Nonlinear lymphangion pressure-volume relationship minimizes edema

Abstract

Lymphangions, the segments of lymphatic vessel between two valves, contract cyclically and actively pump, analogous to cardiac ventricles. Besides having a discernable systole and diastole, lymphangions have a relatively linear end-systolic pressure-volume relationship (with slope E(max)) and a nonlinear end-diastolic pressure-volume relationship (with slope E(min)). To counter increased microvascular filtration (causing increased lymphatic inlet pressure), lymphangions must respond to modest increases in transmural pressure by increasing pumping. To counter venous hypertension (causing increased lymphatic inlet and outlet pressures), lymphangions must respond to potentially large increases in transmural pressure by maintaining lymph flow. We therefore hypothesized that the nonlinear lymphangion pressure-volume relationship allows transition from a transmural pressure-dependent stroke volume to a transmural pressure-independent stroke volume as transmural pressure increases. To test this hypothesis, we applied a mathematical model based on the time-varying elastance concept typically applied to ventricles (the ratio of pressure to volume cycles periodically from a minimum, E(min), to a maximum, E(max)). This model predicted that lymphangions increase stroke volume and stroke work with transmural pressure if E(min) < E(max) at low transmural pressures, but maintain stroke volume and stroke work if E(min)= E(max) at higher transmural pressures. Furthermore, at higher transmural pressures, stroke work is evenly distributed among a chain of lymphangions. Model predictions were tested by comparison to previously reported data. Model predictions were consistent with reported lymphangion properties and pressure-flow relationships of entire lymphatic systems. The nonlinear lymphangion pressure-volume relationship therefore minimizes edema resulting from both increased microvascular filtration and venous hypertension.

Lymph Transport in Rat Mesenteric Lymphatics Experiencing Edemagenic Stress

“…Interestingly, flow rate is greatest at this time point (33‐39 minutes) as well, which correlates to our previous work and findings from Quick et al . who illustrated the conduit behavior of lymphatic vessels . Thus, our results illustrate increased pumping as an immediate response to edemagenic stress followed by a “conduit‐like” response in the long term to accommodate the increased lymph volume.…”

Passive Pressure–Diameter Relationship and Structural Composition of Rat Mesenteric Lymphangions

“…The stiffness transition at this threshold was sharper than that seen by Ohhashi et al 10 in larger vessels and a different species. Venugopal et al 11 used the latter data in fitting a combination of two straight lines to the pressure-volume relationship of a relaxed lymphangion. We believe that our constitutive equation is superior for future models of lymph flow in that it has continuous derivatives.…”

“…However, they did not describe their findings in a constitutive equation. Venugopal et al 11 published a mathematical model describing the nonlinear pressure-volume relation of lymphatic vessels with a piecewise-linear function. While this is a good first approximation, functions with continuous derivatives are closer in spirit to the biology and more suitable for purposes such as network modeling.…”

Multiscale Modelling of Lymphatic Drainage

“…In terms of this modelling, lymph vessels differ from arteries in one very important respect; whilst arterial walls are compliant they are also passive, so the response of the system can be modelled by finding suitable fixed values for L, C and R. Lymphangion walls are actively contractile, contributing to the pumping; and in fact the determination and modelling of this is a significant part of modelling the system as a whole. Venugopal, Quick and collaborators [34,35,[55][56][57] developed a more sophisticated lumped parameter representation of the lymph system using the circuit given in Fig. 7 with the parameters being time-varying.…”

“…Venugopal and collaborators demonstrate a similar effect for lymphatic networks, showing that a ratio of 1:26 for the upstream and downstream lengths optimises lymph flow for symmetric networks. The same authors have also investigated the effect of linear and non-linear contractile behaviour on the pumping effect [57], a significant issue in understanding the response of lymphangions to increasing transmural pressure, for example in response to edema.…”