Network Scale Modeling of Lymph Transport and Its Effective Pumping Parameters

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.

Transport Barriers Influence the Activation of Anti-Tumor Immunity: A Systems Biology Analysis

Effective anti-cancer immune responses require activation of one or more naïve T cells. If the correct naïve T cell encounters its cognate antigen presented by an antigen presenting cell, then the T cell can activate and proliferate. Here, mathematical modeling is used to explore the possibility that immune activation in lymph nodes is a rate-limiting step in anti-cancer immunity and can affect response rates to immune checkpoint therapy. The model provides a mechanistic framework for optimizing cancer immunotherapy and developing testable solutions to unleash anti-tumor immune responses for more patients with cancer. The results show that antigen production rate and trafficking of naïve T cells into the lymph nodes are key parameters and that treatments designed to enhance tumor antigen production can improve immune checkpoint therapies. The model underscores the potential of radiation therapy in augmenting tumor immunogenicity and neoantigen production for improved ICB therapy, while emphasizing the need for careful consideration in cases where antigen levels are already sufficient to avoid compromising the immune response.

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.

Changes of thoracic duct flow and morphology in an animal model of elevated central venous pressure

Objective: Investigation of lymph fluid dynamics in thoracic duct during central venous pressure elevation.

Background: Lymphatic flow is affected by elevated central venous pressure (CVP) in congestive heart failure. The changes of thoracic duct (TD) lymph flow have not been studied chronically in the setting of elevated CVP. This study is to investigate fluid dynamics and remodeling of the TD in the elevated CVP animal model.

Methods: A flow probe was implanted on the swine TD (n = 6) and tricuspid regurgitation (TR) was created by cutting tricuspid chordae percutaneously. Six swine were used as control group animals. The TD flow was measured for 2 weeks (baseline) before TR and 4 weeks postop-TR surgery. Arterial pressure and CVP were measured. The pressure and flow in the TD were measured percutaneously. Histological and morphological analyses were performed.

Results: TR resulted in an increase in CVP from 4.2 ± 2.6 to 10.1 ± 4.3 mmHg (p < 0.05). The lymph flow in the TD increased from 0.78 ± 1.06 before TR to 8.8 ± 4.8 ml/min (p < 0.05) 2 days post-TR and remained plateau for 4 weeks, i.e., the TD flow remained approximately 8–11 fold its baseline. Compared to the 8.1 ± 3.2 mmHg control group, the TD average pressures at the lymphovenous junction increased to 14.6 ± 5.7 mmHg in the TR group (p < 0.05). The TD diameter and wall thickness increased from 3.35 ± 0.37 mm and 0.06 ± 0.01 mm in control to 4.32 ± 0.57 mm and 0.26 ± 0.02 mm (p < 0.05) in the TR group, respectively.

Conclusion: The elevated CVP results in a significant increase in TD flow and pressure which causes the TD’s outward remodeling and thickening. Our study implicates that the outward remodeling may result in the TD valve incompetence due to failure coaptation of leaflets.

Safety and Feasibility of a Kinesiotape Application for Secondary Hand Lymphedema: A Case Series

Background: The safety and feasibility of using kinesiotape as a short-term alternative treatment to compression garments or gloves for hand lymphedema have not been examined. The aim of this study was to examine if kinesiotape could maintain size and extracellular fluid (ECF) volume of the hand and forearm, as well as upper limb function and quality of life for women with secondary hand lymphedema. Methods and Results: Six women with secondary hand lymphedema underwent pretreatment measurements, including hand and digit size using a tape measure; ECF volume using bioimpedance spectroscopy; and patient-reported outcome measurements of upper limb function and quality of life. Kinesiotape was then applied to the dorsum of the hand and left for 48 h, during which participants were asked not to wear compression garments. Posttreatment measurements were completed after kinesiotape removal. Changes in measurements were compared to the smallest detectable change (SDC). Hand size did not change more than the SDC; however, a single affected digit increased in circumference by more than the SDC. Changes of the whole arm ECF volume were less than the SDC. The ECF volume of the dorsum of the hand increased in one and decreased in another participant. The forearm ECF volume decreased in two participants. Upper limb function and quality of life did not change. No adverse event was reported. Conclusion: Short-term kinesiotape use appears to be safe in maintaining the physical presentation of hand lymphedema. However, these results should be examined in a larger sample. The feasibility of using kinesiotape as an alternative treatment to compression requires further investigation. Clinical Trial Registration number: ACTRN12618001232224p, July 23, 2018 retrospectively registered.

