INVESTIGATION OF THE NON-MARKOVITY SPECTRUM

AS A COGNITIVE PROCESSING MEASURE

OF DEEP BRAIN MICROELECTRODE RECORDINGS

P. A. Meehan

, P. A. Bellette

A. P. Bradley

, J. E. Castner

, H. J.Chenery

, D. A. Copland

J. D.Varghese

, T. Coyne

and P. A. Silburn

School of Mechanical Engineering, Faculty of Engineering, The University of Queensland, St Lucia, 4072, Australia

School of Information Technology and Electrical Engineering, Faculty of Engineering, The University of Queensland

St Lucia, 4072, Australia

School of Health and Rehabilitation Sciences, Faculty of Health Sciences, The University of Queensland

St Lucia, 4072, Australia

School of Health and Rehabilitation Sciences and Centre for Clinical Research, Faculty of Health Sciences

The University of Queensland, St Lucia, 4072, Australia

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

Neurologist, The University of Queensland Centre for Clinical Neuroscience

The Royal Brisbane and Women’s Hospital, Brisbane, Australia

Keywords: non-Markovity, Deep Brain, Micro-electrode recordings, Linguistics, Synchrony, Neural networks.

Abstract: Previous research has shown that changes in complexity-based measures of deep brain (DB) microelectrode

recordings (MER) from conscious human patients, show correlations with different linguistic tasks. These

statistical mechanics based measures are further expanded in this research to look at the spectra of an

adapted non-Markovity parameter in different frequency ranges as a measure of synchronous neuronal

networked behaviour. Results presented show statistically significant interaction between hemisphere of

recording, epoch of brain function and semantic category in the fast frequency range (80-200Hz).

Processing of similar semantic words appeared to be associated with increased synchrony in the left hand

hemisphere. Evidence for substantial left and right hemispherical interactions was found. Similar, but less

important trends were found in the beta band (10-30Hz). Significant but less specific correlations were also

found in the theta (4-10Hz) and gamma (30-80Hz) frequency bands.

1 INTRODUCTION

The detection and understanding of brain

functioning based on the direct measurement and

stimulation of the neural electrical activity remains a

seemingly intractable problem due to the complexity

of the neural network. Primarily experimental and

surgical observations have underpinned

breakthroughs in brain activity measurement and

disorder treatment via controlled electrical

stimulation of the brain to greatly alleviate

debilitating neurological disorders. In particular,

Deep Brain Stimulation (DBS) has emerged as a

successful treatment for several chronic neurological

and movement disorders such as Parkinson's disease

(PD), depression, dystonia, epilepsy, Tourette

syndrome and recently Alzheimer's disease. Deep

brain stimulation surgery also provides a unique

opportunity to record the electrical activity of

targeted neural structures while functionally awake

patients perform tasks in a controlled setting. These

developments have spawned recent research

identifying meaningful deep brain functional

behaviour in neural clusters using microelectrode

recordings (MER) and local field potential (LFP)

measurements from implanted electrodes. An

example recording of deep brain electrical activity in

the present research is illustrated in Figure 1

(Meehan and Bellette, 2009).

In deep brain surgery, microelectrodes are

pinpoint-positioned to transmit electrical impulses

from a pacemaker-like device to correct the troubled

area and often produce radical and instantaneous

144

Meehan P., Bellette P., Bradley A., Castner J., Chenery H., Copland D., Varghese J., Coyne T. and Silburn P..

INVESTIGATION OF THE NON-MARKOVITY SPECTRUM AS A COGNITIVE PROCESSING MEASURE OF DEEP BRAIN MICROELECTRODE

RECORDINGS.

DOI: 10.5220/0003133001440150

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 144-150

ISBN: 978-989-8425-35-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

transformations in patient symptoms. Although

demonstrably very effective on many patients, a full

understanding of how DBS affects brain functioning

is yet to be obtained. There is an urgent need to

underpin the recent surgical success of DBS with

detailed and systematic investigations of how

electrode stimulation works, what neural circuitry is

affected and how behaviour change is correlated

with stimulator position and their frequency and

amplitude characteristics. Presently, the outcomes of

DBS surgery are very much dependent upon the

experience and intuition of the surgical team –

further insight into the mechanistic foundations of

these neural signals has the potential to lead to more

predictable (and successful) patient outcomes.

