Computational modelling of the coupled electro-mechanical behaviour of neurons

Recent experimental evidence has uncovered complex biophysical phenomena accompanying the electrical activity of nervous cells. Now emerging theories refer to the electric pulse, i.e. the Action Potential (AP), as an electro-mechanical phenomenon, highlighting its multi-disciplinary nature. Due to its complexity, a unified theory explaining the multiphysics behind neural electrical activity has not yet appeared in the literature. Thus, neural electrical activity and its associated mechanics are frequently studied independently. This work aims at broadening the understanding of electro-mechanical neural activity in relation to brain injuries. Focus is given to injuries that initiate Diffuse Axonal Injury (DAI), a progressive pathogenesis that induces damage at the cellular level. The work performed in this thesis proposes a coupled 3D electro-mechanical modelling framework to investigate the interaction between neural electrical activity and neural structural mechanics in finite element analysis, considering DAI-induced electrical changes following brain injury. This work is based on a novel approach for simulating the interdependence of multi-domain phenomena, where electrical conduction is implemented through the use of electro-thermal equivalences, as the most appropriate and computationally efficient way to couple the electrical and mechanical domains in finite element analysis. The nerve modelling framework developed in this thesis is capable of simulating the real-time electro-mechanical phenomena of electrostriction and piezoelectricity, and their effects on the AP, which have been observed experimentally in the nerve membrane. It includes a modulated threshold for activation of the AP and independent alteration of the neural electrical properties as a function of (elastic and plastic) strain, voltage, space and time. This modelling approach is assessed and validated against experimental observations and data from the literature. A multiscale approach is then taken to investigate brain injury, by linking the nerve modelling framework at the microscale with a structural mechanics model of the head at the macroscale that is capable of simulating head impacts. The combined use of these models replicates both the neural micro-electro-mechanical environment and the brain macro-mechanical environment. The work considers the electro-mechanical behaviour of nerve fibres and fibre bundles, both with and without a myelin layer. The results of the simulations indicate that the structure of the nerve fibre is critically important in determining its electro-mechanical behaviour. Results also show that the insulating layer around myelinated fibres plays an important mechanical role during loading, by redistributing plastic strains within the nerve, and protecting the fibre from mechanical failure and electrophysiological impairments. Additionally, an analysis of the electro-mechanical behaviour in fibres of different calibre and type, reveals that disconnection is more likely to occur in fibres with large diameters because of elastic strains, while plastic strains seem to affect unmyelinated fibres with small calibre to a greater extent. The work reported in this thesis may contribute to the advancement of computational neuro electro-mechanics, leading to an enhancement in the understanding of the link between mechanical and electrical phenomena. It has also generated further insights into the electro-mechanical effects of nerve trauma due to brain injury that could have implications for improving the diagnosis and treatment of DAI. In the long-term, this modelling approach could also be used for studying communication between dendritic cells to aid the understanding of the alteration of neural networks as a result of injury or disease