Synthetic hydrogels engineered to promote collecting lymphatic vessel sprouting

The lymphatic vasculature is an essential component of the body's circulation providing a network of vessels to return fluid and proteins from the tissue space to the blood, to facilitate immune ce-ll and antigen transport to lymph nodes, and to take up dietary lipid from the intestine. The development of biomaterial-based strategies to facilitate the growth of lymphatics either for regenerative purposes or as model system to study lymphatic biology is still in its nascent stages. In particular, platforms that encourage the sprouting and formation of lymphatic networks from collecting vessels are particularly underdeveloped. Through implementation of a modular, poly(ethylene glycol) (PEG)-based hydrogel, we explored the independent contributions of matrix elasticity, degradability, and adhesive peptide presentation on sprouting of implanted segments of rat lymphatic collecting vessels. An engineered hydrogel with 680 Pa elasticity, 2.0 mM RGD adhesive peptide, and full susceptibility to protease degradability produced the highest levels of sprouting relative to other physicochemical matrix properties. This engineered hydrogel was then utilized as a scaffold to facilitate the implantation of a donor vessel that functionally grafted into the host vasculature. This hydrogel provides a promising platform for facilitating lymphangiogenesis in vivo or as a means to understand the cellular mechanisms involved in the sprout process during collecting lymphatic vessel collateralization.

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

The lymph node (LN) is a vital organ of the lymphatic and immune system that enables timely detection, response, and clearance of harmful substances from the body. Each LN comprises of distinct substructures, which host a plethora of immune cell types working in tandem to coordinate complex innate and adaptive immune responses. An improved understanding of LN biology could facilitate treatment in LN-associated pathologies and immunotherapeutic interventions, yet at present, animal models, which often have poor physiological relevance, are the most popular experimental platforms. Emerging biomaterial engineering offers powerful alternatives, with the potential to circumvent limitations of animal models, for in-depth characterization and engineering of the lymphatic and adaptive immune system. In addition, mathematical and computational approaches, particularly in the current age of big data research, are reliable tools to verify and complement biomaterial works. In this review, we first discuss the importance of lymph node in immunity protection followed by recent advances using biomaterials to create in vitro/vivo LN-mimicking models to recreate the lymphoid tissue microstructure and microenvironment, as well as to describe the related immuno-functionality for biological investigation. We also explore the great potential of mathematical and computational models to serve as in silico supports. Furthermore, we suggest how both in vitro/vivo and in silico approaches can be integrated to strengthen basic patho-biological research, translational drug screening and clinical personalized therapies. We hope that this review will promote synergistic collaborations to accelerate progress of LN-mimicking systems to enhance understanding of immuno-complexity.

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.

Mathematical Modeling of Lymph Node Drainage Function by Neural Network

The lymph node (LN) represents a key structural component of the lymphatic system network responsible for the fluid balance in tissues and the immune system functioning. Playing an important role in providing the immune defense of the host organism, LNs can also contribute to the progression of pathological processes, e.g., the spreading of cancer cells. To gain a deeper understanding of the transport function of LNs, experimental approaches are used. Mathematical modeling of the fluid transport through the LN represents a complementary tool for studying the LN functioning under broadly varying physiological conditions. We developed an artificial neural network (NN) model to describe the lymph node drainage function. The NN model predicts the flow characteristics through the LN, including the exchange with the blood vascular systems in relation to the boundary and lymphodynamic conditions, such as the afferent lymph flow, Darcy’s law constants and Starling’s equation parameters. The model is formulated as a feedforward NN with one hidden layer. The NN complements the computational physics-based model of a stationary fluid flow through the LN and the fluid transport across the blood vessel system of the LN. The physical model is specified as a system of boundary integral equations (IEs) equivalent to the original partial differential equations (PDEs; Darcy’s Law and Starling’s equation) formulations. The IE model has been used to generate the training dataset for identifying the NN model architecture and parameters. The computation of the output LN drainage function characteristics (the fluid flow parameters and the exchange with blood) with the trained NN model required about 1000-fold less central processing unit (CPU) time than computationally tracing the flow characteristics of interest with the physics-based IE model. The use of the presented computational models will allow for a more realistic description and prediction of the immune cell circulation, cytokine distribution and drug pharmacokinetics in humans under various health and disease states as well as assisting in the development of artificial LN-on-a-chip technologies.

