Optimal lymphatic vessel structure

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.

Opportunities for Studying the Hydrodynamic Context for Breast Cancer Cell Spread Through Lymph Flow

The lymphatic system serves as the primary route for the metastatic spread of breast cancer cells (BCCs). A scarcity of information exists with regard to the advection of BCCs in lymph flow and a fundamental understanding of the response of BCCs to the forces in the lymphatics needs to be established. This review summarizes the flow environment metastatic BCCs are exposed to in the lymphatics. Special attention is paid to the behavior of cells/particles in microflows in an attempt to elucidate the behavior of BCCs under lymph flow conditions (Reynolds number <1).

Optimal postnodal lymphatic network structure that maximizes active propulsion of lymph

The lymphatic system acts to return lower-pressured interstitial fluid to the higher-pressured veins by a complex network of vessels spanning more than three orders of magnitude in size. Lymphatic vessels consist of lymphangions, segments of vessels between two unidirectional valves, which contain smooth muscle that cyclically pumps lymph against a pressure gradient. Whereas the principles governing the optimal structure of arterial networks have been identified by variations of Murray's law, the principles governing the optimal structure of the lymphatic system have yet to be elucidated, although lymph flow can be identified as a critical parameter. The reason for this deficiency can be identified. Until recently, there has been no algebraic formula, such as Poiseuille's law, that relates lymphangion structure to its function. We therefore employed a recently developed mathematical model, based on the time-varying elastance model conventionally used to describe ventricular function, that was validated by data collected from postnodal bovine mesenteric lymphangions. From this lymphangion model, we developed a model to determine the structure of a lymphatic network that optimizes lymph flow. The model predicted that there is a lymphangion length that optimizes lymph flow and that symmetrical networks optimize lymph flow when the lymphangions downstream of a bifurcation are 1.26 times the length of the lymphangions immediately upstream. Measured lymphangion lengths (1.14 +/- 0.5 cm, n = 74) were consistent with the range of predicted optimal lengths (0.1-2.1 cm). This modeling approach was possible, because it allowed a structural parameter, such as length, to be treated as a variable.