Algebraic formula predicting interstitial fluid pressure homeostasis from the interaction of microvascular filtration and lymphatic transport

Abstract

Interstitial fluid pressure remains relatively low despite fairly large increases in capillary and lymphatic outlet pressures. This maintenance of interstitial fluid pressure imposes competing requirements on lymphatic function. Edema results when lymph flow fails to adequately increase when interstitial fluid pressure rises, or when lymph flow fails to stay constant when lymphatic outlet pressure rises. This critical insight has not been incorporated in mathematical models that predict interstitial fluid pressures arising from the interaction of microvascular filtration and lymphatic transport. Although critical approximations made it possible to predict interstitial fluid pressure with a general algebraic formula, the assumption that lymph flow is equally sensitive to interstitial and outlet pressures neglects a fundamental homeostatic mechanism. Therefore, the purpose of the present work was to develop an algebraic formula predicting interstitial fluid pressure homeostasis that incorporates a differential sensitivity of lymph flow to interstitial and outlet pressures. A new model was constructed using three simple assumptions: 1) equilibrium is established when microvascular filtration into the interstitium equals lymph flow out of the interstitium, 2) microvascular filtration is governed by the Starling‐Landis equation, and 3) lymphatic flow increases linearly with interstitial fluid pressure and decreases linearly with lymphatic outlet pressure. Interstitial fluid pressure was solved algebraically as a function of capillary and lymphatic outlet pressures, as well as the microvascular filtration coefficient, protein reflection coefficient, and two new empirical parameters characterizing lymphatic function. Adding complexity to the model reproduces interstitial fluid pressure homeostasis with perturbations in capillary or lymphatic outlet pressures. Nonetheless, because interstitial fluid pressure is expressed as a simple algebraic formula, the results retain generality beyond a particular assumed set of parameters, make explicit how parameters interact synergistically, and enable new methods to derive values of critical parameters from experimental data.