A dual-clock-driven model of lymphatic muscle cell pacemaking to emulate knock-out of Ano1 or IP3R.

Lymphatic system defects are involved in a wide range of diseases, including obesity, cardiovascular disease, and neurological disorders, such as Alzheimer's disease. Fluid return through the lymphatic vascular system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, which are in turn driven by electrochemical oscillations that cause rhythmic action potentials and associated surges in intracellular calcium ion concentration. There is an incomplete understanding of the mechanisms involved in these repeated events, restricting the development of pharmacological treatments for dysfunction. Previously, we proposed a model where autonomous oscillations in the membrane potential (M-clock) drove passive oscillations in the calcium concentration (C-clock). In this paper, to model more accurately what is known about the underlying physiology, we extend this model to the case where the M-clock and the C-clock oscillators are both active but coupled together, thus both driving the action potentials. This extension results from modifications to the model's description of the IP3 receptor, a key C-clock mechanism. The synchronised dual-driving clock behaviour enables the model to match IP3 receptor knock-out data, thus resolving an issue with previous models. We also use phase-plane analysis to explain the mechanisms of coupling of the dual clocks. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of some causes of lymphoedema.

IP3R1 underlies diastolic ANO1 activation and pressure-dependent chronotropy in lymphatic collecting vessels.

Pressure-dependent chronotropy of murine lymphatic collecting vessels relies on the activation of the Ca2+-activated chloride channel encoded by Anoctamin 1 (Ano1) in lymphatic muscle cells. Genetic ablation or pharmacological inhibition of ANO1 results in a significant reduction in basal contraction frequency and essentially complete loss of pressure-dependent frequency modulation by decreasing the rate of the diastolic depolarization phase of the ionic pacemaker in lymphatic muscle cells (LMCs). Oscillating Ca2+ release from sarcoendoplasmic reticulum Ca2+ channels has been hypothesized to drive ANO1 activity during diastole, but the source of Ca2+ for ANO1 activation in smooth muscle remains unclear. Here, we investigated the role of the inositol triphosphate receptor 1 (Itpr1; Ip3r1) in this process using pressure myography, Ca2+ imaging, and membrane potential recordings in LMCs of ex vivo pressurized inguinal-axillary lymphatic vessels from control or Myh11CreERT2;Ip3r1fl/fl (Ip3r1ismKO) mice. Ip3r1ismKO vessels had significant reductions in contraction frequency and tone but an increased contraction amplitude. Membrane potential recordings from LMCs of Ip3r1ismKO vessels revealed a depressed diastolic depolarization rate and an elongation of the plateau phase of the action potential (AP). Ca2+ imaging of LMCs using the genetically encoded Ca2+ sensor GCaMP6f demonstrated an elongation of the Ca2+ flash associated with an AP-driven contraction. Critically, diastolic subcellular Ca2+ transients were absent in LMCs of Ip3r1ismKO mice, demonstrating the necessity of IP3R1 activity in controlling ANO1-mediated diastolic depolarization. These findings indicate a critical role for IP3R1 in lymphatic vessel pressure-dependent chronotropy and contractile regulation.

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.

Modeling flow in embryonic lymphatic vasculature: what is its role in valve development?

A majority of lymphatic valves tend to form in proximity to vessel junctions, and it is often proposed that disturbed flow at junctions creates oscillating shear stress that leads to accumulation of transcription factors which bring about valvogenesis at these sites. In images of networks of dorsal skin lymphatics from embryonic mice (day E16), we compared simulated fluid flow patterns and observed distributions of the transcription factor Prox1, which is implicated in valve formation. Because of creeping-flow conditions, flow across vessel junctions was not 'disturbed', and within a given vessel, shear stress varied inversely with local conduit width. Prox1 concentration was indeed localised to vessel end-regions, but over three networks was not consistently correlated with the vessel normalised-distance distribution of either fluid shear stress or shear-stress axial gradient. These findings do not support the presently accepted mechanism for the role of flow in valve localisation.

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.

Demonstration and Analysis of the Suction Effect for Pumping Lymph from Tissue Beds at Subatmospheric Pressure.

