Valve-related modes of pump failure in collecting lymphatics: numerical and experimental investigation

The Lymphatic Vascular System: Does Nonuniform Lymphangion Length Limit Flow-Rate?

A previously developed model of a lymphatic vessel as a chain of lymphangions was investigated to determine whether lymphangions of unequal length reduce pumping relative to a similar chain of equal-length ones. The model incorporates passive elastic and active contractile properties taken from ex vivo measurements, and intravascular lymphatic valves as transvalvular pressure-dependent resistances to flow with hysteresis and transmural pressure-dependent bias to the open state as observed experimentally. Coordination of lymphangion contractions is managed by marrying an autonomous transmural pressure-dependent pacemaker for each lymphangion with bidirectional transmission of activation signals between lymphangions, qualitatively matching empirical observations. With eight lymphangions as used here and many nonlinear constraints, the model is capable of complex outcomes. The expected flow-rate advantage conferred by longer lymphangions everywhere was confirmed. However, the anticipated advantage of uniform lymphangions over those of unequal length, compared in chains of equal overall length, was not found. A wide variety of dynamical outcomes was observed, with the most powerful determinant being the adverse pressure difference, rather than the arrangement of long and short lymphangions. This work suggests that the wide variation in lymphangion length which is commonly observed in collecting lymphatic vessels does not confer disadvantage in pumping lymph.

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 dual-clock-driven model of lymphatic muscle cell pacemaking to emulate knock-out of Ano1 or IP3R

Lymphatic system defects are involved in a wide range of diseases, including obesity, cardiovascular disease, and neurological disorders, such as Alzheimer's disease. Fluid return through the lymphatic vascular system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, which are in turn driven by electrochemical oscillations that cause rhythmic action potentials and associated surges in intracellular calcium ion concentration. There is an incomplete understanding of the mechanisms involved in these repeated events, restricting the development of pharmacological treatments for dysfunction. Previously, we proposed a model where autonomous oscillations in the membrane potential (M-clock) drove passive oscillations in the calcium concentration (C-clock). In this paper, to model more accurately what is known about the underlying physiology, we extend this model to the case where the M-clock and the C-clock oscillators are both active but coupled together, thus both driving the action potentials. This extension results from modifications to the model's description of the IP3 receptor, a key C-clock mechanism. The synchronised dual-driving clock behaviour enables the model to match IP3 receptor knock-out data, thus resolving an issue with previous models. We also use phase-plane analysis to explain the mechanisms of coupling of the dual clocks. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of some causes of lymphoedema.

A 1D model characterizing the role of spatiotemporal contraction distributions on lymph transport

Lymphedema is a condition in which lymph transport is compromised. The factors that govern the timing of lymphatic contractions are largely unknown; however, these factors likely play a central role in lymphatic health. Computational models have proven useful in quantifying changes in lymph transport; nevertheless, there is still much unknown regarding the regulation of contractions. The purpose of this paper is to utilize computational modeling to examine the role of pacemaking activity in lymph transport. A 1D fluid-solid modeling framework was utilized to describe the interaction between the contracting vessel and the lymph flow. The distribution of contractions along a three-lymphangion chain in time and space was determined by specifying the pacemaking sites and parameters obtained from experimentation. The model effectively replicates the contractility patterns in experiments. Quantitatively, the flow rates were measured at 5.44 and 2.29 [Formula: see text], and the EF values were 78% and less than 33% in the WT and KO models, respectively, which are consistent with the literature. Applying pacemaking parameters in this modeling framework effectively captures lymphatic contractile wave propagations and their relation to lymph transport. It can serve as a motivation for conducting novel studies to evaluate lymphatic pumping function during the development of lymphedema.

