Christopher D. Bertram

The spontaneous, phasic contractions of collecting lymphatic vessels are critical for lymph transport and interstitial fluid homeostasis. Phasic contractions are initiated by action potentials in lymphatic muscle and conduct along the vessel to trigger contraction waves. Contractions are regulated by pressure and shear stress (SS), but only limited aspects of that regulation are understood. Numerical models predict that pressure promotes retrograde propagation of contraction waves, whereas nitric oxide (NO) production associated with phasic contractions (pulsatile NO) promotes antegrade conduction and extends the pressure range over which contractions propel lymph. These predictions were tested using 3−4‐valve segments of rat mesenteric lymphatic vessels using pressure myography and protocols that imposed forward flow, elevated inflow pressure (P_in) or elevated outflow pressure (P_out), each with/without intact NO signalling. NO bioavailability and flow‐induced responses were enhanced by l‐arginine supplementation. Spatiotemporal maps generated from video images were used to quantify the direction and extent of contraction wave conduction. Our results show that (1) contraction waves are normally biased towards retrograde conduction at equal P_in/P_out levels. (2) P_in elevation promotes antegrade conduction, whereas P_out elevation promotes retrograde conduction. (3) Imposed flow is inhibitory, reducing contraction amplitude and frequency and limiting the extent of contraction wave conduction without a significant effect on conduction direction. (4) Pulsatile NO does not significantly influence the conduction direction or extend the pressure range over which spontaneous contractions occur. Our findings support the idea that pressure is the dominant regulator of lymphatic pacemaking and pumping, with pulsatile NO having only minimal influence. image Key points: The degree to which spontaneous, phasic contractions of lymphatic collecting vessels are regulated by pressure and shear stress is not fully understood. Numeric models predict that nitric oxide (NO) production associated with phasic contractions (pulsatile NO) promotes antegrade conduction of contraction waves, whereas pressure elevation promotes retrograde conduction; pulsatile NO production is also thought to extend the pressure range over which phasic contractions occur. Ex vivo methods were used to control pressure/flow in 3−4 valve segments of collecting lymphatics from rat mesentery, with preserved or inhibited NO signalling. The relatively long vessel segments limited the absolute levels of imposed flow/SS, so l‐arginine supplementation was used to enhance NO bioavailability. Our findings support a scheme whereby pressure is by far the dominant mechanism determining the pacemaking site of lymphatic collectors, and challenge existing dogma about the importance of pulsatile NO production in regulating their behaviour.

Lymphatic system failures contribute to cardiovascular and various other diseases. A critical function of the lymphatic vascular system is the active pumping of fluid from the interstitium back into the blood circulation by periodic contractions of lymphatic muscle cells (LMCs) in the vessel walls. As in cardiac pacemaking, these periodic contractions can be interpreted as occurring due to linked pacemaker oscillations in the LMC membrane potential (M-clock) and calcium concentration (C-clock). We previously reported a minimal model of synchronized dual-clock-driven oscillations. While this qualitatively replicated the period of oscillations under different conditions, it did not replicate the action potential shape as it varied under those conditions, particularly as regards the extent or lack of a systolic plateau. Here, we modify the model to replicate the plateau behaviour. Using phase-plane analysis we show two qualitatively different dynamical mechanisms that could account for plateau formation, one largely M-clock-driven, the other largely C-clock-driven. The second case occurs with the introduction of a ryanodine receptor; in both cases, we find improved predictions for calcium levels. With enhanced fidelity to the experimental data, the improved model has the potential to help determine opportunities for pharmacological treatment of lymphatic system pumping defects.

