Terminal lymphatics: the potential "lethal corner" in the distribution of tissue pO2

BACKGROUND: Terminal lymphatic fluid is the compartment furthest removed from the oxygen supply, and therefore should present the lowest pO(2) in the tissue due to oxygen consumption by the tissue and the lymphatic vessel wall. METHODS AND RESULTS: The distribution of pO(2) was determined in the tissue, the lymphatic microvessels, and arterioles and venules of the hamster chamber window model, which is studied without anesthesia with the tissue isolated from the environment. Lymphatic fluid pO(2) was measured with the phosphorescence oxygen quenching method. Small terminal lymphatic fluid pO(2) was 18.4 +/- 2.6 mmHg, and 18.0 +/- 2.4 mmHg in collecting lymphatics. Tissue pO(2) averaged 24.6 +/- 2.7 mmHg. The significant difference between tissue and intralymphatic pO(2) was due in part to the presence of an oxygen gradient across the lymphatic wall, which ranged from 3.7 +/- 1.3 mmHg for terminal lymphatics, to 6.0 +/- 1.2 mmHg for collecting lymphatics. This gradient is assumed to be due to the oxygen consumption by the cellular component of the lymphatic wall. CONCLUSION: The increased vessels wall gradient found in collecting lymphatics was reconciled by the findings that these microlymphatic vessels tend to be contiguous to the arterioles, whereas the terminal lymphatics are dispersed in the tissue. These findings indicate that terminal lymphatic present the lowest oxygen tension in the tissue, and therefore are the locations at risk to develop anoxia when the microvascular oxygen supply becomes limited.     

A model for mechanics of primary lymphatic valves

Recent experimental evidence indicates that lymphatics have two valve systems, a set of primary valves in the wall of the endothelial cells of initial lymphatics and a secondary valve system in the lumen of the lymphatics. While the intralymphatic secondary valves are well described, no analysis of the primary valves is available. We propose a model for primary lymphatics valves at the junctions between lymphatic endothelial cells. The model consists of two overlapping endothelial extensions at a cell junction in the initial lymphatics. One cell extension is firmly attached to the adjacent connective tissue while the other cell extension is not attached to the interstitial collagen. It is free to bend into the lumen of the lymphatic when the lymphatic pressure falls below the adjacent interstitial fluid pressure. Thereby the cell junction opens a gap permitting entry of interstitial fluid into the lymphatic lumen. When the lymphatic fluid pressure rises above the adjacent interstitial fluid pressure, the endothelial extensions contact each other and the junction is closed preventing fluid reflow into the interstitial space. The model illustrates the mechanics of valve action and provides the first time a rational analysis of the mechanisms underlying fluid collection in the initial lymphatics and lymph transport in the microcirculation.     

Modeling flow in collecting lymphatic vessels: one-dimensional flow through a series of contractile elements

The lymphatic system comprises a series of elements, lymphangions, separated by valves and possessed of active, contractile walls to pump interstitial fluid from its collection in the terminal lymphatics back to the main circulation. Despite its importance, there is a dearth of information on the fluid dynamics of the lymphatic system. In this article, we describe linked experimental and computational work aimed at elucidating the biomechanical properties of the individual lymphangions. We measure the static and dynamic mechanical properties of excised bovine collecting lymphatics and develop a one-dimensional computational model of the coupled fluid flow/wall motion. The computational model is able to reproduce the pumping behavior of the real vessel using a simple contraction function producing fast contraction pulses traveling in the retrograde direction to the flow.     

