Extracellular matrix alignment by cells: discrete and continuous models compared

The basic event in the formation of scar tissue in a wound is the remodelling of extracellular matrix by fibroblasts cells. These cells enter the wound from surrounding tissue, break down the fibrin-based blood clot, and replace it with a collagen-based matrix. The orientation of the new collagen fibres involves a complex interplay between cells and matrix: cells tend to move along collagen fibres, and also reorient fibres towards their direction of movement. I will discuss and compare two different approaches to modelling this process of fibre reorientation by fibroblasts. I will describe a discrete formulation in which each cell is represented as a separate entity, within a continuum of collagen fibres. I will compare this with a continuous model with densities of cells and matrix that are functions of space and orientation. The two approaches offer different insights into the process of matrix alignment and I will discuss their implications for scar tissue formation.