Mechanics of interstitial-lymphatic fluid transport: theoretical foundation and experimental validation

Interstitial fluid movement is intrinsically linked to lymphatic drainage. However, their relationship is poorly understood, and associated pathologies are mostly untreatable. In this work we test the hypothesis that bulk tissue fluid movement can be evaluated in situ and described by a linear biphasic theory which integrates the regulatory function of the lymphatics with the mechanical stresses of the tissue. To accomplish this, we develop a novel experimental and theoretical model using the skin of the mouse tail. We then use the model to demonstrate how interstitial–lymphatic fluid movement depends on a balance between the elasticity, hydraulic conductivity, and lymphatic conductance as well as to demonstrate how chronic swelling (edema) alters the equipoise between tissue fluid balance parameters. Specifically, tissue fluid equilibrium is perturbed with a continuous interstitial infusion of saline into the tip of the tail. The resulting gradients in tissue stress are measured in terms of interstitial fluid pressure using a servo-null system. These measurements are then fit to the theory to provide in vivo estimates of the tissue hydraulic conductivity, elastic modulus, and overall resistance to lymphatic drainage. Additional experiments are performed on edematous tails to show that although chronic swelling causes an increase in the hydraulic conductivity, its greatly increased distensibility (due to matrix remodeling) dampens the driving forces for fluid movement and leads to fluid stagnation. This model is useful for examining potential treatments for edema and lymphatic disorders as well as substances which may alter tissue fluid balance and/or lymphatic drainage.     

Multiscale modeling of angiogenic tumor growth,progression, and therapy

Biophysics - A mathematical model of angiogenic tumor growth in tissue with account of bevacizumab therapy was developed. The model accounts for convective flows that occur in dense tissue under...     

Lymphangiogenesis in post-natal tissue remodeling: lymphatic endothelial cell connection with its environment

The main physiological function of the lymphatic vasculature is to maintain tissue fluid homeostasis. Lymphangiogenesis or de novo lymphatic formation is closely associated with tissue inflammation in adults (i.e. wound healing, allograft rejection, tumor metastasis). Until recently, research on lymphangiogenesis focused mainly on growth factor/growth factor-receptor pathways governing this process. One of the lymphatic vessel features is the incomplete or absence of basement membrane. This close association of endothelial cells with the underlying interstitial matrix suggests that cell–matrix interactions play an important role in lymphangiogenesis and lymphatic functions. However, the exploration of interaction between extracellular matrix (ECM) components and lymphatic endothelial cells is in its infancy. Herein, we describe ECM–cell and cell–cell interactions on lymphatic system function and their modification occurring in pathologies including cancer metastasis.     

Vascular endothelial growth factor inhibition: Conflicting roles in tumor growth

Angiogenesis, the physiological process of sprouting of new blood vessels from pre-existing ones, is a key biological feature of almost all cancers. Among the multitude of factors driving tumor angiogenesis, vascular endothelial growth factor (VEGF) is the most potent, exerting myriad effects on vascular pruning and sprouting, permeability, network formation, proliferation, and cell death. Despite the initial unimpressive clinical performance of anti-VEGF antibody (bevacizumab) as cancer monotherapy, clear improvements in clinical outcomes following combination bevacizumab and chemotherapy regimens and multi-targeted VEGF receptor tyrosine kinase inhibitors (sorafenib and sunitinib) in select tumor types have established VEGF-targeted agents as an effective means of controlling cancer growth. Prolongation of overall survival and cure with these agents, however, remains elusive. Moreover, recent data has revealed key differences in the therapeutic and biological tumor response to antibody versus receptor kinase VEGF inhibitors and suggested, at least pre-clinically, that VEGF blockade in certain circumstances may actually promote more aggressive tumor growth. Given the diverse mechanisms and potentially opposing roles of VEGF neutralization in cancer biology, identification of novel biomarkers predictive of in vivo angiogenic responses may hold the key to optimizing therapeutic outcomes of anti-VEGF therapy in future cancer patients.     

