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

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 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-draining nanoparticles deliver Bay K8644 payload to lymphatic vessels and enhance their pumping function

Dysfunction of collecting lymphatic vessel pumping is associated with an array of pathologies. S-(-)-Bay K8644 (BayK), a small-molecule agonist of L-type calcium channels, improves vessel contractility ex vivo but has been left unexplored in vivo because of poor lymphatic access and risk of deleterious off-target effects. When formulated within lymph-draining nanoparticles (NPs), BayK acutely improved lymphatic vessel function, effects not seen from treatment with BayK in its free form. By preventing rapid drug access to the circulation, NP formulation also reduced BayK's dose-limiting side effects. When applied to a mouse model of lymphedema, treatment with BayK formulated in lymph-draining NPs, but not free BayK, improved pumping pressure generated by intact lymphatic vessels and tissue remodeling associated with the pathology. This work reveals the utility of a lymph-targeting NP platform to pharmacologically enhance lymphatic pumping in vivo and highlights a promising approach to treating lymphatic dysfunction.

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.

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.

Imaging technology of the lymphatic system

The lymphatic system plays critical roles in tissue fluid homeostasis and immunity and has been implicated in the development of many different pathologies, ranging from lymphedema, the spread of cancer to chronic inflammation. In this review, we first summarize the state-of-the-art of lymphatic imaging in the clinic and the advantages and disadvantages of these existing techniques. We then detail recent progress on imaging technology, including advancements in tracer design and injection methods, that have allowed visualization of lymphatic vessels with excellent spatial and temporal resolution in preclinical models. Finally, we describe the different approaches to quantifying lymphatic function that are being developed and discuss some emerging topics for lymphatic imaging in the clinic. Continued advancements in lymphatic imaging technology will be critical for the optimization of diagnostic methods for lymphatic disorders and the evaluation of novel therapies targeting the lymphatic system.

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.

Axial stretch regulates rat tail collecting lymphatic vessel contractions

Lymphatic contractions play a fundamental role in maintaining tissue and organ homeostasis. The lymphatic system relies on orchestrated contraction of collecting lymphatic vessels, via lymphatic muscle cells and one-way valves, to transport lymph from the interstitial space back to the great veins, against an adverse pressure gradient. Circumferential stretch is known to regulate contractile function in collecting lymphatic vessels; however, less is known about the role of axial stretch in regulating contraction. It is likely that collecting lymphatic vessels are under axial strain in vivo and that the opening and closing of lymphatic valves leads to significant changes in axial strain throughout the pumping cycle. The purpose of this paper is to quantify the responsiveness of lympatic pumping to altered axial stretch. In situ measurements suggest that rat tail collecting lymphatic vessels are under an axial stretch of ~1.24 under normal physiological loads. Ex vivo experiments on isolated rat tail collecting lymphatics showed that the contractile metrics such as contractile amplitude, frequency, ejection fraction, and fractional pump flow are sensitive to axial stretch. Multiphoton microscopy showed that the predominant orientation of collagen fibers is in the axial direction, while lymphatic muscle cell nuclei and actin fibers are oriented in both circumferential and longitudinal directions, suggesting an axial component to contraction. Taken together, these results demonstrate the significance of axial stretch in lymphatic contractile function, suggest that axial stretch may play an important role in regulating lymph transport, and demonstrate that changes in axial strains could be an important factor in disease progression.

Lymphatic remodelling in response to lymphatic injury in the hind limbs of sheep

Contractile activity in the lymphatic vasculature is essential for maintaining fluid balance within organs and tissues. However, the mechanisms by which collecting lymphatics adapt to changes in fluid load and how these adaptations influence lymphatic contractile activity are unknown. Here we report a model of lymphatic injury based on the ligation of one of two parallel lymphatic vessels in the hind limb of sheep and the evaluation of structural and functional changes in the intact, remodelling lymphatic vessel over a 42-day period. We show that the remodelled lymphatic vessel displayed increasing intrinsic contractile frequency, force generation and vessel compliance, as well as decreasing flow-mediated contractile inhibition via the enzyme endothelial nitric oxide synthase. A computational model of a chain of lymphatic contractile segments incorporating these adaptations predicted increases in the flow-generation capacity of the remodelled vessel at the expense of normal mitochondrial function and elevated oxidative stress within the lymphatic muscle. Our findings may inform interventions for mitigating lymphatic muscle fatigue in patients with dysfunctional lymphatics.

