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.

In Defense of Current Concepts and Applications of Clearance in Drug Development and Therapeutics.

Clearance is one of the most widely quoted and applied pharmacokinetic concepts in drug development and therapy. Its foundations and associated models of drug elimination are well embedded and accepted within the scientific community. Recently, however, the prevailing views that have held us in good stead for the past almost 50 years have been challenged with the argument that organ clearance should not be based on elimination rate, now defined by extraction across the liver divided by incoming or systemic concentration, as in current practice, but rather, by the mean concentration of drug within the blood in the organ, which is model-dependent. We argue that all needed parameters already exist, and that the proposed new approach to organ clearance is confusing and unnecessary. SIGNIFICANCE STATEMENT: Clearance concepts are widely applied in drug development and therapy. Historically, hepatic clearance has been defined as the ratio of rate of elimination divided by ingoing blood concentration. Recently, this approach has been challenged arguing that clearance should be referenced to blood concentration within the liver extrapolation (IVIVE). There is no need for additional, a feature that corresponds to intrinsic clearance of the chosen clearance model, a widely accepted parameter in physiologically based pharmacokinetic (PBPK) and in vitro to in vivo extrapolation (IVIVE). There is no need for additional, confusing clearance terms, which offer no material benefit.

Intracellular and Intraorgan Concentrations of Small Molecule Drugs: Theory, Uncertainties in Infectious Diseases and Oncology, and Promise.

The distribution of a drug within the body should be considered as involving movement of unbound drug between the various aqueous spaces of the body. At true steady state, even for a compound of restricted lipoidal permeability, unbound concentrations in all aqueous compartments (blood, extracellular, and intracellular) are considered identical, unless a compartment has a clearance/transport process. In contrast, total drug concentrations may differ greatly, reflecting binding or partitioning into constituents of each compartment. For most highly lipid permeable drugs, this uniform unbound concentration is expected to apply. However, many compounds have restricted lipoidal permeability and are subjected to transport/clearance processes causing a gradient between intracellular and extracellular unbound concentrations even at steady state. Additional concerns arise where the drug target resides in a site of limited vascularity. Many misleading assumptions about drug concentrations and access to drug targets are based on total drug. Correction, if made, is usually by measuring tissue binding, but this is limited by the lack of homogenicity of the organ or compartment. Rather than looking for technology to measure the unbound concentration it may be better to focus on designing high lipoidal permeable molecules with a high chance of achieving a uniform unbound drug concentration. It is hoped this paper will stimulate greater understanding of the path from circulation to cell interior, and thereby in part avoid or minimize the need to provide the experimentally very determining, and sometimes still questionable, answer to this problem.

Physiologically-based pharmacokinetics in drug development and regulatory science.

The application of physiologically-based pharmacokinetic (PBPK) modeling is coming of age in drug development and regulation, reflecting significant advances over the past 10 years in the predictability of key pharmacokinetic (PK) parameters from human in vitro data and in the availability of dedicated software platforms and associated databases. Specific advances and contemporary challenges with respect to predicting the processes of drug clearance, distribution, and absorption are reviewed, together with the ability to anticipate the quantitative extent of PK-based drug-drug interactions and the impact of age, genetics, disease, and formulation. The value of this capability in selecting and designing appropriate clinical studies, its implications for resource-sparing techniques, and a more holistic view of the application of PK across the preclinical/clinical divide are considered. Finally, some attention is given to the positioning of PBPK within the drug development and approval paradigm and its future application in truly personalized medicine.

Target Reserve and Turnover Parameters Determine Rightward Shift of Enalaprilat Potency From its Binding Affinity to the Angiotensin Converting Enzyme.

Drug effects are often assumed to be directly proportional to the fraction of occupied targets. However, for a number of antagonists that exhibit target-mediated drug disposition (TMDD), such as angiotensin-converting enzyme (ACE) inhibitors, drug binding to the target at low concentrations may be significant enough to influence pharmacokinetics but insufficient to elicit a drug response (i.e., differences in drug-target binding affinity and potency). In this study, a pharmacokinetic/pharmacodynamic model for enalaprilat was developed in humans to provide a theoretical framework for assessing the relationship between ex vivo drug potency (IC50) and in vivo target-binding affinity (KD). The model includes competitive binding of angiotensin I and enalaprilat to ACE and accounts for the circulating target pool. Data were obtained from the literature, and model fitting and parameter estimation were conducted using maximum likelihood in ADAPT5. The model adequately characterized time-courses of enalaprilat concentrations and four biomarkers in the renin-angiotensin system and provided estimates for in vivo KD (0.646 nM) and system-specific parameters, such as total target density (32.0 nM) and fraction of circulating target (19.8%), which were in agreement with previous reports. Model simulations were used to predict the concentration-effect curve of enalaprilat, revealing a 6.3-fold increase in IC50 from KD. Additional simulations demonstrated that target reserve and degradation parameters are key factors determining the extent of shift of enalaprilat ex vivo potency from its in vivo binding affinity. This may be a common phenomenon for drugs exhibiting TMDD and has implications for translating binding affinity to potency in drug development.