Expression of aquaporin-4 in human supratentorial meningiomas with peritumoral brain edema and correlation of VEGF with edema formation

Peritumoral brain edema is a common complication of meningiomas. It is believed that vascular endothelial growth factor (VEGF), as an angiogenic factor, plays a vital role in edema formation. Aquaporin-4 (AQP4) is a small integral membrane protein that regulates water in the normal brain. However, the expression of AQP4 and its relationship to VEGF in edematous meningiomas are not well known. We studied tumor specimens of 59 human supratentorial meningiomas. Western blot analysis was used to detect the expression of AQP4, and double-labeling immunofluorescence histochemical staining was performed to determine the relationship between AQP4 and VEGF. The AQP4 expression was significantly higher in the edema group, in which the protein level was correlated with the extent of edema. Greater VEGF expression was also observed in the edema group, and a relationship between AQP4 and VEGF was found. We conclude that AQP4 is involved in peritumoral brain edema formation in meningiomas and is also closely related to the expression of VEGF.     

Genesis and pathogenesis of lymphatic vessels

The lymphatic system is generally regarded as supplementary to the blood vascular system, in that it transports interstitial fluid, macromolecules, and immune cells back into the blood. However, in insects, the open hemolymphatic (or lymphohematic) system ensures the circulation of immune cells and interstitial fluid through the body. The Drosophila homolog of the mammalian vascular endothelial growth factor receptor (VEGFR) gene family is expressed in hemocytes, suggesting a close relationship to the endothelium that develops later in phylogeny. Lymph hearts are typical organs for the propulsion of lymph in lower vertebrates and are still transiently present in birds. The lymphatic endothelial marker VEGFR-3 is transiently expressed in embryonic blood vessels and is crucial for their development. We therefore regard the question of whether the blood vascular system or the lymphatic system is primary or secondary as open. Future molecular comparisons should be performed without any bias based on the current prevalence of the blood vascular system over the lymphatic system. Here, we give an overview of the structure, function, and development of the lymphatics, with special emphasis on the recently discovered lymphangiogenic growth factors.     

Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy

Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of patients still remains less than half. Recent studies have indicated that bevacizumab, an anti-VEGF drug used in treatment of several other cancer types, may be effective for treating neuroblastoma as well. However, its effect on neuroblastoma has not been well characterized. While traditional experiments are costly and time-consuming, mathematical models are capable of simulating complex systems quickly and inexpensively. In this study, we present a model of vascular tumor growth of neuroblastoma IMR-32 that is complex enough to replicate experimental data across a range of tumor cell properties measured in a suite of in vitro and in vivo experiments. The model provides quantitative insight into tumor vasculature, predicting a linear relationship between vasculature and tumor volume. The tumor growth model was coupled with known pharmacokinetics and pharmacodynamics of the VEGF blocker bevacizumab to study its effect on neuroblastoma growth dynamics. The results of our model suggest that total administered bevacizumab concentration per week, as opposed to dosage regimen, is the major determining factor in tumor suppression. Our model also establishes an exponentially decreasing relationship between administered bevacizumab concentration and tumor growth rate.     

Visualisation and stereological assessment of blood and lymphatic vessels

The physiological processes involved in tissue development and regeneration also include the parallel formation of blood and lymphatic vessel circulations which involves their growth, maturation and remodelling. Both vascular systems are also frequently involved in the development and progression of pathological conditions in tissues and organs. The blood vascular system circulates oxygenated blood and nutrients at appropriate physiological levels for tissue survival, and efficiently removes all waste products including carbon dioxide. This continuous network consists of the heart, aorta, arteries, arterioles, capillaries, post-capillary venules, venules, veins and vena cava. This system exists in an interstitial environment together with the lymphatic vascular system, including lymph nodes, which aids maintenance of body fluid balance and immune surveillance. To understand the process of vascular development, vascular network stability, remodelling and/or regression in any research model under any experimental conditions, it is necessary to clearly and unequivocally identify and quantify all elements of the vascular network. By utilising stereological methods in combination with cellular markers for different vascular cell components, it is possible to estimate parameters such as surface density and surface area of blood vessels, length density and length of blood vessels as well as absolute vascular volume. This review examines the current strategies used to visualise blood vessels and lymphatic vessels in two- and three-dimensions and the basic principles of vascular stereology used to quantify vascular network parameters.     

