Saturable First-Pass Metabolism: Dose-Dependent Bioavailability

Oral Dose

Entering concentration C_u 4.0 mg/L

Enzyme Kinetics (CYP450)

Max metabolic capacity V_max 60 mg/h

Affinity constant K_m 3.0 mg/L

Hepatic Blood Flow

Flow Q 81 L/h

Live Readouts

Extraction ratio E

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Bioavailability F

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Hepatic clearance CL_h

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Enzyme occupancy θ

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Bioavailability F vs. dose C_u (marker = current dose)

How it works

The liver is modeled as one well-stirred compartment (venous-equilibrium model) that a drug crosses once on its way from gut to systemic circulation. Unlike a fixed-clearance drug, this one saturates its own metabolizing enzymes at clinically relevant oral concentrations — the defining feature of capacity-limited ("saturable" or "nonlinear") first-pass metabolism, seen clinically with propranolol, verapamil and high-dose lidocaine.

Intrinsic clearance:  CLint(Cu) = Vmax / (Km + Cu)
Extraction ratio:     E = CLint / (Q + CLint)
Hepatic clearance:    CLh = Q · E
Oral bioavailability: F = 1 − E
Site occupancy:       θ = Cu / (Km + Cu)

Low dose (Cu ≪ Km): CLint ≈ Vmax/Km is nearly constant → E is dose-independent → F is flat, "linear" kinetics.
High dose (Cu ≫ Km): enzyme sites are saturated (θ→1), CLint falls toward Vmax/Cu → E drops → F rises faster than dose itself. Each additional mg swallowed survives the liver more easily than the last — systemic exposure grows disproportionately, which is why some drugs need careful dose-titration rather than simple linear scaling.
Vmax slider — total enzymatic capacity (enzyme induction/inhibition, CYP450 genotype).
Km slider — substrate affinity (lower Km = enzyme binds the drug more readily at low concentration).
Q slider — hepatic blood flow (falls in cirrhosis, heart failure, portosystemic shunting).

Spheres are individual drug molecules: they spawn in the portal vein, pass through the glowing enzyme lattice inside the liver lobule (color = occupancy θ), and each is metabolized (fades out) or survives to the hepatic vein with probability equal to the instantaneous E and 1−E computed from the formulas above.

Drug molecule Metabolized (removed) Escapes to systemic circulation

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