape parameter c is varied to

control the neuron behaviour; with ≪1 generating

bursting, =1 Poissonian and ≫1 periodic

behaviour. The parameter 



controls the refractory

time of the neuron and set to 5 ms, preventing

another action potential occurring for the same

neuron in this period. The first spike for each neuron

uses =1 with 



=0. Each time series is convolved

with the EAP for an STN neuron by taking the

product in the frequency domain. The time series

data for each neuron are then superimposed to create

the voltage at the electrode.

2.2.2 Neuron Dynamics

Using a PP model for the neural network, the

dynamics of each neuron have been reduced to an

‘on’ or ‘off’ state. To develop the correct response

for a neuron when in the ‘on’ state, conductance

models such as the Hodgkin and Huxley (HH)

model can be used to generate the behaviour of the

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

individual neuron, when an action potential occurs.

The HH model can calculate the extracellular

currents around a neuron which is required for

determining the voltage seen by an electrode. It has

previously been demonstrated STN cells can be

simulated effectively using this type of model

(Terman, et al., 2002). More computationally

efficient mathematical models of neurons are not

considered since these types of models cannot

always reproduce the correct shape of the action

potential waveform, and this feature is important

when considering the windowed power spectrum.

Figure 3: The extracellular current used for each neuron

generated using equation (3).

The STN cell is modelled using a single

compartment conductance based model described by

a modified version of the HH equation, based on

(Feng, et al., 2007; Rubin & Terman, 2004; Terman,

et al., 2002):









=−



(

−



)

−







(

−



)

−









ℎ

(

−



)

−











(

−



)

−









(

−



)

(3)

where 



is the membrane capacitance and set to

1 

⁄

; 



,



are the leak conductance and

reversal potential (2.25/



and −60.0

respectively); 



,



are the 



conductance and

equilibrium potential (45/



and −80.0

respectively); 



,



are the 



conductance and

equilibrium potential (37.5/



and 55.0

respectively); 



is a low-threshold T-type Ca

conductance (0.5/



); and 



,



are a high-

threshold Ca

conductance and a Ca

equilibrium

potential (0.5/



and 140.0 respectively).

The gating variables , , ℎ, and  follow the

differential equations given in (Terman, et al., 2002)

using the parameters given in their table 1. The

dynamics of a single neuron are modelled in

NEURON (Hines & Carnevale, 1997) using

equation (3) to generate the extracellular current

during an action potential, shown in figure 3. 

2.2.3 Neuron/Electrode Interaction

The electrode senses the neuron dynamics through

the electric field that propagates from the neuron.

This electric field is known as the extracellular

action potential (EAP). The EAP is generated by

ionic currents around the active neuron. As the EAP

propagates through the extracellular space to the

electrode it will pass through regions of space with

different conductivity and permittivity. This will

cause filtering effects along with attenuation of the

field. This means that the electrode will record a

different EAP for each neuron depending upon the

distance from the electrode and the media in

between.

The complex impedance (



(



)

) for the

interaction of each neuron with the electrode over

the range of radii is calculated by (Bedard, Kroger,

& Destexhe, 2004),





(



)



()











(



)



(



)



(



)



(



)

′





(4)

where  is the conductivity in the extracellular

medium,  is the permittivity in the extracellular

medium and R is the spherical radial size of each

neuron. An exponentially decaying conductance



(



)

=

(



)





(

1−



)











,

(5)

with a space constant =500, cell radius

=10, conductivity at the cell 

(



)

1.5/ and a normalized low amplitude

conductivity 



=2×10



; and a constant

normalized permittivity =10



/ were used

following Bedard (2004). The EAP waveform in the

frequency domain for each neuron is calculated

using the complex impedance and the FFT of the

extracellular current.

The voltage (



), in terms of the frequency

components, at the electrode caused by a neuron is

then calculated using Ohm’s law (Bedard, et al.,

2004),





()=







(),

(6)

where 



is the frequency component of the current

at the neuron.

