The Effects of Exterior Boundary Conditions in Tumor Tissues Fluid Transport under Heating Conditions

Modeling flow field in tumor cells interstitial space is of primary importance, because of the importance of the advection in macromolecule drug delivery. Cell deformation has also to be taken into account because of the forces caused by the fluid; if the cell is not isothermal, this deformation can be also strongly affected by temperature fields. In this paper, the effects of boundary conditions on a tumor cell periphery with an internal heat source are investigated. The tumor cell is modeled as a deformable sph ere, in which two phases can be distinguished. The fluid phase is the interstitial fluid, while the rest of the tumor is modeled as the solid phase, including also capillaries and tissues. Transient state governing equations for mass, momentum and energy a re written for both phases, by also considering tumor deformation under the linear elastic material assumption. A situation of Tumor Blood Flow (TBF) rapid decay is considered, while the heat source is modeled as a radial decay function. Boundary conditions for the energy equation are varied on external surface of the sphere, in order to appreciate the effects of the surrounding on flow nd temperature fields inside the tumor. After scaling equations, a finite element scheme is employed for the numerical solution. Results are shown for different dimensionless parameters, showing in which case external boundary conditions strongly affect tumor cell flow fields and have to be given the right consideration.