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J Mol Model. 2006 Jul;12(5):641-8. Epub 2006 Mar 23.

Numerical simulation and graphical analysis of in vitro benign tumor growth: application of single-particle state bosonic matter equation with length scaling.

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Department of Chemistry, Cleveland State University, Cleveland, OH 44115, USA.


We describe the application of a non-linear single-particle state bosonic condensate equation to simulate multicellular tumor growth by treating it as a coupling of two classical wave equations with real components. With one component representing the amplitude of the cells in their volume growth phase and the other representing the amplitude of the cells in their proliferation or mitosis phase, the two components of the coupled equation feed each other during the time evolution and are coupled together through diffusion and other linear and non-linear terms. The features of quiescent and necrotic cells, which result from poor nutrient diffusion into a tumor, have been found to correspond quite well to experimental data when they are modeled as depending on higher cell density. Classical hallmarks of benign tumor growth, such as the initial rapid growth, followed by a dramatic collapse in the proliferating cell count and a strong re-growth thereafter appear quite encouragingly in the theoretical results. A tool for graphical analysis of the tumor simulation results has been developed to provide morphological information about tumors at various growth stages. The model and the graphical analysis can be extended further to create an effective tool to predict/monitor tumor growth.

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