2.2.4 Electrical Processing

To properly analyse a MER the effects of the

electrical equipment, on the recording, need to be

included. These effects include the introduction of

noise, such as that due to sampling rate, clock

AN EFFICIENT STOCHASTIC BASED MODEL FOR SIMULATING MICROELECTRODE RECORDINGS OF THE

DEEP BRAIN - Modelling and Analysis

stability and thermal noise, and any filtering that

occurs. These issues could greatly affect the ability

of a measure to differentiate the neuronal behaviour

from the electrical effects.

The first such noise source is the noise present

from thermal fluctuation of electrons in the

microelectrode (Akingba, Wang, Chen, Neves, &

Montemago, 2003). This type of noise is known as

Johnson-Nyquist noise and is characterized by

having zero mean voltage and a variance dependant

on the temperature, resistance and frequency

bandwidth.

The phase noise is not considered in this analysis

due to the stability of the 10 MHz clock typically

used and the comparatively small sample rate of 24

kHz. Digitization noise can be accounted for by

producing the final MER of the simulation with the

same time step that the patient data is recorded at.

Finally any filters can be added using the filter

transfer function in the post processing of the MER

simulation.

Thermal noise on the electrode is added as white

noise using

〈



〉

=0,

(7)

〈





〉

=4



Δ



(8)

where 



is Boltzmann’s constant,  is the

temperature,  is the resistance,Δ is the bandwidth

and

〈〉

is the time average, it is found that for a 0.5

MΩ resistor at body temperature (37

C) the thermal

noise can be between 10-30% of the size of the

neural signal.

The recording is filtered with a 6

order low

pass Butterworth filter with a corner frequency of 5

kHz and a 3

order high pass filter with a corner

frequency of 500 Hz. The final MER from the

simulation is produced with a sample rate of 24 kHz

to create the same digitization effects as present in

the patient data.

2.3 Simplified Analytical Model

of Micro-Electrode Recordings

The MER may be analytically modelled by a

superposition of independent spike trains, equivalent

to the numerical model using a point process. The

PSD for a PP model will be a filtered version of the

PSD for the EAP waveform. For independent

overlapping pulse trains, with the same shape

waveform for each pulse, it has been shown (Banta,

1964) that the power spectrum (



()) for the MER

can be written as





()=



(



)









−2









(



)



(



)

,

(9)

where () is the PSD of the waveform, () is

the characteristic function (Fourier transform) of the

probability distribution for the aggregate spiking

statistics,  is the number of pulses per unit time and

 is the amplitude of the pulses with



representing

the ensemble average.

Although this equation for the PSD takes into

account the attenuation caused by the extracellular

medium on the spike waveform it does not take into

account the frequency filtering effects.

This equation can however be used to see

expected behaviour of different simulations. The

bracketed term can be thought of as a filter, which is

a function of the spiking probability, applied to the

waveform PSD. By looking at this term the filtering

effects caused by the different probability functions

can be examined.

2.4 Procedure for Comparison of

Numerical and Experimental

Results

The most intuitive way to analyse the noise of an

MER is to look at the PSD. This was first done by in

1979 (McNames, 2004) using a circuit equivalent of

a Fourier Transform (FT). In recent years analysis of

MERs has progressed into the digital domain. The

majority of these techniques still involve analysis of

the PSD.

Neuron spiking behaviour can be examined

through MER PSDs. It was shown how 



behaviour in the PSD can arise from shot noise type

behaviour of neurons spiking (Milstein, Mormann,

Fried, & Koch, 2009), while 



behaviour may be

due to filtering by reactive extracellular media, or

due to complex self-organized critical phenomena

(Bedard & Destexhe, 2009).

Complex measures have been used to look at

MERs, and it has been shown that some techniques,

such as the Non-Markov parameter (NMP) relate to

the PSD (Varghese, et al., 2011).

The windowed PSD will not capture transient

behaviour in the MER. To view this transient

behaviour a spectrogram can be used. This involves

dividing the signal into smaller time bins. The PSD

is taken for each time bin to see the PSD as a

function of time for the MER.

A windowed PSD is taken of the time series data

from the simulation using a Gaussian window with

an 



width of 1/50

of the signal length. The PSD

is then averaged of 5 trials of the simulation with the

same firing statistics. This is compared to the

windowed PSD of a three second signal averaged

over 5 recordings.

