Cortical waves and post‐stroke brain stimulation

Abstract

A neural field model with different activation and inhibition connectivity and response functions is considered. Stability analysis of a homogeneous in space solution determines the conditions of the emergence of stationary periodic solutions and of periodic travelling waves. Various regimes of wave propagation are illustrated in numerical simulations. The influence of external stimulation on the wave properties is investigated.

To the Thomson Cross Section of Light Scattered by a Moving Particle

“…The final result represented in a simple form (10). Our derivation is valid for scattering of long laser wavelets ( 1 M  ), when the radiation, emitted in selected direction is a quasi-monochromatic one and could be described by functions (7). This is due to the fact that W. Pauli considered the case when the particles in each beam have the same energy.…”

“…it does not depend on choice of functions(7) corresponding to oscillations of particles in transverse and longitudinal directions with respect to theirs velocities and could be calculated as the photon flux of scattered radiation to the density of incoming laser flux is e. the cross-section of scattering of laser photons by moving par-…”

Cortical stimulation in aphasia following ischemic stroke: toward model-guided electrical neuromodulation

“…The model proposed below (1.1)-(1.3) is a particular case of the existing models (see, e.g., Senk et al 2018). In its simplest form, this model represents a single integro-differential equation for the electric potential in the cortex (Bessonov et al 2018(Bessonov et al , 2019Beuter et al 2018). For example, the model suggested in Bessonov et al 2018 differs by the diffusion term describing additional conduction mechanisms (see Buskila et al 2019 for additional information).…”

“…(1.1) with the rate determined by a positive constant σ . Let us also note that more complete models can be considered, containing diffusion term, or a system of two equations instead of the single equation (Bessonov et al 2018. Numerical simulations are carried out in a bounded interval with periodic boundary conditions.…”

“…In addition, it offers an opportunity to calculate in quasi-real time the stimulation signal to be injected. Finally, it facilitates the computation of the stimulation parameters in a closed-loop design (Beuter et al 2014(Beuter et al , 2018Bessonov et al 2018Bessonov et al , 2019. Regarding electrical stimulation, Voigt et al (2018) show that activity elicited by low-current intracortical micro-stimulation "modulates induced cortical responses to a sensory stimulus in the primary auditory cortex" (Page 1).…”