The effect of respiration and body position on terminal thoracic duct diameter and the lymphovenous junction: An exploratory ultrasound study

The thoracic duct (TD) drains most of the body's lymph back to the venous system via its lymphovenous junction (LVJ), playing a pivotal role in fluid homeostasis, fat absorption and the systemic immune response. The respiratory cycle is thought to assist with lymph flow, but the precise mechanism underpinning terminal TD lymph flow into the central veins is not well understood. The aim of this study was to use ultrasonography (US) to explore the relationship between terminal TD lymph flow, the respiratory cycle, and gravity. The left supraclavicular fossa was scanned in healthy non-fasted volunteers using high-resolution (13-5 MHz) US to identify the terminal TD and the presence of a lymphovenous valve (LVV). The TD's internal diameter was measured in relation to respiration (inspiration vs. expiration) and body positioning (supine vs. Trendelenburg). The terminal TD was visualized in 20/33 (61%) healthy volunteers. An LVV was visualized in only 4/20 (20%) cases. The mean terminal TD diameter in the supine position was 1.7 mm (range 0.8-3.1 mm); this increased in full inspiration (mean 1.8 mm, range 0.9-3.2 mm, p < 0.05), and in the Trendelenburg position (mean 1.8 mm, range 1.2-3.1 mm, p < 0.05). The smallest mean terminal TD diameter occurred in full expiration (1.6 mm, range 0.7-3.1 mm, p < 0.05). Respiration and gravity impact the terminal TD diameter. Due to the challenges of visualizing the TD and LVJ, other techniques such as dynamic magnetic resonance imaging will be required to fully understand the factors governing TD lymph flow.

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.

Fluid pumping of peristaltic vessel fitted with elastic valves

Using numerical simulations, we probe the fluid flow in an axisymmetric peristaltic vessel fitted with elastic bi-leaflet valves. In this biomimetic system that mimics the flow generated in lymphatic vessels, we investigate the effects of the valve and vessel properties on pumping performance of the valved peristaltic vessel. The results indicate that valves significantly increase pumping by reducing backflow. The presence of valves, however, increases the viscous resistance therefore requiring greater work compared to valveless vessels. The benefit of the valves is the most significant when the fluid is pumped against an adverse pressure gradient and for low vessel contraction wave speeds. We identify the optimum vessel and valve parameters leading to the maximum pumping efficiency. We show that the optimum valve elasticity maximizes the pumping flow rate by allowing the valve to block more effectively the backflow while maintaining low resistance during the forward flow. We also examine the pumping in vessels where the vessel contraction amplitude is a function of the adverse pressure gradient as found in lymphatic vessels. We find that in this case the flow is limited by the work generated by the contracting vessel, suggesting that the pumping in lymphatic vessels is constrained by the performance of lymphatic muscle. Given the regional heterogeneity of valve morphology observed throughout the lymphatic vasculature, these results provide insight into how these variations might facilitate efficient lymphatic transport in the vessel's local physiologic context.

Go with the flow: modeling unique biological flows in engineered in vitro platforms

Interest in recapitulating in vivo phenomena in vitro using organ-on-a-chip technology has grown rapidly and with it, attention to the types of fluid flow experienced in the body has followed suit. These platforms offer distinct advantages over in vivo models with regards to human relevance, cost, and control of inputs (e.g., controlled manipulation of biomechanical cues from fluid perfusion). Given the critical role biophysical forces play in several tissues and organs, it is therefore imperative that engineered in vitro platforms capture the complex, unique flow profiles experienced in the body that are intimately tied with organ function. In this review, we outline the complex and unique flow regimes experienced by three different organ systems: blood vasculature, lymphatic vasculature, and the intestinal system. We highlight current state-of-the-art platforms that strive to replicate physiological flows within engineered tissues while introducing potential limitations in current approaches.

Characterization of rat tail lymphatic contractility and biomechanics: incorporating nitric oxide-mediated vasoregulation