Cyclosporine inhibition of hepatic and intestinal CYP3A4, uptake and efflux transporters: application of PBPK modeling in the assessment of drug-drug interaction potential.

PURPOSE: To apply physiologically-based pharmacokinetic (PBPK) modeling to investigate the consequences of reduction in activity of hepatic and intestinal uptake and efflux transporters by cyclosporine and its metabolite AM1. METHODS: Inhibitory potencies of cyclosporine and AM1 against OATP1B1, OATP1B3 and OATP2B1 were investigated in HEK293 cells +/- pre-incubation. Cyclosporine PBPK model implemented in Matlab was used to assess interaction potential (+/- metabolite) against different processes (uptake, efflux and metabolism) in liver and intestine and to predict quantitatively drug-drug interaction with repaglinide. RESULTS: Cyclosporine and AM1 were potent inhibitors of OATP1B1 and OATP1B3, IC(50) ranging from 0.019-0.093 µM following pre-incubation. Cyclosporine PBPK model predicted the highest interaction potential against liver uptake transporters, with a maximal reduction of >70% in OATP1B1 activity; the effect on hepatic efflux and metabolism was minimal. In contrast, 80-97% of intestinal P-gp and CYP3A4 activity was reduced due to the 50-fold higher cyclosporine enterocytic concentrations relative to unbound hepatic inlet. The inclusion of AM1 resulted in a minor increase in the predicted maximal reduction of OATP1B1/1B3 activity. Good predictability of cyclosporine-repaglinide DDI and the impact of dose staggering are illustrated. CONCLUSIONS: This study highlights the application of PBPK modeling for quantitative prediction of transporter-mediated DDIs with concomitant consideration of P450 inhibition.

Correction for nonspecific binding to various components of ultrafiltration apparatus and impact on estimating in vivo rat clearance for a congeneric series of 5-ethyl, 5-n-alkyl barbituric acids.

Accurately predicting in vivo metabolic clearance from in vitro liver microsomes or hepatocytes requires a good understanding of the factors contributing to the prediction. Although much work has concentrated on deriving scaling factors and optimizing the metabolic stability techniques for consistency and rigor, it is only relatively recently that the importance of binding to microsomes and hepatocytes has been appreciated. Ultrafiltration is often used to estimate binding to plasma proteins and microsomes, but the level of nonspecific binding (NSB) to the ultrafiltration apparatus has not been adequately described. We derive an equation to correct for NSB and demonstrate that this can significantly affect the estimate of binding to microsomes and improve the accuracy of scaling to in vivo clearance for a series of barbiturates.

Measurement of binding of basic drugs to acidic phospholipids using surface plasmon resonance and incorporation of the data into mechanistic tissue composition equations to predict steady-state volume of distribution.

Acidic phospholipid binding plays an important role in determining the tissue distribution of basic drugs. This article describes the use of surface plasmon resonance to measure binding affinity (K(D)) of three basic drugs to phosphatidylserine, a major tissue acidic phospholipid. The data are incorporated into mechanistic tissue composition equations to allow prediction of the steady-state volume of distribution (V(ss)). The prediction accuracy of V(ss) using this approach is compared with the original methodology described by Rodgers et al. (J Pharm Sci 94:1259-1276), in which the binding to acidic phospholipids is calculated from the blood/plasma concentration ratio (BPR). The compounds used in this study [amlodipine, propranolol, and 3-dimethylaminomethyl-4-(4-methylsulfanyl-phenoxy)-benzenesulfonamide (UK-390957)] showed higher affinity binding to phosphatidylserine than to phosphatidylcholine. When the binding affinity to phosphatidylserine was incorporated into mechanistic tissue composition equations, the V(ss) was more accurately predicted for all three compounds by using the surface plasmon resonance measurement than by using the BPR to estimate acidic phospholipid binding affinity. The difference was particularly marked for UK-390957, a sulfonamide that has a high BPR due to binding to carbonic anhydrase. The novel approach described in this article allows the binding affinity of drugs to an acidic phospholipid (phosphatidylserine) to be measured directly and demonstrates the utility of the binding data in the prediction of V(ss).