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255–318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667–2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

     

Inhibition of active lymph pump by simulated microgravity in rats

During spaceflight the normal head-to-foot hydrostatic pressure gradients are eliminated and body fluids shift toward the head, resulting in a diminished fluid volume in the legs and an increased fluid volume in the head, neck, and upper extremities. Lymphatic function is important in the maintenance of normal tissue fluid volume, but it is not clear how microgravity influences lymphatic pumping. We performed a detailed evaluation of the influence of simulated microgravity on lymphatic diameter, wall thickness, elastance, tone, and other measures of phasic contractility in isolated lymphatics. Head-down tail suspension (HDT) rats were used to simulate the effects of microgravity. Animals were exposed to HDT for 2 wk, after which data were collected and compared with the control non-HDT group. Lymphatics from four regional lymphatic beds (thoracic duct, cervical, mesenteric, and femoral lymphatics) were isolated, cannulated, and pressurized. Input and output pressures were adjusted to apply a range of transmural pressures and flows to the lymphatics. Simulated microgravity caused a potent inhibition of pressure/stretch-stimulated pumping in all four groups of lymphatics. The greatest inhibition was found in cervical lymphatics. These findings presumably are correlated to the cephalic fluid shifts that occur in HDT rats as well as those observed during spaceflight. Flow-dependent pump inhibition was increased after HDT, especially in the thoracic duct. Mesenteric lymphatics were less strongly influenced by HDT, which may support the idea that lymph hydrodynamic conditions in the mesenteric lymphatic during HDT are not dramatically altered.     

Measurement of Cytosolic Ca2+ in Isolated Contractile Lymphatics

Lymphatic vessels comprise a multifunctional transport system that maintains fluid homeostasis, delivers lipids to the central circulation, and acts as a surveillance system for potentially harmful antigens, optimizing mucosal immunity and adaptive immune responses¹. Lymph is formed from interstitial fluid that enters blind-ended initial lymphatics, and then is transported against a pressure gradient in larger collecting lymphatics. Each collecting lymphatic is made up of a series of segments called lymphangions, separated by bicuspid valves that prevent backflow. Each lymphangion possesses a contractile cycle that propels lymph against a pressure gradient toward the central circulation². This phasic contractile pattern is analogous to the cardiac cycle, with systolic and diastolic phases, and with a lower contraction frequency⁴. In addition, lymphatic smooth muscle generates tone and displays myogenic constriction and dilation in response to increases and decreases in luminal pressure, respectively⁵. A hybrid of molecular mechanisms that support both the phasic and tonic contractility of lymphatics are thus proposed.Contraction of smooth muscle is generally regulated by the cytosolic Ca²⁺ concentration ([Ca²⁺]_i) plus sensitivity to Ca^2+, of the contractile elements in response to changes in the environment surrounding the cell⁶. [Ca²⁺]_i is determined by the combination of the movement of Ca²⁺ through plasma membrane ligand or voltage gated Ca²⁺ channels and the release and uptake of Ca²⁺ from internal stores. Cytosolic Ca²⁺ binds to calmodulin and activates enzymes such as myosin light chain (MLC) kinase (MLCK), which in turn phosphorylates MLC leading to actin-myosin-mediated contraction⁸. However, the sensitivity of this pathway to Ca²⁺ can be regulated by the MLC phosphatase (MLCP)⁹. MLCP activity is regulated by Rho kinase (ROCK) and the myosin phosphatase inhibitor protein CPI-17.Here, we present a method to evaluate changes in [Ca²⁺]_i over time in isolated, perfused lymphatics in order to study Ca²⁺-dependent and Ca²⁺-sensitizing mechanisms of lymphatic smooth muscle contraction. Using isolated rat mesenteric collecting lymphatics we studied stretch-induced changes in [Ca²⁺]_i and contractile activity. The isolated lymphatic model offers the advantage that pressure, flow, and the chemical composition of the bath solution can be tightly controlled. [Ca²⁺]_i was determined by loading lymphatics with the ratiometric, Ca²⁺-binding dye Fura-2. These studies will provide a new approach to the broader problem of studying the different molecular mechanisms that regulate phasic contractions versus tonic constriction in lymphatic smooth muscle.     