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

Spectrograms are produced with the same time

intervals used for the windowed PSD. The

spectrograms consist of a series of instantaneous

PSD over each time interval. The spectrograms are

then used to compare the stationary behaviour of the

power spectrum for different ISI probability

distributions and the patient data.

3 RESULTS AND DISCUSSION

The results from the numerical simulations are

presented in this section and are then compared to

the experimental results and analytical predictions.

Subsection 3.1 summarises the numerical results and

provides a comparison with MERs acquired from

patients. The time series, windowed power spectrum

and spectrogram for three different simulation

parameters are used. Subsection 3.2 includes details

of the results from the simple analytical model,

comparing how the power spectrum of the EAP is

modified under the different spiking statistics used

to produce the MERs from the numerical models.

3.1 Numerical and Experimental

Results Comparison

The time series of voltage from the simulations has

been plotted for three different firing probability

distributions and compared to a patient recording

(Figure 4). For ≅1 the time series have similar

features to the patient data. Differences can only be

seen for large deviations from =1. As case

examples for their characteristic behaviour extreme

cases of  have been used. As ≪1, bursting

behaviour is visible in the time series and for ≫1

periodic spiking becomes apparent.

Figure 4: Comparison of a) Patient MER to simulations

with b)=1 , c) ≪1and d) ≫1.

The simulations were calculated at a rate of 6

milli seconds per neuron per second of

computational time, a 200 fold increase on

dynamical models that reproduce accurate waveform

shapes (Long & Fang, 2010).

Figure 5: Overlap of the real patient windowed PSD over

the windowed PSD of the simulation for =1.

Figure 6: Overlap of the real patient windowed PSD over

the windowed PSD of the simulation for ≫1.

Figure 7: Overlap of the real patient windowed PSD over

the windowed PSD of the simulation for ≪1.

The windowed PSD for all three simulations and

the patient recordings, seen in figures 5, 6 & 7, have

three main regions. The first region is the filter drop

off above 5 kHz. This feature is present in all 4

PSDs with good agreement between patient data and

simulations. The thermal noise term added is white

AN EFFICIENT STOCHASTIC BASED MODEL FOR SIMULATING MICROELECTRODE RECORDINGS OF THE

DEEP BRAIN - Modelling and Analysis

noise and as such adds the same power to every

frequency, shifting the PSD up. This effect is

removed by normalizing the power spectrum to

integrate to unity. The other electrical effects; high

and low pass filtering; do however alter the

normalized power spectrum, seen by the sharp

falloff in power in this region.

The second region is the behaviour at high

frequencies (100-5000 Hz). The two simulations

with ≤1 have good agreement with patient data in

this region shown in figures 5 & 7. The simulation

with ≫1 (figure 6) has structure in this region that

can be explained as harmonics of features in the low

frequency region. The overall shape in this region is

dominated by the waveform of the EAP.

The final region of interest is in the region below

100 Hz. This region is thought to contain

information of the Local field potential (LFP).

Experimentally this region has an electronic filter,

with a slow drop off. For ≫1 this region has a

sharp peak at 10 Hz, the simulated spike rate, and

then has peaks at the harmonic frequencies of n10

Hz, where n is an integer. The other two cases have

anomalous peaks in this region similar to the 20 Hz

peak in the patient data. This beta band peak (12-30

Hz) has been seen in PD MER recordings previously

and has been implicated in the pathological state

(Eusebio & Brown, 2009).

Besides the PSD for ≫1, the problem with

comparing the average PSD is that they appear very

similar between 100-5000 Hz with differences

below 100 Hz. Another method to examine the

spectral properties of an MER is to look at the

spectrogram, figure 8, and to observe changes in the

power spectrum over time.

From the spectrogram for the typical patient

MER recording it can be seen that the PSD changes

in time. These recordings show the feature in the

beta band appearing and disappearing through the

recording.

When the numerical simulations were performed

with ≫1, the PSD appears periodic stationary.

This behaviour can be seen in figure 8 d). When c is

set to one or below features of the PSD appears to

change in time in the beta band. This is similar

behaviour to the PSD for the patient data.

