We present a generic model to investigate alignment due to cell movement with spefic application to collagen fibre alignment in wound healing. In particular, alignment in two orthogonal directions is considered. Numerical simulation are presented to show how alignment is affected by key parameter min the model. from a travelling wave analysis of a simplified one-dimensional version of the model we derive a first order ordinary differential equation to describe the time evolution of aligment. We conclude that in the wound healing context,faster healing wounds result in more aligment and hence more serve scarring. It is shown how the model can be extended to included orientation dependent Kinetics,multipkle cell types and several extracellular matrix materials.
Olsen, L., Maini, P. K., Sherratt, J. A., & Marchant, B. (1998). Simple Modelling of Extracellular Matrix Alignment in Dermal Wound Healing I. Cell Flux Induced Alignment. Journal of Theoretical Medicine, 1(3), 175–192. https://doi.org/10.1080/10273669808833018