Model of traveling waves in a neural environment with asymmetric interneuronal connections

About the author:

Malkov Ivan Nikolaevich, postgraduate student, junior lecturer, University of Tyumen, Tyumen, Russia
i.n.malkov@yandex.ru, https://orcid.org/0000-0001-5845-5591

Abstract:

This study investigates the propagation dynamics of a traveling wave on the human neocortex, elicited by the stimulation of the median nerve. The primary objective is to evaluate the hypothesis of radially asymmetric wave propagation, with variability contingent upon the directional curvature of the activation function. We employ an Amari-type mathematical model within the framework of neural field theory, wherein the activation velocity of neuronal populations — modulated by the curvature parameter of the activation function — varies with the direction of wave propagation. For the reconstruction of the traveling wave, we utilize an individual-specific anatomical model of the cerebral cortex, derived from high-resolution magnetic resonance imaging (MRI), ensuring precise accuracy of spatial localization of electrical processes in the cerebral cortex. The outcomes of the radially asymmetric propagation model are juxtaposed with those predicated on radially symmetric wave propagation assumptions. Our findings indicate that incorporating directional variability in the curvature parameter of the activation function gives significant improvements in modeling accuracy, as validated by comparative analysis of approximation errors against empirical magnetoencephalographic (MEG) data. Furthermore, the dynamics of electrical potentials on the neocortical surface are graphically represented, illustrating the results of both approximation approaches on the subject-specific anatomical model.

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