Nitric oxide formation by lymphatic bulb and valves is a major regulatory component of lymphatic pumping

Microscopic lymphatics produce nitric oxide (NO) during contraction as flow shear activates the endothelial cells. The valve leaflets and bulbous valve housing contain a large amount of endothelial nitric oxide synthase (eNOS) due both to many endothelial cells and increased expression of eNOS. Direct NO measurements indicate the valve area has a 30-50% higher NO concentration ([NO]) than tubular regions although both regions generate equivalent relative increases in [NO] with each contraction. We hypothesize that 1) the greater eNOS and [NO] of the bulb region would have greater effects to lower pumping activity of the overall lymphatic than occurs in tubular regions and 2), the elevated [NO] in the bulb region may be because of high NO production in the valve leaflets that diffuses to the wall of the bulb. Measurement of [NO] with a micropipette inside the lymphatic bulb revealed the valve leaflets generate ~50% larger [NO] than the bulb wall in the in vivo rat mesenteric lymphatics. The valves add NO to the lymph that quickly diffuses to the bulb wall. Bradykinin locally released iontophoretically from a micropipette on both bulbs and tubes increased the [NO] in a dose-dependent manner up to ~50%, demonstrating agonist activation of the NO pathway. However, pumping output determined by contraction frequency and stroke volume decreased much more for the bulb than tubular areas in response to the bradykinin. In effect, NO generation by the bulb area and its valves limits the pumped flow of the total lymphatic by lowering frequency and stroke volume of individual contractions.     

A Model for Fluid Drainage by the Lymphatic System

This study investigates the fluid flow through tissues where lymphatic drainage occurs. Lymphatic drainage requires the use of two valve systems, primary and secondary. Primary valves are located in the initial lymphatics. Overlapping endothelial cells around the circumferential lining of lymphatic capillaries are presumed to act as a unidirectional valve system. Secondary valves are located in the lumen of the collecting lymphatics and act as another unidirectional valve system; these are well studied in contrast to primary valves. We propose a model for the drainage of fluid by the lymphatic system that includes the primary valve system. The analysis in this work incorporates the mechanics of the primary lymphatic valves as well as the fluid flow through the interstitium and that through the walls of the blood capillaries. The model predicts a piecewise linear relation between the drainage flux and the pressure difference between the blood and lymphatic capillaries. The model describes a permeable membrane around a blood capillary, an elastic primary lymphatic valve and the interstitium lying between the two.     

Length-tension relationships of small arteries, veins, and lymphatics from the rat mesenteric microcirculation

The passive and active length-tension relationships of isolated rat mesenteric lymphatics ( approximately 150 microm ID), and adjacent small arteries ( approximately 240 microm) and veins ( approximately 275 microm) were compared under isometric conditions using a wire myograph. About 60% of the lymphatic vessels developed spontaneous contractions in physiological saline solution at nominal preload. To maximally activate smooth muscle, 145 mM K(+) + 5 x 10(-5) M norepinephrine was used for arteries, and 145 mM K(+) + 1 x 10(-6) M substance P was used for lymphatics and veins. In response, arteries exhibited monotonic force development to a plateau level, whereas lymphatics and veins showed biphasic force development, consisting of a transient force peak followed by partial relaxation to a plateau over approximately 5 min. The passive and the active length-tension curves were similar in shape among all three vessels. However, the maximal active tension of arteries (3.4 +/- 0.42 mN/mm) was significantly greater than peak active tension (0.59 +/- 0.04 mN/mm) or plateau tension (0.20 +/- 0.04 mN/mm) in small veins and greater than peak active tension (0.34 +/- 0.02 mN/mm) or plateau tension (0.21 +/- 0.02 mN/mm) in lymphatics. Maximal active medial wall stress was similar between lymphatics and veins but was approximately fivefold higher in small arteries. For lymphatics, the pressure calculated from the optimal preload was significantly higher than that found previously in isobaric studies of isolated lymphatics, suggesting the capacity to operate at higher than normal pressures for increased responsiveness. Our results represent the first mechanical comparisons of arterial, venous, and lymphatic vessels in the same vasculature.     

