A switch curve can be used to realize the disturbance in feedback form. The switch curve has a general analytic form for second order systems. This closed analytic form requires less computational effort and gives an intuitive feeling for how the switch curve will change with the other parameters. Nutrient Concentration in and Around a Vascularized Tumor with a Necrotic Core Abstract Nutrients are essential for the development of tumors. In a similar manner, glucose plays a role in the development of necrosis, and also controls cellular viability.
Tumors initially rely on diffusion for nutrient, oxygen, and waste transport.
Eventually the nutrient concentration at the center of the tumor can fall below a critical level, resulting in a decrease in cell proliferation, slow growth rate and possibly even cell death. Thus, the tumor may develop what is known as a necrotic core, or inactive region in the center of the tumor. This presentation focuses on the distribution of nutrient for a tumor penetrated by a capillary network - a basic model of vascularization on a tumor with a necrotic core. The inclusion of such a nutrient source adds complexities to the problem at hand. Physically this models the effects of immersion of a tumor into a nutrient bath, or similarly the addition of nutrient to the tissue surrounding the tumor.