Hepatic clearance and oral bioavailability

The liver clears blood by first-pass extraction; the well-stirred model sets the extraction ratio E and oral bioavailability F = 1 − E. For propranolol the engine gives E ≈ 0.75, F ≈ 0.25 (clearance 1125 mL/min). High-E drugs are flow-limited (clearance flow-elasticity ≈ 0.90), low-E drugs capacity-limited (≈ 0.10). Grade [F]/[L].

Hepatic extraction is E = fu·CLint/(QH + fu·CLint) and oral bioavailability is F = 1 − E. As intrinsic clearance rises, E sweeps 0→1 and F falls 1→0; propranolol sits at E ≈ 0.75, F ≈ 0.25, matching the cited high-extraction tracer.

First-pass extraction sets bioavailability

The liver is the clearance class. In the well-stirred model the fraction removed in one pass is E, so the orally available fraction is F = 1 − E.

Flow-limited vs capacity-limited

Sweeping intrinsic clearance, E rises monotonically from ~0 to ~1 and F falls accordingly. The regimes separate by the canonical discriminant — hepatic-clearance flow-elasticity d(ln CL)/d(ln Q): for high-extraction drugs ≈ 0.90 (clearance tracks blood flow), for low-extraction drugs ≈ 0.10 (clearance set by fu·CLint, flow-independent). Propranolol (E ≈ 0.75, F ≈ 0.25) is correctly flow-limited.