First-order approximation for the pressure-flow relationship of spontaneously contracting lymphangions

Computational fluid dynamic modeling of the lymphatic system: a review of existing models and future directions

Historically, research into the lymphatic system has been overlooked due to both a lack of knowledge and limited recognition of its importance. In the last decade however, lymphatic research has gained substantial momentum and has included the development of a variety of computational models to aid understanding of this complex system. This article reviews existing computational fluid dynamic models of the lymphatics covering each structural component including the initial lymphatics, pre-collecting and collecting vessels, and lymph nodes. This is followed by a summary of limitations and gaps in existing computational models and reasons that development in this field has been hindered to date. Over the next decade, efforts to further characterize lymphatic anatomy and physiology are anticipated to provide key data to further inform and validate lymphatic fluid dynamic models. Development of more comprehensive multiscale- and multi-physics computational models has the potential to significantly enhance the understanding of lymphatic function in both health and disease.

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.

Aqueous outflow regulation - 21st century concepts

We propose an integrated model of aqueous outflow control that employs a pump-conduit system in this article. Our model exploits accepted physiologic regulatory mechanisms such as those of the arterial, venous, and lymphatic systems. Here, we also provide a framework for developing novel diagnostic and therapeutic strategies to improve glaucoma patient care. In the model, the trabecular meshwork distends and recoils in response to continuous physiologic IOP transients like the ocular pulse, blinking, and eye movement. The elasticity of the trabecular meshwork determines cyclic volume changes in Schlemm's canal (SC). Tube-like SC inlet valves provide aqueous entry into the canal, and outlet valve leaflets at collector channels control aqueous exit from SC. Connections between the pressure-sensing trabecular meshwork and the outlet valve leaflets dynamically control flow from SC. Normal function requires regulation of the trabecular meshwork properties that determine distention and recoil. The aqueous pump-conduit provides short-term pressure control by varying stroke volume in response to pressure changes. Modulating TM constituents that regulate stroke volume provides long-term control. The aqueous outflow pump fails in glaucoma due to the loss of trabecular tissue elastance, as well as alterations in ciliary body tension. These processes lead to SC wall apposition and loss of motion. Visible evidence of pump failure includes a lack of pulsatile aqueous discharge into aqueous veins and reduced ability to reflux blood into SC. These alterations in the functional properties are challenging to monitor clinically. Phase-sensitive OCT now permits noninvasive, quantitative measurement of pulse-dependent TM motion in humans. This proposed conceptual model and related techniques offer a novel framework for understanding mechanisms, improving management, and development of therapeutic options for glaucoma.

Lymphatic System Flows

The supply of oxygen and nutrients to tissues is performed by the blood system, and involves a net leakage of fluid outward at the capillary level. One of the principal functions of the lymphatic system is to gather this fluid and return it to the blood system to maintain overall fluid balance. Fluid in the interstitial spaces is often at subatmospheric pressure, and the return points into the venous system are at pressures of approximately 20 cmH₂O. This adverse pressure difference is overcome by the active pumping of collecting lymphatic vessels, which feature closely spaced one-way valves and contractile muscle cells in their walls. Passive vessel squeezing causes further pumping. The dynamics of lymphatic pumping have been investigated experimentally and mathematically, revealing complex behaviours indicating that the system performance is robust against minor perturbations in pressure and flow. More serious disruptions can lead to incurable swelling of tissues called lymphœdema.

Opportunities for Studying the Hydrodynamic Context for Breast Cancer Cell Spread Through Lymph Flow

The lymphatic system serves as the primary route for the metastatic spread of breast cancer cells (BCCs). A scarcity of information exists with regard to the advection of BCCs in lymph flow and a fundamental understanding of the response of BCCs to the forces in the lymphatics needs to be established. This review summarizes the flow environment metastatic BCCs are exposed to in the lymphatics. Special attention is paid to the behavior of cells/particles in microflows in an attempt to elucidate the behavior of BCCs under lymph flow conditions (Reynolds number <1).

OCT Study of Mechanical Properties Associated with Trabecular Meshwork and Collector Channel Motion in Human Eyes

