Electrothermal Equivalent Three-Dimensional Finite-Element Model of a Single Neuron

Objective: We propose a novel approach for modelling the interdependence of electrical and mechanical phenomena in nervous cells, by using electrothermal equivalences in finite element (FE) analysis so that existing thermomechanical tools can be applied. Methods: First, the equivalence between electrical and thermal properties of the nerve materials is established, and results of a pure heat conduction analysis performed in Abaqus CAE Software 6.13-3 are validated with analytical solutions for a range of steady and transient conditions. This validation includes the definition of equivalent active membrane properties that enable prediction of the action potential. Then, as a step toward fully coupled models, electromechanical coupling is implemented through the definition of equivalent piezoelectric properties of the nerve membrane using the thermal expansion coefficient, enabling prediction of the mechanical response of the nerve to the action potential. Results: Results of the coupled electromechanical model are validated with previously published experimental results of deformation for squid giant axon, crab nerve fibre, and garfish olfactory nerve fibre. Conclusion: A simplified coupled electromechanical modelling approach is established through an electrothermal equivalent FE model of a nervous cell for biomedical applications. Significance: One of the key findings is the mechanical characterization of the neural activity in a coupled electromechanical domain, which provides insights into the electromechanical behaviour of nervous cells, such as thinning of the membrane. This is a first step toward modelling three-dimensional electromechanical alteration induced by trauma at nerve bundle, tissue, and organ levels.