Many tissues exhibit subatmospheric interstitial pressures under normal physiologic conditions. The mechanisms by which the lymphatic system extracts fluid from these tissues against the overall pressure gradient are unknown. We address this important physiologic issue by combining experimental measurements of contractile function and pressure generation with a previously validated mathematical model. We provide definitive evidence for the existence of 'suction pressure' in collecting lymphatic vessels, which manifests as a transient drop in pressure downstream of the inlet valve following contraction. This suction opens the inlet valve and is required for filling in the presence of low upstream pressure. Positive transmural pressure is required for this suction, providing the energy required to reopen the vessel. Alternatively, external vessel tethering can serve the same purpose when the transmural pressure is negative. Suction is transmitted upstream, allowing fluid to be drawn in through initial lymphatics. Because suction plays a major role in fluid entry to the lymphatics and is affected by interstitial pressure, our results introduce the phenomenon as another important factor to consider in the study of lymphoedema and its treatment.

Consequences of intravascular lymphatic valve properties: a study of contraction timing in a multi-lymphangion model.

The observed properties of valves in collecting lymphatic vessels include transmural pressure-dependent bias to the open state and hysteresis. The bias may reduce resistance to flow when the vessel is functioning as a conduit. However, lymphatic pumping implies a streamwise increase in mean pressure across each valve, suggesting that the bias is then potentially unhelpful. Lymph pumping by a model of several collecting lymphatic vessel segments (lymphangions) in series, which incorporated these properties, was investigated under conditions of adverse pressure difference while varying the refractory period between active muscular contractions and the inter-lymphangion contraction delay. It was found that many combinations of the timing parameters and the adverse pressure difference led to one or more intermediate valves remaining open instead of switching between open and closed states during repetitive contraction cycles. Cyclic valve switching was reliably indicated if the mean pressure in a lymphangion over a cycle was higher than that in the lymphangion upstream, but either lack of or very brief valve closure could cause mean pressure to be lower downstream. Widely separated combinations of refractory period and delay time were found to produce the greatest flow-rate for a given pressure difference. The efficiency of pumping was always maximized by a long refractory period and lymphangion contraction starting when the contraction of the lymphangion immediately upstream was peaking. By means of an ex vivo experiment, it was verified that intermediate valves in a chain of pumping lymphangions can remain open, while the lymphangions on either side of the open valve continue to execute contractions.

Parameter sensitivity analysis of a lumped-parameter model of a chain of lymphangions in series.

Any disruption of the lymphatic system due to trauma or injury can lead to edema. There is no effective cure for lymphedema, partly because predictive knowledge of lymphatic system reactions to interventions is lacking. A well-developed model of the system could greatly improve our understanding of its function. Lymphangions, defined as the vessel segment between two valves, are the individual pumping units. Based on our previous lumped-parameter model of a chain of lymphangions, this study aimed to identify the parameters that affect the system output the most using a sensitivity analysis. The system was highly sensitive to minimum valve resistance, such that variations in this parameter caused an order-of-magnitude change in time-average flow rate for certain values of imposed pressure difference. Average flow rate doubled when contraction frequency was increased within its physiological range. Optimum lymphangion length was found to be some 13-14.5 diameters. A peak of time-average flow rate occurred when transmural pressure was such that the pressure-diameter loop for active contractions was centered near maximum passive vessel compliance. Increasing the number of lymphangions in the chain improved the pumping in the presence of larger adverse pressure differences. For a given pressure difference, the optimal number of lymphangions increased with the total vessel length. These results indicate that further experiments to estimate valve resistance more accurately are necessary. The existence of an optimal value of transmural pressure may provide additional guidelines for increasing pumping in areas affected by edema.

Passive pressure-diameter relationship and structural composition of rat mesenteric lymphangions.

