Abstract
Tissue growth is due to cell division and death within the tissue. A first approach is to study cell division and death as processes of cell population dynamics. Cell division and death rates are then introduced, and a Fokker-Planck equation can be written to describe the statistics of the number of cells in the tissue. The key parameter is the growth rate, which is the difference between cell division and death rates. If the growth rate is positive, the number of cells grows exponentially. The stochasticity of cell division and death introduces noise, which is multiplicative noise for cell number.
Another classical growth model that has been proposed for bacteria is a growth front propagation model. If only cell diffusion and death are taken into account, the front is described by the Fisher-Kolmogorov equations, which enable the propagation velocity to be calculated.
A final important parameter is the regulation of growth by mechanical properties, as proposed by Boris Shraiman. Cell growth and death rates depend on cell pressure in the tissue. The rate of division decreases with pressure, while the rate of cell death increases. There is then a homeostatic pressure for which both rates are equal ; the growth rate is zero and the tissue is in a stationary state. This pressure is an important characteristic of the tissue.
