Mathematical modeling of cell adhesion in tissue engineering using continuum models

Key factors in the formation of cell aggregates in tissue engineering and other fields are the cell-cell and cell-matrix interactions. Other important factors are culture conditions such as nutrient and oxygen supply and the characteristics of the environment (medium versus hydrogel). As mathematical models are increasingly used to investigate biological phenomena, it is important that processes such as cell adhesion are adequately described in the models. Recently a technique was developed to incorporate cell-cell and cell-matrix adhesion in continuum models through the use of non-local terms. In this study we apply this technique to model adhesion in a cell-in-gel culture set-up often found in tissue engineering applications. We briefly describe the biological issues underlying this study and the various modeling techniques used to capture adhesive behaviour. We furthermore elaborate on the numerical techniques that were developed in the course of this study. Finally, we consider a tissue engineering model that describes the spatiotemporal evolution of the concentration of cells, matrix, hydrogel, matrix degrading enzymes and oxygen/ nutrients in a cell-in-gel culture system. Sensitivity analyses indicate a clear influence of the different adhesive processes on the final cell and collagen density and distribution, demonstrating the significance of cell adhesion in tissue engineering and the potential of the proposed mathematical technique.status: accepte