A Mathematical Model for Brain Tissue

Open Access
Author:
Lapsansky, Bradford Joseph
Area of Honors:
Engineering Science
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Corina Stefania Drapaca, Thesis Supervisor
  • Francesco Costanzo, Faculty Reader
  • Judith A Todd, Faculty Reader
  • Corina Stefania Drapaca, Honors Advisor
Keywords:
  • 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.