Mass transfer modeling of solid tumor growth for therapy evaluation and prognosis

Simulation of tumor evolution at the macroscopic, tissue scale can be applied to cancer treatment optimization. This paper aims to gain deeper insight into the dynamics of tumor growth at this scale and to develop predictive, quantitative mathematical models which can be used as a decision tool supporting oncologists and surgeons. This preliminary model describes tumor progression as mass transfer governed by partial differential equations, incorporating a multi-species logistic growth/decay law to account for the production of necrosis and the interaction with therapy. The set of governing equations is integrated by a commercial platform of Finite Element Method. After a validation study with literature data on a hepatocellular carcinoma, a sensitivity analysis was conducted by including the driving source terms (growth rates, drug efficiency and its delivery/availability). Results suggest that, in the first two months of therapy, tumor volume progress is related nonlinearly so that a mere 10% of stronger/weaker cancer malignancy lead to doubling/halving the tumor volume, the increment of drug efficiency by 25% lead to a 60% decrease of the volume, while a smaller efficiency by 25% lead to a sudden run-away of the disease. Finally, the optimal administration pattern for chemoembolization was found with a 4-points therapy delivery on the same side with respect to the Region of Interest.