High-Resolution Method for The Analysis of Electrophysiological Activities

Khalil EL KHAMLICHI DRISSI1*, Christophe PASQUIER1, Claire FAURE1 and Kamal KERROUM1, Benoit SION2, Lénaïc MONCONDUIT2 and Alain ESCHALIER2

1Institut Pascal, CNRS-UMR 6602, F-63171, Clermont-Ferrand, France

2Neuro-dol, Inserm U1107, University of Auvergne *drissi@univ-bpclermont.fr

INTRODUCTION To better understand the physiopathological mechanisms of pain or to evaluate the

effectiveness of analgesic substances, response of unitary neurons in animal model or cortical response in human to peripheral stimulations can be analyzed using electrophysiological recordings such as the electroneurogram (ENG) or electroencephalogram (EEG). The analysis of ENG involves measuring the spike frequency, the amplitude and nerve conduction velocity after applying peripheral stimulations but little is known about the spontaneous nerve activity.

In peripheral nerves, we try to extract predictive signals of activity in primary afferent fibers by distinguishing the type of nociceptors AMH (Aδ myelinated fibers) and MHC (unmyelinated C fibers). The method used in this work is called Matrix Pencil Method (MPM) and is usually referred to as a high-resolution technique. The method provides one to identify non-stationary signals, even in the presence of numerical or measurement noise, respectively. The basis functions are complex exponentials with corresponding damping factor. Those functions are rather appropriate to identify electromagnetic waves or distributed currents or voltages with an optimal number of elements. The method is applied either in time domain, in frequency domain or in space domain allowing one to identify the original signal by means of a limited number of singular values, poles and residues. In our case, MPM is applied to analyze the spontaneous nerve activity, nerves simultaneously conveying a lot of information afferent and efferent axons via various functionalities. To extract relevant information, it is essential to discriminate groups of axons within the nerve. Such discrimination takes a place in a particularly difficult context since the measured neural signals are of very low amplitude and in a rather noisy environment by the surrounding natural activity.

ENG AND EEG ANALYSIS

Moreover in pain field, by using a Fourier transform or wavelets analysis, EEG provides information about the oscillatory frequencies or the magnitude and duration of evoked potentials [1]. However, these studies do not account for the nonlinear dynamical behavior exhibited by the very large scale of neuronal interactions. Indeed, a physical and multidimensional system as the Human Brain, may exhibit complex dynamics that can be governed by a global mechanism. These dynamics can be long lasting modified by pathologies such as chronic pains. Thus, even if the EEG seems similar between healthy subjects and migraine patients, differences can be observed when visual stimulations are present and it is likely that differences also exist in the absence of stimulation. Besides, neurons undergo a broad range of regimes including periodic, quasi-periodic, non-periodic, and chaotic during their communications with each other via spike and burst. Moving from one regime to another could be the signature of the transition from a physiological state to a pathological one.

As electrophysiological techniques [2] offer the highest possible temporal and spatial resolutions for exploring brain mechanisms, in particular those related to chronic pain, we need powerful mathematical tools to carry out the proper analysis of the neuronal activity. Our goal is to compare peripheral nerve activity (ENG) during rest and tactile stimulus conditions, and on the other hand to compare the EEG of healthy subjects to migraine patients. Preliminary results allowed us to verify the method to be applicable to electrophysiological recordings of nerves and EEG. HIGH RESOLUTION METHOD

Matrix Pencil Method (MPM) is based on an adaptive subspace analysis and the exponentially damped sinusoids model. Subspace based signal analysis involves splitting the observations into a set of desired (hr) and a set of disturbing components (br), which can be viewed in terms of signal and noise subspaces. This approach has been widely studied in the fields of adaptive filtering, source localization, or parameter estimation [3]. The eigenvalue decomposition (EVD) and the singular value decomposition (SVD) are commonly used in subspace estimation.

After the sampling procedure, the observed response can be written as follows [4]:

y! kT! = h! kT! + b! kT! ≈ R!z!! + b! kT!

!

!!!

                                             (1)

where T! is the sampling period, h! kT! is the signal, and b! kT! is the noise, with: R! = a! e!!!          r = 1,2,… ,M                                                                                                                                 2 z! = e!!!! = e(!!!!!!)!!          r = 1,2,… ,M.                                                                                        (3)

CONCLUSIONS

As the use of proposed technique has been already demonstrated to be successful in different research areas (Radar signature, Load monitoring, Sonar waves classification), promising results in the study of Electrophysiological activities are expected.

This project aims to develop: - A high-resolution method, reliable, rapid and reproducible to analyze the activity of peripheral fibers Aδ and C transporting nociceptive information from peripheral nervous system; - An evaluation tool for in vivo antalgic therapy; - An efficient tool to analyze cortical activities to extract specific identifiers for migraine pain. ACKNOWLEDGMENTS This interdisciplinary and exploratory project is supported by the CNRS, Blaise Pascal University and University of Auvergne.

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