Mathematical models for ameboid cell motility and model based inverse problems.

摘要

In this interdisciplinary work which is a combination of mathematics, biology and engineering, discrete and continuum models for ameboid cell movement, together with the corresponding inverse problem formulations are introduced and discussed. The discrete model uses classical mechanical tools and the continuum model uses viscoelastic fluid dynamics. The models are analyzed qualitatively and quantitatively.; Based on the models, the inverse problems can be posed: depending on the constitutive relations and governing equations, what kind of characteristic properties must the model parameters and unknowns have in order to reproduce a given movement of the cell, provided that position or the velocity field is given? The inverse problems which were not previously addressed in the area of cell motility are also analyzed.; The inverse problems provide the model parameters that give some insight, principally into the mechanical aspect, but also, through scientific reasoning, into chemical and biophysical aspects of the cell.; The discrete model consists of a system of second-order ordinary differential equations with the corresponding inverse problem, which can be written as a linear algebraic system. The continuum model, in the one-dimensional case, is a system of six nonlinear partial differential equations of mixed type including parabolic, hyperbolic, and elliptic equations with a free boundary formulation. The inverse problem for the continuum model has two parts: finding the unknowns for a given velocity field, which is done analytically, and parameter estimation, which is done numerically.