Pharmacokinetic–pharmacodynamic modelling and simulation using the electrical circuit simulation program spice2

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.

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.

Pharmacodynamic modelling of drug-induced ventilatory depression and automatic drug dosing in conscious sedation

In conscious sedation (CS) procedures, the patient is sedated but retains the ability to breathe spontaneously. Drug-induced ventilatory depression represents a dangerous side effect of CS, possibly leading to hypoventilation and subsequent hypoxia. In this work, we propose a new pharmacodynamic model for drug-induced ventilatory depression. The model presents a parsimonious structure and shows good agreement with experimental data for different drugs. In addition, we explore the innovative idea of regulating drug infusion during CS by means of a feedback control system based on measurements of transcutaneous partial pressure of CO(2). In simulations, the controller proves able to maintain a predefined target of CO(2) despite pain, external disturbances and inter-patient variability in the sensibility to the drug. The implementation of the controller during CS procedures would improve clinical practice minimizing the occurrence of drug-induced ventilatory depression by tailoring drug infusion to patient's needs.

Calculation of steady-state distribution delay between central and peripheral compartments in two-compartment models with infusion regimen

A lag time may exist between blood drug concentration and drug effect. Various factors can contribute to the lag time, among which the drug distribution delay is a significant one. The drug distribution delay can also exist between different compartments. An equation was derived to calculate the steady-state drug concentration delay between central and peripheral compartments in a two-compartment model with infusion regimen.

Another integrated form of the Michaelis-Menten equation, its analogy to electrical circuit model and implications for active transporters

The Michaelis-Menten equation is integrated versus concentration to study active transporters. The integrated equation is analogous to compartmental and electrical circuit models. Simulation of the integrated equation suggests that an active transporter can run backwards and produce energy.