A computational model coupling mechanics and electrophysiology in spinal cord injury

Abstract

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differentiated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specifically, the direct relations between brain and spinal cord tissue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanisticbased damage criteria, simulated function-based damage criteria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus providing a link between mechanical trauma and subsequent functional deficits.

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

“…[19,28], see Table 1. An explicit scheme was used for solving the electrophysiological ion channel dynamics variables of the HH boundary condition equations.…”

“…This model follows the approach proposed by Jérusalem et al [19] to model the ion channel left shift related damage. In this model, Equation (30) is also used but the reversal potentials of the ion channels are modified to reflect such damage, see Equation (31).…”

“…In order to validate the electrophysiological implementation of the CT and HH boundary conditions, both were modelled separately and, in the absence of deformation, validated against the results of two other numerical codes: Neurite, a 1D finite difference framework for mechanical electrophysiological coupling [19,28], and a Matlab 1D FE code with CT and HH applied as boundary conditions in a similar fashion, and solved using the Newton-Raphson iterative scheme, see Appendix B for the full study and Appendix C for the Matlab 1D code.…”

“…To this end, Jérusalem et al [19] proposed a 1D finite difference model to capture the longitudinal strain and strain rate dependence of electrophysiological alteration by relating the N a V and voltage gated potassium (K V ) ion channels dynamics to the strain in the membrane. This model aimed at capturing the recovery of CAP amplitude up to 30 minutes post white matter stretch in experiments conducted by Shi and Whitebone [7].…”

“…Their model considers the extracellular matrix, membrane and intracellular matrix as separate element types. The strain based electrophysiology damage model proposed by Jérusalem et al [19] was adopted in this model but the ion channel dynamics damage was not directly linked to the deformation. While the 3D FE approach allows for multiple loading modes, the required spatial discretisation of the axonal membrane (approximately a thousandth of the axon diameter) for a fully geometrically conserving model remains computationally expensive.…”