3D finite element formulation for mechanical–electrophysiological coupling in axonopathy

Abstract

Traumatic injuries to the central nervous system (brain and spinal cord) have recently been put under the spotlight because of their devastating socio-economical cost. At the cellular scale, recent research efforts have focussed on primary injuries by making use of models aimed at simulating mechanical deformation induced axonal electrophysiological deficits. The overwhelming majority of these models only consider axonal stretching as a loading mode, while other modes of deformation such as crushing or mixed modes – highly relevant in spinal cord injury – are left unmodelled. To this end, we propose here a novel 3D finite element framework coupling mechanics and electrophysiology by considering the electrophysiological Hodgkin–Huxley and Cable Theory models as surface boundary conditions introduced directly in the weak form, hence eliminating the need to geometrically account for the membrane in its electrophysiological contribution. After validation against numerical and experimental results, the approach is leveraged to model an idealised axonal dislocation injury. The results show that the sole consideration of induced longitudinal stretch following transverse loading of a node of Ranvier is not necessarily enough to capture the extent of axonal electrophysiological deficit and that the non-axisymmetric loading of the node participates to a larger extent to the subsequent damage. On the contrary, a similar transverse loading of internodal regions was not shown to significantly worsen with the additional consideration of the non-axisymmetric loading mode.