Pseudo-chemical Mathematical Model for Tumor Growth Based on the Cancer Stem Cell Hypothesis

摘要

We present a simple pseudo-chemical mathematical model for tumor growth based on the CSC hypothesis, derived using a chemical reaction engineering approach. Each event related to cell division or death of each one of three cell subpopulations (CSCs, progenitor cells, and differentiated cells) is represented and modeled as a chemical reaction. This approach resulted in a set of analytically solvable ordinary differential equations that describes the time evolution of each cell subpopulation and the overall tumor growth. Model parameters were estimated by fitting to five data sets corresponding to different in vitro and in vivo tumor growth scenarios. Results show that asymmetric and symmetric divisions of CSCs are of major importance for tumor maintenance and that, not only specific targeting, but also induction of differentiation of CSCs, could be highly effective therapeutic strategies against tumor growth.