American Institute of Mathematical Sciences

Advanced
2005, 2(3): 421-436. doi: 10.3934/mbe.2005.2.421

Using Mathematical Modeling as a Resource in Clinical Trials

Evans K. Afenya 1,

1. 

Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, United States

Received  January 2005 Revised  May 2005 Published  August 2005

In light of recent clinical developments, the importance of mathematical modeling in cancer prevention and treatment is discussed. An existing model of cancer chemotherapy is reintroduced and placed within current investigative frameworks regarding approaches to treatment optimization. Areas of commonality between the model predictions and the clinical findings are investigated as a way of further validating the model predictions and also establishing mathematical foundations for the clinical studies. The model predictions are used to propose additional ways that treatment optimization could enhance the clinical processes. Arising out of these, an expanded model of cancer is proposed and a treatment model is subsequently obtained. These models predict that malignant cells in the marrow and peripheral blood exhibit the tendency to evolve toward population levels that enable them to replace normal cells in these compartments in the untreated case. In the case of dose-dense treatment along with recombinant hematopoietic growth factors, the models predict a situation in which normal and abnormal cells in the marrow and peripheral blood are obliterated by drug action, while the normal cells regain their growth capabilities through growth-factor stimulation.
Keywords: clinical trials., leukemia, mathematical modeling, cancer.
Mathematics Subject Classification: 92D3.
Citation: Evans K. Afenya. Using Mathematical Modeling as a Resource in Clinical Trials. Mathematical Biosciences & Engineering, 2005, 2 (3) : 421-436. doi: 10.3934/mbe.2005.2.421
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