Mathematical modeling of stem cell proliferation.

The mathematical models prevalently used to represent stem cell proliferation do not have the level of accuracy that might be desired. The hyperbolastic growth models promise a greater degree of precision in representing data of stem cell proliferation. The hyperbolastic growth model H3 is applied to experimental data in both embryonic stem cells and adult mesenchymal stem cells. In the embryonic stem cells the results are compared with other popular models, including the Deasy model, which is used prevalently for stem cell growth. In the case of modelling adult mesenchymal stem cells, H3 is also successfully applied to describe the proliferative index. We demonstrated that H3 can accurately represent the dynamics of stem cell proliferation for both embryonic and adult mesenchymal stem cells. We also recognize the importance of additional factors, such as cytokines, in determining the rate of growth. We propose the question of how to extend H3 to a multivariable model that can include the influence of growth factors.