Regular and stochastic behavior of Parkinsonian pathological tremor signals

Yulmetyev, Renat M.; Demin, Sergey; Panischev, O. Yu.; Hänggi, Peter; Тимашев, С. Ф.; Vstovsky, G. V.

doi:10.1016/j.physa.2006.01.077

Cited by 34 publications

(30 citation statements)

References 72 publications

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“…We perform this analysis to understand how sensitive this parameter is to specific variation in the measured power spectra. This provides insight into what changes, in terms of spectral properties, the ZF-NMP 1 was detecting in the measured complex systems analyzed in [5,12,14,15].…”

Section: Explicit Calculation Of Zf-nmp 1 For Physical Systemsmentioning

confidence: 97%

“…The nth memory power spectrum can then be constructed in a modular fashion from the measured power spectrum M 0 (ω) using Eqs. (10), (13), and (15). For signals with memory kernel spectrums with decay rates O(ω −4 ) or greater, or equivalently with memory autocorrelation functions belonging to the C 1 or greater set this has a particularly simple form:…”

Section: Non-markov Parametersmentioning

confidence: 99%

“…In these complex systems the NMP * john.varghese@uqconnect.edu.au has been developed as an informational tool to analyze the degree of randomness or "Markovity" of the system. Particular attention has been paid to the zero-frequency value of the first-order NMP (ZF-NMP 1 ) [5,12,14,15], which in a similar sense to the Shannon information entropy maps the Markovity of a system interacting with its environment to a scale from unity for non Markov processes (the transition to the next state is history dependent) to infinity for purely Markov processes (the transition to the next state is history independent) [11]. In specific applications the quantification of this randomness has proved useful as a metric of discrimination between different states in complex systems.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the non-Markov parameter in continuous-time signal processing

et al. 2014

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The use of statistical complexity metrics has yielded a number of successful methodologies to differentiate and identify signals from complex systems where the underlying dynamics cannot be calculated. The Mori-Zwanzig framework from statistical mechanics forms the basis for the generalized non-Markov parameter (NMP). The NMP has been used to successfully analyze signals in a diverse set of complex systems. In this paper we show that the Mori-Zwanzig framework masks an elegantly simple closed form of the first NMP, which, for C 1 smooth autocorrelation functions, is solely a function of the second moment (spread) and amplitude envelope of the measured power spectrum. We then show that the higher-order NMPs can be constructed in closed form in a modular fashion from the lower-order NMPs. These results provide an alternative, signal processing-based perspective to analyze the NMP, which does not require an understanding of the Mori-Zwanzig generating equations. We analyze the parametric sensitivity of the zero-frequency value of the first NMP, which has been used as a metric to discriminate between states in complex systems. Specifically, we develop closed-form expressions for three instructive systems: band-limited white noise, the output of white noise input to an idealized all-pole filter,f and a simple harmonic oscillator driven by white noise. Analysis of these systems shows a primary sensitivity to the decay rate of the tail of the power spectrum.

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Section: Explicit Calculation Of Zf-nmp 1 For Physical Systemsmentioning

confidence: 97%

Section: Non-markov Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of the non-Markov parameter in continuous-time signal processing

et al. 2014

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“…The motivation for using the NMP is based on its previous success of differentiating states of complex biological systems, such as healthy and post-myocardial infarction hearts based on ECG recordings [67] and, more saliently for this thesis, attempting to differentiate Parkinsonian tremor under different treatment modalities (Levodopa and DBS) based on signals obtained from velocity transducing laser recordings [68].…”

Section: Introductionmentioning

confidence: 99%

“…Particular attention has been paid to the Zero Frequency value of the first order NMP (ZF-NMP 1 ) [67], [111], [113], [114] which in a similar sense to the Shannon information entropy, maps the Markovity of a system interacting with its environment to a scale from unity for non Markov processes (the transition to the next state is history dependent) to infinity for purely Markov processes (the transition to the next state is history independent) [110]. In specific applications the quantification of this randomness has proved useful as a metric of discrimination between different states in complex systems.…”

Section: Introductionmentioning

confidence: 99%

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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