Nonlinear analysis techniques, successfully used

for characterizing other biological activity such as

heart rate variability, may provide further insight

into deep brain functioning. The nonlinear, aperiodic

patterns exhibited in biological signals have

motivated many researchers to investigate the use of

nonlinear analysis techniques for insight into

complex behaviour. Typical chaos measures can

quantify the fractal geometry of the aperiodic signal

and/or its exponential sensitivity to input, but require

careful application and interpretation. In many real

complex systems, signals rarely strictly fulfil the

theoretical requirements for using a large range of

these measures of being noise free and stationary.

Hence methods from statistical mechanics, focused

on the complex dynamics of systems exposed to

random fluctuations, may be more applicable than

low-dimensional chaos measures. For example, the

analysis of measured time series using the Hurst

exponent has been applied to a variety of complex

biological processes (Knezevic and Martinis, 2006),

including spike inter-arrival times of subthalamic

nucleus (STN) activity of Rhesus Monkeys (Darbin

et al, 2006) to identify different forms of behaviour.

Alternatively, Yulmeteyev et al. (2000) have

investigated various physical and biological systems

using the so-called Non-Markovity parameter

(NMP) and Relaxation Parameter (RP) arising from

a discrete version of the Zwanzig-Mori chain of

equations (see for example Zwanzig, 2001). This

same method of analysis has also been applied to

Parkinson’s Disease gait and finger tremor data

(Yulmetyev, 2006). This analysis shows a low NMP

for untreated PD patients,( i.e., regular behaviour),

and an increase,( i.e., more chaotic behaviour), when

under DBS or medication. Although interesting,

these measurements are far removed from their

source in the brain and limited to lower level motor

function. The present team recently extended this

Figure 1: Typical micro-electrode recording (MER) of the

field potential of the network of neurons surrounding a

point (in the subthalamic nucleus) deep in the brain, taken

during deep brain stimulation surgery. Larger diameter

macro-electrodes are similarly used for long term

stimulation and recording of local field potentials (LFPs)

encompassing larger volumes of the brain.

research using a range of these measures on direct

deep brain microelectrode recordings to reveal

signatures of higher level cognitive language

processing (Meehan et al 2010). It also provided

evidence for important networked brain activity

remote to local MER spiking activity and brain

activity correlates in unfiltered deep brain

recordings. In addition, increasing evidence is

emerging as to the importance of neural synchrony

in higher order cognition (Engel et al, 2001). This

recent work provides the foundation for the current

research in which the analysis is extended and

performed over renowned neurophysiological

frequency bands. In particular, traditional

electroencephalographic (EEG) brain electrical

activity measurements from the scalp has long

indicated characteristic frequency rhythms

associated with different human behaviour (ie Beta

band waves of 10-30Hz associated with motor

function). Hence the present paper focuses on the

identification of similar correlations within the deep

brain that are yet to be fully measured and

investigated.

INVESTIGATION OF THE NON-MARKOVITY SPECTRUM AS A COGNITIVE PROCESSING MEASURE OF DEEP

BRAIN MICROELECTRODE RECORDINGS

145

2 NON-MARKOVITY

PARAMETER AS A MEASURE

OF SYNCHRONY

A biological neural network is a complex system

composed of numerous neurons with a vast array of

interconnections. These systems are found to operate

on multiple time scales and involve non-linear

interaction of many degrees of freedom. When the

electrodynamics of the neural network are examined

via a microelectrode recording, the superposition of

the activity of the spiking neurons may be

considered to result in essentially a weighted

average of the neural activity in the vicinity of the

electrode. These observations motivate the use of

ideas from the framework of statistical mechanics in

understanding and interpreting the recorded signals.