Lymphatic contractile dysfunction in mouse models of Cantú Syndrome with KATP channel gain-of-function

Cantú Syndrome (CS) is an autosomal dominant disorder caused by gain-of-function (GoF) mutations in the Kir6.1 and SUR2 subunits of KATP channels. KATP overactivity results in a chronic reduction in arterial tone and hypotension, leading to other systemic cardiovascular complications. However, the underlying mechanism of lymphedema, developed by >50% of CS patients, is unknown. We investigated whether lymphatic contractile dysfunction occurs in mice expressing CS mutations in Kir6.1 (Kir6.1[V65M]) or SUR2 (SUR2[A478V], SUR2[R1154Q]). Pressure myograph tests of contractile function of popliteal lymphatic vessels over the physiological pressure range revealed significantly impaired contractile strength and reduced frequency of spontaneous contractions at all pressures in heterozygous Kir6.1[V65M] vessels, compared to control littermates. Contractile dysfunction of intact popliteal lymphatics in vivo was confirmed using near-infrared fluorescence microscopy. Homozygous SUR2[A478V] vessels exhibited profound contractile dysfunction ex vivo, but heterozygous SUR2[A478V] vessels showed essentially normal contractile function. However, further investigation of vessels from all three GoF mouse strains revealed significant disruption in contraction wave entrainment, decreased conduction speed and distance, multiple pacemaker sites, and reversing wave direction. Tests of 2-valve lymphatic vessels forced to pump against an adverse pressure gradient revealed that all CS-associated genotypes were essentially incapable of pumping under an imposed outflow load. Our results show that varying degrees of lymphatic contractile dysfunction occur in proportion to the degree of molecular GoF in Kir6.1 or SUR2. This is the first example of lymphatic contractile dysfunction caused by a smooth muscle ion channel mutation and potentially explains the susceptibility of CS patients to lymphedema.

A vascular smooth muscle-specific integrin-α8 Cre mouse for lymphatic contraction studies that allows male-female comparisons and avoids visceral myopathy

Introduction: The widely-used, tamoxifen-inducible, smooth muscle (SM)-specific Cre, Myh11-CreER^T2 , suffers from two disadvantages: 1) it is carried on the Y-chromosome and thus only effective for gene deletion in male mice, and 2) it recombines in both vascular and non-vascular SM, potentially leading to unwanted or confounding gastrointestinal phenotypes. Here, we tested the effectiveness of a new, SM-specific Cre, based on the integrin α8 promoter (Itga8-CreER^T2 ), that has been recently developed and characterized, to assess the effects of Cav1.2 deletion on mouse lymphatic SM function. Methods: Cav1.2 (the L-type voltage-gated calcium channel) is essential for lymphatic pacemaking and contraction and its deletion using either Myh11-CreER^T2 or Itga8-CreER^T2 abolished spontaneous lymphatic contractions. Mouse lymphatic contractile function was assessed using two ex vivo methods. Results: Myh11-CreER^T2 ; Cav1.2 ^f/f mice died of gastrointestinal obstruction within 20 days of the first tamoxifen injection, preceded by several days of progressively poor health, with symptoms including weight loss, poor grooming, hunched posture, and reduced overall activity. In contrast, Itga8-CreER^T2 ; Cav1.2 ^f/f mice survived for >80 days after induction and were in normal health until the time of sacrifice for experimental studies. Cav1.2 deletion was equally effective in male and female mice. Discussion: Our results demonstrate that Itga8-CreER ^T2 can be used to effectively delete genes in lymphatic smooth muscle while avoiding potentially lethal visceral myopathy and allowing comparative studies of lymphatic contractile function in both male and female mice.

Lymphatic Collecting Vessel: New Perspectives on Mechanisms of Contractile Regulation and Potential Lymphatic Contractile Pathways to Target in Obesity and Metabolic Diseases

Obesity and metabolic syndrome pose a significant risk for developing cardiovascular disease and remain a critical healthcare challenge. Given the lymphatic system's role as a nexus for lipid absorption, immune cell trafficking, interstitial fluid and macromolecule homeostasis maintenance, the impact of obesity and metabolic disease on lymphatic function is a burgeoning field in lymphatic research. Work over the past decade has progressed from the association of an obese phenotype with Prox1 haploinsufficiency and the identification of obesity as a risk factor for lymphedema to consistent findings of lymphatic collecting vessel dysfunction across multiple metabolic disease models and organisms and characterization of obesity-induced lymphedema in the morbidly obese. Critically, recent findings have suggested that restoration of lymphatic function can also ameliorate obesity and insulin resistance, positing lymphatic targeted therapies as relevant pharmacological interventions. There remain, however, significant gaps in our understanding of lymphatic collecting vessel function, particularly the mechanisms that regulate the spontaneous contractile activity required for active lymph propulsion and lymph return in humans. In this article, we will review the current findings on lymphatic architecture and collecting vessel function, including recent advances in the ionic basis of lymphatic muscle contractile activity. We will then discuss lymphatic dysfunction observed with metabolic disruption and potential pathways to target with pharmacological approaches to improve lymphatic collecting vessel function.

