Three phase flow dynamics in tumor growth

Existing tumor models generally consider only a single pressure for all the cell phases. Here, a three-fluid model originally proposed by the authors is further developed to allow for different pressures in the host cells (HC), the tumor cells (TC) and the interstitial fluid (IF) phases. Unlike traditional mixture theory models, this model developed within the thermodynamically constrained averaging theory contains all the necessary interfaces. Appropriate constitutive relationships for the pressure difference among the three fluid phases are introduced with respect to their relative wettability and fluid–fluid interfacial tensions, resulting in a more realistic modeling of cell adhesion and invasion. Five different tumor cases are studied by changing the interfacial tension between the three liquid phases, adhesion and dynamic viscosity. Since these parameters govern the relative velocities of the fluid phases and the adhesion of the phases to the extracellular matrix significant changes in tumor growth are observed. High interfacial tensions at the TC–IF and TC–HC interface support the lateral displacement of the healthy tissue in favor of a rapid growth of the malignant mass, with a relevant amount of HC which cannot be pushed out by TC and remain in place. On the other hand, lower TC–IF and TC–HC interfacial tensions tend to originate a more compact and dense tumor mass with a slower growth rate of the overall size. This novel computational model emphasizes the importance of characterizing the TC–HC interfacial properties to properly predict the temporal and spatial pattern evolution of tumor.