Nonlinear lymphangion pressure-volume relationship minimizes edema

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.

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.

Lymph transport in rat mesenteric lymphatics experiencing edemagenic stress

OBJECTIVE

To assess lymphatic flow adaptations to edema, we evaluated lymph transport function in rat mesenteric lymphatics under normal and increased fluid volume (edemagenic) conditions in situ.

METHODS

Twelve rats were infused with saline (intravenous infusion, 0.2 mL/min/100 g body weight) to induce edema. We intravitally measured mesenteric lymphatic diameter and contraction frequency, as well as lymphocyte velocity and density before, during, and after infusion.

RESULTS

A 10-fold increase in lymphocyte velocity (0.1-1 mm/s) and a sixfold increase in flow rate (0.1-0.6 μL/min), were observed post infusion, respectively. There were also increases in contraction frequency and fractional pump flow one minute post infusion. Time-averaged wall shear stress increased 10 fold post infusion to nearly 1.5 dynes/cm(2) . Similarly, maximum shear stress rose from 5 to 40 dynes/cm(2) .

CONCLUSIONS

Lymphatic vessels adapted to edemagenic stress by increasing lymph transport. Specifically, the increases in lymphatic contraction frequency, lymphocyte velocity, and shear stress were significant. Lymph pumping increased post infusion, though changes in lymphatic diameter were not statistically significant. These results indicate that edemagenic conditions stimulate lymph transport via increases in lymphatic contraction frequency, lymphocyte velocity, and flow. These changes, consequently, resulted in large increases in wall shear stress, which could then activate NO pathways and modulate lymphatic transport function.

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.

Modelling the lymphatic system: challenges and opportunities

The lymphatic system is a vital part of the circulatory and immune systems, and plays an important role in homeostasis by controlling extracellular fluid volume and in combating infection. Nevertheless, there is a notable disparity in terms of research effort expended in relation to the treatment of lymphatic diseases in contrast to the cardiovascular system. While similarities to the cardiovascular system exist, there are considerable differences in their anatomy and physiology. This review outlines some of the challenges and opportunities for those engaged in modelling biological systems. The study of the lymphatic system is still in its infancy, the vast majority of the models presented in the literature to date having been developed since 2003. The number of distinct models and their variants are few in number, and only one effort has been made thus far to study the entire lymphatic network; elements of the lymphatic system such as the nodes, which act as pumps and reservoirs, have not been addressed by mathematical models. Clearly, more work will be necessary in combination with experimental verification in order to progress and update the knowledge on the function of the lymphatic system. As our knowledge and understanding of its function increase, new and more effective treatments of lymphatic diseases are bound to emerge.