A. Bakhtiarydavijani A Macroscale Mechano-physiological Internal State Variable (MPISV) Model for Neuronal Membrane Damage with Subscale Microstructural Effects

Bakhtiarydavijani, A., Murphy, M. A., Prabhu, R., Fonville, T. R., & Horstemeyer, M. (2021). A. Bakhtiarydavijani A Macroscale Mechano-physiological Internal State Variable (MPISV) Model for Neuronal Membrane Damage with Subscale Microstructural Effects. Multiscale Biomechanical Modeling of the Brain. Cambridge, Massachusetts: Academic Press. 119-138. DOI:10.1016/B978-0-12-818144-7.00003-7.

In this chapter, we develop thermodynamically consistent mechano-physiological internal state variable (MPISV) damage rate equations that bridge neuronal membrane mechanoporation from the nanoscale to the microscale. Traumatic brain injuries inherently affect multiple length scales of heterogeneous structures starting at the nanoscale, such as neuronal membrane mechanoporation, and can causally affect different multiscale structures at the macroscale level. Our proposed macroscale continuum, multiscale MPISV damage equations are strain rate, stress state, and history dependent. Coupled with Nernst–Planck diffusion equations, we measure the disruption of neuronal ion homeostasis using an analytical model. Our modeling approach admits the effects of microstructural features related to neuronal injuries in a manner that is thermodynamically consistent with MPISV theory and can be implemented into microscale neuron models to accurately define neuronal injury thresholds.