Quantifying Strain State Effect on Neuronal Membrane Damage

Murphy, M. A., Mun, S., Baskes, M. I., Horstemeyer, M., & Prabhu, R. (2018). Quantifying Strain State Effect on Neuronal Membrane Damage. 18th U.S. National Congress for Theoretical and Applied Mechanics. Rosemont, IL.

Abstract

INTRODUCTION Globally, ten million people are estimated to suffer from traumatic brain injury (TBI) every year. To better simulate TBI using finite element analysis, a mechano-physiological internal state variable (MPISV) material model that incorporates both mechanical and physiological effects is needed. One important TBI-related physiological effect is membrane mechanoporation. Membrane damage due to mechanoporation can be calculated as the product of pore nucleation and growth. Using the MPISV material model, these damage properties can be used to capture mechanoporation damage in macroscale brain models. The current study examines the damage resulting from mechanoporation on multiple strain states. METHODS A membrane structure containing seventy-two 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) phospholipids and 9,070 TIP3P water molecules was equilibrated for ten nanoseconds using the program LAMMPS and the CHARMM36 all-atom lipid force field. The equilibrated structure was subjected to constant velocity tensile deformations in the x and y (in-plane) dimensions. X and y strain rates were determined so that all strain states had a von Mises strain rate of 5.5 × 108 s-1. The z dimension was allowed to relax freely during deformations. Structure failure was assumed to occur when water fully penetrated the bilayer and formed a chain of water through both bilayer leaflets. Structure coordinates were output every 5 ps and visualized using OVITO. For analysis, 3x3x1 (a total of 9 boxes) periodic images were used to create intact images of all pores from the top view. An in-house MATLAB function was used to remove duplicate pores, record pore properties, and calculate damage. Additionally, strains corresponding to the first appearance of pores large enough for water molecules and calcium ions were recorded. RESULTS AND CONCLUSIONS Results show the strain state significantly affected mechanoporation-related pore nucleation and growth and, therefore, the resulting damage. The equibiaxial and non-equibiaxial cases exhibited statistically similar damage responses and were the most damaging. The damage response magnitude in the strip biaxial case was lower and required considerably higher strains to start increasing. The uniaxial case resulted in the least damage with a minimal response. These results emphasize the potential for the phospholipids to flow in a deforming structure. Hence, strain states that greater restrict the ability of the phospholipids to move freely in the membrane result in higher damage at lower strains. Further, pore growth will be mapped using a membrane forming limit diagram to demonstrate nanoscale membrane strain limits that may result in physiological damage.