Phase 0/microdosing approaches: time for mainstream application in drug development?

Phase 0 approaches - which include microdosing - evaluate subtherapeutic exposures of new drugs in first-in-human studies known as exploratory clinical trials. Recent progress extends phase 0 benefits beyond assessment of pharmacokinetics to include understanding of mechanism of action and pharmacodynamics. Phase 0 approaches have the potential to improve preclinical candidate selection and enable safer, cheaper, quicker and more informed developmental decisions. Here, we discuss phase 0 methods and applications, highlight their advantages over traditional strategies and address concerns related to extrapolation and developmental timelines. Although challenges remain, we propose that phase 0 approaches be at least considered for application in most drug development scenarios.

Hepatic clearance concepts and misconceptions: Why the well-stirred model is still used even though it is not physiologic reality?

The liver is the most important drug metabolizing organ, endowed with a plethora of metabolizing enzymes and transporters to facilitate drug entry and removal via metabolism and/or biliary excretion. For this reason, much focus surrounds the development of clearance concepts, which are based on normalizing the rate of removal to the input or arterial concentration. By so doing, some authors have recently claimed that it implies one specific model of hepatic elimination, namely, the widely used well-stirred or venous equilibration model (WSM). This commentary challenges this claim and aims to provide a comprehensive discussion of not only the WSM but other currently applied hepatic clearance models - the parallel tube model (PTM), the dispersion model (DM), the zonal liver model (ZLM), and the heterogeneous capillary transit time model of Goresky and co-workers (GM). The WSM, PTM, and DM differ in the patterns of internal blood flow, assuming bulk, plug, and dispersive flows, respectively, which render different degrees of mixing within the liver that are characterized by the magnitudes of the dispersion number (DN), resulting in different implications concerning the (unbound) substrate concentration in liver (CuH). Early models assumed perfusion rate-limited distribution, which have since been modified to include membrane-limited transport. The recent developments associated with the misconceptions and the sensitivity of the models are hereby addressed. Since the WSM has been and will likely remain widely used, the pros and cons of this model relative to physiological reality are further discussed.

Interleukin-1 receptor antagonist penetrates human brain at experimentally therapeutic concentrations.

The proinflammatory cytokine interleukin (IL)-1 mediates several forms of experimentally induced acute brain injury and has been implicated in chronic neurodegenerative disorders. The IL-1 receptor antagonist, IL-1RA, protects rodents against ischaemic brain injury, but its molecular mass (17 kDa) potentially limits the brain penetration of peripherally administered IL-1RA. We therefore sought to identify whether therapeutically effective concentrations of IL-1RA in the rat were also achieved in brain of patients with subarachnoid haemorrhage (SAH), using a peripheral administration regime that had proved to be safe and reduce peripheral inflammation in patients after stroke. An intravenous bolus of IL-1RA, followed by infusion, was administered to rats after induction of focal cerebral ischaemia. The effects of IL-1RA on brain ischaemia and the concentrations achieved in cerebrospinal fluid (CSF), were determined. Interleukin-1 receptor antagonist was similarly administered to patients with SAH, and CSF was sampled via external ventricular drains. In rats, IL-1RA significantly reduced brain injury induced by focal cerebral ischaemia. The plasma IL-1RA concentrations reached 12+/-2 microg/mL by 30 mins, and CSF concentrations were maintained between 91 and 232 ng/mL between 1 and 24 h of infusion. In patients with SAH, IL-1RA reached a steady-state plasma concentration of 22+/-4 microg/mL by 15 mins, and CSF concentrations were maintained at 78 to 558 ng/mL between 1 and 24 h. Intravenous delivery of IL-1RA leads to CSF concentrations in patients comparable to those that are neuroprotective in rats, and might therefore be of therapeutic benefit.

Pharmacokinetic modelling of interleukin-1 receptor antagonist in plasma and cerebrospinal fluid of patients following subarachnoid haemorrhage.