The lymphatic system transports lymph from the interstitial space back to the great veins via a series of orchestrated contractions of chains of lymphangions. Biomechanical models of lymph transport, validated with ex vivo or in vivo experimental results, have proved useful in revealing novel insight into lymphatic pumping; however, a need remains to characterize the contributions of vasoregulatory compounds in these modelling tools. Nitric oxide (NO) is a key mediator of lymphatic pumping. We quantified the active contractile and passive biaxial biomechanical response of rat tail collecting lymphatics and changes in the contractile response to the exogenous NO administration and integrated these findings into a biomechanical model. The passive mechanical response was characterized with a three-fibre family model. Nonlinear regression and non-parametric bootstrapping were used to identify best-fit material parameters to passive cylindrical biaxial mechanical data, assessing uniqueness and parameter confidence intervals; this model yielded a good fit (R² = 0.90). Exogenous delivery of NO via sodium nitroprusside (SNP) elicited a dose-dependent suppression of contractions; the amplitude of contractions decreased by 30% and the contraction frequency decreased by 70%. Contractile function was characterized with a modified Rachev-Hayashi model, introducing a parameter that is related to SNP concentration; the model provided a good fit (R² = 0.89) to changes in contractile responses to varying concentrations of SNP. These results demonstrated the significant role of NO in lymphatic pumping and provide a predictive biomechanical model to integrate the combined effect of mechanical loading and NO on lymphatic contractility and mechanical response.

A computational model of a network of initial lymphatics and pre-collectors with permeable interstitium

Initial lymphatic vessels are made up of overlapped endothelial cells that act as unidirectional valves enabling one-way drainage of tissue fluid into the lumen of the initial lymphatics when there is a favourable pressure gradient. Initial lymphatics subsequently drain this fluid into the collecting lymphatics. This paper describes a computational model for a network of passive rat mesenteric lymphatic vessels with sparse secondary valves. The network was simulated with the secondary valves both operational and non-operational. The effects on the cycle-mean outflow-rate from the network of both inflammation and the resistance of the surrounding interstitium were considered. The cycle-mean outflow-rate is sensitive to vessel stiffness. If the influence of primary-valve resistance is reduced relative to that of interstitial resistance and intravascular resistance, there is no absolute advantage of extrinsic pumping, since maximum outflow-rate occurs when vessels are rigid. However, there is relative advantage, in that the outflow-rate at intermediate stiffness is higher with the secondary valves functioning than when they are deactivated. If primary-valve resistance dominates, then extrinsic pumping of non-rigid vessels provides absolute advantage. The nonlinear relation between pressure drop and flow-rate of the endothelial primary valves, combined with downstream compliance and pulsatile external pressure, constitutes a separate mechanism of pumping. By enabling the consideration of interactions between multiple phenomena (primary valves, secondary valves, a real network geometry with multiple branches, deformable vessel walls, interstitial resistance and external pressures), the model offers a perspective for delineating physiological phenomena that have not yet been fully linked to the biomechanics of fluid flow through initial lymphatic networks.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved.

Simultaneous measurements of lymphatic vessel contraction, flow and valve dynamics in multiple lymphangions using optical coherence tomography

Lymphatic dysfunction is involved in many diseases including lymphedema, hypertension, autoimmune responses, graft rejection, atherosclerosis, microbial infections, cancer and cancer metastasis. Expanding our knowledge of lymphatic system function can lead to a better understanding of these disease processes and improve treatment options. Here, optical coherence tomography (OCT) methods were used to reveal intraluminal valve dynamics in 3 dimensions, and measure lymph flow and vessel contraction simultaneously in 3 neighboring lymphangions of the afferent collecting lymphatic vessels to the popliteal lymph node in mice. Flow measurements were based on Doppler OCT techniques in combination with exogenous lymph labeling by Intralipid. Through these imaging methods, it is possible to study lymphatic function and pumping more comprehensively. These capabilities can lead to a better understanding of the regulation and dysregulation of lymphatic vessels in health and disease. The image depicts the dynamic measurements of lymphatic valves, lymphatic vessels cross-sectional area and lymph velocity simultaneously measured in vivo with optical coherence tomography.

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.

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.

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.

Modulation of mesenteric collecting lymphatic contractions by σ1-receptor activation and nitric oxide production

