Mechanical Properties of Lymphangions that Optimize Stroke Work in a Lymphatic Network

Abstract

Lymphangions, the functional units of a lymphatic vessel bound by two valves, actively contract and relax to pump lymph. Like cardiac ventricles, stroke work (SW) of a lymphangion depends on filling pressure, outlet pressure, systolic contractility and diastolic stiffness. Although radii, contractilities and stiffnesses vary by several order of magnitude, inlet and outlet pressures are surprisingly similar in rat and bovine mesenteric lymphangions when stroke work is maximized. Therefore, the purpose of the present work was to derive a general algebraic formula that relates optimal inlet and outlet pressures to critical mechanical properties of lymphangions. The pressure‐volume relationships of lymphangions, like ventricles, are characterized by time‐varying elastance. An algebraic solution for stroke work was formulated assuming linear relationships in terms of three functional parameters: 1) end‐systolic elastance (Ees), 2) end‐diastolic elastance (Eed) and 3) the difference between end‐diastolic and end‐systolic unstressed volumes (ΔVo). The resulting formula for SW reproduces maximal stroke work for particular inlet and outlet pressures. The formulas for optimal inlet and outlet pressures are functions of two critical quantities: EesΔVo and Ees/Eed. Furthermore, the values of these two quantities are conserved when using parameters characterizing rat and bovine mesenteric lymphatic vessels. The surprising implication is that the mechanical properties of each lymphangion in a lymphatic network can be predicted with a simple assumption: lymphangions in a network have a maximum stroke work at similar transmural pressures. Furthermore, the algebraic solutions provide a novel tool to predict how mechanical properties might adapt to maintain optimal stroke work with acute and chronic perturbations.