Modelling secondary lymphatic valves with a flexible vessel wall: how geometry and material properties combine to provide function

Pacemaking in the lymphatic system

Lymphatic collecting vessels exhibit spontaneous phasic contractions that are critical for lymph propulsion and tissue fluid homeostasis. This rhythmic activity is driven by action potentials conducted across the lymphatic muscle cell (LMC) layer to produce entrained contractions. The contraction frequency of a lymphatic collecting vessel displays exquisite mechanosensitivity, with a dynamic range from <1 to >20 contractions per minute. A myogenic pacemaker mechanism intrinsic to the LMCs was initially postulated to account for pressure-dependent chronotropy. Further interrogation into the cellular constituents of the lymphatic vessel wall identified non-muscle cell populations that shared some characteristics with interstitial cells of Cajal, which have pacemaker functions in the gastrointestinal and lower urinary tracts, thus raising the possibility of a non-muscle cell pacemaker. However, recent genetic knockout studies in mice support LMCs and a myogenic origin of the pacemaker activity. LMCs exhibit stochastic, but pressure-sensitive, sarcoplasmic reticulum calcium release (puffs and waves) from IP3R1 receptors, which couple to the calcium-activated chloride channel Anoctamin 1, causing depolarisation. The resulting electrical activity integrates across the highly coupled lymphatic muscle electrical syncytia through connexin 45 to modulate diastolic depolarisation. However, multiple other cation channels may also contribute to the ionic pacemaking cycle. Upon reaching threshold, a voltage-gated calcium channel-dependent action potential fires, resulting in a nearly synchronous calcium global calcium flash within the LMC layer to drive an entrained contraction. This review summarizes the key ion channels potentially responsible for the pressure-dependent chronotropy of lymphatic collecting vessels and various mechanisms of IP3R1 regulation that could contribute to frequency tuning.

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.

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.

The Microvascular-Lymphatic Interface and Tissue Homeostasis: Critical Questions That Challenge Current Understanding

Lymphatic and blood microvascular networks play critical roles in the clearance of excess fluid from local tissue spaces. Given the importance of these dynamics in inflammation, tumor metastasis, and lymphedema, understanding the coordinated function and remodeling between lymphatic and blood vessels in adult tissues is necessary. Knowledge gaps exist because the functions of these two systems are typically considered separately. The objective of this review was to highlight the coordinated functional relationships between blood and lymphatic vessels in adult microvascular networks. Structural, functional, temporal, and spatial relationships will be framed in the context of maintaining tissue homeostasis, vessel permeability, and system remodeling. The integration across systems will emphasize the influence of the local environment on cellular and molecular dynamics involved in fluid flow from blood capillaries to initial lymphatic vessels in microvascular networks.

Multiple aspects of lymphatic dysfunction in an ApoE -/- mouse model of hypercholesterolemia

Introduction: Rodent models of cardiovascular disease have uncovered various types of lymphatic vessel dysfunction that occur in association with atherosclerosis, type II diabetes and obesity. Previously, we presented in vivo evidence for impaired lymphatic drainage in apolipoprotein E null (ApoE ^-/- ) mice fed a high fat diet (HFD). Whether this impairment relates to the dysfunction of collecting lymphatics remains an open question. The ApoE ^-/- mouse is a well-established model of cardiovascular disease, in which a diet rich in fat and cholesterol on an ApoE deficient background accelerates the development of hypercholesteremia, atherosclerotic plaques and inflammation of the skin and other tissues. Here, we investigated various aspects of lymphatic function using ex vivo tests of collecting lymphatic vessels from ApoE ^+/+ or ApoE ^-/- mice fed a HFD. Methods: Popliteal collectors were excised from either strain and studied under defined conditions in which we could quantify changes in lymphatic contractile strength, lymph pump output, secondary valve function, and collecting vessel permeability. Results: Our results show that all these aspects of lymphatic vessel function are altered in deleterious ways in this model of hypercholesterolemia. Discussion: These findings extend previous in vivo observations suggesting significant dysfunction of lymphatic endothelial cells and smooth muscle cells from collecting vessels in association with a HFD on an ApoE-deficient background. An implication of our study is that collecting vessel dysfunction in this context may negatively impact the removal of cholesterol by the lymphatic system from the skin and the arterial wall and thereby exacerbate the progression and/or severity of atherosclerosis and associated inflammation.

Mathematical Modeling of Lymph Node Drainage Function by Neural Network

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

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.