Portosystemic shunt and first-pass escape

A portosystemic shunt lets a fraction s of portal blood bypass the hepatocytes, so oral bioavailability becomes F=1−(1−s)E. The slope dF/ds equals the extraction ratio E exactly, so high-extraction drugs are most affected (slope 0.75 vs 0.09 for a low-E drug). Grade [F], a corollary of the clearance result.

Shunting routes part of the portal flow around the liver, escaping first pass. The oral bioavailability is F=1−(1−s)E and its sensitivity to the shunt fraction is dF/ds=E — so flow-limited high-extraction drugs gain the most (here F rises 0.25→0.85) while low-extraction drugs barely change.

Bypassing the first pass

Portal hypertension opens porto-systemic collaterals, so a fraction s of orally absorbed drug reaches the systemic circulation without crossing hepatocytes. The bypassed fraction escapes extraction entirely, giving F = s + (1−s)(1−E) = 1−(1−s)E.

High-extraction drugs gain the most

The sensitivity to the shunt is exactly dF/ds = E. For the high-extraction drug (E=0.75) bioavailability rises steeply 0.25→0.85 as s goes 0→0.8 (slope 0.75); for a low-extraction drug (E=0.09) it barely moves (slope 0.09). This is a direct corollary of the clearance flow-elasticity result in §6 — flow-limited drugs are the ones whose first pass a shunt can steal — and it matches the clinical observation that shunting raises the bioavailability of moderate-to-high-extraction drugs toward unity (PLOS One; Frontiers in Medicine 2022).