Gatenby, R. A. and Maini, P. K. and Gawlinski, E. T. (2002) Analysis of tumor as an inverse problem provides a novel theoretical framework for understanding tumor biology and therapy. Applied Mathematics Letters, 15 (3). pp. 339-345.
We use a novel “inverse problem” technique to construct a basic mathematical model of the interacting populations at the tumor-host interface. This approach assumes that invasive cancer is a solution to the set of state equations that govern the interactions of transformed and normal cells. By considering the invading tumor edge as a traveling wave, the general form of the state equations can be inferred. The stability of this traveling wave solution imposes constraints on key biological quantities which appear as parameters in the model equations. Based on these constraints, we demonstrate the limitations of traditional therapeutic strategies in clinical oncology that focus solely on killing tumor cells or reducing their rate of proliferation. The results provide insights into fundamental mechanisms that may prevent these approaches from successfully eradicating most common cancers despite several decades of research. Alternative therapies directed at modifying the key parameters in the state equations to destabilize the propagating solution are proposed.
|Uncontrolled Keywords:||Mathematical modeling; Tumor host interaction; Tumor invasion; Tumor therapy|
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||20 Nov 2006|
|Last Modified:||20 Jul 2009 14:21|
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