Mathematical model for cancer cell invasion of tissue

Abstract

Cancer cell invasion of tissue is a complex biological process which during cell migration through extracellular matrix, facilitated by the secretion of degradative enzymes, is a central process. Cells can be deform their cytoplasm to produce pseudopodia, anchor these pseudopodia to neighbouring spatial locations in the tissue and detach earlier bonds, to enable them to move and therefore migrate in a specified direction. Genetic mutations, chemoattractant gradient or a lack of nutrients in their current location can stimulate cell motility and cause them to migrate, thereby invading new territory. In this paper, we propose a hybrid discrete-continuum model to study the early growth of solid tumour and their ability to degrade and migrate into the surrounding extracellular matrix. Considering the importance of chemoattractant gradients in the invasion process, the model consists of a system of partial differential equations describing the interactions of enzyme and the surrounding matrix. Having formulated, then the system has been simplified to simpler system which give an analytical solution in Fourier series. Results from simulation show that the degradation of the extracellular matrix mirrors the tumour’s growth. High enzyme concentrations, which cause maximum degradation of extracellular matrix leads to a rise in concentration of attractant and growth factors causes cells to migrate outward and to proliferate. Finally concluding remarks are made and recommendation for future work are indicated in the last section.