Impairments in the intrinsic contractility of mesenteric collecting lymphatics in a rat model of metabolic syndrome

Numerous studies on metabolic syndrome (MetSyn), a cluster of metabolic abnormalities, have demonstrated its profound impact on cardiovascular and blood microvascular health; however, the effects of MetSyn on lymphatic function are not well understood. We hypothesized that MetSyn would modulate lymphatic muscle activity and alter muscularized lymphatic function similar to the impairment of blood vessel function associated with MetSyn, particularly given the direct proximity of the lymphatics to the chronically inflamed adipose depots. To test this hypothesis, rats were placed on a high-fructose diet (60%) for 7 wk, and their progression to MetSyn was assessed through serum insulin and triglyceride levels in addition to the expression of metabolic and inflammatory genes in the liver. Mesenteric lymphatic vessels were isolated and subjected to different transmural pressures while lymphatic pumping and contractile parameters were evaluated. Lymphatics from MetSyn rats had significant negative chronotropic effects at all pressures that effectively reduced the intrinsic flow-generating capacity of these vessels by ～50%. Furthermore, lymphatics were remodeled to a significantly smaller diameter in the animals with MetSyn. Wire myograph experiments demonstrated that permeabilized lymphatics from the MetSyn group exhibited a significant decrease in force generation and were less sensitive to Ca(2+), although there were no significant changes in lymphatic muscle cell coverage or morphology. Thus, our data provide the first evidence that MetSyn induces a remodeling of collecting lymphatics, thereby effectively reducing their potential load capabilities and impairing the intrinsic contractility required for proper lymph flow.     

Smooth muscle-endothelial cell communication activates Reelin signaling and regulates lymphatic vessel formation

Active lymph transport relies on smooth muscle cell (SMC) contractions around collecting lymphatic vessels, yet regulation of lymphatic vessel wall assembly and lymphatic pumping are poorly understood. Here, we identify Reelin, an extracellular matrix glycoprotein previously implicated in central nervous system development, as an important regulator of lymphatic vascular development. Reelin-deficient mice showed abnormal collecting lymphatic vessels, characterized by a reduced number of SMCs, abnormal expression of lymphatic capillary marker lymphatic vessel endothelial hyaluronan receptor 1 (LYVE-1), and impaired function. Furthermore, we show that SMC recruitment to lymphatic vessels stimulated release and proteolytic processing of endothelium-derived Reelin. Lymphatic endothelial cells in turn responded to Reelin by up-regulating monocyte chemotactic protein 1 (MCP1) expression, which suggests an autocrine mechanism for Reelin-mediated control of endothelial factor expression upstream of SMC recruitment. These results uncover a mechanism by which Reelin signaling is activated by communication between the two cell types of the collecting lymphatic vessels--smooth muscle and endothelial cells--and highlight a hitherto unrecognized and important function for SMCs in lymphatic vessel morphogenesis and function.     

Flow fields generated by peristaltic reflex in isolated guinea pig ileum: impact of contraction depth and shoulders

The guinea pig ileum responds to distension with characteristic wall movements, luminal pressure gradients, and outflow (the peristaltic reflex). To date, little is known about whether the peristaltic reflex generates flow events other than laminar flow. Here we used a numerical method to solve for the flow generated by moving walls to assess occlusive contractions (case 1), nonocclusive contractions (case 2), and contractions with steep shoulders (case 3) for which visual parameters of wall movements are published. We found that all three contraction cases produced pressure differentials across the coapting segment, downstream and reverse flow, and vortical flow patterns that redistributed particles and mixed liquids. Contractions generated pressures and shear stresses, particularly along the moving section of the wall. The nonocclusive contraction was much less effective than the occlusive contraction with the steep shoulders; the occlusive contraction with flat shoulders had an intermediate effect. Our analysis shows that even peristaltic contractions produce not only laminar flow but also many flow events likely to promote digestion and absorption. The visual patterns of contractions impact the patterns of luminal flow, and precise definition of wall movements is critical to quantify the fluid mechanical consequences of intestinal contractions.     

Non-equilibrium allele frequency spectra via spectral methods

A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related populations require high-performance algorithms to determine the likelihood of different demographic scenarios that could have shaped the observed neutral single nucleotide polymorphism (SNP) allele frequency spectrum. In many areas of applied mathematics, Fourier Transforms and Spectral Methods are firmly established tools to analyze spectra of signals and model their dynamics as solutions of certain Partial Differential Equations (PDEs). When spectral methods are applicable, they have excellent error properties and are the fastest possible in high dimension; see Press et al. (2007). In this paper we present an explicit numerical solution, using spectral methods, to the forward Kolmogorov equations for a Wright–Fisher process with migration of K populations, influx of mutations, and multiple population splitting events.     

