This 2D companion uses the exact same 4-compartment ODE model as the 3D lab — liver, gallbladder, intestinal lumen and portal-return pools — only drawn as a flat flow diagram instead of a 3D scene:
d(liver)/dt = synth + portal->liver − liver->gb
d(gb)/dt = liver->gb − gb->intestine
d(intestine)/dt = gb->intestine − intestine->portal
d(portal)/dt = intestine->portal − portal->liver
synth = max(min, BASE − gain × portal->liver flow)
Each duct's flow rate scales with how much is left in its source pool (Michaelis-style availability term), so pools never go negative and the loop self-stabilizes. The circle fill level of each organ tracks its own pool size in grams, and particle count/speed on every duct is driven directly by that leg's instantaneous flow — not decoration.
The two intervention toggles change the model, not just the picture: a bile acid sequestrant binds bile in the gut and cuts the intestine→portal reabsorption rate to about 15%, and simulated terminal ileum resection removes the dedicated transporter almost entirely. Both starve the FXR feedback loop of its signal, so CYP7A1 synthesis in the liver ramps up to compensate — visible directly in the Synthesis rate and FXR suppression readouts.