Traumatic brain injuries (TBI) are among the leading causes of death and permanent
disability worldwide. Recent experimental observations suggest that damage in brain
tissue involves complex local as well as nonlocal chemomechanical interactions that
happen on multiple spatiotemporal scales. Biomechanical models of TBI existing in
the literature do not incorporate either electrochemical or multiscaling features.
Given that neurons are the brain cells responsible for electrochemical signaling
on multiplexed temporal scales we propose a novel mathematical model of
neuronal electromechanics that uses a constrained Lagrangian formulation and
Hamilton’s principle to couple Newton’s law of motion for a linear viscoelastic
Kelvin–Voigt solid-state neuron and the classic Hodgkin–Huxley equations of
the electronic neuron. We will use fractional order derivatives of variable
order to model multiple temporal scales. Numerical simulations of possible
damage dynamics in neurons due to mechanical trauma will be presented and
discussed.
