Fall 2019 – General Formulas Predicting Interstitial Flows, Pressures, and Concentrations in Solid Tumors

Interstitial flows, pressures, and concentrations are critical variables affecting growth and treatment of solid tumors. Experimental approaches to identify fundamental principles governing tumor transport are limited, because these variables emerge from the complex interaction of microvascular filtration into the tumor interstitium, lymphatic drainage, and transudation from the tumor. Existing tumor computational models must assume a specific set of parameter values to solve equations numerically, which makes results impossible to generalize for different tumor morphologies and tissue types. Although investigators have developed general algebraic formulas for interstitial transport, they have neglected transudation. Therefore, the purpose of the present work is to derive general algebraic formulas for these critical tumor variables from a modified tumor model that includes transudation and lymphatic drainage. We therefore assumed a lumped three-compartment model to characterize tumors with various degrees of vascularization. Fluid filtration, solute flow, and lymph flow were characterized by the Starling-Landis and Drake-Lane equations, respectively. By assuming constant interstitial protein concentrations, algebraic formulas predicting interstitial flows and hydrostatic pressures could be derived. By alternatively assuming constant interstitial pressures, algebraic formulas for interstitial flows and protein concentrations could be derived. In each set of formulas, the critical variables are explicitly related to standard fluid balance parameters: filtration coefficients, protein reflection coefficients, and lymphatic resistance. This modeling approach provides a complement to animal models by providing novel insights into how tumor various tumor properties can affect transport and concentrations of nutrients, inflammatory mediators, apoptotic factors, angiogenic factors and drugs.