Multiple aspects of lymphatic dysfunction in an ApoE -/- mouse model of hypercholesterolemia

Introduction: Rodent models of cardiovascular disease have uncovered various types of lymphatic vessel dysfunction that occur in association with atherosclerosis, type II diabetes and obesity. Previously, we presented in vivo evidence for impaired lymphatic drainage in apolipoprotein E null (ApoE ^-/- ) mice fed a high fat diet (HFD). Whether this impairment relates to the dysfunction of collecting lymphatics remains an open question. The ApoE ^-/- mouse is a well-established model of cardiovascular disease, in which a diet rich in fat and cholesterol on an ApoE deficient background accelerates the development of hypercholesteremia, atherosclerotic plaques and inflammation of the skin and other tissues. Here, we investigated various aspects of lymphatic function using ex vivo tests of collecting lymphatic vessels from ApoE ^+/+ or ApoE ^-/- mice fed a HFD. Methods: Popliteal collectors were excised from either strain and studied under defined conditions in which we could quantify changes in lymphatic contractile strength, lymph pump output, secondary valve function, and collecting vessel permeability. Results: Our results show that all these aspects of lymphatic vessel function are altered in deleterious ways in this model of hypercholesterolemia. Discussion: These findings extend previous in vivo observations suggesting significant dysfunction of lymphatic endothelial cells and smooth muscle cells from collecting vessels in association with a HFD on an ApoE-deficient background. An implication of our study is that collecting vessel dysfunction in this context may negatively impact the removal of cholesterol by the lymphatic system from the skin and the arterial wall and thereby exacerbate the progression and/or severity of atherosclerosis and associated inflammation.

A Mathematical Description of the Flow in a Spherical Lymph Node

The motion of the lymph has a very important role in the immune system, and it is influenced by the porosity of the lymph nodes: more than 90% takes the peripheral path without entering the lymphoid compartment. In this paper, we construct a mathematical model of a lymph node assumed to have a spherical geometry, where the subcapsular sinus is a thin spherical shell near the external wall of the lymph node and the core is a porous material describing the lymphoid compartment. For the mathematical formulation, we assume incompressibility and we use Stokes together with Darcy-Brinkman equation for the flow of the lymph. Thanks to the hypothesis of axisymmetric flow with respect to the azimuthal angle and the use of the stream function approach, we find an explicit solution for the fully developed pulsatile flow in terms of Gegenbauer polynomials. A selected set of plots is provided to show the trend of motion in the case of physiological parameters. Then, a finite element simulation is performed and it is compared with the explicit solution.

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.

Pump efficacy in a two-dimensional, fluid-structure interaction model of a chain of contracting lymphangions

The transport of lymph through the lymphatic vasculature is the mechanism for returning excess interstitial fluid to the circulatory system, and it is essential for fluid homeostasis. Collecting lymphatic vessels comprise a significant portion of the lymphatic vasculature and are divided by valves into contractile segments known as lymphangions. Despite its importance, lymphatic transport in collecting vessels is not well understood. We present a computational model to study lymph flow through chains of valved, contracting lymphangions. We used the Navier-Stokes equations to model the fluid flow and the immersed boundary method to handle the two-way, fluid-structure interaction in 2D, non-axisymmetric simulations. We used our model to evaluate the effects of chain length, contraction style, and adverse axial pressure difference (AAPD) on cycle-mean flow rates (CMFRs). In the model, longer lymphangion chains generally yield larger CMFRs, and they fail to generate positive CMFRs at higher AAPDs than shorter chains. Simultaneously contracting pumps generate the largest CMFRs at nearly every AAPD and for every chain length. Due to the contraction timing and valve dynamics, non-simultaneous pumps generate lower CMFRs than the simultaneous pumps; the discrepancy diminishes as the AAPD increases. Valve dynamics vary with the contraction style and exhibit hysteretic opening and closing behaviors. Our model provides insight into how contraction propagation affects flow rates and transport through a lymphangion chain.