UNLABELLED: What is already known about this subject? The naturally occurring interlukin-1 receptor antagonist (IL-1RA) markedly protects rodents against ischaemic, excitotoxic and traumatic brain injury, suggesting it may be of therapeutic value. When administered intravenously to patients soon after stroke, IL-1RA is safe and reduces the peripheral inflammatory response. However, IL-1RA is a large protein (17 kDa), which may limit brain penetration, thereby limiting its potential utility in brain injury. What this study adds. The purpose of these experiments was to determine the pharmacokinetics of IL-1RA in cerebrospinal fluid (CSF) of patients, to allow modelling that would aid development of therapeutic regimens. Peripherally administered IL-1RA crosses slowly into and out of the CSF of patients with subarachnoid haemorrhage and, at steady state, CSF IL-1RA concentration (range 115-886 ng ml(-1)) was similar to that found to be neuroprotective in rats (range 91-232 ng ml(-1)), although there was considerable variability among patients. However, there is a large concentration gradient of IL-1RA between plasma and CSF. These CSF:plasma data are consistent with very low permeation of IL-1RA into the CSF and elimination kinetics from it controlled by the volumetric turnover of CSF. AIM: The naturally occurring interlukin-1 receptor antagonist (IL-1RA) markedly protects rodents against ischaemic, excitotoxic and traumatic brain injury, suggesting it may be of therapeutic value. The aim was to determine the pharmacokinetics of IL-1RA in cerebrospinal fluid (CSF) of patients, to allow modelling that would aid development of therapeutic regimens. METHODS: When administered intravenously to patients soon after stroke, IL-1RA is safe and reduces the peripheral inflammatory response. However, IL-1RA is a large protein (17 kDa), which may limit brain penetration, thereby limiting its potential utility in brain injury. In seven patients with subarchnoid haemorrhage (SAH), IL-1RA was administered by intravenous bolus, then infusion for 24 h, and both blood and CSF, via external ventricular drains, were sampled during and after stopping the infusion. RESULTS: Plasma steady-state concentrations were rapidly attained and maintained throughout the infusion, whereas CSF concentrations rose slowly towards a plateau during the 24-h infusion, reaching at best only 4% of that in plasma. Plasma kinetic parameters were within the literature range. Modelling of the combined data yielded rate constants entering and leaving the CSF of 0.0019 h(-1)[relative standard error (RSE) = 19%] and 0.1 h(-1) (RSE = 19%), respectively. CONCLUSIONS: Peripherally administered IL-1RA crosses slowly into and out of the CSF of patients with SAH. However, there is a large concentration gradient of IL-1RA between plasma and CSF. These CSF:plasma data are consistent with very low permeation of IL-1RA into the CSF and elimination kinetics from it controlled by the volumetric turnover of CSF.

Commentary on "The Universally Unrecognized Assumption in Predicting Drug Clearance and Organ Extraction Ratio".

Among pharmacokinetic concepts, clearance has been the most widely applied in clinical pharmacology and drug development. With so much written on the subject it might be thought that there is nothing more to say. So it is noteworthy that some basic aspects related to hepatic clearance, and specifically the most popular model, the well-stirred model, have been challenged by Benet et al. This commentary examines the challenge and provides our views.

Past, Present, and Future of Bioequivalence: Improving Assessment and Extrapolation of Therapeutic Equivalence for Oral Drug Products.

The growth in the utilization of systems thinking principles has created a paradigm shift in the regulatory sciences and drug product development. Instead of relying extensively on end product testing and one-size-fits-all regulatory criteria, this new paradigm has focused on building quality into the product by design and fostering the development of product-specific, clinically relevant specifications. In this context, this commentary describes the evolution of bioequivalence regulations up to the current day and discusses the potential of applying a Bayesian-like approach, considering all relevant prior knowledge, to guide regulatory bioequivalence decisions in a patient-centric environment.

Importance of target-mediated drug disposition for small molecules.

Target concentration is typically not considered in drug discovery. However, if targets are expressed at relatively high concentrations and compounds have high affinity, such that most of the drug is bound to its target, in vitro screens can give unreliable information on compound affinity. In vivo, a similar situation will generate pharmacokinetic (PK) profiles that deviate greatly from those normally expected, owing to target binding affecting drug distribution and clearance. Such target-mediated drug disposition (TMDD) effects on small molecules have received little attention and might only become apparent during clinical trials, with the potential for data misinterpretation. TMDD also confounds human microdosing approaches by providing therapeutically unrepresentative PK profiles. Being aware of these phenomena will improve the likelihood of successful drug discovery and development.

