Mathematical Models of Cancer Evolution and Cure

Since the pioneering work of Salmon and Durie, the availability of a quantitative measure of malignant cell burden in multiple myeloma has been used to make clinical predictions and to model tumor cell growth. Here, we analyzed a large set of tumor response data from three randomized controlled clinical trials (total sample size n=1,469 evaluable patients) to establish and validate a novel mathematical model of MM cell dynamics based on responses to bortezomib-based chemotherapy regimens. Dynamics of treatment response in newly diagnosed patients were most consistent with a mathematical model postulating the existence of two tumor cell subpopulations, “myeloma progenitor cells" and “myeloma differentiated cells”. Differential treatment responses were observed with significant tumoricidal effects on myeloma differentiated cells and less clear effects on myeloma progenitor cells. We validated this model using a second trial of newly diagnosed MM patients and a third trial of refractory patients. When applying our model to data of relapsed MM patients, we found that a hybrid mathematical model incorporating both a MM differentiation hierarchy and clonal evolution best explains the tumor response patterns in all patients. The clinical data, together with mathematical modeling, suggest that bortezomib-based therapy exerts a selection pressure on myeloma cells that can shape the disease phenotype, thereby generating further inter-patient variability. This model may be a useful tool for improving the rational design of chemotherapy regimens in multiple myeloma.