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Full-Text Articles in Physical Sciences and Mathematics
Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo
Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo
Mathematics & Statistics Theses & Dissertations
Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.
It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …
Mathematical Models Of Prevascular Tumor Growth By Diffusion, Sophia A. Maggelakis
Mathematical Models Of Prevascular Tumor Growth By Diffusion, Sophia A. Maggelakis
Mathematics & Statistics Theses & Dissertations
A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly straightforward comparisons with experimental or clinical data (as it becomes available), yet they are mathematically sophisticated enough to capture the main biological phenomena of interest.
The tumor growth and cell proliferation rate are assumed to depend on the local concentrations of nutrients and inhibitory factors. The effects of geometry and spatially non-uniform inhibitor production and non-uniform nutrient consumption …