In particular, Yulmeteyev et al. (2000) developed a

Statistical Parameter of Non-Markovity (NMP),

based on a discretisation of the Zwanzig-Mori chain

of differential equations, expressed as,

∆

∆

=





(



)

−





(



)



(

−

)





(1)

Where a is the autocorrelation of the recorded time

series, M is the first “memory function”, λ

and Λ

are the relaxation parameters, τ is the sample period

and m is the length of the time series. Physically, the

use of the Zwanzig-Mori chain to describe the

system is equivalent to assuming that the underlying

dynamics are of the form of a Generalized Langevin

Equation (GLE) (see Zwanzig, 2001), where the rate

of change of the macroscopic variable, in this case

MER voltage, is driven by a random input and is

restricted by a generalized friction that depends on

the previous state of the system, This is analogous to

a “memory” of the system, explaining the naming of

the memory function.

From the autocorrelation and initial conditions,

equation (1) may be solved recursively to yield the

first memory function. In previous research (Meehan

and Bellette, 2009) the MER data was analyzed by

only looking at the zeroth frequency component of

the ratio of the magnitude of the Discrete Fourier

Transforms (DFT) of the autocorrelation function

and the first memory function, i.e. evaluating the

value of,



(



)

(())

(())

(2)

when ω = 0, where F indicates the DFT. The

purpose of examining the ratios of these two

functions is to provide a scale of the degree of non-

Markovity in the underlying process. When the

future state of the process depends strongly on the

historical values the NMP will be low, whereas if it

only depends on the current state the NMP will be

high.

The relationship of the raw NMP measure of (2)

to synchronous networked neuronal behavior in

frequency bands used in neural biosignal analysis, is

not so clear. Also recent application of this measure

on Deep Brain MER has been shown to provide non-

normal, highly skewed distributions over a large

number of baseline measurements of patients.

Hence, in this research this measure has been

developed further as a measure of neural synchrony

to enable application over the spectrum of

frequencies traditionally used in neurophysiology,

being θ (4-10Hz), β (10-30Hz), γ (30-80Hz), fast

(80-200Hz) and very fast (200-600Hz). Note that

lower frequency bands were not investigated due to

sample length restrictions. More specifically, we

define a non-Markov spectral measure of synchrony

as,

() = 1/



max[

(



)

]

(3)

where max[] refers to the maximum value of the

NMP spectrum within the bandwidth being

investigated. Note that the Sync measure of (3) is

equivalent to a simple type of Box-Cox

transformation of the NMP to normalize statistical

data. It is also meaningful in that it provides a more

direct measure of normalized synchronous behavior

whereby Sync>=1 indicates synchronous behaviour

and Sync<<1 indicates complex behavior.

3 EXPERIMENTAL PROCEDURE

MERs prior to DBS implantation were taken during

a semantic categorization task whereby participants

categorised 2 words as having the same or different

linguistic meaning. In particular, participants were

informed of the task instructions requiring them to

make a decision as to whether a series of word pairs

belonged to the same semantic category (of either

animals or household objects) or whether the word

pairs belonged to different semantic categories (i.e.,

one animal and one household object). Participants

were required to manually respond using the

ipsilateral (same side) hand to the side of STN MER

acquisition. A response was made by pressing one

button to identify same word pairs and an alternate

button to identify different word pairs.

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146

A trial commenced with the auditory

presentation of the first word followed by and inter-

stimulus interval (ISI) of 1000 ms and then the

auditory presentation of the second word. A trial

ended when the participant made a response.

Approximately 3 seconds lapsed before the onset of

the next trial. Participants completed the task on two

occasions with list one being presented when MERs

were acquired from the left STN and list two

presented when MERs were acquired from the right

STN. Each participant became familiar with the

semantic categorisation task and completed a

practice consisting of 14 unique trials, the day before

their surgery.

666 Micro-Electrode Recordings (MERs) were

taken from the STN of 8 patients prior to DBS

implantation. They were taken on both left and right

hemispheres. The recordings are grouped into 3

sampling epochs, which are as follows;

1. Baseline: Prior to a semantic categorization

task

2. Stimulus Presentation: Listening to two words

from either the same or different semantic

categories.

3. Response: via pressing a button for their

categorization of the words as belonging to

either same or different semantic categories.

STN targeting was completed using fused MRI

and stereotactic CT images displayed by Radionics

(Radionics, Inc., Burlington, MA, USA) or

Stealthstation (Medtronic Inc., Minneapolis, MN).