Microanatomy of the intestinal lymphatic system

The intestinal lymphatic system comprises two noncommunicating lymphatic networks: one containing the lacteals draining the villi and the connecting submucosal lymphatic network and one containing the lymphatics that drain the intestine muscular layer. These systems deliver lymph into a common network of collecting lymphatics originating near the mesenteric border. The intestinal lymphatic system serves vital functions in the regulation of tissue fluid homeostasis, immune surveillance, and the transport of nutrients; conversely, this system is affected by, and directly contributes to, disease processes within the intestine. Recent discoveries of specific lymphatic markers, factors promoting lymphangiogenesis, and factors selectively affecting the development of intestinal lymphatics, hold promise for unlocking the role of lymphatics in the pathogenesis of diseases affecting the intestine and for intestinal lymphatic selective therapies. Vital to progress in understanding how the intestinal lymphatic system functions is the integration of recent advances identifying molecular pathways for lymphatic growth and remodeling with advanced imaging modalities to observe lymphatic function and dysfunction in vivo.     

Contractions of the lymphangion under low filling conditions and the absence of stretching stimuli. The possibility of the sucking effect

Regulation of the function of the lymphatic pump is tightly connected to the degree of filling of the lymphangion. This mechanism is one of the principle ways that the lymphatics self-regulate lymph transport. But interpretation of the causes and consequences of this regulation is still far from perfect. The issue of whether automatism of electrical activity of the lymphatic smooth muscle cells or the distension of the cell membranes first causes depolarization, is a principal question which needs answering in order to understand the control of lymph transport. In our experiments with perfused isolated bovine mesenteric lymphangions, different values of lymph pressure were simulated. For this purpose, lowfrequency sinusoidal fluctuations of the input pressure were applied to lymphangions under conditions of regulated filling. A poor correlation was seen between lymph pressure fluctuations and lymphangion contractions, as well as between the rate of lymphangion filling and contractions. We observed stable spontaneous contractions of both bovine and rat mesenteric lymphangions at 0 cm of water intralymphatic pressure, and in the absence of distension stimuli (both radial and axial stretch). Under conditions of low filling, contractions of bovine lymphangions produced negative intralymphatic pressure and a suction effect. The automatism is an inherent feature of the lymphatic smooth muscle cells. Distension of the lymphangion modulates the electrical characteristics of the membranes and thus the contractile mechanisms in lymphangions.     

Validation of a patient-specific one-dimensional model of the systemic arterial tree

The aim of this study is to develop and validate a patient-specific distributed model of the systemic arterial tree. This model is built using geometric and hemodynamic data measured on a specific person and validated with noninvasive measurements of flow and pressure on the same person, providing thus a patient-specific model and validation. The systemic arterial tree geometry was obtained from MR angiographic measurements. A nonlinear viscoelastic constitutive law for the arterial wall is considered. Arterial wall distensibility is based on literature data and adapted to match the wave propagation velocity of the main arteries of the specific subject, which were estimated by pressure waves traveling time. The intimal shear stress is modeled using the Witzig-Womersley theory. Blood pressure is measured using applanation tonometry and flow rate using transcranial ultrasound and phase-contrast-MRI. The model predicts pressure and flow waveforms in good qualitative and quantitative agreement with the in vivo measurements, in terms of wave shape and specific wave features. Comparison with a generic one-dimensional model shows that the patient-specific model better predicts pressure and flow at specific arterial sites. These results obtained let us conclude that a patient-specific one-dimensional model of the arterial tree is able to predict well pressure and flow waveforms in the main systemic circulation, whereas this is not always the case for a generic one-dimensional model.     

