This is the 2D companion to the 3D lymphangion-chain simulator, computed independently from the same governing equations rather than a flattened render of the 3D scene. The 3D version shows the chain as an orbit-camera view of swelling/squeezing bulbs. Here the identical per-segment pressure-volume ODE system drives a space-time kymograph — a scrolling strip where the horizontal axis is position along the chain, the vertical axis is time (newest at the bottom), and colour encodes local segment pressure. This is the same recording technique physiologists actually use on isolated lymphatic vessels under a microscope: a kymograph directly reveals the contraction wave as a diagonal band travelling from segment 1 toward the outlet, its slope literally equal to the conduction velocity of the peristaltic wave — a measurement with no equivalent view in the 3D model.
Segment pressure: P = P0 + k(V - V0) + Pactive(t)
Valve flow: Q = G·ΔP (forward, ΔP ≥ 0)
Q = -G(1-c)·|ΔP| (reflux, if valve incompetent)
Volume update: dV/dt = Qin - Qout
Stretch-frequency
coupling (myogenic): ω_eff = ω_base·(1 + β·strain)
- Lymph formation rate — how fast interstitial fluid enters the first lymphangion (net capillary filtration feeding the initial lymphatics).
- Valve competence — fraction of each valve's closure that holds against back-pressure. Below 100% some fluid regurgitates every cycle — the same mechanism behind valvular lymphedema — and shows up on the kymograph as a bright band bleeding backward (upstream) instead of a clean forward diagonal.
- Downstream pressure — afterload at the outlet. Raising it steepens (slows) the wave near the outlet as segments there work harder against a bigger gradient.
- Pacemaker rate — baseline phasic contraction frequency. The myogenic stretch-frequency coupling means a segment that fills faster also contracts sooner, visible on the kymograph as the wave's diagonal bending when upstream congestion builds.
The row of discs above the kymograph shows the same seven segments at the current instant — radius scaled to volume, colour scaled to pressure — with the valves between them as small triangles that flip from green (forward flow) to red (reflux) exactly like the 3D version's valve rings; the kymograph beneath is what makes the travelling-wave physics directly measurable over time.