Brain Triphasic Model Continuum Mixture Mathematical Linearized Linear
Abstract:
Brain tissue is very sensitive to both mechanical forces and chemical imbalances.
These imbalances can cause functional and/or structural changes of the tissue
which can lead to the onset and evolution of neurological diseases. Accurate mathematical
models of brain chemo-biomechanics that increase our understanding of
both healthy tissue and disease mechanisms in the brain greatly aid the development
of better diagnostic and therapeutic tools and protocols. This thesis models
the brain as a mixture material made of three phases: solid, fluid, and ionic.
The equations that govern the chemo-biomechanics of the brain are linearized and
considered in a limiting one-dimensional case so that the accuracy of numerical
solutions developed for these equations may be verified by using an analytic solutions
represented as Fourier series. The model is then coupled to the classic
Hodgkin-Huxley equations to predict the displacement field of neurons as a result
of an applied electric potential.