We report the use of a high-resolution optical coherence tomography (OCT) imaging platform to identify and quantify pressure-dependent aqueous outflow system (AOS) tissue relationships and to infer mechanical stiffness through examination of tissue properties in ex vivo human eyes. Five enucleated human eyes are included in this study, with each eye prepared with four equal-sized quadrants, each encompassing 90 degrees of the limbal circumference. In radial limbal segments perfusion pressure within Schlemm’s canal (SC) is controlled by means of a perfusion cannula inserted into the canal lumen, while the other end of the cannula leads to a reservoir at a height that can control the pressure in the cannula. The OCT system images the sample with a spatial resolution of about 5 μm from the trabecular meshwork (TM) surface. Geometric parameters are quantified from the 2D OCT images acquired from the sample subjected to controlled changes in perfusion pressures; parameters include area and height of the lumen of SC, collector channel entrances (CCE) and intrascleral collector channels (ISCC). We show that 3D OCT imaging permits the identification of 3-D relationships of the SC, CCE and ISCC lumen dimensions. Collagen flaps or leaflets are found at CCE that are attached or hinged at only one end, whilst the flaps are connected to the TM by cylindrical structures spanning SC. Increasing static SC pressures resulted in SC lumen enlargement with corresponding enlargement of the CCE and ISCC lumen. Pressure-dependent SC lumen area and height changes are significant at the 0.01 levels for ANOVA, and at the 0.05 for both polynomial curves and Tukey paired comparisons. Dynamic measurements demonstrate a synchronous increase in SC, CCE and ISCC lumen height in response to pressure changes from 0 to 10, 30 or 50 mm Hg, respectively, and the response time is within the 50-millisecond range. From the measured SC volume and corresponding IOP values, we demonstrate that an elastance curve can be developed to infer the mechanical stiffness of the TM by means of quantifying pressure-dependent SC volume changes over a 2 mm radial region of SC. Our study finds pressure-dependent motion of the TM that corresponds to collagen leaflet configuration motion at CCE; the synchronous tissue motion also corresponds with synchrony of SC and CCE lumen dimension changes.

Estimation of the Pressure Drop Required for Lymph Flow through Initial Lymphatic Networks

BACKGROUND

Lymphatic function is critical for maintaining interstitial fluid balance and is linked to multiple pathological conditions. While smooth muscle contractile mechanisms responsible for fluid flow through collecting lymphatic vessels are well studied, how fluid flows into and through initial lymphatic networks remains poorly understood. The objective of this study was to estimate the pressure difference needed for flow through an intact initial lymphatic network.

METHODS AND RESULTS

Pressure drops were computed for real and theoretical networks with varying branch orders using a segmental Poiseuille flow model. Vessel geometries per branch order were based on measurements from adult Wistar rat mesenteric initial lymphatic networks. For computational predications based on real network geometries and combinations of low or high output velocities (2 mm/s, 4 mm/s) and viscosities (1 cp, 1.5 cp), pressure drops were estimated to range 0.31-2.57 mmHg. The anatomical data for the real networks were also used to create a set of theoretical networks in order to identify possible minimum and maximum pressure drops. The pressure difference range for the theoretical networks was 0.16-3.16 mmHg.

CONCLUSIONS

The results support the possibility for suction pressures generated from cyclic smooth muscle contractions of upstream collecting lymphatics being sufficient for fluid flow through an initial lymphatic network.

Mesenteric lymphatic vessels adapt to mesenteric venous hypertension by becoming weaker pumps

Lymphangions, the segments of lymphatic vessels between two adjacent lymphatic valves, actively pump lymph. Acute changes in transmural pressure and lymph flow have profound effects on lymphatic pump function in vitro. Chronic changes in pressure and flow in vivo have also been reported to lead to significant changes in lymphangion function. Because changes in pressure and flow are both cause and effect of adaptive processes, characterizing adaptation requires a more fundamental analysis of lymphatic muscle properties. Therefore, the purpose of the present work was to use an intact lymphangion isovolumetric preparation to evaluate changes in mesenteric lymphatic muscle mechanical properties and the intracellular Ca(2+) in response to sustained mesenteric venous hypertension. Bovine mesenteric veins were surgically occluded to create mesenteric venous hypertension. Postnodal mesenteric lymphatic vessels from mesenteric venous hypertension (MVH; n = 6) and sham surgery (Sham; n = 6) animals were isolated and evaluated 3 days after the surgery. Spontaneously contracting MVH vessels generated end-systolic active tension and end-diastolic active tension lower than the Sham vessels. Furthermore, steady-state active tension and intracellular Ca(2+) concentration levels in response to KCl stimulation were also significantly lower in MVH vessels compared with those of the Sham vessels. There was no significant difference in passive tension in lymphatic vessels from the two groups. Taken together, these results suggest that following 3 days of mesenteric venous hypertension, postnodal mesenteric lymphatic vessels adapt to become weaker pumps with decreased cytosolic Ca(2+) concentration.

Functional adaptation of bovine mesenteric lymphatic vessels to mesenteric venous hypertension

Lymph flow is the primary mechanism for returning interstitial fluid to the blood circulation. Currently, the adaptive response of lymphatic vessels to mesenteric venous hypertension is not known. This study sought to determine the functional responses of postnodal mesenteric lymphatic vessels. We surgically occluded bovine mesenteric veins to create mesenteric venous hypertension to elevate mesenteric lymph flow. Three days after surgery, postnodal mesenteric lymphatic vessels from mesenteric venous hypertension (MVH; n = 7) and sham surgery (Sham; n = 6) group animals were evaluated and compared. Contraction frequency (MVH: 2.98 ± 0.75 min(-1); Sham: 5.42 ± 0.81 min(-1)) and fractional pump flow (MVH: 1.14 ± 0.30 min(-1); Sham: 2.39 ± 0.32 min(-1)) were significantly lower in the venous occlusion group. These results indicate that postnodal mesenteric lymphatic vessels adapt to mesenteric venous hypertension by reducing intrinsic contractile activity.

