Note on a diffusion model of tissue growth
The growth of cell population is governed by a conservation law of mass or cell volume. The assumptions and analytical details on how to derive the conservation law have been discussed e.g. by \textit{H. Greenspan} [Studies Appl. Math. 51, 317-340 (1972; Zbl 0257.92001), and Growth 38, 81 ff (1974)] and only a summary of results is given here. Following Greenspan, we consider the growth of a cell culture in a small tube with a small constant cross sectional area, \(\alpha\), and the three interfacial heights \(z_ 0(t)\), \(z_ g(t)\), \(z_ i(t)\) to separate the cell culture from the ambient medium, dividing from nondividing cells, and living from dead cells, respectively.
scientific article; zbMATH DE number 4160543