Open Access. Powered by Scholars. Published by Universities.®
Other Biochemistry, Biophysics, and Structural Biology Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
- Publication
- Publication Type
Articles 1 - 2 of 2
Full-Text Articles in Other Biochemistry, Biophysics, and Structural Biology
Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe
Master's Theses
In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …
Modeling Human Immune Response To The Lyme Disease-Causing Bacteria, Yevhen Rutovytskyy
Modeling Human Immune Response To The Lyme Disease-Causing Bacteria, Yevhen Rutovytskyy
Honors Scholar Theses
The purpose of this project is to develop and analyze a mathematical model
for the pathogen-host interaction that occurs during early Lyme disease.
Based on the known biophysics of motility of Borrelia burgdorferi and a
simple model for the immune response, a PDE model was created which tracks
the time evolution of the concentrations of bacteria and activated immune
cells in the dermis. We assume that a tick bite inoculates a highly
localized population of bacteria into the dermis. These bacteria can
multiply and migrate. The diffusive nature of the migration is assumed and
modeled using the heat equation. Bacteria …