Objective: Intravascular lymphatic valves often occur in proximity to vessel junctions. It is commonly held that disturbed flow at junctions is responsible for accumulation of valve‐forming cells (VFCs) at these locations as the initial step in valve creation, and the one which explains the association with these sites. However, evidence in favor is largely limited to cell culture experiments.Methods: We acquired images of embryonic lymphatic vascular networks from day E16.5, when VFC accumulation has started but the developing valve has not yet altered the local vessel geometry, stained for Prox1, which co‐localizes with Foxc2. Using finite‐element computational fluid mechanics, we simulated the flow through the networks, under conditions appropriate to this early development stage. Then we correlated the Prox1 distributions with the distributions of simulated fluid shear and shear stress gradient.Results: Across a total of 16 image sets, no consistent correlation was found between Prox1 distribution and the local magnitude of fluid shear, or its positive or negative gradient.Conclusions: This, the first direct semi‐empirical test of the localization hypothesis to interrogate the tissue from in vivo at the critical moment of development, does not support the idea that a feature of the local flow determines valve localization.

A previously developed model of a lymphatic vessel as a chain of lymphangions was investigated to determine whether lymphangions of unequal length reduce pumping relative to a similar chain of equal-length ones. The model incorporates passive elastic and active contractile properties taken from ex vivo measurements, and intravascular lymphatic valves as transvalvular pressure-dependent resistances to flow with hysteresis and transmural pressure-dependent bias to the open state as observed experimentally. Coordination of lymphangion contractions is managed by marrying an autonomous transmural pressure-dependent pacemaker for each lymphangion with bidirectional transmission of activation signals between lymphangions, qualitatively matching empirical observations. With eight lymphangions as used here and many nonlinear constraints, the model is capable of complex outcomes. The expected flow-rate advantage conferred by longer lymphangions everywhere was confirmed. However, the anticipated advantage of uniform lymphangions over those of unequal length, compared in chains of equal overall length, was not found. A wide variety of dynamical outcomes was observed, with the most powerful determinant being the adverse pressure difference, rather than the arrangement of long and short lymphangions. This work suggests that the wide variation in lymphangion length which is commonly observed in collecting lymphatic vessels does not confer disadvantage in pumping lymph.

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.

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 Myh11CreER^T2;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.

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.

Lymphoedema, a common dysfunction of the lymphatic system, results in fluid accumulating between cells. Fluid return through the lymphatic vascular system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, driven by electrochemical oscillations causing rhythmic action potentials and associated surges in intracellular calcium ion concentration. There is 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, and thus both driving the action potentials. This extension results from modifications to the model for the IP ₃ receptor, a key C-clock mechanism. The synchronized dual-driving clock behaviour enables the model to match IP ₃ receptor knock-out data, resolving an issue with previous models. We also use phase-plane analysis to explain the mechanisms for the dual-clock coupling. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of lymphoedema.

Lymphoedema develops due to chronic dysfunction of the lymphatic vascular system which results in fluid accumulation between cells. The condition is commonly acquired secondary to diseases such as cancer or the therapies associated with it. The primary driving force for fluid return through the lymphatic vasculature is provided by contractions of the muscularized lymphatic collecting vessels, driven by electrical oscillations. However, there is an incomplete understanding of the molecular and bioelectric mechanisms involved in lymphatic muscle cell excitation, hampering the development and use of pharmacological therapies. Modelling in silico has contributed greatly to understanding the contributions of specific ion channels to the cardiac action potential, but modelling of these processes in lymphatic muscle remains limited. Here, we propose a model of oscillations in the membrane voltage (M-clock) and intracellular calcium concentrations (C-clock) of lymphatic muscle cells. We modify a model by Imtiaz and colleagues to enable the M-clock to drive the C-clock oscillations. This approach differs from typical models of calcium oscillators in lymphatic and related cell types, but is required to fit recent experimental data. We include an additional voltage dependence in the gating variable control for the L-type calcium channel, enabling the M-clock to oscillate independently of the C-clock. We use phase-plane analysis to show that these M-clock oscillations are qualitatively similar to those of a generalised FitzHugh-Nagumo model. We also provide phase plane analysis to understand the interaction of the M-clock and C-clock oscillations. The model and methods have the potential to help determine mechanisms and find targets for pharmacological treatment of lymphoedema.