A multi-scale model for determining the effects of pathophysiology and metabolic disorders on tumor growth

The search for efficient chemotherapy drugs and other anti-cancer treatments would benefit from a deeper understanding of the tumor microenvironment (TME) and its role in tumor progression. Because in vivo experimental methods are unable to isolate or control individual factors of the TME and in vitro models often do not include all the contributing factors, some questions are best addressed with systems biology mathematical models. In this work, we present a new fully-coupled, agent-based, multi-scale mathematical model of tumor growth, angiogenesis and metabolism that includes important aspects of the TME spanning subcellular-, cellular- and tissue-level scales. The mathematical model is computationally implemented for a three-dimensional TME, and a double hybrid continuous-discrete (DHCD) method is applied to solve the governing equations. The model recapitulates the distinct morphological and metabolic stages of a solid tumor, starting with an avascular tumor and progressing through angiogenesis and vascularized tumor growth. To examine the robustness of the model, we simulated normal and abnormal blood conditions, including hyperglycemia/hypoglycemia, hyperoxemia/hypoxemia, and hypercarbia/hypocarbia – conditions common in cancer patients. The results demonstrate that tumor progression is accelerated by hyperoxemia, hyperglycemia and hypercarbia but inhibited by hypoxemia and hypoglycemia; hypocarbia had no appreciable effect. Because of the importance of interstitial fluid flow in tumor physiology, we also examined the effects of hypo- or hypertension, and the impact of decreased hydraulic conductivity common in desmoplastic tumors. The simulations show that chemotherapy-increased blood pressure, or reduction of interstitial hydraulic conductivity increase tumor growth rate and contribute to tumor malignancy.