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Using Mathematical Modeling as a Resource in Clinical Trials

1. Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126

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.
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Keywords clinical trials.; leukemia; mathematical modeling; cancer

Citation: Evans K. Afenya. Using Mathematical Modeling as a Resource in Clinical Trials. Mathematical Biosciences and Engineering, 2005, 2(3): 421-436. doi: 10.3934/mbe.2005.2.421


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Copyright Info: 2005, Evans K. Afenya, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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