A novel mouse tail lymphedema model for observing lymphatic pump failure during lymphedema development

It has been suggested that many forms of secondary lymphedema in humans are driven by a progressive loss of lymphatic pump function after an initial risk-inducing event. However, the link between pump failure and disease progression has remained elusive due to experimental challenges in the clinical setting and a lack of adequate animal models. Using a novel surgical model of lymphatic injury, we track the adaptation and functional decline of the lymphatic network in response to surgery. This model mimics the histological hallmarks of the typical mouse tail lymphedema model while leaving an intact collecting vessel for analysis of functional changes during disease progression. Lymphatic function in the intact collecting vessel negatively correlated with swelling, while a loss of pumping pressure generation remained even after resolution of swelling. By using this model to study the role of obesity in lymphedema development, we show that obesity exacerbates acquired lymphatic pump failure following lymphatic injury, suggesting one mechanism through which obesity may worsen lymphedema. This lymphatic injury model will allow for future studies investigating the molecular mechanisms leading to lymphedema development.

Endothelin-1 inhibits size dependent lymphatic clearance of PEG-based conjugates after intra-articular injection into the rat knee

Clearance of particles from the knee is an essential mechanism to maintain healthy joint homeostasis and critical to the delivery of drugs and therapeutics. One of the limitations in developing disease modifying drugs for joint diseases, such as osteoarthritis (OA), has been poor local retention of the drugs. Enhancing drug retention within the joint has been a target of biomaterial development, however, a fundamental understanding of joint clearance pathways has not been characterized. We applied near-infrared (NIR) imaging techniques to assess size-dependent in vivo clearance mechanisms of intra-articular injected, fluorescently-labelled polyethylene glycol (PEG-NIR) conjugates. The clearance of 2 kDa PEG-NIR (τ = 171 ± 11 min) was faster than 40 kDa PEG-NIR (τ = 243 ± 16 min). 40 kDa PEG-NIR signal was found in lumbar lymph node while 2 kDa PEG-NIR signal was not. Thus, these two conjugates may be cleared through different pathways, i.e. lymphatics for 40 kDa PEG-NIR and venous for 2 kDa PEG-NIR. Endothelin-1 (ET-1), a potent vasoconstrictor of vessels, is elevated in synovial fluid of OA patients but, its effects on joint clearance are unknown. Intra-articular injection of ET-1 dose-dependently inhibited the clearance of both 2 kDa and 40 kDa PEG-NIR. ET-1 caused a 1.63 ± 0.17-fold increase in peak fluorescence for 2 kDa PEG-NIR and a 1.85 ± 0.15-fold increase for 40 kDa PEG-NIR; and ET-1 doubled their clearance time constants. The effects of ET-1 were blocked by co-injection of ET receptor antagonists, bosentan or BQ-123. These findings provide fundamental insight into retention and clearance mechanisms that should be considered in the development and delivery of drugs and biomaterial carriers for joint diseases. STATEMENT OF SIGNIFICANCE: This study demonstrates that in vivo knee clearance can be measured using NIR technology and that key factors, such as size of materials and biologics, can be investigated to define joint clearance mechanisms. Therapies targeting regulation of joint clearance may be an approach to treat joint diseases like osteoarthritis. Additionally, in vivo functional assessment of clearance may be used as diagnostics to monitor progression of joint diseases.

Lymphatic Vessel Network Structure and Physiology

The lymphatic system is comprised of a network of vessels interrelated with lymphoid tissue, which has the holistic function to maintain the local physiologic environment for every cell in all tissues of the body. The lymphatic system maintains extracellular fluid homeostasis favorable for optimal tissue function, removing substances that arise due to metabolism or cell death, and optimizing immunity against bacteria, viruses, parasites, and other antigens. This article provides a comprehensive review of important findings over the past century along with recent advances in the understanding of the anatomy and physiology of lymphatic vessels, including tissue/organ specificity, development, mechanisms of lymph formation and transport, lymphangiogenesis, and the roles of lymphatics in disease. © 2019 American Physiological Society. Compr Physiol 9:207-299, 2019.