Cortical waves and post‐stroke brain stimulation

Nikolai Bessonov (1) , Anne Beuter (2) , Sergei Trofimchuk (3) , Vitaly Volpert (4, 5)

1 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
2 IMS - Laboratoire de l'intégration, du matériau au système
3 Instituto de Matemática y Física - Universidad de Talca
4 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
5 MMCS - Modélisation mathématique, calcul scientifique

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.

Mots clés: brain stimulation; integro-differential equation; neural field model; waves

Domaines: Equations aux dérivées partielles [math.AP]

Nikolai Bessonov, Anne Beuter, Sergei Trofimchuk, Vitaly Volpert. Cortical waves and post‐stroke brain stimulation. Mathematical Methods in the Applied Sciences, 2019, 42 (11), pp.3912-3928. ⟨10.1002/mma.5620⟩. ⟨hal-02363412⟩