This is a 2D phase-space companion to the 3D organ-on-chip model — same two-compartment pharmacokinetics, no rendered chip. The left chart is a live scrolling strip chart of the exact same ODEs the 3D model integrates:
dC_L/dt = [ -Q·C_L - Vmax·C_L/(Km+C_L) ] / V_L
dC_T/dt = [ Q·(C_L - C_T) ] / V_T
The right panel is a genuinely different computation, not a picture of the chip at all: because C_T never feeds back into C_L, the liver chamber's ODE is separable in C_L, so the total fraction of a bolus dose that the liver metabolizes before any of it can flow onward — the hepatic extraction ratio ER — reduces to a closed-form integral over concentration rather than time:
ER(Q,Vmax,Km,Dose) = (V_L / Dose) · ∫₀^C0 [ 1 − Q / (Q + Vmax/(Km+C)) ] dC, C0 = Dose/V_L
Bioavailability F = 1 − ER
The field sweeps every combination of flow rate Q (x-axis) and metabolic capacity Vmax (y-axis) at the current dose and Km, colouring each cell by its resulting bioavailability F. It is recomputed live whenever dose or Km changes, and the bright marker tracks today's actual Q/Vmax slider setting — so you can see first-pass metabolism as a boundary in parameter space (low Q + high Vmax ⇒ near-total hepatic extraction) rather than as a particle animation.
- Inject Bolus Dose — adds Dose/VL to the liver chamber and starts a fresh trace on the strip chart.
- Flow rate Q — sweeps the drug through faster, giving enzymes less contact time and raising bioavailability; moves the marker left/right on the field.
- Vmax / Km — the liver's metabolic capacity and substrate affinity; raising Vmax or lowering Km lowers bioavailability. Vmax moves the marker up/down; Km reshapes the whole field.