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Based on the mass balance (conservation) equation and the ubiquitous ¼ power law in biological allometry, we derive a general governing equation for organism growth. It is the same as a previously published model by West et al., which was developed using a conservation of total energy formalism with respect to the maintenance of already existing tissue and newly created one. In the present model, the energy/nutrition (including oxygen) supply or consumption in metabolism is reflected in the production and death rates. We start by dividing an organism into different small systems which have identical cells and then unite them by introducing similarity of growth. Normal cells follow the rules for similarity of growth but tumor cells may not. This model is applied to tumor therapy. We model the response of tumor cells to the major standard tumor treatments: surgery, radiation and chemotherapy. This model explains the survival curves quite well (better than all previous models). Also, it consistently explains cell response to high and low LET (linear energy transfer) radiations. This work shows that the LQ model is an approximate result of the present model under specific conditions. Tumor interstitial fluid pressure (TIFP) has the potential to predict tumor response to non-surgical cancer treatments such as radiation and chemotherapies. We present the mathematical framework for a quantitative, non-invasive measure of TIFP. It describes the distribution of interstitial fluid pressure in three distinct tumor regions: vascularized tumor rim, central tumor region and normal tissue. We demonstrate that the acquisition of serial images of a tumor after the injection of a contrast agent can provide a non-invasive and potentially quantitative measure of TIFP.
Liu, Long Jian, "Study Regarding Properties of Solid Tumors in Mammals" (2013). Electronic Theses and Dissertations. 4742.