Determining the combined effect of the lymphatic valve leaflets and sinus on resistance to forward flow

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.

A human initial lymphatic chip reveals distinct mechanisms of primary lymphatic valve dysfunction in acute and chronic inflammation

Interstitial fluid uptake and retention by lymphatic vessels (LVs) play a role in maintaining interstitial fluid homeostasis. While it is well-established that intraluminal lymphatic valves in the collecting LVs prevent fluid backflow (secondary lymphatic valves), a separate valve system in the initial LVs that only permits interstitial fluid influx into the LVs, preventing fluid leakage back to the interstitium (primary lymphatic valves), remains incompletely understood. Although lymphatic dysfunction is commonly observed in inflammation and autoimmune diseases, how the primary lymphatic valves are affected by acute and chronic inflammation has scarcely been explored and even less so using in vitro lymphatic models. Here, we developed a human initial lymphatic vessel chip where interstitial fluid pressure and luminal fluid pressure are controlled to examine primary lymph valve function. In normal conditions, lymphatic drainage (fluid uptake) and permeability (fluid leakage) in engineered LVs were maintained high and low, respectively, which was consistent with our understanding of healthy primary lymph valves. Next, we examined the effects of acute and chronic inflammation. Under the acute inflammation condition with a TNF-α treatment (2 hours), degradation of fibrillin and impeded lymphatic drainage were observed, which were reversed by treatment with anti-inflammatory dexamethasone. Surprisingly, the chronic inflammation condition (repeated TNF-α treatments during 48 hours) deposited fibrillin to compensate for the fibrillin loss, showing no change in lymphatic drainage. Instead, the chronic inflammation condition led to cell death and disruption of lymphatic endothelial cell-cell junctions, increasing lymphatic permeability and fluid leakage. Our human lymphatic model shows two distinct mechanisms by which primary lymphatic valve dysfunction occurs in acute and chronic inflammation.

Effect of valve spacing on peristaltic pumping

Peristaltic fluid pumping due to a periodically propagating contraction wave in a vessel fitted with one-way elastic valves is investigated numerically. It is concluded that the valve spacing within the vessel relative to the contraction wavelength plays a critical role in providing efficient pumping. When the valve spacing does not match the wavelength, the valves open asynchronously and the volume of the vessel segments bounded by two consecutive valves changes periodically, thereby inducing volumetric fluid pumping. The volumetric pumping leads to higher pumping flowrate and efficiency against an adverse pressure gradient. The optimum pumping occurs when the ratio of valve spacing to contraction wavelength is about2/3. This pumping regime is characterized by a longer period during which the valves are open. The results are useful for further understanding the pumping features of lymphatic system and provide insight into the design of biomimetic pumping devices.

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.

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.

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.

The mechanical responses of advecting cells in confined flow

Fluid dynamics have long influenced cells in suspension. Red blood cells and white blood cells are advected through biological microchannels in both the cardiovascular and lymphatic systems and, as a result, are subject to a wide variety of complex fluidic forces as they pass through. In vivo, microfluidic forces influence different biological processes such as the spreading of infection, cancer metastasis, and cell viability, highlighting the importance of fluid dynamics in the blood and lymphatic vessels. This suggests that in vitro devices carrying cell suspensions may influence the viability and functionality of cells. Lab-on-a-chip, flow cytometry, and cell therapies involve cell suspensions flowing through microchannels of approximately 100-800  μ m. This review begins by examining the current fundamental theories and techniques behind the fluidic forces and inertial focusing acting on cells in suspension, before exploring studies that have investigated how these fluidic forces affect the reactions of suspended cells. In light of these studies' findings, both in vivo and in vitro fluidic cell microenvironments shall also be discussed before concluding with recommendations for the field.

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.

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

The lymphatic system contains intraluminal leaflet valves that function to bias lymph flow back towards the heart. These valves are present in the collecting lymphatic vessels, which generally have lymphatic muscle cells and can spontaneously pump fluid. Recent studies have shown that the valves are open at rest, can allow some backflow, and are a source of nitric oxide (NO). To investigate how these valves function as a mechanical valve and source of vasoactive species to optimize throughput, we developed a mathematical model that explicitly includes Ca²⁺ -modulated contractions, NO production and valve structures. The 2D lattice Boltzmann model includes an initial lymphatic vessel and a collecting lymphangion embedded in a porous tissue. The lymphangion segment has mechanically-active vessel walls and is flanked by deformable valves. Vessel wall motion is passively affected by fluid pressure, while active contractions are driven by intracellular Ca²⁺ fluxes. The model reproduces NO and Ca²⁺ dynamics, valve motion and fluid drainage from tissue. We find that valve structural properties have dramatic effects on performance, and that valves with a stiffer base and flexible tips produce more stable cycling. In agreement with experimental observations, the valves are a major source of NO. Once initiated, the contractions are spontaneous and self-sustained, and the system exhibits interesting non-linear dynamics. For example, increased fluid pressure in the tissue or decreased lymph pressure at the outlet of the system produces high shear stress and high levels of NO, which inhibits contractions. On the other hand, a high outlet pressure opposes the flow, increasing the luminal pressure and the radius of the vessel, which results in strong contractions in response to mechanical stretch of the wall. We also find that the location of contraction initiation is affected by the extent of backflow through the valves.

