Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010Mathematical modeling in the medical sciences
|Page(s)||40 - 62|
|Published online||28 April 2010|
Modeling the Cancer Stem Cell Hypothesis
Department of Mathematics and Statistics, California State University
2 Department of Chemical Engineering ,Vanderbilt University
3 Department of Chemistry, Tennessee State University
4 Department of Cancer Biology, Vanderbilt University
5 Department of Mathematics, Vanderbilt University
* Corresponding author. E-mail:
Solid tumors and hematological cancers contain small population of tumor cells that are believed to play a critical role in the development and progression of the disease. These cells, named Cancer Stem Cells (CSCs), have been found in leukemia, myeloma, breast, prostate, pancreas, colon, brain and lung cancers. It is also thought that CSCs drive the metastatic spread of cancer. The CSC compartment features a specific and phenotypically defined cell population characterized with self-renewal (through mutations), quiescence or slow cycling, overexpression of anti-apoptotic proteins, multidrug resistance and impaired differentiation. CSCs show resistance to a number of conventional therapies, and it is believed that this explains why it is difficult to completely eradicate the disease and why recurrence is an ever-present threat. A hierarchical phenomenological model is proposed based on eight compartments following the stem cell lineage at the normal and cancer cell levels. As an empirical test, the tumor grading and progression, typically collected in the pathologic lab, is used to correlate the outcome of this model with the tumor development stages. In addition, the model is able to quantitatively account for the temporal development of the population of observed cell types. Two types of therapeutic treatment models are considered, with dose-density chemotherapy (a pulsatile scenario) as well as continuous, metronomic delivery. The drug hit is considered at the stem cell progenitor and early differentiated specialized cell levels for both normal and cancer cells, while the quiescent stem cell and fully differentiated compartments are considered favorable outcome for cancer treatment. Circulating progenitors are neglected in this analysis. The model provides a number of experimentally testable predictions. The relative importance of the cell kill and survival is demonstrated through a deterministic parametric study. The significance of the stem cell compartment is underlined based on this simulation study. This predictive mathematical model for cancer stem cell hypothesis is used to understand tumor responses to chemotherapeutic agents and judge the efficacy.
Mathematics Subject Classification: 92C37 / 92C50 / 34F05
Key words: Stem cell / mathematical model / hypothesis / cancer therapy
© EDP Sciences, 2010
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