Abstract
In 1999, Hahnfeldt et al. proposed a mathematical model for tumor growth as dictated by reciprocal communications between tumor and its associated vasculature, introducing the idea that a tumor is supported by a dynamic, rather than a static, carrying capacity. In this original paper, the carrying capacity was equated with the variable tumor vascular support resulting from the net effect of tumor-derived angiogenesis stimulators and inhibitors. This dynamic carrying capacity model was further abstracted and developed in our recent publication to depict the more general situation where there is an interaction between the tumor and its supportive host tissue; in that case, as a function of host aging (Benzekry et al., 2014). This allowed us to predict a range of host changes that may be occurring with age that impact tumor dynamics. More generally, the basic formalism described here can be (and has been), extended to the therapeutic context using additional optimization criteria (Hahnfeldt et al., 1999). The model depends on three parameters: One for the tumor cell proliferation kinetics, one for the stimulation of the stromal support, and one for its inhibition, as well as two initial conditions. We describe here the numerical method to estimate these parameters from longitudinal tumor volume measurements.