Multiscale Model of Brain Gray Matter
Multiscale Modeling of Gray Matter
The goal of the present model is to determine the stress-strain behavior and neuronal damage in gray matter of the brain. The gray matter may be considered a two phase material constituting of neuronal cell bodies or soma and ExtraCellular Matrix (ECM). The model will develop constitutive relations based on the microstructure of the gray matter at different length scales and the effect of the ECM on it.
In order to define the constitutive relations in the macroscale, the density effects and texture of the mesoscale between the ECM and neurons needs to be considered. The mechancial properties of neuron must be determined in the micro scale. The damage in the neuron must be determined in the nanoscale, and will be determined by considering the effects of the cytoskeleton on mechanical properties and lipid bilayer poration. The properties of the lipid bilayer need to be determined by considering the forces of each protein on each other. These forces must be determined from the quantum scale using Density Functional Theory (DFT) simulations.
DFT simulations carried out in the quantum scale are used to determine the forces acting between the proteins. These will be passed up into the atomic scale and used to determine the properties of the lipid bilayer. LAMMPS simulations carried out in the atomic scale will then be used to determine poration and their growth. the lipid bilayer properties and pore nucleation must be passed onto the microscale where damage must be defined on a single neuron. Membrane damage and the mechancial properties of the neuron will then be pushed up into the mesoscale where the microstructure of the gray matter consisting the ECM are considered. Finite element analysis carried out on the combination of the neurons and the ECM will be used to a constitutive equation at the macroscale. The resulting equation will be used on the finite element analysis of the human brain and validated by comparison to existing experimental data.