Valve-related modes of pump failure in collecting lymphatics: numerical and experimental investigation

Abstract

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 intralymphangion 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.

Contraction of collecting lymphatics: organization of pressure-dependent rate for multiple lymphangions

“…any lymphangion can initiate contractions, at a rate which depends nonlinearly on the local pressure, as in our single-lymphangion model (Bertram et al 2017)…”

“…Since we preferred to avoid the creation of a large array to hold this information, a second scheme was devised, which tracked these quantities only in the moving time window where they were needed. The scheme encapsulated the following rules: any lymphangion can initiate contractions, at a rate which depends nonlinearly on the local pressure, as in our single-lymphangion model (Bertram et al 2017)activation signals commanding the start of contraction are propagated to adjacent lymphangions,the propagation time between lymphangions is an adjustable constant ( t p ),during a refractory period which begins at contraction start and ends after contraction end, a further contraction cannot be provoked, and arriving activation signals are extinguished,the cut part-lymphangions beyond the outermost valves in the chain participate in the signal generation and propagation, but do not contract.…”

“…The plotted quantity of each curve in the second panel is the activation (ranging between 0 and 1). In the full pumping model this waveform controls how the pressure/diameter relationship varies smoothly from the curve which applies when the vessel is passive to that which applies at the peak of contraction, and back again; see Bertram et al (2017) for further details.…”

“…In papers since 2011, our group has reported the progressive development and application of a lumped-parameter model of collecting lymphatic vessels. The model, for which equations are given in Appendix 1, has been adapted to situations ranging from emulation of pump limits in an isolated single-lymphangion segment (Bertram et al 2017), through investigation of optimal pumping in multi-lymphangion chains (Bertram et al 2016b), to performance prediction for idealised lymphatic networks (Jamalian et al 2016). The model adheres closely to recent biological observations of lymphatic behaviour, for instance in its treatment of the inter-lymphangion valves (Davis et al 2011; Bertram et al 2014a; Bertram et al 2014b).…”

“…We have previously incorporated a contraction repetition rate that depends on transmural pressure into a model of an excised lymphatic vascular segment that consists of just one whole lymphangion including its bounding valves (Bertram et al 2017). Data on contraction frequency vs. transmural pressure were taken from an experiment involving recording of spontaneous twitch contractions at various levels of constant and equal inlet and outlet pressure from an isolated rat mesenteric collecting lymphatic vessel segment.…”