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 behaviors that indicate that the system performance is robust against minor perturbations in pressure and flow. More serious disruptions can lead to incurable swelling of tissues called lymphedema.

An existing lumped-parameter model of multiple lymphangions (lymphatic vascular segments) in series is adapted for the incorporation of recent physiological measurements of lymphatic vascular properties. The new data show very marked nonlinearity of the passive pressure–diameter relation during distension, relative to comparable blood vessels, and complex valve behaviour. Since lymph is transported as a result of either the active contraction or the passive squeezing of vascular segments situated between two one-way valves, the performance of these valves is of primary importance. The valves display hysteresis (the opening and closing pressure drop thresholds differ), a bias to staying open (both state changes occur when the trans-valve pressure drop is adverse) and pressure-drop threshold dependence on transmural pressure. These properties, in combination with the strong nonlinearity that valve operation represents, have in turn caused intriguing numerical problems in the model, and we describe numerical stratagems by which we have overcome the problems. The principal problem is also generalised into a relatively simple mathematical example, for which solution detail is provided using two different solvers.

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.

Lymph is transported along collecting lymphatic vessels by intrinsic and extrinsic pumping. The walls have muscle of a type intermediate between blood-vascular smooth muscle and myocardium; a contracting segment between two valves (a lymphangion) constitutes a pump. This intrinsic mechanism is investigated ex vivo in isolated, spontaneously contracting, perfused segments subjected to controlled external pressures. The reaction to varying afterload is probed by slowly ramping up the outlet pressure until pumping fails. Often the failure occurs when the contraction raises intra-lymphangion pressure insufficiently to overcome the outlet pressure, open the outlet valve and cause ejection, but many segments fail by other means, the mechanisms of which are not clear. We here elucidate those mechanisms by resort to a numerical model. Experimental observations are paired with comparable findings from computer simulations, using a lumped-parameter model that incorporates previously measured valve properties, plus new measurements of active contractile and passive elastic properties, and the dependence of contraction frequency on transmural pressure, all taken from isobaric twitch contraction experiments in the same vessel. Surprisingly, the model predicts seven different possible modes of pump failure, each defined by a different sequence of valve events, with their occurrence depending on the parameter values and boundary conditions. Some, but not all, modes were found experimentally. Further model investigation reveals routes by which a vessel exhibiting one mode of failure might under altered circumstances exhibit another.