Direct evidence that the VEGF-specific antibody bevacizumab has antivascular effects in human rectal cancer

The effects of vascular endothelial growth factor (VEGF) blockade on the vascular biology of human tumors are not known. Here we show here that a single infusion of the VEGF-specific antibody bevacizumab decreases tumor perfusion, vascular volume, microvascular density, interstitial fluid pressure and the number of viable, circulating endothelial and progenitor cells, and increases the fraction of vessels with pericyte coverage in rectal carcinoma patients. These data indicate that VEGF blockade has a direct and rapid antivascular effect in human tumors.     

Mechanoinduction of lymph vessel expansion

In the mammalian embryo, few mechanical signals have been identified to influence organ development and function. Here, we report that an increase in the volume of interstitial or extracellular fluid mechanically induces growth of an organ system, that is, the lymphatic vasculature. We first demonstrate that lymph vessel expansion in the developing mouse embryo correlates with a peak in interstitial fluid pressure and lymphatic endothelial cell (LEC) elongation. In 'loss-of-fluid' experiments, we then show that aspiration of interstitial fluid reduces the length of LECs, decreases tyrosine phosphorylation of vascular endothelial growth factor receptor-3 (VEGFR3), and inhibits LEC proliferation. Conversely, in 'gain-of-fluid' experiments, increasing the amount of interstitial fluid elongates the LECs, and increases both VEGFR3 phosphorylation and LEC proliferation. Finally, we provide genetic evidence that β1 integrins are required for the proliferative response of LECs to both fluid accumulation and cell stretching and, therefore, are necessary for lymphatic vessel expansion and fluid drainage. Thus, we propose a new and physiologically relevant mode of VEGFR3 activation, which is based on mechanotransduction and is essential for normal development and fluid homeostasis in a mammalian embryo.     

Vascular Endothelial Growth Factor C-Induced Lymphangiogenesis Decreases Tumor Interstitial Fluid Pressure and Tumor

Characteristically, most solid tumors exhibit an increased tumor interstitial fluid pressure (TIFP) that directly contributes to the lowered uptake of macromolecular therapeutics into the tumor interstitium. Abnormalities in the tumor-associated lymph vessels are a central brick in the development and prolonged sustaining of an increased TIFP. In the current study, vascular endothelial growth factor C (VEGF-C) was used to enhance tumor-associated lymphangiogenesis as a new mechanism to actively reduce the TIFP by increased lymphatic drainage of the tumor tissue. Human A431 epidermoid vulva carcinoma cells were inoculated in NMRI nu/nu mice to generate a xenograft mouse model. Seven days after tumor cell injection, VEGF-C was peritumorally injected to induce lymphangiogenesis. Tumor growth and TIFP was lowered significantly over time in VEGF-C-treated tumors in comparison to control or VEGF-A-treated animals. These data demonstrate for the first time that actively induced lymphangiogenesis can lower the TIFP in a xenograft tumor model and apparently reduce tumor growth. This model represents a novel approach to modulate biomechanical properties of the tumor interstitium enabling a lowering of TIFP in vivo.     

Developmental and pathological lymphangiogenesis: from models to human disease

The lymphatic vascular system, the body’s second vascular system present in vertebrates, has emerged in recent years as a crucial player in normal and pathological processes. It participates in the maintenance of normal tissue fluid balance, the immune functions of cellular and antigen trafficking and absorption of fatty acids and lipid-soluble vitamins in the gut. Recent scientific discoveries have highlighted the role of lymphatic system in a number of pathologic conditions, including lymphedema, inflammatory diseases, and tumor metastasis. Development of genetically modified animal models, identification of lymphatic endothelial specific markers and regulators coupled with technological advances such as high-resolution imaging and genome-wide approaches have been instrumental in understanding the major steps controling growth and remodeling of lymphatic vessels. This review highlights the recent insights and developments in the field of lymphatic vascular biology.     

Mathematical model of blood and interstitial flow and lymph production in the liver

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal ‘classic’ lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules’ thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the non-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5 % more than if the entire surface were covered by the Glisson–peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations.     