This analysis suggests that ≅1 qualitatively

represents the patient data the best from the options

tried. This supports the idea that spiking behaviour

in a large network appears Poisson (Câteau & Reyes,

2006; McNames, 2004; Stevens & Zador, 1998).

3.2 Analytical Predictions

The results from equation (5) show the effect of

changes in the aggregate probability distribution.

Equation (5) can be thought of as a spike waveform

filter that is dependent on the probability distribution

through



(



)

1−

(



)



⁄

. Figure 9 shows the

frequency behaviour of equation (5) for different

values of

, if the statistics follow a Weibull

distribution.

For ≫1 and =1 figure 9 shows the

frequency filtering effects due to the spiking

statistics are flat and will not add noticeable features

in the PSD below 100 Hz. This analytical model

doesn’t take into account the frequency filtering of

Figure 8: Spectrograms with the region displaying beta band behaviour boxed in red, a) patient MER showing transient beta

band behaviour, b) simulations ≪1 showing transient beta band behaviour, c) =1 showing transient beta band

behaviour and d)≫1 showing periodic behaviour.

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

more distant neurons by the extracellular medium.

Figure 9 a) shows how the extracellular medium

model acts as a low pass filter. For these reasons this

model is not sufficient to describe the features seen

in the numerical simulations below 100 Hz.

Figure 9: a) The filter function of the extracellular medium

at 0.2. Inserts b)-d) show the comparison of the power

spectrum of the EAP with the MER power spectrum from

the analytical model, b) the MER PSD for =1 modelled

by equation (9), it can be seen that for this distribution the

results of the MER and EAP PSDs are in agreement, c) the

MER PSD for ≫1 modelled by equation (9), d) the

MER PSD ≪1 modelled by equation (9).

For ≫1 the 10 Hz peak with harmonic peaks

in the numerical simulation can be seen in the

frequency effects from equation (9), shown in figure

9, if the aggregate probability distribution maintains

the single neuron ISI probability shape.

The problem with this analysis is that we have

assumed that the distribution controlling the ISIs is

stationary in time. Equation (9) cannot account for

ISI distributions that change in time. The non-

stationary nature of the real patient PSD could

suggest that the probability distribution describing

the neuron firing may not be stationary. This

behaviour can alternatively be explained by the

probabilistic nature of the simulation and the time

period the PSD is taken over. This is demonstrated

by the simulations using the PP model showing

similar non stationary behaviour under the same

analysis, even though the probability distribution of

ISIs was stationary in time.

4 CONCLUSIONS

MERs were efficiently simulated using a PP model

with a conductance model for generating the EAP,

taking into account extracellular frequency filtering

and attenuation; and the effects of the recording

electronics. The simulations perform approximately

200 times faster than using a Hodgkin and Huxley

model for all of the neuron dynamics (Long & Fang,

2010). With this computationally efficient model

very good agreement was achieved when comparing

the windowed PSD of the simulated MERs with real

patient data for frequencies above 100 Hz.

Below 100 Hz the PSD of patient MERs are not

stationary, which can be reproduced using a time

stationary probability distribution for the ISI. Since

the model is a probabilistic model that treats the

neurons as point sources rather than a full dynamical

model, the neurons are either in an ‘on’ or ‘off’

state. This means it cannot produce neural features

such as sub-threshold oscillations and cellular

activity such as synaptic currents. These features

may be critical for describing the features below

100Hz sufficiently.

The analytical model using the results from

Banta (1964) showed features that were present in

the simulations, such as the harmonic structure

present in the windowed PSD for simulations with

≫1. This type of analysis could allow for

characterization of the ISI probabilities of patient

MERs from the windowed PSD.

To account for the features in the beta band (10-

35 Hz) more complex models; including explicit

network interactions and full cell dynamics, such as

sub-threshold oscillations, may be required.

Future work could include performing the

inverse problem of finding the shape and rate

parameters that best describe a patient MER. The

results from this study could be used to find markers

that may be applicable in the clinical environment

for optimising DBS and potentially operating in a

feedback controller.

ACKNOWLEDGEMENTS

The authors are greatly indebted to PD specialists of

St. Andrew’s War Memorial and The Wesley

Hospitals, Australia for their motivation, guidance,

interdisciplinary expertise and funding.

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