Modulation of fluid pumping in isolated bovine mesenteric lymphatics by a thromboxane/endoperoxide analogue

A thromboxane/endoperoxide analogue (compound U46619) is known to stimulate phasic and tonic contractions in quiescent bovine lymphatic vessels and enhance contractile activity in spontaneously active vessels. In order to determine how these effects relate to changes in fluid propulsion by the lymphatics, we have assessed the effects of U46619 on the ability of isolated bovine mesenteric lymphatics to pump fluid in vitro. Bovine lymphatic segments (up to 8 cm in length with a minimum of 4 valves) were cannulated at both ends and fluid input provided from a reservoir. Flow through the vessels was regulated by intraluminal pressures. On average, changes in transmural pressures up to 8 cm H2O resulted in enhanced pumping; pressures above this level depressed flow. The dominant effect of U46619 (added to the reservoir) was to depress pumping; 10(-7) and 10(-9)M decreased flow at all transmural pressures tested; 10(-8)M had a dual effect, slightly inhibiting flow at low transmural pressures and enhancing flow at higher pressures. These results suggest that thromboxane may stimulate or inhibit lymphatic pumping depending on the concentration of the agent and the transmural pressure applied to the vessel. These effects may relate to its ability to induce variable changes in luminal diameter and frequency and force of contractions.     

A model of a radially expanding and contracting lymphangion

The lymphatic system is an extensive vascular network featuring valves and contractile walls that pump interstitial fluid and plasma proteins back to the main circulation. Immune function also relies on the lymphatic system's ability to transport white blood cells. Failure to drain and pump this excess fluid results in edema characterized by fluid retention and swelling of limbs. It is, therefore, important to understand the mechanisms of fluid transport and pumping of lymphatic vessels. Unfortunately, there are very few studies in this area, most of which assume Poiseuille flow conditions. In vivo observations reveal that these vessels contract strongly, with diameter changes of the order of magnitude of the diameter itself over a cycle that lasts typically 2-3s. The radial velocity of the contracting vessel is on the order of the axial fluid velocity, suggesting that modeling flow in these vessels with a Poiseuille model is inappropriate. In this paper, we describe a model of a radially expanding and contracting lymphatic vessel and investigate the validity of assuming Poiseuille flow to estimate wall shear stress, which is presumably important for lymphatic endothelial cell mechanotransduction. Three different wall motions, periodic sinusoidal, skewed sinusoidal and physiologic wall motions, were investigated with steady and unsteady parabolic inlet velocities. Despite high radial velocities resulting from the wall motion, wall shear stress values were within 4% of quasi-static Poiseuille values. Therefore, Poiseuille flow is valid for the estimation of wall shear stress for the majority of the lymphangion contractile cycle.     

Simulation of a chain of collapsible contracting lymphangions with progressive valve closure

The aim of this investigation was to achieve the first step toward a comprehensive model of the lymphatic system. A numerical model has been constructed of a lymphatic vessel, consisting of a short series chain of contractile segments (lymphangions) and of intersegmental valves. The changing diameter of a segment governs the difference between the flows through inlet and outlet valves and is itself governed by a balance between transmural pressure and passive and active wall properties. The compliance of segments is maximal at intermediate diameters and decreases when the segments are subject to greatly positive or negative transmural pressure. Fluid flow is the result of time-varying active contraction causing diameter to reduce and is limited by segmental viscous and valvular resistance. The valves effect a smooth transition from low forward-flow resistance to high backflow resistance. Contraction occurs sequentially in successive lymphangions in the forward-flow direction. The behavior of chains of one to five lymphangions was investigated by means of pump function curves, with variation of valve opening parameters, maximum contractility, lymphangion size gradation, number of lymphangions, and phase delay between adjacent lymphangion contractions. The model was reasonably robust numerically, with mean flow-rate generally reducing as adverse pressure was increased. Sequential contraction was found to be much more efficient than synchronized contraction. At the highest adverse pressures, pumping failed by one of two mechanisms, depending on parameter settings: either mean leakback flow exceeded forward pumping or contraction failed to open the lymphangion outlet valve. Maximum pressure and maximum flow-rate were both sensitive to the contractile state; maximum pressure was also determined by the number of lymphangions in series. Maximum flow-rate was highly sensitive to the transmural pressure experienced by the most upstream lymphangions, suggesting that many feeding lymphatics would be needed to supply one downstream lymphangion chain pumping at optimal transmural pressure.