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.
| Identifer | oai:union.ndltd.org:wpi.edu/oai:digitalcommons.wpi.edu:etd-theses-1743 |
| Date | 05 May 2006 |
| Creators | Branco, Dorothy M |
| Contributors | Roger Y. Lui, Advisor, , |
| Publisher | Digital WPI |
| Source Sets | Worcester Polytechnic Institute |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses (All Theses, All Years) |
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