Mathematical modeling provides the predictive ability to understand the metabolic reprogramming and complex pathways that mediate cancer cells’ proliferation. We present a mathematical model using a multiscale, multicellular approach to simulate avascular tumor growth, applied to pancreatic cancer. The model spans three distinct spatial and temporal scales. At the extracellular level, reaction diffusion equations describe nutrient concentrations over a span of seconds. At the cellular level, a lattice-based energy driven stochastic approach describes cellular phenomena including adhesion, proliferation, viability and cell state transitions, occurring on the timescale of hours. At the sub-cellular level, we incorporate a detailed kinetic model of intracellular metabolite dynamics on the timescale of minutes, which enables the cells to uptake and excrete metabolites and use the metabolites to generate energy and building blocks for cell growth. This is a particularly novel aspect of the model. Certain defined criteria for the concentrations of intracellular metabolites lead to cancer cell growth, proliferation and necrosis. Overall, we model the evolution of the tumor in both time and space. Starting with a cluster of tumor cells, the model produces an avascular tumor that quantitatively and qualitatively mimics experimental measurements of multicellular tumor spheroids. Through our model simulations, we can investigate the response of individual intracellular species under a metabolic perturbation and investigate how that response contributes to the response of the tumor as a whole. The predicted response of intracellular metabolites under various targeted strategies are difficult to resolve with experimental techniques. Thus, the model can give novel predictions as to the response of the tumor as a whole, identifies potential therapies to impede tumor growth, and predicts the effects of those therapeutic strategies. In particular, the model provides quantitative insight into the dynamic reprogramming of tumor cells at the intracellular level in response to specific metabolic perturbations. Overall, the model is a useful framework to study targeted metabolic strategies for inhibiting tumor growth.
Binding and interstitial penetration of liposomes within avascular tumor spheroids
