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 Copley, Faculty Reader
Corina Stefania Drapaca, Thesis 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.