Lymphangions, segments of lymphatic vessels bounded by valves, have characteristics of both ventricles and arteries. They can act primarily like pumps when actively transporting lymph against a pressure gradient. They also can act as conduit vessels when passively transporting lymph down a pressure gradient. This duality has implications for clinical treatment of several types of edema, since the strategy to optimize lymph flow may depend on whether it is most beneficial for lymphangions to act as pumps or conduits. To address this duality, we employed a simple computational model of a contracting lymphangion, predicted the flows at both positive and negative axial pressure gradients, and validated the results with in vitro experiments on bovine mesenteric vessels. This model illustrates that contraction increases flow for normal axial pressure gradients. With edema, limb elevation, or external compression, however, the pressure gradient might reverse, and lymph may flow passively down a pressure gradient. In such cases, the valves may be forced open during the entire contraction cycle. The vessel thus acts as a conduit, and contraction has the effect of increasing resistance to passive flow, thus inhibiting flow rather than promoting it. This analysis may explain a possible physiological benefit of the observed flow-mediated inhibition of the lymphatic pump at high flow rates.

The lymphatic system returns interstitial fluid to the central venous circulation, in part, by the cyclical contraction of a series of "lymphangion pumps" in a lymphatic vessel. The dynamics of individual lymphangions have been well characterized in vitro; their frequencies and strengths of contraction are sensitive to both preload and afterload. However, lymphangion interaction within a lymphatic vessel has been poorly characterized because it is difficult to experimentally alter properties of individual lymphangions and because the afterload of one lymphangion is coupled to the preload of another. To determine the effects of lymphangion interaction on lymph flow, we adapted an existing mathematical model of a lymphangion (characterizing lymphangion contractility, lymph viscosity, and inertia) to create a new lymphatic vessel model consisting of several lymphangions in series. The lymphatic vessel model was validated with focused experiments on bovine mesenteric lymphatic vessels in vitro. The model was then used to predict changes in lymph flow with different time delays between onset of contraction of adjacent lymphangions (coordinated case) and with different relative lymphangion contraction frequencies (noncoordinated case). Coordination of contraction had little impact on mean flow. Furthermore, orthograde and retrograde propagations of contractile waves had similar effects on flow. Model results explain why neither retrograde propagation of contractile waves nor the lack of electrical continuity between lymphangions adversely impacts flow. Because lymphangion coordination minimally affects mean flow in lymphatic vessels, lymphangions have flexibility to independently adapt to local conditions.

Lymphangions, the segments of lymphatic vessels between valves, exhibit structural characteristics in common with both ventricles and arteries. Although once viewed as passive conduits like arteries, it has become well established that lymphangions can actively pump lymph against an axial pressure gradient from low-pressure tissues to the great veins of the neck. A recently reported mathematical model, based on fundamental principles, predicted that lymphangions can transition from pump to conduit behavior when outlet pressure falls below inlet pressure. In this case, the axial pressure gradient becomes the major source of energy for the propulsion of lymph, despite the presence of cyclical contraction. In fact, flow is augmented when cyclical contractions are abolished. We therefore used an in vitro preparation to confirm these findings and to test the hypothesis that lymphangion contraction inhibits flow when outlet pressure falls below inlet pressure. Bovine postnodal mesenteric lymphatic vessels harvested from an abattoir were subjected to an inlet pressure of 5.0 cmH(2)O and an outlet pressure that decreased from 6.5 to 3.5 cmH(2)O under control conditions, stimulated with U-46619 (a thromboxane analog) and relaxed with calcium-free solution. Under control conditions, lymphatic flow markedly increased as outlet pressure fell below inlet pressure. In this case, the slopes of the flow versus axial pressure gradient increased with calcium-free conditions (61%, n = 8, P = 0.016) and decreased with U-46619 stimulation (21%, n = 5, P = 0.033). Our findings indicate that the stimulation of lymphatic contractility does indeed inhibit lymphatic flow when vessels act like conduits.

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...