The STN target was established through the

identification of the anterior commissure (AC) and

posterior commissure (PC) resulting in

anteroposterior, lateral, and vertical coordinates.The

location of the STN was confirmed when a

neurologist and neurosurgeon verified characteristic

STN firing patterns and visually by post-operative

CT. Once the optimal STN location was established

intraoperatively, participants completed an auditory

semantic categorisation task with the simultaneous

acquisition of MERs. Prior to participation in the

language task, patients were deemed to be

sufficiently alert to perform the standard clinical

assessments used during surgery for DBS. 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).

Despite the known presence of a filter with a corner

frequency at 500Hz, an examination of the power

spectra of the measured signals revealed that there is

no distinct cut-off and significant power is still

present in lower frequency ranges. Thus an

examination of the possible Non-Markovity effects

in the lower frequency ranges is valid, since there is

still a non-negligible signal in these frequency

bands. It should also be noted that a linear filter

produces a known constant effect on the NMP

spectra that should not change for the different

experimental test conditions.

The data files for the 666 individual

microelectrode recordings taken under the various

experimental conditions were labeled with the

individual conditions for patient number, semantic

condition (same or different), recording side (left or

right) and recording epoch (baseline, listening and

responding). The data was then automatically

processed using the new NMP spectral analysis

method described in II and the results recorded using

the unique data label for subsequent statistical

analysis. The method of statistical analysis

employed was a linear mixed model analysis with

recording epoch, recording side and semantic

condition considered as fixed effects and the patient

considered to be a random effect to determine

correlations between the NMP measure and

semantic task outcomes. It is noted that the raw

NMP measure (2) of the data failed the

Kolmogorov-Smirnov normality test while the Sync

measure (3) passed.

4 RESULTS AND DISCUSSION

A sample of the time and frequency domain raw ME

recordings in three time epochs (see section 3.) can

be seen in Figure 2 including separate zoom-ins to

show small scale detail.

Also included is a delay embedding

representation of the phase space, from which

traditional low dimensional chaos measures were

previously taken (Meehan and Bellette, 2009). These

measures indicated the MER behaviour in the

present data is characterised by very high

dimensional chaos but could not discern meaningful

changes as a function of semantic condition or

left/right sided recordings. For the general linear

model of the frequency band NMP data it was found

that a statistically significant 3 way interaction was

found in the fast frequency range (p=0.004, 80-

200Hz band) between measurement side, recording

epoch and semantic word category. The average

results for these categories are shown in figure 3.

INVESTIGATION OF THE NON-MARKOVITY SPECTRUM AS A COGNITIVE PROCESSING MEASURE OF DEEP

BRAIN MICROELECTRODE RECORDINGS

147

Figure 2 Raw MER (a) Time domain (b) Frequency domain and (c) Phase Spaces for each epoch. Epoch 1 NMP =

1.83±1.99, Epoch 2 NMP = 0.92±0.08 and Epoch 3 NMP = 0.79±0.15. (Epoch 1: baseline prior to task, Epoch 2: listening

to task, Epoch 3: response).

Post-hoc pair-wise comparisons show that for the

fast band statistically significant differences were

seen on the left side recording in the responding

phase for the same and different semantic conditions

(p=0.041). On the right side recording significant

differences are observed for the same and different

word categories in both the listening and responding

epochs (listening, p=0.048 and responding,

p=0.001).

Figure 3: Average NMP-Synchrony measure in fast

frequency range (80-200Hz) for baseline, listening and

responding epochs, for left and right hand side recordings

and for same and different semantic word categories

showing significant (p=0.0001) 3 factor interaction. Error

bar indicates SEM.

Since the left hemisphere is typically associated with

linguistic processing we focus on the left-side

recordings initially. It can be seen that for the left

side recording, an increase in synchrony (decrease in

complexity) was observed for the same semantic

(word-meaning) category during the responding

phase. This is consistent with recent research

indicating the important use of synchrony associated

with top-down selection processes during higher

order cognition (Engel, 2001) i.e. neurons that

respond to the same meaning fire in temporal

synchrony. It is interesting to note that this finding

was reversed in the right side recording, indicating

important left-right hemispherical interactions are

also occurring during semantic processing. These

results provide stronger evidence of higher order

cognition occurring in the STN associated with

semantic processing. In particular, traditional EEG

analysis has long associated high frequency brain

rhythms with binding of different populations of

neurons together into a network for the purpose of

carrying out a certain higher order cognitive or

motor function.

