The effects of valve leaflet mechanics on lymphatic pumping assessed using numerical simulations

A quasilinear hyperbolic one-dimensional model of the lymph flow through a lymphangion with valve dynamics and a contractile wall

This paper presents a one-dimensional model that describes fluid flow in lymphangions, the segments of lymphatic vessels between valves, using quasilinear hyperbolic systems. The model incorporates a phenomenological pressure-cross-sectional area relationship based on existing literature. Numerical solutions of the differential equations align with known results, offering insights into lymphatic flow dynamics. This model enhances the understanding of lymph movement through the lymphatic system, driven by lymphangion contractions.

Numerical investigation on flow-induced wall shear stress variation of metastatic cancer cells in lymphatics with elastic valves

Hematogenous metastasis occurs when cancer cells detach from the extracellular matrix in the primary tumor into the bloodstream or lymphatic system. Elucidating the response of metastatic tumor cells in suspension to the flow conditions in lymphatics with valves from a mechanical/fluidic perspective is necessary. A physiologically relevant computational model of a lymphatic vessel with valves was constructed using fully coupled fluid-cell-vessel interactions to investigate the effects of lymphatic vessel contractility, valve properties, and cell size and stiffness on the variations in magnitude and gradient of the flow-induced wall shear stress (WSS) experienced by suspended tumor cells. Results indicated that the maximum WSSmax increased with the increments in cell diameter, vessel contraction amplitude, and valve stiffness. The decrease in vessel contraction period and valve aspect ratio also increased the maximum WSSmax. The influence of the properties of the valve on the WSS was more significant among the factors mentioned above. The maximum WSSmax acting on the cancer cell when the cell reversed the direction of its motion in the valve region increased by 0.5-1.4 times that before the cell entered the valve region. The maximum change in WSS was in the range of 0.004-0.028 Pa/µm depending on the factors studied. They slightly exceeded the values associated with breast cancer cell apoptosis. The results of this study provide biofluid mechanics-based support for mechanobiological research on the metastasis of metastatic cancer cells in suspension within the lymphatics.

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.

Lymphatic Imaging and Intervention in Congenital Heart Disease

The lymphatic system plays a central role in some of the most devastating complications associated with congenital heart defects. Diseases like protein-losing enteropathy, plastic bronchitis, postoperative chylothorax, and chylous ascites are now proven to be lymphatic in origin. Novel imaging modalities, most notably, noncontrast magnetic resonance lymphangiography and dynamic contrast-enhanced magnetic resonance lymphangiography, can now depict lymphatic anatomy and function in all major lymphatic compartments and are essential for modern therapy planning. Based on the new pathophysiologic understanding of lymphatic flow disorders, innovative minimally invasive procedures have been invented during the last few years with promising results. Abnormal lymphatic flow can now be redirected with catheter-based interventions like thoracic duct embolization, selective lymphatic duct embolization, and liver lymphatic embolization. Lymphatic drainage can be improved through surgical or interventional techniques such as thoracic duct decompression or lympho-venous anastomosis.

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.

An Enhanced 3D Model of Intravascular Lymphatic Valves to Assess Leaflet Apposition and Transvalvular Differences in Wall Distensibility

Lymphatic valves operate in a fluid-dynamically viscous environment that has little in common with that of cardiac valves, and accordingly have a different, axially lengthened, shape. A previously developed 3D fluid/structure interaction model of a lymphatic valve was extended to allow the simulation of stages of valve closure after the leaflets come together. This required that the numerical leaflet be prevented from passing into space occupied by the similar other leaflet. The resulting large deflections of the leaflet and lesser deflections of the rest of the valve were mapped as functions of the transvalvular pressure. In a second new development, the model was reconstructed to allow the vessel wall to have different material properties on either side of where the valve leaflet inserts into the wall. As part of this, a new pre-processing scheme was devised which allows easier construction of models with modified valve dimensions, and techniques for successfully interfacing the CAD software to the FE software are described. A two-fold change in wall properties either side of the leaflet made relatively little difference to valve operation apart from affecting the degree of sinus distension during valve closure. However, the numerically permitted strains were modest (<14%), and did not allow examination of the large-scale highly nonlinear elastic properties exhibited by real lymphatic vessels. A small series of murine popliteal, mesenteric, and inguinal-axillary lymphatic vessel segments containing a valve were experimentally investigated ex vivo. The pressure–diameter curves measured just upstream and just downstream of the valve were parameterised by computing the difference in tubular distensibility at three values of transmural pressure. In the popliteal and mesenteric segments, it was found that the distensibility was usually greater just downstream, i.e., in the sinus region, than upstream, at low and intermediate transmural pressure. However, there was wide variation in the extent of difference, and possible reasons for this are discussed.