Recently, it has been reported that a σ-receptor antagonist could reduce inflammation-induced edema. Lymphatic vessels play an essential role in removing excess interstitial fluid. We tested the hypothesis that activation of σ-receptors would reduce or weaken collecting lymphatic contractions. We used isolated, cannulated rat mesenteric collecting lymphatic vessels to study contractions in response to the σ-receptor agonist afobazole in the absence and presence of different σ-receptor antagonists. We used RT-PCR and Western blot analysis to investigate whether these vessels express the σ1-receptor and immunofluorescence confocal microscopy to examine localization of the σ1-receptor in the collecting lymphatic wall. Using N-nitro-l-arginine methyl ester (l-NAME) pretreatment before afobazole in isolated lymphatics, we tested the role of nitric oxide (NO) signaling. Finally, we used 4-amino-5-methylamino-2',7'-difluorofluorescein diacetate fluorescence as an indicator to test whether afobazole increases NO release in cultured lymphatic endothelial cells. Our results show that afobazole (50-150 µM) elevated end-systolic diameter and generally reduced pump efficiency and that this response could be partially blocked by the σ1-receptor antagonists BD 1047 and BD 1063 but not by the σ2-receptor antagonist SM-21. σ1-Receptor mRNA and protein were detected in lysates from isolated rat mesenteric collecting lymphatics. Confocal images with anti-σ1-receptor antibody labeling suggested localization in the lymphatic endothelium. Blockade of NO synthases with l-NAME inhibited the effects of afobazole. Finally, afobazole elicited increases in NO production from cultured lymphatic endothelial cells. Our findings suggest that the σ1-receptor limits collecting lymphatic pumping through a NO-dependent mechanism.NEW & NOTEWORTHY Relatively little is known about the mechanisms that govern contractions of lymphatic vessels. σ1-Receptor activation has been shown to reduce the fractional pump flow of isolated rat mesenteric collecting lymphatics. The σ1-receptor was localized mainly in the endothelium, and blockade of nitric oxide synthase inhibited the effects of afobazole.

Demonstration and Analysis of the Suction Effect for Pumping Lymph from Tissue Beds at Subatmospheric Pressure

Many tissues exhibit subatmospheric interstitial pressures under normal physiologic conditions. The mechanisms by which the lymphatic system extracts fluid from these tissues against the overall pressure gradient are unknown. We address this important physiologic issue by combining experimental measurements of contractile function and pressure generation with a previously validated mathematical model. We provide definitive evidence for the existence of 'suction pressure' in collecting lymphatic vessels, which manifests as a transient drop in pressure downstream of the inlet valve following contraction. This suction opens the inlet valve and is required for filling in the presence of low upstream pressure. Positive transmural pressure is required for this suction, providing the energy required to reopen the vessel. Alternatively, external vessel tethering can serve the same purpose when the transmural pressure is negative. Suction is transmitted upstream, allowing fluid to be drawn in through initial lymphatics. Because suction plays a major role in fluid entry to the lymphatics and is affected by interstitial pressure, our results introduce the phenomenon as another important factor to consider in the study of lymphoedema and its treatment.

The relationship between lymphangion chain length and maximum pressure generation established through in vivo imaging and computational modeling

The intrinsic contraction of collecting lymphatic vessels serves as a pumping system to propel lymph against hydrostatic pressure gradients as it returns interstitial fluid to the venous circulation. In the present study, we proposed and validated that the maximum opposing outflow pressure along a chain of lymphangions at which flow can be achieved increases with the length of chain. Using minimally invasive near-infrared imaging to measure the effective pumping pressure at various locations in the rat tail, we demonstrated increases in pumping pressure along the length of the tail. Computational simulations based on a microstructurally motivated model of a chain of lymphangions informed from biaxial testing of isolated vessels was used to provide insights into the pumping mechanisms responsible for the pressure increases observed in vivo. These models suggest that the number of lymphangions in the chain and smooth muscle cell force generation play a significant role in determining the maximum outflow pressure, whereas the frequency of contraction has no effect. In vivo administration of nitric oxide attenuated lymphatic contraction, subsequently lowering the effective pumping pressure. Computational simulations suggest that the reduction in contractile strength of smooth muscle cells in the presence of nitric oxide can account for the reductions in outflow pressure observed along the lymphangion chain in vivo. Thus, combining modeling with multiple measurements of lymphatic pumping pressure provides a method for approximating intrinsic lymphatic muscle activity noninvasively in vivo while also providing insights into factors that determine the extent that a lymphangion chain can transport fluid against an adverse pressure gradient. NEW & NOTEWORTHY Here, we report the first minimally invasive in vivo measurements of the relationship between lymphangion chain length and lymphatic pumping pressure. We also provide the first in vivo validation of lumped parameter models of lymphangion chains previously developed through data obtained from isolated vessel testing.

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).

