Effect of number of number of lymphangions (<i>n</i>_v).

<p>(A) Pump function curves for branching networks with <i>n</i>_v = 1–14 (associated <i>L</i>_s = 0.3–4.2 cm). Under favorable pressure differences (Δ<i>P</i> < 0) maximum flow rate was achieved with <i>n</i>_v = 1 because additional valves increased the resistance. Flow rate increased with <i>n</i>_v when Δ<i>P</i> > 16 cmH₂O. (B) Flow waveforms versus time for networks with <i>n</i>_v = 2, 4, and 8 at Δ<i>P</i> = 16 cmH₂O. Networks with larger <i>n</i>_v benefit from additional valves to maintain the pressures required to keep downstream valves open in the presence of an adverse Δ<i>P</i>.</p

Effect of time delay between contractions of adjacent lymphangions in branching networks with <i>n</i>_v = 4.

<p>(A) Pump function curves for synchronized pumping (Δ<i>t</i>_g = Δ<i>t</i>_v = 0 s), time delay only at the junctions (Δ<i>t</i>_v = 0, Δ<i>t</i>_g = 0.5 s), and the baseline case (Δ<i>t</i>_g = Δ<i>t</i>_v = 0.5 s) at <i>p</i>_a − <i>p</i>_e = 4 cmH₂O (solid lines) and <i>p</i>_a − <i>p</i>_e = 3 cmH₂O (dashed). (B) vs. Δ<i>t</i>_v (Δ<i>t</i>_g = Δ<i>t</i>_v): effect of transmural pressure via (variation of <i>p</i>_e) at Δ<i>P</i> = 3 cmH₂O. Solid line: forward propagating contraction wave, dashed line: reverse propagating contraction wave.</p

Network structure.

<p>(A) Top: Schematic view of the branching network structure with three generations of bifurcating vessels. The network pumps the fluid from inlets (<i>p</i>_a) to the outlet (<i>p</i>_b). The network is formed by seven vessels arranged in a bifurcating pattern (index 0101–0304). Each vessel is composed of multiple lymphangions and the number of lymphangions per vessel (<i>n</i>_v) is the same for all the vessels in the network. Bottom: Electrical analogy schematic of one of the junctions in the network. (B) Diagram of the algorithm for solving the system of equations and the behavior of the main governing equations. <i>t</i>_ITP is the initial transient period after which a consistent periodic solution is achieved.</p

Effect of transmural pressure (via <i>p</i>_e). vs. external pressure at Δ<i>P</i> = 3, 10, 16 cmH₂O for branching networks with <i>n</i>_v = 2 (dot-dashed), <i>n</i>_v = 4 (solid), and <i>n</i>_v = 8 (dotted).

<p> The top axis indicates transmural pressure. Peak flow rate occurred at higher values of <i>p</i>_eas pressure difference increased. Inlet pressure <i>p</i>_a was constant and equal to 6 cmH₂O.</p

Timing of contractions.

<p><i>M</i>_<i>t</i> (<i>t</i>) vs. time for branching network with four lymphangions per vessel (<i>n</i>_v = 4). Bottom panel: vessels 0301–0304. Mid panel: vessels 0201 and 0202. Top panel: vessel 0101. Δ<i>t</i>_v is the time delay between contractions of adjacent lymphangions in one vessel; Δ<i>t</i>_g is the time delay between two subsequent generations (at the junction). Specified time course for the contraction of an individual lymphangion (normalized <i>M</i>_<i>t</i> (<i>t</i>) vs. time) is presented.</p

Effect of time delay between contractions of adjacent lymphangions in branching networks with <i>n</i>_v = 4 when Δ<i>t</i>_g = Δ<i>t</i>_v.

<p>(A) Pump function curves as Δ<i>t</i>_v increased from 0 to 3.5 by steps of 1.0 s (Increasing <i>p</i>_b). (B) <i></i>vs. Δ<i>t</i>_v: effect of pressure difference across the network. Flow rate response as Δ<i>t</i>_v incrementally increased from 0 to 3.5 s. For reverse travelling waves (dashed line) equivalent time delay in the reverse direction is presented as 3.5 –(Δ<i>t</i>_g = Δ<i>t</i>_v).</p

Simulation conditions for all the cases studied here.

<p>Simulation conditions for all the cases studied here.</p

Effect of diastolic period (<i>t</i>_r).

<p>(A) Pump function curves for a branching network with <i>n</i>_v = 4 as <i>t</i>_r increased from 0 to 3.5 s. Diastolic period was advantageous to pumping, particularly at low Δ<i>P</i>, because relaxed vessels present less impedance to incoming flow. (B) Combined effect of diastolic period, contraction period (<i>t</i>_c), and number of lymphangions per vessel (<i>n</i>_v) at Δ<i>P</i> = 3 cmH₂O.</p

Parameters used in the numerical model, including their definition and baseline value.

<p>Parameters used in the numerical model, including their definition and baseline value.</p

Volumetric renderings of collagen and elastin layers within in the lymphatic vessel wall imaged using multiphoton microscopy.

<p>(A) Collagen signal as viewed from the interior of the vessel. (B) Elastin signal as viewed from the interior of the vessel. The bottom panels show composite renderings of collagen (white) and elastin (green) within the interior surface of the vessel (C) and the exterior surface (D). Volumetric renderings of multiphoton image data were performed using the software FluoRender [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183222#pone.0183222.ref025" target="_blank">25</a>]. Scale bar 100 μm.</p