Mathematical model of blood and interstitial flow and lymph production in the liver

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal ‘classic’ lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules’ thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the non-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5 % more than if the entire surface were covered by the Glisson–peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations.

Modelling the lymphatic system: challenges and opportunities

The lymphatic system is a vital part of the circulatory and immune systems, and plays an important role in homeostasis by controlling extracellular fluid volume and in combating infection. Nevertheless, there is a notable disparity in terms of research effort expended in relation to the treatment of lymphatic diseases in contrast to the cardiovascular system. While similarities to the cardiovascular system exist, there are considerable differences in their anatomy and physiology. This review outlines some of the challenges and opportunities for those engaged in modelling biological systems. The study of the lymphatic system is still in its infancy, the vast majority of the models presented in the literature to date having been developed since 2003. The number of distinct models and their variants are few in number, and only one effort has been made thus far to study the entire lymphatic network; elements of the lymphatic system such as the nodes, which act as pumps and reservoirs, have not been addressed by mathematical models. Clearly, more work will be necessary in combination with experimental verification in order to progress and update the knowledge on the function of the lymphatic system. As our knowledge and understanding of its function increase, new and more effective treatments of lymphatic diseases are bound to emerge.

Osteopathic lymphatic pump techniques to enhance immunity and treat pneumonia

Pneumonia is a common cause of morbidity and mortality worldwide. While antibiotics are generally effective for the treatment of infection, the emergence of resistant strains of bacteria threatens their success. The osteopathic medical profession has designed a set of manipulative techniques called lymphatic pump techniques (LPT), to enhance the flow of lymph through the lymphatic system. Clinically, LPT is used to treat infection and oedemaand might be an effective adjuvant therapy in patients with pneumonia.The immune system uses the lymphatic and blood systems to survey to rid the body of pathogens; however, only recently have the effects of LPT on the lymphatic and immune systems been investigated. This short review highlightsclinical and basic science research studies that support the use of LPT to enhance the lymphatic and immune systems and treat pneumonia, and discusses the potential mechanisms by which LPT benefits patients with pneumonia.

Lymphatic pump treatment enhances the lymphatic and immune systems

The osteopathic medical profession has long advocated the use of osteopathic lymphatic pump treatments (LPT) to improve lymphatic circulation, reduce edema and combat infectious disease. However, until recently, there was no scientific evidence that LPT enhances function of the lymphatic and immune systems. This review discusses the physiological functions of the lymphatic system, the ability of LPT to increase lymph flow under normal and experimental conditions, the clinical benefits of LPT, current research models for the study of LPT and the potential mechanisms by which LPT enhances lymphatic and immune function.

Engineering the Lymphatic System

The recent advances in our understanding of lymphatic physiology and the role of the lymphatics in actively regulating fluid balance, lipid transport, and immune cell trafficking has been furthered in part through innovations in imaging, tissue engineering, quantitative biology, biomechanics, and computational modeling. Interdisciplinary and bioengineering approaches will continue to be crucial to the progression of the field, given that lymphatic biology and function are intimately woven with the local microenvironment and mechanical loads experienced by the vessel. This is particularly the case in lymphatic diseases such as lymphedema where the microenvironment can be drastically altered by tissue fibrosis and adipocyte accumulation. In this review we will highlight contributions engineering and mechanics have made to lymphatic physiology and will discuss areas that will be important for future research.

Nonlinear lymphangion pressure-volume relationship minimizes edema

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.

Human thoracic duct in vitro: diameter-tension properties, spontaneous and evoked contractile activity

