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Difficulty: Very hardPharmacokinetic and Pharmacodynamic Principles

A 54-year-old man is maintained on an oral lipophilic beta-blocker for heart failure. The drug is eliminated exclusively via hepatic metabolism. It is completely absorbed across the gastrointestinal epithelium (fa=1.0f_a = 1.0) with no intestinal wall metabolism. Pharmacokinetic profiling reveals the drug has a baseline hepatic extraction ratio (EHE_H) of 0.800.80. The patient's hepatic blood flow (QQ) is estimated at 1,500 mL/min1,500 \text{ mL/min}.

The patient is subsequently diagnosed with latent tuberculosis and started on rifampin, a potent cytochrome P450 inducer. This induction increases the beta-blocker's hepatic intrinsic clearance (CLintCL_{int}) by exactly 50%50\%. Assuming the well-stirred model of hepatic clearance and that hepatic blood flow remains constant, what is the patient's new absolute oral bioavailability of the beta-blocker? Express your answer as a percentage rounded to one decimal place.

Answer: 14.3 %

Answer

14.3
The drug's absolute oral bioavailability (FF) depends on the fraction absorbed (faf_a) and the fraction escaping hepatic extraction (1−EH1 - E_H). Because fa=1.0f_a = 1.0, F=1−EHF = 1 - E_H. For a high-extraction drug, intrinsic clearance (CLintCL_{int}) is much larger than hepatic blood flow (QQ). Using the well-stirred model equation EH=CLintQ+CLintE_H = \frac{CL_{int}}{Q + CL_{int}}, the initial CLintCL_{int} is calculated to be 6,000 mL/min6,000 \text{ mL/min}. A 50%50\% induction increases CLintCL_{int} to 9,000 mL/min9,000 \text{ mL/min}. Recalculating EHE_H yields 900010500=0.8571\frac{9000}{10500} = 0.8571. The new bioavailability is 1−0.8571=0.14281 - 0.8571 = 0.1428, which is 14.3%14.3\%. This non-linear shift illustrates why patients on high-extraction drugs are highly sensitive to enzyme induction during oral therapy.

Step-by-Step Solution

1
Calculate initial oral bioavailability (FF).
F=1−0.80=0.20F = 1 - 0.80 = 0.20
Since the drug is 100% absorbed (fa=1f_a = 1) without gut wall metabolism, systemic bioavailability depends purely on escaping first-pass hepatic extraction.
2
Calculate baseline intrinsic clearance (CLintCL_{int}).
CLint=6,000 mL/minCL_{int} = 6,000 \text{ mL/min}
Applying the well-stirred model (EH=CLintQ+CLintE_H = \frac{CL_{int}}{Q + CL_{int}}), we rearrange to solve for CLintCL_{int}: 0.80=CLint1500+CLint0.80 = \frac{CL_{int}}{1500 + CL_{int}}.
3
Determine the new CLintCL_{int} after CYP induction.
NewCLint=9,000 mL/minNew CL_{int} = 9,000 \text{ mL/min}
Rifampin induces the enzyme, increasing the baseline intrinsic clearance by 50%50\% (6000×1.56000 \times 1.5).
4
Calculate the new hepatic extraction ratio (EHE_H).
NewEH=90001500+9000=900010500≈0.8571New E_H = \frac{9000}{1500 + 9000} = \frac{9000}{10500} \approx 0.8571
We must substitute the new intrinsic clearance back into the well-stirred model equation, keeping blood flow (QQ) constant at 1500 mL/min1500 \text{ mL/min}.
5
Calculate final bioavailability (FF).
NewF=1−0.8571=0.142857  ⟹  14.3%New F = 1 - 0.8571 = 0.142857 \implies 14.3\%
The new systemic exposure is the fraction that escapes the newly elevated first-pass hepatic extraction.

Key Concept

Well-stirred model of hepatic clearance and first-pass effect
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Topics

Pharmacokinetic and Pharmacodynamic Principles

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