The advection of microparticles, MCF-7 and MDA-MB-231 breast cancer cells in response to very low Reynolds numbers

The lymphatic system is an extensive vascular network that serves as the primary route for the metastatic spread of breast cancer cells (BCCs). The dynamics by which BCCs travel in the lymphatics to distant sites, and eventually establish metastatic tumors, remain poorly understood. Particle tracking techniques were employed to analyze the behavior of MCF-7 and MDA-MB-231 BCCs which were exposed to lymphatic flow conditions in a 100 μm square microchannel. The behavior of the BCCs was compared to rigid particles of various diameters (η = d_p/H= 0.05-0.32) that have been used to simulate cell flow in lymph. Parabolic velocity profiles were recorded for all particle sizes. All particles were found to lag the fluid velocity, the larger the particle the slower its velocity relative to the local flow (5%-15% velocity lag recorded). A distinct difference between the behavior of BCCs and particles was recorded. The BCCs travelled approximately 40% slower than the undisturbed flow, indicating that morphology and size affects their response to lymphatic flow conditions (Re < 1). BCCs adhered together, forming aggregates whose behavior was irregular. At lymphatic flow rates, MCF-7s were distributed uniformly across the channel in comparison to the MDA-MB-231 cells which travelled in the central region (88% of cells found within 0.35 ≤ W ≤ 0.64), indicating that metastatic MDA-MB-231 cells are subjected to a lower range of shear stresses in vivo. This suggests that both size and deformability need to be considered when modelling BCC behavior in the lymphatics. This finding will inform the development of in vitro lymphatic flow and metastasis models.

Synchronization and Random Triggering of Lymphatic Vessel Contractions

The lymphatic system is responsible for transporting interstitial fluid back to the bloodstream, but unlike the cardiovascular system, lacks a centralized pump-the heart–to drive flow. Instead, each collecting lymphatic vessel can individually contract and dilate producing unidirectional flow enforced by intraluminal check valves. Due to the large number and spatial distribution of such pumps, high-level coordination would be unwieldy. This leads to the question of how each segment of lymphatic vessel responds to local signals that can contribute to the coordination of pumping on a network basis. Beginning with elementary fluid mechanics and known cellular behaviors, we show that two complementary oscillators emerge from i) mechanical stretch with calcium ion transport and ii) fluid shear stress induced nitric oxide production (NO). Using numerical simulation and linear stability analysis we show that the newly identified shear-NO oscillator shares similarities with the well-known Van der Pol oscillator, but has unique characteristics. Depending on the operating conditions, the shear-NO process may i) be inherently stable, ii) oscillate spontaneously in response to random disturbances or iii) synchronize with weak periodic stimuli. When the complementary shear-driven and stretch-driven oscillators interact, either may dominate, producing a rich family of behaviors similar to those observed in vivo.

For decades, cardiovascular physiology has been an area of intense research, and we have a fundamental understanding of the mechanisms the heart uses to drive blood flow through the distributed network of vessels in the body. The lymphatic system is now receiving similar attention as more is learned about its functional role in disease processes. The importance of the lymphatic system in collecting excess fluid from tissues and returning it to the blood is well known, but how the lymph flow is regulated without a central pump is poorly understood. Each segment of collecting lymphatic vessel can independently contract yielding a network of distributed pump/conduits. This paper shows how the lymphatic muscle cells that squeeze fluid along the lymphatic vessels can be effectively regulated using only chemical and mechanical signals that they receive from their immediate microenvironment. Using stability theory and the tools of nonlinear dynamics we identify two complementary oscillators that respond to stretch of the vessel wall and shear of fluid flowing over the vessel wall. Numerical simulations of the combined oscillators show that they have characteristics well suited to the regulation of distributed systems in general and may have application in other biological and physical contexts.

Lymphatic pumping: mechanics, mechanisms and malfunction

A combination of extrinsic (passive) and intrinsic (active) forces move lymph against a hydrostatic pressure gradient in most regions of the body. The effectiveness of the lymph pump system impacts not only interstitial fluid balance but other aspects of overall homeostasis. This review focuses on the mechanisms that regulate the intrinsic, active contractions of collecting lymphatic vessels in relation to their ability to actively transport lymph. Lymph propulsion requires not only robust contractions of lymphatic muscle cells, but contraction waves that are synchronized over the length of a lymphangion as well as properly functioning intraluminal valves. Normal lymphatic pump function is determined by the intrinsic properties of lymphatic muscle and the regulation of pumping by lymphatic preload, afterload, spontaneous contraction rate, contractility and neural influences. Lymphatic contractile dysfunction, barrier dysfunction and valve defects are common themes among pathologies that directly involve the lymphatic system, such as inherited and acquired forms of lymphoedema, and pathologies that indirectly involve the lymphatic system, such as inflammation, obesity and metabolic syndrome, and inflammatory bowel disease.