Physiologically Based Pharmacokinetic Model Qualification and Reporting Procedures for Regulatory Submissions: A Consortium Perspective.

This work provides a perspective on the qualification and verification of physiologically based pharmacokinetic (PBPK) platforms/models intended for regulatory submission based on the collective experience of the Simcyp Consortium members. Examples of regulatory submission of PBPK analyses across various intended applications are presented and discussed. European Medicines Agency (EMA) and US Food and Drug Administration (FDA) recent draft guidelines regarding PBPK analyses and reporting are encouraging, and to advance the use and acceptability of PBPK analyses, more clarity and flexibility are warranted.

Influence of erythrocytes on the hepatic distribution kinetics of urea and thiourea.

The role of erythrocyte on the hepatic distribution kinetics of urea and thiourea was investigated in the in situ isolated perfused rat liver. Perfusion experiments were conducted using Krebs-bicarbonate buffer delivered via the portal vein in a single pass mode at a total flow rate of 15 ml/min. With urea, superimposable unimodal effluent curves were obtained in the presence and absence of erythrocytes, indicating that its distribution kinetics is not affected by erythrocytes. With thiourea, effluent curves were unimodal in the absence of erythrocytes but bimodal in the presence of erythrocytes. The maximum frequency output at the first peak increased from 0.017+/-0.002 to 0.042+/-0.006 s(-1) with an increase in the bolus hematocrit from 0.40 to 0.75, indicating that some thiourea fraction is retained by the erythrocytes on transit through the liver. Although the fractional output associated with the first peak was very similar (11.9% versus 11.5%), whether the perfusate contained unlabelled thiourea or not, this fraction was reduced from 17 to 5% with a decrease in the incubation time before injection from 30 min to 40s. However, there was no evidence for a capacity limitation; a 30-min period of pre-incubation of either radiolabelled thiourea alone or combined with a high concentration of unlabelled thiourea had minimal effect on effluent profiles.

Use of microdosing to predict pharmacokinetics at the therapeutic dose: experience with 5 drugs.

OBJECTIVES: A volunteer trial was performed to compare the pharmacokinetics of 5 drugs--warfarin, ZK253 (Schering), diazepam, midazolam, and erythromycin--when administered at a microdose or pharmacologic dose. Each compound was chosen to represent a situation in which prediction of pharmacokinetics from either animal or in vitro studies (or both) was or is likely to be problematic. METHODS: In a crossover design volunteers received (1) 1 of the 5 compounds as a microdose labeled with radioactive carbon (carbon 14) (100 microg), (2) the corresponding (14)C-labeled therapeutic dose on a separate occasion, and (3) simultaneous administration of an intravenous (14)C-labeled microdose and an oral therapeutic dose for ZK253, midazolam, and erythromycin. Analysis of (14)C-labeled drugs in plasma was done by use of HPLC followed by accelerator mass spectrometry. Liquid chromatography-tandem mass spectrometry was used to measure plasma concentrations of ZK253, midazolam, and erythromycin at therapeutic concentrations, whereas HPLC-accelerator mass spectrometry was used to measure warfarin and diazepam concentrations. RESULTS: Good concordance between microdose and therapeutic dose pharmacokinetics was observed for diazepam (half-life [t((1/2))] of 45.1 hours, clearance [CL] of 1.38 L/h, and volume of distribution [V] of 90.1 L for 100 microg and t((1/2)) of 35.7 hours, CL of 1.3 L/h, and V of 123 L for 10 mg), midazolam (t((1/2)) of 4.87 hours, CL of 21.2 L/h, V of 145 L, and oral bioavailability [F] of 0.23 for 100 microg and t((1/2)) of 3.31 hours, CL of 20.4 L/h, V of 75 L, and F of 0.22 for 7.5 mg), and development compound ZK253 (F = <1% for both 100 microg and 50 mg). For warfarin, clearance was reasonably well predicted (0.17 L/h for 100 microg and 0.26 L/h for 5 mg), but the discrepancy observed in distribution (67 L for 100 microg and 17.9 L for 5 mg) was probably a result of high-affinity, low-capacity tissue binding. The oral microdose of erythromycin failed to provide detectable plasma levels as a result of possible acid lability in the stomach. Absolute bioavailability for the 3 compounds examined yielded excellent concordance with data from the literature or data generated in house. CONCLUSION: Overall, when used appropriately, microdosing offers the potential to aid in early drug candidate selection.