Theoretical &amp;amp; experimental analysis of the Non Markov Parameter to detect low frequency synchronisation in time series analysis

Varghese, John J.; Weegink, Kristian J.; Bellette, P. A.; Coyne, Terry; Silburn, Peter A.; Meehan, Paul A.

doi:10.1109/iembs.2011.6090743

Cited by 3 publications

(6 citation statements)

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“…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).…”

Section: Procedures For Comparison Of Numerical and Experimental Resultsmentioning

confidence: 99%

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Investigation of using firing time renewal processes for modelling and analysis of single point microelectrode recordings of the subthalamic nucleus

Weegink¹

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Microelectrode recordings (MER) involve insertion of an electrode, approximately 50 micrometers at the tip, into deep brain structures and recording the electrical activity. It is commonly used in surgeries to accurately determine the location of a target for deep brain stimulation (DBS). A common target for this type of procedure is the subthalamic nucleus (STN), identified by a unique spiking pattern and a change in the background noise level compared to surrounding structures. This change in background noise level indicates that the noise is composed of neuronal sources. This thesis aims to develop a model to determine what extent the volume of neurons around the electrode contribute to an MER. The potential usefulness of the model as a biomarker for the behaviour of the STN is then explored. The model for the STN MER involves simulating thousands of neurons by assuming they follow a renewal process. This assumption requires that the timing between a single neuron's spikes (inter-spike interval-ISI) are independent and identically distributed (IID). The model is tuned to intraoperative recordings to determine the best simulation parameters. To investigate the usefulness of the model as a biomarker of STN behaviour, the IID assumption is relaxed by introducing synchronization between neurons or changing their spike timings to be driven by a dynamical model of the basal ganglia. Fitting the parameters of the renewal process model to these extended models is then used to see if they can reliably describe the new behaviour. The results show firstly that a volume of ~1mm 3 , or on the order of 10,000 neurons, are required to simulate an STN MER that best describes patient data. This result indicates that the background noise of MERs is in fact partly caused by neuronal sources. The speed of the renewal model, faster than real time, allowed many simulations (Ο(10 6)) with different parameters to be created for tuning and verification of the model. The Weibull distribution is used as a parameterized ISI distribution for the renewal model and was found to reliably describe the simulations when the IID assumptions were relaxed. The first example of this was when neurons had synchronized firing times. In this case the Weibull distribution reliably fit the underlying ISI distribution for different realizations of the same simulation parameters. Finally, the thesis shows that using a neural mass model of the basal ganglia to generate the STN firing times, that the renewal model can differentiate between certain cortical inputs. This motivates future investigation into using the parameters from fitting a renewal model to an MER as biomarkers.

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“…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).…”

Section: Procedures For Comparison Of Numerical and Experimental Resultsmentioning

confidence: 99%

“…Recent work has shown that with the correct measure, correlations between MER recordings and patient response to symantic tests has been demonstrated (P. A. Paul A. Meehan et al, 2011;Varghese et al, 2011).…”

Section: Suggestions For Further Researchmentioning

confidence: 99%

Investigation of using firing time renewal processes for modelling and analysis of single point microelectrode recordings of the subthalamic nucleus

Weegink¹

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“…structure, which has a non zero λ value, was considered in [115]. A full derivation of the functional form of this λ n relaxation parameters is provided in section A.1.…”

Section: Mori-zwanzig Kinetic Equationsmentioning

confidence: 99%

“…These results suggest that signal metrics to differentiate complex systems can be developed by analysing different properties of the measured power spectrum. The previous success of the NMP [67], [106], [111], [112], [115] helps elucidate specifically what properties (spectral spread and DC offset) should be explored, but does not necessarily require Mori-Zwanzig theory to interpret the results.…”

Section: Analysis Of the Non-markov Parametersmentioning

confidence: 99%

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Probing the sub-thalamic nucleus: development of bio-markers from very Local Field Potentials

Varghese¹

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Deep Brain Stimulation (DBS) surgery for neuro-psychiatric disorders involves the insertion of Micro Electrode Recording (MER) targeting probes into a specific location in the patient's brain to confirm the precise location of the candidate nucleus for the stimulation therapy.The unique geometry and electrical properties of these MERs probes, when inserted into neuron dense tissue such as the Sub-thalamic Nucleus (STN) results in the acquisition of signals which typically contain contributions from the spiking behaviour of multiple nearby neurons in addition to a low frequency component similar to the Local Field Potentials (LFP) generated by more distant neurons (over length scales smaller than typical LFPs). We refer to these signals acquired from the MER probes, which contain both some of the nearby (resolvable) spikes and these smaller scale LFPs as very Local Field Potentials (vLFPs).The unique signal contributions to the vLFPs raise the immediate question what contribution of the signal is best used in order to characterise (in terms of identifying the underlying physiology or detecting changes of) the state of the STN. In this thesis we develop methodologies to analyse vLFPs using both model based and model free analysis of the entire (nearby spiking, distant spiking and non-spiking contributions) vLFP and only the nearby spiking neurons.We apply concepts from Mori-Zwanzig non-equillibrium kinetic theory to develop modelfree estimates of the entire vLFP. With this approach we show that the Non-Markov Parameter (NMP) can be used to identify statistically significant changes in the electrical behaviour of the STN when presented with different neuro-linguistic stimuli. We show that these changes are due to variations in the low frequency bands associated with the power spectrum of the vLFP.We then develop a model-based analysis of the entire vLFP using the renewal theory of stochastic processes. We show that when the ensemble of neural processes forming the vLFP satisfy the assumptions of an independent renewal process model, given a measurement of ii the power spectrum, the common probability distribution driving the spiking statistics of the individual neurons can be identified. We show with simulation that, when the assumptions of the model are satisfied, this approach can outperform state of the art spike sorting algorithms in the challenging situation of identifying the spiking statistics when an unknown number of neurons with near identical spike shapes contribute to the vLFP.Finally we develop spike-only analysis by constructing spike sorting strategies using convex optimisation and clustering theory to identify the precise timing and shapes of the spikes associated with individual neurons nearby to the MER probe. With this approach the spike detection and clustering is performed using a Basis Pursuit De-Noising (BPDN) strategy which is a subset of ℓ 1 regularised least squares techniques. We show that this method outperforms state of the art spike sorting algorithms for a range of signal to n...

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

Weegink¹,

Varghese²,

Bellette³

et al. 2012

Proceedings of the International Conference on Bio-Inspired Systems and Signal Processing

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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 recreated using this efficient model in real time.

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Theoretical & experimental analysis of the Non Markov Parameter to detect low frequency synchronisation in time series analysis

Cited by 3 publications

References 13 publications

Investigation of using firing time renewal processes for modelling and analysis of single point microelectrode recordings of the subthalamic nucleus

Investigation of using firing time renewal processes for modelling and analysis of single point microelectrode recordings of the subthalamic nucleus

Probing the sub-thalamic nucleus: development of bio-markers from very Local Field Potentials

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

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