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.

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.

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.

Integrated geometric and mechanical analysis of an image-based lymphatic valve

Lymphatic valves facilitate the lymphatic system's role in maintaining fluid homeostasis. Malformed valves are found in several forms of primary lymphœdema, resulting in incurable swelling of the tissues and immune dysfunction. Their experimental study is complicated by their small size and operation in low pressure and low Reynolds number environments. Mathematical models of these structures can give insight and complement experimentation. In this work, we present the first valve geometry reconstructed from confocal imagery and used in the construction of a subject-specific model in a closing mode. A framework is proposed whereby an image is converted into a valve model. An FEA study was performed to identify the significance of the shear modulus, the consequences of smoothing the leaflet surface and the effect of wall motion on valve behaviour. Smoothing is inherent to any analysis from imagery. The nature of the image, segmentation and meshing all cause attenuation of high-frequency features. Smoothing not only causes loss of surface area but also the loss of high-frequency geometric features which may reduce stiffness. This work aimed to consider these effects and inform studies by taking a manual reconstruction and through manifold harmonic analysis, attenuating higher frequency features to replicate lower resolution images or lower degree-of-freedom reconstructions. In conclusion, two metrics were considered: trans-valvular pressure required to close the valve, ΔP_c, and the retrograde volume displacement after closure. The higher ΔP_c, the greater the volume of lymph that will pass through the valve during closure. Retrograde volume displacement after closure gives a metric of compliance of the valve and for the quality of the valve seal. In the case of the image-specific reconstructed valve, removing features with a wavelength longer than four μm caused changes in ΔP_c. Varying the shear modulus from 10 kPa to 60 kPa caused a 3.85-fold increase in the retrograde volume displaced. The inclusion of a non-rigid wall caused ΔP_c to increase from 1.56 to 2.52 cmH₂O.

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).

Towards the prediction of flow-induced shear stress distributions experienced by breast cancer cells in the lymphatics

Tumour metastasis in the lymphatics is a crucial step in the progression of breast cancer. The dynamics by which breast cancer cells (BCCs) travel in the lymphatics remains poorly understood. The goal of this work is to develop a model capable of predicting the shear stresses metastasising BCCs experience using numerical and experimental techniques. This paper models the fluidic transport of large particles ([Formula: see text] where [Formula: see text] is the particle diameter and W is the channel width) subjected to lymphatic flow conditions ([Formula: see text]), in a [Formula: see text] microchannel. The feasibility of using the dynamic fluid body interaction (DFBI) method to predict particle motion was assessed, and particle tracking experiments were performed. The experiments found that particle translational velocity decreased from the undisturbed fluid velocity with increasing particle size (5-14% velocity lag for [Formula: see text]). DFBI simulations were found to better predict particle behaviour than theoretical predictions; however, mesh restrictions in the near-wall region ([Formula: see text]) result in computationally expensive models. The simulations were in good agreement with the experiments ([Formula: see text] difference) across the channel ([Formula: see text]), with differences up to 25% in the near-wall region. Particles experience a range of shear stresses (0.002-0.12 Pa) and spatial shear gradients ([Formula: see text]) depending on their size and radial position. The predicted shear gradients are far in excess of values associated with BCC apoptosis ([Formula: see text]). Increasing our understanding of the shear stress magnitudes and gradients experienced by BCCs could be leveraged to elucidate whether a particular BCC size or location exists that encourages metastasis within the lymphatics.

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.

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.

Microparticle image velocimetry approach to flow measurements in isolated contracting lymphatic vessels

We describe the development of an optical flow visualization method for resolving the flow velocity vector field in lymphatic vessels in vitro. The aim is to develop an experimental protocol for accurately estimating flow parameters, such as flow rate and shear stresses, with high spatial and temporal resolution. Previous studies in situ have relied on lymphocytes as tracers, but their low density resulted in a reduced spatial resolution whereas the assumption that the flow was fully developed in order to determine the flow parameters of interest may not be valid, especially in the vicinity of the valves, where the flow is undoubtedly more complex. To overcome these issues, we have applied the time-resolved microparticle image velocimetry (μ -PIV) technique, a well-established method that can provide increased spatial and temporal resolution that this transient flow demands. To that end, we have developed a custom light source, utilizing high-power light-emitting diodes, and associated control and image processing software. This paper reports the performance of the system and the results of a series of preliminary experiments performed on vessels isolated from rat mesenteries, demonstrating, for the first time, the successful application of the μ -PIV technique in these vessels.