Modelling secondary lymphatic valves with a flexible vessel wall: how geometry and material properties combine to provide function

A three-dimensional finite-element fluid/structure interaction model of an intravascular lymphatic valve was constructed, and its properties were investigated under both favourable and adverse pressure differences, simulating valve opening and valve closure, respectively. The shear modulus of the neo-Hookean material of both vascular wall and valve leaflet was varied, as was the degree of valve opening at rest. Also investigated was how the valve characteristics were affected by prior application of pressure inflating the whole valve. The characteristics were parameterised by the volume flow rate through the valve, the hydraulic resistance to flow, and the maximum sinus radius and inter-leaflet-tip gap on the plane of symmetry bisecting the leaflet, all as functions of the applied pressure difference. Maximum sinus radius on the leaflet-bisection plane increased with increasing pressure applied to either end of the valve segment, but also reflected the non-circular deformation of the sinus cross section caused by the leaflet, such that it passed through a minimum at small favourable pressure differences. When the wall was stiff, the inter-leaflet gap increased sigmoidally during valve opening; when it was as flexible as the leaflet, the gap increased more linearly. Less pressure difference was required both to open and to close the valve when either the wall or the leaflet material was more flexible. The degree of bias of the valve characteristics to the open position increased with the inter-leaflet gap in the resting position and with valve inflation pressure. The characteristics of the simulated valve were compared with those specified in an existing lumped-parameter model of one or more collecting lymphangions and used to estimate a revised value for the constant in that model which controls the rate of valve opening/closure with variation in applied pressure difference. The effects of the revised value on the lymph pumping efficacy predicted by the lumped-parameter model were evaluated.

Inhibition of contraction strength and frequency by wall shear stress in a single-lymphangion model

The phasic contractions of collecting lymphatic vessels are reduced in strength and occur at diminished frequency when the favourable pressure difference and the resulting antegrade flow create large fluid shear stresses at the luminal surface. This paper describes a minimal phenomenological model of this mechanism, that is applied to a previously validated numerical model of a phasically contracting lymphangion. The parameters of the inhibition model are quantitatively matched to observations in isolated segments of rat lymphatic vessel, first for mesenteric lymphatics then for thoracic duct, and outcomes from the numerical model are then qualitatively compared with recent observations in isolated segments of rat thoracic duct.

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh-Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.

Contraction of collecting lymphatics: organization of pressure-dependent rate for multiple lymphangions

The paper describes the extension of a previously developed model of pressure-dependent contraction rate to the case of multiple lymphangions. Mechanical factors are key modulators of active lymphatic pumping. As part of the evolution of our lumped-parameter model to match experimental findings, we have designed an algorithm whereby the time until the next contraction depends on lymphangion transmural pressure in the contraction just completed. The functional dependence of frequency on pressure is quantitatively matched to isobaric contraction experiments on isolated lymphatic segments. When each of several lymphangions is given this ability, a scheme for their coordination must be instituted to match the observed synchronization. Accordingly, and in line with an experiment on an isolated lymphatic vessel segment in which we measured contraction sequence and conduction delay, we took the fundamental principle to be that local timing can be overridden by signals to initiate contraction that start in adjacent lymphangions, conducted with a short delay. The scheme leads to retrograde conduction when the lymphangion chain is pumping against an adverse pressure difference, but antegrade conduction when contractions occur with no or a favourable pressure difference. Abolition of these conducted signals leads to chaotic variation of cycle-mean flow-rate from the chain, diastolic duration in each lymphangion, and inter-lymphangion delays. Chaotic rhythm is also seen under other circumstances. Because the model responds to increasing adverse pressure difference by increasing the repetition rate of contractions, it maintains time-average output flow-rate better than one with fixed repetition rate.