A thermodynamically consistent electro-chemo-mechanical theory for modeling axonal swelling

Abstract In the present study, for the first time, a thermodynamically consistent large deformation theory is developed to model the multi physics problem of axonal swelling which is the hallmark of most of the brain diseases. To this end, first, relevant axonal compartments are explained and then the corresponding model parts are introduced. Next, the problem is formulated as an open thermodynamic system and the consequent constitutive and evolution equations are extracted utilizing the balance laws. Here, a multiplicative decomposition of the deformation gradient is used to capture the active behavior of the axonal actin cortex. After that, specific free energy functions are given for the model parts to complete the framework. Finally, while the developed model is general and can be extended to cover other types of axonal swellings, for the sake of briefness, two swelling modes are explored in the present study: swelling due to hypo-osmotic shocks and volume expansions because of actomyosin disruptions. To this end, three relevant sets of experimental data available in the literature are chosen to be investigated; free equilibrium swelling of squid axoplasm, transient swelling of PC12 neurites due to hypo-osmotic shocks and steady state as well as transient swellings of embryonic Drosophila axons due to blocking myosin motors. Comparative study between model predictions with realistic estimated parameters and the corresponding experimental data demonstrates that the model can successfully predict both axonal swellings. The key findings of this study are as follows: first, it is shown that the kinetics of axonal swelling is surface limited and hence there is no need to consider the details of water diffusion inside the axoplasm. In fact, the axoplasm swelling can be considered instantaneous in the presence of the axolemma barrier. Second, axonal swelling happens mainly in its radial direction due to its structural and geometrical constraints. Third, the multiphasic nature of the axoplasm can be accurately modeled as an ideal polyelectrolyte hydrogel and finally the active contractile forces can be ignored for volume expansions due to hypo-osmotic shocks as the osmotic pressures are much bigger than the corresponding stresses due to active deformations.