Title page for ETD etd-050506-164020

Document Type thesis

Author Name Branco, Dorothy M

URN etd-050506-164020

Title Nonlinear Optimization of a Stochastic Function in a Cell Migration Model

Degree MS

Department Mathematical Sciences

Advisors
Roger Lui, Advisor

Keywords
minimization
derivatives
correlation
cell migration

Date of Presentation/Defense 2006-05-05

Availability unrestricted

Abstract
The basis for many biological processes such as cell division and differentiation, immune responses, and tumor metastasis depends upon the cell's ability to migrate effectively. A mathematical model for simulating cell
migration can be useful in identifying the underlying contributing factors to the crawling motions observed in
different types of cells. We present a cell migration model that simulates the 2D motion of amoeba, fibroblasts,
keratocytes, and neurons according to a set of input parameters. In the absence of external stimuli the pattern
of cell migration follows a persistent random walk which necessitates for several stochastic components in the
mathematical model. Consequently, the cell metrics which provide a quantitative description of the cell motion
varies between simulations. First we examine different methods for computing the error observed between the
output metrics generated by our model and a set of target cell metrics. We also investigate ways of minimizing
the variability of the output by varying the number of iterations within a simulation. Finally we apply finite
differences, Hooke and Jeeves, and Nelder-Mead minimization methods to our nonlinear stochastic function to search
for optimal input values.

Files
dbranco.pdf

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Document Type	thesis
Author Name	Branco, Dorothy M
URN	etd-050506-164020
Title	Nonlinear Optimization of a Stochastic Function in a Cell Migration Model
Degree	MS
Department	Mathematical Sciences
Advisors	Roger Lui, Advisor
Keywords	minimization derivatives correlation cell migration
Date of Presentation/Defense	2006-05-05
Availability	unrestricted
Abstract The basis for many biological processes such as cell division and differentiation, immune responses, and tumor metastasis depends upon the cell's ability to migrate effectively. A mathematical model for simulating cell migration can be useful in identifying the underlying contributing factors to the crawling motions observed in different types of cells. We present a cell migration model that simulates the 2D motion of amoeba, fibroblasts, keratocytes, and neurons according to a set of input parameters. In the absence of external stimuli the pattern of cell migration follows a persistent random walk which necessitates for several stochastic components in the mathematical model. Consequently, the cell metrics which provide a quantitative description of the cell motion varies between simulations. First we examine different methods for computing the error observed between the output metrics generated by our model and a set of target cell metrics. We also investigate ways of minimizing the variability of the output by varying the number of iterations within a simulation. Finally we apply finite differences, Hooke and Jeeves, and Nelder-Mead minimization methods to our nonlinear stochastic function to search for optimal input values.
Files	dbranco.pdf