BACKGROUND: Lymph flow depends on both the rate of lymph production by tissues and the extent of passive and active pumping. Here we aim to characterize the passive mechanical properties of a lymphangion in both mid-lymphangion and valve segments to assess regional differences along a lymphangion, as well as evaluating its structural composition. METHODS AND RESULTS: Mesenteric lymphatic vessels were isolated and cannulated in a microchamber for pressure-diameter (P-D) testing. Vessels were inflated from 0 to 20 cmH(2)O at a rate of 4 cmH(2)O/min, and vessel diameter was continuously tracked, using an inverted microscope, video camera, and custom LabVIEW program, at both mid-lymphangion and valve segments. Isolated lymphatic vessels were also pressure-fixed at 2 and 7 cmH(2)O and imaged using a nonlinear optical microscope (NLOM) to obtain collagen and elastin structural information. We observed a highly nonlinear P-D response at low pressures (3-5 cmH(2)O), which was modeled using a three-parameter constitutive equation. No significant difference in the passive P-D response was observed between mid-lymphangion and valve regions. NLOM imaging revealed an inner elastin layer and outer collagen layer at all locations. Lymphatic valve leaflets were predominantly elastin with thick axially oriented collagen bands at the insertion points. CONCLUSIONS: We observed a highly nonlinear P-D response at low pressures (3-5 cmH(2)O) and developed the first constitutive equation to describe the passive P-D response for a lymphangion. The passive P-D response did not vary among regions, in agreement with the composition of elastin and collagen in the lymphatic wall.

Three-dimensional ray tracing through curvilinear interfaces with application to laser Doppler anemometry in a blood analogue fluid.

Prediction of the effects of refractive index (RI) mismatch on laser Doppler anemometer (LDA) measurements within a curvilinear cavity (an artificial ventricle) was achieved by developing a general technique for modelling the paths of the convergent beams of the LDA system using 3D vector geometry. Validated by ray tracing through CAD drawings, the predicted maximum tolerance in RI between the solid model and the working fluid was +/- 0.0005, equivalent to focusing errors commensurate with the geometric and alignment uncertainties associated with the flow model and the LDA arrangement. This technique supports predictions of the effects of refraction within a complex geometry. Where the RI mismatch is unavoidable but known, it is possible not only to calculate the true position of the measuring volume (using the probe location and model geometry), but also to estimate degradation in signal quality arising from differential displacement and refraction of the laser beams.

Flow-induced oscillation of collapsed tubes and airway structures.

The self-excited oscillation of airway structures and flexible tubes in response to flow is reviewed. The structures range from tiny airways deep in the lung causing wheezing at the end of a forced expiration, to the pursed lips of a brass musical instrument player. Other airway structures that vibrate include the vocal cords (and their avian equivalent, the syrinx) and the soft palate of a snorer. These biological cases are compared with experiments on and theories for the self-excited oscillation of flexible tubes conveying a flow on the laboratory bench, with particular reference to those observations dealing with the situation where the inertia of the tube wall is dominant. In each case an attempt is made to summarise the current state of understanding. Finally, some outstanding challenges are identified.

Transitional flow at the venous anastomosis of an arteriovenous graft: potential activation of the ERK1/2 mechanotransduction pathway.

We present experimental and computational results that describe the level, distribution, and importance of velocity fluctuations within the venous anastomosis of an arteriovenous graft. The motivation of this work is to understand better the importance of biomechanical forces in the development of intimal hyperplasia within these grafts. Steady-flow in vitro studies (Re = 1060 and 1820) were conducted within a graft model that represents the venous anastomosis to measure velocity by means of laser Doppler anemometry. Numerical simulations with the same geometry and flow conditions were conducted by employing the spectral element technique. As flow enters the vein from the graft, the velocity field exhibits flow separation and coherent structures (weak turbulence) that originate from the separation shear layer. We also report results of a porcine animal study in which the distribution and magnitude of vein-wall vibration on the venous anastomosis were measured at the time of graft construction. Preliminary molecular biology studies indicate elevated activity levels of the extracellular regulatory kinase ERK1/2, a mitogen-activated protein kinase involved in mechanotransduction, at regions of increased vein-wall vibration. These findings suggest a potential relationship between the associated turbulence-induced vein-wall vibration and the development of intimal hyperplasia in arteriovenous grafts. Further research is necessary, however, in order to determine if a correlation exists and to differentiate the vibration effect from that of flow related effects.