Further to this interaction, there were also

significant 3 way interactions noted in the frequency

bands lower than the fast band, in the theta, beta and

gamma bands (θ 4-10Hz, β 10-30Hz, γ 30-80Hz,

respectively). In particular, the most significant of

these; the beta band; is shown in Figure 4. Pair-wise

comparisons revealed the same trend for the beta

band data as the fast band, i.e. a significant

difference between same and different on the left

recording in the responding epoch (p=0.010), and in

Patient 34 Raw MER

FFT of Patient 34 Raw

Frequenc

(

)

Time

(

)

-2.6

-2.1

-0.4

0.5

Phase s

ace E

och 1

Phase s

ace E

och 2

Phase s

ace E

och 3

0.4

-0.4

0.4

-0.4

n-4

Baseline

0.4

0.45

0.5

0.55

Sync(ω) = Max NMP(ω)

-1

Fast (80-200Hz)

Listening Responding

0.4

0.45

0.5

0.55

Baseline

0.4

0.45

0.5

0.55

Listening Responding

0.4

0.45

0.5

0.55

Different

Same

Left Side Recordings

Right Side Recordings

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148

both the listening and responding epochs for the

right side recording (p<0.001 for both cases).”

Figure 4: Average NMP-Synchrony measure in beta band

(10-30Hz) for baseline, listening and responding epochs,

for left and right hand side recordings and for same and

different semantic word categories showing significant

(p=0.001) 3 factor interaction. Error bar indicates SEM.

Figure 4 shows similar trends to the fast

frequency band results of figure 3. In particular,

there is a significant difference in the level of

synchrony during the response on the left and right

hand hemispheres between same and different

semantic conditions. Interestingly, these results

indicate substantial beta band activity associated

with the semantic task although it is noted that the

task included a motor activity i.e. button push (in the

responding phase). In addition, it should be

highlighted that the MER were taken from PD

patients. In particular, recent research (ie

Weinberger et al, 2006 and Chen et al 2010) has

highlighted enhanced beta band synchrony

associated with STN local field potential (LFP)

recordings from PD patients using power spectra and

complexity-based analyses of Parkinson’s disease

patients. It is therefore of interest to perform a

similar investigation using LFP data in future

research for comparison.

These results give an experimental basis for

further investigations of biological neural networks

under a statistical mechanics framework. Previous

benchmarking tests (Meehan et al 2010) have shown

that the NMP and RP of an MER time series may be

related to the mean and variance of underlying

neuron spike rates, however a deeper understanding

of the physiological basis for these and other

Synchrony/Complexity measures is desired.

5 CONCLUSIONS

The spectrum of a new non-markovity based

synchrony measure from statistical mechanics has

been applied to deep brain micro-electrode

recordings from the STN of Parkinson’s disease

patients performing a semantic categorization task.

The results presented show statistically significant 3-

way interaction between hemisphere of recording,

recording epoch and semantic category in the fast

frequency range (80-200Hz). Processing of similar

semantic words appeared to be associated with

increased synchrony in the left hand hemisphere

typically associated with language processing. Less

specific correlations are also found in the lower

frequency bands with the beta band (10-30Hz)

showing similar trends to fast frequency range.

These results highlight the role that the STN may

play in linguistic and well as motor tasks. Such

statistical mechanics models, which may be

validated against real data such as that used in this

research, may be a useful tool in gaining further

understanding of biological neural networks and

may provide avenues of investigation into the

mechanics of dysfunction such as Parkinson’s

disease, deep brain stimulation and fundamental

insights into cognitive processes in the brain.

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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Baseline

0.6

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Sync(ω) = Max NMP(ω)

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Beta (10-30Hz)

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BRAIN MICROELECTRODE RECORDINGS

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