A model for mechanics of primary lymphatic valves

Recent experimental evidence indicates that lymphatics have two valve systems, a set of primary valves in the wall of the endothelial cells of initial lymphatics and a secondary valve system in the lumen of the lymphatics. While the intralymphatic secondary valves are well described, no analysis of the primary valves is available. We propose a model for primary lymphatics valves at the junctions between lymphatic endothelial cells. The model consists of two overlapping endothelial extensions at a cell junction in the initial lymphatics. One cell extension is firmly attached to the adjacent connective tissue while the other cell extension is not attached to the interstitial collagen. It is free to bend into the lumen of the lymphatic when the lymphatic pressure falls below the adjacent interstitial fluid pressure. Thereby the cell junction opens a gap permitting entry of interstitial fluid into the lymphatic lumen. When the lymphatic fluid pressure rises above the adjacent interstitial fluid pressure, the endothelial extensions contact each other and the junction is closed preventing fluid reflow into the interstitial space. The model illustrates the mechanics of valve action and provides the first time a rational analysis of the mechanisms underlying fluid collection in the initial lymphatics and lymph transport in the microcirculation.     

Modeling flow in collecting lymphatic vessels: one-dimensional flow through a series of contractile elements

The lymphatic system comprises a series of elements, lymphangions, separated by valves and possessed of active, contractile walls to pump interstitial fluid from its collection in the terminal lymphatics back to the main circulation. Despite its importance, there is a dearth of information on the fluid dynamics of the lymphatic system. In this article, we describe linked experimental and computational work aimed at elucidating the biomechanical properties of the individual lymphangions. We measure the static and dynamic mechanical properties of excised bovine collecting lymphatics and develop a one-dimensional computational model of the coupled fluid flow/wall motion. The computational model is able to reproduce the pumping behavior of the real vessel using a simple contraction function producing fast contraction pulses traveling in the retrograde direction to the flow.     

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.

     

Study of tumor blood perfusion and its variation due to vascular normalization by anti-angiogenic therapy based on 3D angiogenic microvasculature

The coupling of intravascular and interstitial flow is a distinct feature of tumor microcirculation, due to high vessel permeability, low osmotic pressure gradient and absence of functional lymphatic system inside tumors. We have previously studied the tumor microcirculation by using a 2D coupled model. In this paper, we extend it to a 3D case with some new considerations, to investigate tumor blood perfusion on a more realist microvasculature, and the effects of vascular normalization by anti-angiogenic therapy on tumor microenvironment.The model predict the abnormal tumor microcirculation and the resultant hostile microenvironment: (1) in the intra-tumoral vessels, blood flows slowly with almost constant pressure values, haematocrit is much lower which contributes to hypoxia and necrosis formation of the tumor centre; (2) the total transvascular flux is at the same order of magnitude as intravascular flux, the intravasation appears inside of the tumor, the ratio of the total amount of intravasation flux to extravasation flux is about 16% for the present model; (3) the interstitial pressure is uniformly high throughout the tumor and drops precipitously at the periphery, which leads to an extremely slow interstitial flow inside the tumor, and a rapidly rising convective flow oozing out from the tumor margin into the surrounding normal tissue. The investigation of the sensitivity of flows to changes in transport properties of vessels and interstitium as well as the vascular density of the vasculature, gains an insight into how normalization of tumor microenvironment by anti-angiogenic therapies influences the blood perfusion.     

A model of a radially expanding and contracting lymphangion

The lymphatic system is an extensive vascular network featuring valves and contractile walls that pump interstitial fluid and plasma proteins back to the main circulation. Immune function also relies on the lymphatic system's ability to transport white blood cells. Failure to drain and pump this excess fluid results in edema characterized by fluid retention and swelling of limbs. It is, therefore, important to understand the mechanisms of fluid transport and pumping of lymphatic vessels. Unfortunately, there are very few studies in this area, most of which assume Poiseuille flow conditions. In vivo observations reveal that these vessels contract strongly, with diameter changes of the order of magnitude of the diameter itself over a cycle that lasts typically 2-3s. The radial velocity of the contracting vessel is on the order of the axial fluid velocity, suggesting that modeling flow in these vessels with a Poiseuille model is inappropriate. In this paper, we describe a model of a radially expanding and contracting lymphatic vessel and investigate the validity of assuming Poiseuille flow to estimate wall shear stress, which is presumably important for lymphatic endothelial cell mechanotransduction. Three different wall motions, periodic sinusoidal, skewed sinusoidal and physiologic wall motions, were investigated with steady and unsteady parabolic inlet velocities. Despite high radial velocities resulting from the wall motion, wall shear stress values were within 4% of quasi-static Poiseuille values. Therefore, Poiseuille flow is valid for the estimation of wall shear stress for the majority of the lymphangion contractile cycle.