The current study characterizes the mechanical properties of the human thoracic duct and demonstrates a role for adrenoceptors, thromboxane, and endothelin receptors in human lymph vessel function. With ethical permission and informed consent, portions of the thoracic duct (2-5 cm) were resected and retrieved at T(7)-T(9) during esophageal and cardia cancer surgery. Ring segments (2 mm long) were mounted in a myograph for isometric tension (N/m) measurement. The diameter-tension relationship was established using ducts from 10 individuals. Peak active tension of 6.24 +/- 0.75 N/m was observed with a corresponding passive tension of 3.11 +/- 0.67 N/m and average internal diameter of 2.21 mm. The equivalent active and passive transmural pressures by LaPlace's law were 47.3 +/- 4.7 and 20.6 +/- 3.2 mmHg, respectively. Subsequently, pharmacology was performed on rings from 15 ducts that were normalized by stretching them until an equivalent pressure of 21 mmHg was calculable from the wall tension. At low concentrations, norepinephrine, endothelin-1, and the thromboxane-A(2) analog U-46619 evoked phasic contractions (analogous to lymphatic pumping), whereas at higher contractions they induced tonic activity (maximum tension values of 4.46 +/- 0.63, 5.90 +/- 1.4, and 6.78 +/- 1.4 N/m, respectively). Spontaneous activity was observed in 44% of ducts while 51% of all the segments produced phasic contractions after agonist application. Acetylcholine and bradykinin relaxed norepinephrine preconstrictions by approximately 20% and approximately 40%, respectively. These results demonstrate that the human thoracic duct can develop wall tensions that permit contractility to be maintained across a wide range of transmural pressures and that isolated ducts contract in response to important vasoactive agents.

Hypertonic saline alters hydraulic conductivity and up-regulates mucosal/submucosal aquaporin 4 in resuscitation-induced intestinal edema

OBJECTIVE

To characterize membrane conductivity by applying mathematical modeling techniques and immunohistochemistry and to localize and predict areas of the bowel where aquaporins may be associated with edema resolution/prevention associated with hypertonic saline. Intestinal edema induced by resuscitation and mesenteric venous hypertension impairs intestinal transit/contractility. Hypertonic saline decreases intestinal edema and improves transit. Aquaporins are water transport membrane proteins that may be up-regulated with edema and/or hypertonic saline.

DESIGN

Laboratory study.

SETTING

University research laboratory.

SUBJECTS

Male Sprague Dawley rats, weighing 270 to 330 g.

INTERVENTIONS

Rats were randomized to control (with and without hypertonic saline) and mesenteric venous hypertension with either 80 mL/kg normal saline (RESUS + VH + VEH) or 80 mL/kg normal saline with hypertonic saline (RESUS + VH + HTS). After 6 hrs, intestinal wet/dry ratios, urine output, peritoneal fluid, and intraluminal fluid were measured. Hydraulic conductivity was calculated from our previously known and published pressure-flow data. The cDNA microarray, Western blot, polymerase chain reaction, and immunohistochemistry studies were conducted for candidate aquaporins and distribution in intestinal edema resolution.

MEASUREMENTS AND MAIN RESULTS

Hypertonic saline decreased edema and increased urine, intraluminal, and peritoneal fluid volume. RESUS + VH favors fluid flux into the interstitium. Hypertonic saline causes increased hydraulic conductivity at the seromuscular and mucosal surfaces at the same time limiting flow into the interstitium. This is associated with increased aquaporin 4 expression in the intestinal mucosa and submucosa.

CONCLUSIONS

Hypertonic saline mitigates intestinal edema development and promotes fluid redistribution secondary to increased membrane conductivity at the mucosal and seromuscular surfaces. This is associated with up-regulation of aquaporin 4 gene expression and protein. Aquaporin 4 may be a useful therapeutic target for strategies to enhance edema resolution.

Balance point characterization of interstitial fluid volume regulation

The individual processes involved in interstitial fluid volume and protein regulation (microvascular filtration, lymphatic return, and interstitial storage) are relatively simple, yet their interaction is exceedingly complex. There is a notable lack of a first-order, algebraic formula that relates interstitial fluid pressure and protein to critical parameters commonly used to characterize the movement of interstitial fluid and protein. Therefore, the purpose of the present study is to develop a simple, transparent, and general algebraic approach that predicts interstitial fluid pressure (P(i)) and protein concentrations (C(i)) that takes into consideration all three processes. Eight standard equations characterizing fluid and protein flux were solved simultaneously to yield algebraic equations for P(i) and C(i) as functions of parameters characterizing microvascular, interstitial, and lymphatic function. Equilibrium values of P(i) and C(i) arise as balance points from the graphical intersection of transmicrovascular and lymph flows (analogous to Guyton's classical cardiac output-venous return curves). This approach goes beyond describing interstitial fluid balance in terms of conservation of mass by introducing the concept of inflow and outflow resistances. Algebraic solutions demonstrate that P(i) and C(i) result from a ratio of the microvascular filtration coefficient (1/inflow resistance) and effective lymphatic resistance (outflow resistance), and P(i) is unaffected by interstitial compliance. These simple algebraic solutions predict P(i) and C(i) that are consistent with reported measurements. The present work therefore presents a simple, transparent, and general balance point characterization of interstitial fluid balance resulting from the interaction of microvascular, interstitial, and lymphatic function.

Lymphatic pump-conduit duality: contraction of postnodal lymphatic vessels inhibits passive flow

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.

Optimal postnodal lymphatic network structure that maximizes active propulsion of lymph

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.