An application of the non-linear bifurcation theory to tumor growth modeling

The purpose of the work reported in this paper was to understand how a few cancerous cells (either from the primary growth, or as result of breaking away from a tumor and lodging in a different part of the body--metastasis) can grow to form a sizable mass and what decides whether such growth will indeed take place. The intermediate region, lying between the molecular (or micro) level to the fully developed (or macro) level, is not readily accessible to experimental observations. A mathematical model with a firm physiological basis has been proposed to develop a unified field theory that bridges the two regimes. The techniques of non-linear global analysis have been used. The global behavior, (which determines the long-term prognosis), is found to be significantly influenced by the presence or absence of two critical bifurcations. Both of these have practical consequences regarding the inception and the cure of the disease. Several conclusions have been drawn which lead to practical suggestions for experimentation. It is predicted that reducing the food intake immediately after an exposure to carcinogens, would lead to a reduced chance of cancer. A preliminary case has been made to lend support to the idea that an absence of snacking (and even periodic fasting) might work as a preventive measure against cancer.