Faculty Advisor

Roger Lui


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.


Worcester Polytechnic Institute

Degree Name



Mathematical Sciences

Project Type


Date Accepted





minimization, derivatives, correlation, cell migration, Cell migration, Mathematical models, Stochastic modeling