Process and System Clearances in Pharmacokinetic Models: Our Basic Clearance Concepts Are Correct

A Continuous Intestinal Absorption Model to Predict Drug Enterohepatic Recirculation in Healthy Humans: Nalbuphine as a Model Substrate

Nalbuphine (NAL) is a κ-agonist/μ-antagonist opioid being developed as an oral extended formulation (ER) for the treatment of chronic cough in idiopathic pulmonary fibrosis and itch in prurigo nodularis. NAL is extensively glucuronidated and likely undergoes enterohepatic recirculation (EHR). The purpose of this work is to develop pharmacokinetic models for NAL absorption and enterohepatic recirculation (EHR). Clinical pharmacokinetic (PK) data sets in healthy subjects from three trials that included IV, oral solution, and ER tablets in fed and fasted state and two published trials were used to parametrize a novel partial differential equation (PDE)-based model, termed "PDE-EHR" model. Experimental inputs included in vitro dissolution and permeability data. The model incorporates a continuous intestinal absorption framework, explicit liver and gall bladder compartments, and compartments for systemic drug disposition. The model was fully PDE-based with well-stirred compartments achieved by rapid diffusion. The PDE-EHR model accurately reproduces NAL concentration-time profiles for all clinical data sets. NAL disposition simulations required inclusion of both parent and glucuronide recirculation. Inclusion of intestinal P-glycoprotein efflux in the simulations suggests that NAL is not expected to be a victim or perpetrator of P-glycoprotein-mediated drug interactions. The PDE-EHR model is a novel tool to predict EHR and food/formulation effects on drug PK. The results strongly suggest that even intravenous dosing studies be conducted in fasted subjects when EHR is suspected. The modeling effort is expected to aid in improved prediction of dosing regimens and drug disposition in patient populations.

An Explanation of Why Dose-Corrected Area Under the Curve for Alternate Administration Routes Can Be Greater than for Intravenous Dosing

It is generally believed that bioavailability (F) calculated based on systemic concentration area under the curve (AUC) measurements cannot exceed 1.0, yet some published studies report this inconsistency. We teach and believe, based on differential equation derivations, that rate of absorption has no influence on measured systemic clearance following an oral dose, i.e., determined as available dose divided by AUC. Previously, it was thought that any difference in calculating F from urine data versus that from systemic concentration AUC data was due to the inability to accurately measure urine data. A PubMed literature search for drugs exhibiting F > 1.0 and studies for which F was measured using both AUC and urinary excretion dose-corrected analyses yielded data for 35 drugs. We show and explain, using Kirchhoff's Laws, that these universally held concepts concerning bioavailability may not be valid in all situations. Bioavailability, determined using systemic concentration measurements, for many drugs may be overestimated since AUC reflects not only systemic elimination but also absorption rate characteristics, which is most easily seen for renal clearance measures. Clearance of drug from the absorption site must be significantly greater than clearance following an iv bolus dose for F(AUC) to correctly correspond with F(urine). The primary purpose of this paper is to demonstrate that studies resulting in F > 1.0 and/or greater systemic vs urine bioavailability predictions may be accurate. Importantly, these explications have no significant impact on current regulatory guidance for bioequivalence testing, nor on the use of exposure (AUC) measures in making drug dosing decisions.

Notes on the Use of Kirchhoff's Laws in Pharmacokinetics

Recent publications by Benet and coworkers, Korzekwa and Nagar, and Rowland et al. signal disagreement regarding the use of Kirchhoff's laws in combining pharmacokinetic parameters, especially clearances and rate constants. Here, it is pointed out that Kirchhoff's laws as applied to pharmacokinetics simply assert that concentrations are well defined and that molar or mass balances hold. The real issue is how to combine parameters for clearance processes in sequence, which may be reversible, irreversible, or even active in either or both directions. It is also demonstrated that Kirchhoff's laws cannot be used to resolve contradictory results observed in liver transport and clearance. Finally, a simple argument is provided relating nonlinear clearance to apparently anomalous bioavailability observations.

Kirchhoff's Laws and Hepatic Clearance, Well-Stirred Model - Is There Common Ground?

Clearance concepts are extensively applied in drug development and drug therapy. The well-stirred model (WSM) of hepatic elimination is the most widely adopted physiologic model in pharmacokinetics owing to its simplicity. A common feature of this organ model is its use to relate hepatic clearance of a compound to the physiologic variables: organ blood flow rate, binding within blood, and hepatocellular metabolic and excretory activities. Recently, Kirchhoff's laws of electrical network have been applied to organ clearance (Pachter et al., 2022; Benet and Sodhi, 2023) with the claim that they yield the same equation for hepatic clearance as the WSM, and that the equation is independent of a mechanistic model. This commentary analyzes this claim and shows that implicit in the application of Kirchhoff's approaches are the same assumptions as those of the WSM. Concern is also expressed in the interpretation of permeability or transport parameters and related equations, as well as the inappropriateness of the corresponding equation defining hepatic clearance. There is no value, and some dangers, in applying Kirchhoff's electrical laws to organ clearance. SIGNIFICANCE STATEMENT: This commentary refutes this claim by Pachter et al. (2022), and Benet and Sodhi, (2023), who suggest that the well-stirred model (WSM) of hepatic elimination, the most widely applied physiologic model of hepatic clearance, provides the same equation as Kirchhoff's laws of electrical network that is independent of a physiologic model. A careful review shows that the claim is groundless and fraught with errors. We conclude that there is no place for the application of Kirchhoff's laws to organ clearance models.