Collective cell migration is an important activity during the process of wound healing. In this thesis, we develop a model of a wound-healing assay using the Cellular Potts Model in the software package Morpheus. In addition, we describe a system of three coupled partial differential equations for different forms of the molecule transforming growth factor β. An analysis of this system shows the existence of a trivial and an infeasible homogeneous steady state solution, but the system does not allow Turing patterns to form. A baseline migration model with circular-shaped fibroblast cells is set up and tested. This model is extended by modeling the elongated shape of fibroblasts, which showed an increased amount of vertical cell movement. An in-depth analysis is performed to investigate the effect of cell length on vertical cell movement. It shows a significant increase in vertical movement when increasing the cell length up to approximately a factor of 2. Lastly, as a proof of concept, the reaction-diffusion system is integrated into the extended model simulating the differentiation of fibroblasts into myofibroblasts.