Lymphangions, the segments of lymphatic vessel between two valves, contract cyclically and actively pump, analogous to cardiac ventricles. Besides having a discernable systole and diastole, lymphangions have a relatively linear end-systolic pressure-volume relationship (with slope E(max)) and a nonlinear end-diastolic pressure-volume relationship (with slope E(min)). To counter increased microvascular filtration (causing increased lymphatic inlet pressure), lymphangions must respond to modest increases in transmural pressure by increasing pumping. To counter venous hypertension (causing increased lymphatic inlet and outlet pressures), lymphangions must respond to potentially large increases in transmural pressure by maintaining lymph flow. We therefore hypothesized that the nonlinear lymphangion pressure-volume relationship allows transition from a transmural pressure-dependent stroke volume to a transmural pressure-independent stroke volume as transmural pressure increases. To test this hypothesis, we applied a mathematical model based on the time-varying elastance concept typically applied to ventricles (the ratio of pressure to volume cycles periodically from a minimum, E(min), to a maximum, E(max)). This model predicted that lymphangions increase stroke volume and stroke work with transmural pressure if E(min) < E(max) at low transmural pressures, but maintain stroke volume and stroke work if E(min)= E(max) at higher transmural pressures. Furthermore, at higher transmural pressures, stroke work is evenly distributed among a chain of lymphangions. Model predictions were tested by comparison to previously reported data. Model predictions were consistent with reported lymphangion properties and pressure-flow relationships of entire lymphatic systems. The nonlinear lymphangion pressure-volume relationship therefore minimizes edema resulting from both increased microvascular filtration and venous hypertension.

The lymphatic system acts to return lower-pressured interstitial fluid to the higher-pressured veins by a complex network of vessels spanning more than three orders of magnitude in size. Lymphatic vessels consist of lymphangions, segments of vessels between two unidirectional valves, which contain smooth muscle that cyclically pumps lymph against a pressure gradient. Whereas the principles governing the optimal structure of arterial networks have been identified by variations of Murray's law, the principles governing the optimal structure of the lymphatic system have yet to be elucidated, although lymph flow can be identified as a critical parameter. The reason for this deficiency can be identified. Until recently, there has been no algebraic formula, such as Poiseuille's law, that relates lymphangion structure to its function. We therefore employed a recently developed mathematical model, based on the time-varying elastance model conventionally used to describe ventricular function, that was validated by data collected from postnodal bovine mesenteric lymphangions. From this lymphangion model, we developed a model to determine the structure of a lymphatic network that optimizes lymph flow. The model predicted that there is a lymphangion length that optimizes lymph flow and that symmetrical networks optimize lymph flow when the lymphangions downstream of a bifurcation are 1.26 times the length of the lymphangions immediately upstream. Measured lymphangion lengths (1.14 +/- 0.5 cm, n = 74) were consistent with the range of predicted optimal lengths (0.1-2.1 cm). This modeling approach was possible, because it allowed a structural parameter, such as length, to be treated as a variable.

The lymphatic system consists of a network of vessels which return interstitial fluid and protein to the blood circulation. Lymphatic vessels can be divided into smaller units called lymphangions, which contain valves and cyclically contract. Under normal conditions, lymphangions can pump lymph up a n axial pressure gradient, much like the heart pumps blood. Also, like the heart, lymphangions a r e sensitive to both preload and afterload. T o describe contraction of the heart independent of preload and afterload, investigators developed the concept of time-varying elastance, which relates chamber pressure and volume in the time domain. To evaluate the applicability of this concept to lymphangions, we analyzed preliminary pressure-volume data from bovine mesenteric lymphangions in vitro. W e found that there were significant limitations to the applicability of the time-varying elastance concept-there is a high degree of variability in contraction strength and frequency, the end-diastolic pressure-volume relationship is highly nonlinear, and the values of maximum and minimum elastance are sensitive to pressure. Nonetheless, normalized elastance curves show a remarkable degree of consistency. Just as the lymphangion is the fundamental building block of the lymphatic system, this simple description of a Iymphangion can form a fundamental building block of a large-scale lymphatic system model.

Lymphatic vessels transport excess interstitial fluid from the low-pressure tissues to the higher pressure veins. The basic structural unit of lymphatic vessels is the lymphangion, a segment of the vessel separated by two unidirectional valves. Lymphangions cyclically contract like ventricles and can actively pump lymph. Lymphangions, as conduit vessels, also can act as arteries, and resist lymph flow. Functional parameters such as pressures, flow, and efficiency are determined by structural parameters like length, radius, and wall thickness. Since these structural parameters are unalterable experimentally, we developed a computational model to study the effect of a particular structural parameter, lymphangion length, to a particular functional variable, lymph flow. The model predicts that flow is a bimodal function of length, exhibiting an optimal length in the same order of magnitude as that observed experimentally. In essence, when the length to radius ratio is small, lymphangions act more like ventricles, where longer lengths yield greater chamber volume and thus lymph pumped. When the length to radius ratio is large, lymphangions act more like arteries, where longer lengths yield greater resistances to flow. This approach provides the means to explore how lymphatic vessel structure is optimized in a variety of conditions.