Interstitial hydraulic conductivity and interstitial fluid pressure for avascular or poorly vascularized tumors

A correct description of the hydraulic conductivity is essential for determining the actual tumor interstitial fluid pressure (TIFP) distribution. Traditionally, it has been assumed that the hydraulic conductivities both in a tumor and normal tissue are constant, and that a tumor has a much larger interstitial hydraulic conductivity than normal tissue. The abrupt transition of the hydraulic conductivity at the tumor surface leads to non-physical results (the hydraulic conductivity and the slope of the TIFP are not continuous at tumor surface). For the sake of simplicity and the need to represent reality, we focus our analysis on avascular or poorly vascularized tumors, which have a necrosis that is mostly in the center and vascularization that is mostly on the periphery. We suggest that there is an intermediary region between the tumor surface and normal tissue. Through this region, the interstitium (including the structure and composition of solid components and interstitial fluid) transitions from tumor to normal tissue. This process also causes the hydraulic conductivity to do the same. We introduce a continuous variation of the hydraulic conductivity, and show that the interstitial hydraulic conductivity in the intermediary region should be monotonically increasing up to the value of hydraulic conductivity in the normal tissue in order for the model to correspond to the actual TIFP distribution. The value of the hydraulic conductivity at the tumor surface should be the lowest in value.