Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-050506-164020

Document Typethesis
Author NameBranco, Dorothy M
TitleNonlinear Optimization of a Stochastic Function in a Cell Migration Model
DepartmentMathematical Sciences
  • Roger Lui, Advisor
  • Keywords
  • minimization
  • derivatives
  • correlation
  • cell migration
  • Date of Presentation/Defense2006-05-05
    Availability unrestricted


    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.

  • dbranco.pdf

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