Quick CM, Venugopal AM, Dongaonkar RM, Laine GA, Stewart RH. First-order approximation for the pressure-flow relationship of spontaneously contracting lymphangions. Am J Physiol Heart Circ Physiol 294: H2144-H2149, 2008. First published March 7, 2008 doi:10.1152/ajpheart.00781.2007.-To return lymph to the great veins of the neck, it must be actively pumped against a pressure gradient. Mean lymph flow in a portion of a lymphatic network has been characterized by an empirical relationship (Pin Ϫ Pout ϭ ϪPp ϩ RLQL), where Pin Ϫ Pout is the axial pressure gradient and QL is mean lymph flow. RL and Pp are empirical parameters characterizing the effective lymphatic resistance and pump pressure, respectively. The relation of these global empirical parameters to the properties of lymphangions, the segments of a lymphatic vessel bounded by valves, has been problematic. Lymphangions have a structure like blood vessels but cyclically contract like cardiac ventricles; they are characterized by a contraction frequency (f ) and the slopes of the enddiastolic pressure-volume relationship [minimum value of resulting elastance (Emin)] and end-systolic pressure-volume relationship [maximum value of resulting elastance (Emax)]. Poiseuille's law provides a first-order approximation relating the pressure-flow relationship to the fundamental properties of a blood vessel. No analogous formula exists for a pumping lymphangion. We therefore derived an algebraic formula predicting lymphangion flow from fundamental physical principles and known lymphangion properties. Quantitative analysis revealed that lymph inertia and resistance to lymph flow are negligible and that lymphangions act like a series of interconnected ventricles. For a single lymphangion, Pp ϭ Pin (Emax Ϫ Emin)/Emin and RL ϭ Emax/f. The formula was tested against a validated, realistic mathematical model of a lymphangion and found to be accurate. Predicted flows were within the range of flows measured in vitro. The present work therefore provides a general solution that makes it possible to relate fundamental lymphangion properties to lymphatic system function. mathematical modeling; edema LYMPHANGIONS ACT as pumps. The function of the lymphatic system is to transport lymph to the great veins of the neck and is necessary for proper interstitial fluid balance (1). Functionally, lymph must be actively pumped against a pressure gradient (18), in contrast with the arterial system where the blood flows from higher pressure arteries to the lower pressure capillaries. Although intestinal motility and skeletal muscle contraction can propel lymph via external compression (19,29), many lymphangions, the sections of a lymphatic vessel between valves (1, 3, 29), can cyclically contract and actively pump lymph when they are engorged (3). Although they are structured like blood vessels and have a discernable tone, lymphangions function like cardiac ventricles (2, 22, 24).Although lymphangion contractility was originally characterized in terms of tone, investigators have used the ventri...