The effects of gravity and compression on interstitial fluid transport in the lower limb

Edema in the limbs can arise from pathologies such as elevated capillary pressures due to failure of venous valves, elevated capillary permeability from local inflammation, and insufficient fluid clearance by the lymphatic system. The most common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy. To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of a lower limb that includes the effects of gravity. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due to lymphatic clearance, and movement through the interstitial space due to both gravity and gradients in interstitial fluid pressure (IFP). From dimensional analysis and numerical solutions of the governing equations we have identified several parameter groups that determine the essential length and time scales involved. We find that gravity can have dramatic effects on the fluid balance in the limb with the possibility that a positive feedback loop can develop that facilitates chronic edema. This process involves localized tissue swelling which increases the hydraulic conductivity, thus allowing the movement of interstitial fluid vertically throughout the limb due to gravity and causing further swelling. The presence of a compression wrap can interrupt this feedback loop. We find that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema development and treatment in a gravity dependent limb.

Lymphotonic activity of Ruscus extract, hesperidin methyl chalcone and vitamin C in human lymphatic smooth muscle cells

OBJECTIVE

Besides actions including their venotonic, anti-inflammatory, and anti-oxidant effects, venoactive drugs are expected to act on edema via their action on lymphatics. The objective of this study was to evaluate the effect of the combination of Ruscus, hesperidin methyl chalcone and Vitamin C (Ruscus/HMC/Vit C) on intracellular calcium mobilization and contraction of human lymphatic smooth muscle cells (LSMCs) to better characterize the mechanism of its lymphotonic activity.

METHODS

Calcium mobilization was evidenced by videomicroscopy analysis of the fluorescence emitted by a specific Ca²⁺ sensitive dye and measured after injection of Ruscus/HMC/Vit C at 0.1, 0.3, 1.0, and 3.0 mg/mL into LSMCs.

RESULTS

Ruscus/HMC/Vit C induced a strong and reproducible concentration-dependent calcium mobilization in LSMCs. On the contrary, another venoactive drug used as comparator, micronized purified flavonoid fraction (MPFF), did not induce calcium mobilization whatever the tested concentration.

CONCLUSION

Although alternative mechanisms of action may result in potential lymphotonic effects, the efficacy of lymphotonic products is nonetheless related to their stimulating effect on the contractile activity of the smooth muscle cells surrounding lymphatic vessels. In the light of the results obtained in this study, the direct effect of Ruscus/HMC/Vit C on LSMC contraction may partially explain its clinical efficacy on lymphotonic activity, as has been observed in terms of objective signs of edema as reported in the recent guidelines on chronic venous disease.

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.

Microfluidic valvular chips and a numerical lymphatic vessel model for the study of lymph transport characteristics

Lymph transport inside lymphatic vessels is highly complex and not yet fully understood. So far, a consensus has not been reached among existing analytical models on how spatiotemporal coordination of contracting adjacent lymphangions affects lymph transport. To understand complex lymph transport, we created a novel microfluidic valvular chip with flexible bicuspid valves and segmental pneumatic pumps based on a microfluidic device with an inside 3D structure made of hydrogels. Inside the chip, water moved unidirectionally when the microfluidic channel was locally compressed, with its velocity profile closely resembling the waveform of lymph observed in vivo. Furthermore, for a systematic and mechanistic study, we constructed a numerical model based on fluid-structure interaction and validated the model via demonstration of similarities in water transport characteristics between the model and the chip. Using this model, we examined various mechanical and time-dependent parameters, such as period, phase delay, sequence, and strength of contractions, valve compliance, fluid viscosity, and pressure differences, for their effects on water transport. Although our model is simplified, it enabled a parametric study that helped clarify the mechano-temporal correlations between compressions of adjacent chambers via transmissions of hydrodynamic forces, which regulate complex lymph transport. Moreover, our chip demonstrated technical advances that enable unidirectional discrete movement of fluid in the picoliter range by phenumatic pumping. The velocity profile is also similar to the pulse waveform of arteries under pathological conditions such as increased aortic stiffness, allowing our chip to be used for in vitro mechanobiology studies of endothelial cells.

Overcoming physiological barriers by nanoparticles for intravenous drug delivery to the lymph nodes

The lymph nodes are major sites of cancer metastasis and immune activity, and thus represent important clinical targets. Although not as well-studied compared to subcutaneous administration, intravenous drug delivery is advantageous for lymph node delivery as it is commonly practiced in the clinic and has the potential to deliver therapeutics systemically to all lymph nodes. However, rapid clearance by the mononuclear phagocyte system, tight junctions of the blood vascular endothelium, and the collagenous matrix of the interstitium can limit the efficiency of lymph node drug delivery, which has prompted research into the design of nanoparticle-based drug delivery systems. In this mini review, we describe the physiological and biological barriers to lymph node targeting, how they inform nanoparticle design, and discuss the future outlook of lymph node targeting.

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.