Clinical Pharmacokinetics & Drug Metabolism
Well-Stirred Hepatic Extraction & First-Pass Formula
Calculate Rowland, Benet, and Graham’s (1973) well-stirred liver Extraction Ratio E_H = (f_u * CL_int) / (Q_H + f_u * CL_int), Hepatic Clearance CL_H, and First-Pass Oral Bioavailability F_H = 1 - E_H.
Distinguish flow-limited high-extraction drugs from capacity-limited low-extraction drugs!
Malcolm Rowland, Leslie Benet, and Garry Graham (1973) established the foundational Well-Stirred Venous-Equilibrium Model of hepatic drug clearance! Given Hepatic_Blood_Flow Q_H (typically ~90 L/hr in adults), Unbound_Free_Blood_Fraction f_u in (0, 1], and Hepatocyte_Intrinsic_Metabolic_Clearance CL_int, the Hepatic Extraction Ratio is E_H = (f_u * CL_int) / (Q_H + f_u * CL_int), Hepatic Blood Clearance is CL_H = Q_H * E_H, and assuming complete gut absorption (F_abs * F_G = 1), Oral First-Pass Hepatic Bioavailability escaping portal extraction is F_H = 1 - E_H = Q_H / (Q_H + f_u * CL_int)!
Verify on Hepatic_Blood_Flow Q_H = 90.0 L/hr (B2), Unbound_Fraction f_u = 0.20 (B3), and Intrinsic_Clearance CL_int = 1,800 L/hr (B4 -> f_u * CL_int = 360 L/hr): Hepatic Extraction Ratio is E_H = 360 / (90 + 360) = 0.8000 (80.0% extracted on a single pass -> High-Extraction Flow-Limited Drug, E_H > 0.70!); Hepatic Clearance is CL_H = 90 * 0.8000 = 72.00 L/hr; and Oral First-Pass Bioavailability is F_H = 1 - 0.8000 = 0.2000 (only 20.0% reaches systemic circulation!). Notice the clinical CYP-inhibition surprise: if an enzyme inhibitor halves CL_int to 900 L/hr (f_u * CL_int = 180), IV clearance drops only -16.7% (72 -> 60 L/hr), yet Oral Bioavailability F_H jumps +50% (0.2000 -> 0.3333, doubling oral AUC/dose ratio)!
| Well-Stirred Liver PK Metric (Q_H=90 L/hr, f_u=0.20, CL_int=1800 L/hr) | Formula | Verified Output |
|---|---|---|
| Hepatic Extraction Ratio (E_H) | (f_u * CL_int) / (Q_H + f_u * CL_int) | 0.8000 (80.00% Extracted) |
| Hepatic Blood Clearance (CL_H) | Q_H * E_H | 72.00 L/hr |
| First-Pass Hepatic Bioavailability (F_H) | 1 - E_H = Q_H / (Q_H + f_u * CL_int) | 0.2000 (20.00% Escapes) |
| Clearance Sensitivity Class | E_H > 0.7 Flow; E_H < 0.3 Capacity | Flow-Limited (High E_H > 0.70) |
Well-Stirred Hepatic Extraction Ratio E_H Formula
Validate Q_H > 0, 0 < f_u <= 1, and CL_int >= 0.
=LET(qh_fl, B2, fu_fr, B3, cl_in, B4, IF(OR(qh_fl <= 0, fu_fr <= 0, fu_fr > 1, cl_in < 0), "Invalid Hepatic Input", ROUND((fu_fr * cl_in) / (qh_fl + fu_fr * cl_in), 4)))First-Pass Survival F_H & Rowland-Tozer Extraction Regime Formula
Test CL_int = 50 L/hr (f_u * CL_int = 10 -> E_H = 10 / 100 = 0.1000 < 0.30) to observe shift to "Capacity-Limited (Low E_H < 0.30)" where CL_H ≈ f_u * CL_int is sensitive to protein binding and CYP activity rather than liver blood flow!
=IF(ISTEXT(E2), E2, IF(E2 > 0.7, "Flow-Limited (High E_H > 0.70)", IF(E2 < 0.3, "Capacity-Limited (Low E_H < 0.30)", "Intermediate Extraction (0.30-0.70)")))Try the example
Use the original values or change them to test your understanding.