Commentary: Pharmacokinetic Theory Must Consider Published Experimental Data.

Recently, we have proposed simple methodology to derive clearance and rate constant equations, independent of differential equations, based on Kirchhoff's Laws, a common methodology from physics used to describe rate-defining processes either in series or parallel. Our approach has been challenged in three recent publications, two published in this journal, but notably what is lacking is that none evaluate experimental pharmacokinetic data. As reviewed here, manuscripts from our laboratory have evaluated published experimental data, demonstrating that the Kirchhoff's Laws approach explains (1) why all of the experimental perfused liver clearance data appear to fit the equation that was previously believed to be the well-stirred model, (2) why linear pharmacokinetic systemic bioavailability determinations can be greater than 1, (3) why renal clearance can be a function of drug input processes, and (4) why statistically different bioavailability measures may be found for urinary excretion versus systemic concentration measurements. Our most recent paper demonstrates (5) how the universally accepted steady-state clearance approach used by the field for the past 50 years leads to unrealistic outcomes concerning the relationship between liver-to-blood Kpuu and hepatic availability FH , highlighting the potential for errors in pharmacokinetic evaluations based on differential equations. The Kirchhoff's Laws approach is applicable to all pharmacokinetic analyses of quality experimental data, those that were previously adequately explained with present pharmacokinetic theory, and those that were not. The publications that have attempted to rebut our position do not address unexplained experimental data, and we show here why their analyses are not valid. SIGNIFICANCE STATEMENT: The Kirchhoff's Laws approach to deriving clearance equations for linear systems in parallel or in series, independent of differential equations, successfully describes published pharmacokinetic data that has previously been unexplained. Three recent publications claim to refute our proposed methodology; these publications only make theoretical arguments, do not evaluate experimental data, and never demonstrate that the Kirchhoff methodology provides incorrect interpretations of experimental pharmacokinetic data, including statistically significant data not explained by present pharmacokinetic theory. We demonstrate why these analyses are invalid.

Does Addition of Protein to Hepatocyte or Microsomal In Vitro Incubations Provide a Useful Improvement in In Vitro-In Vivo Extrapolation Predictability?

Accurate prediction of in vivo hepatic clearance is an essential part of successful and efficient drug development; however, many investigators have recognized that there are significant limitations in the predictability of clearance with a tendency for underprediction for primarily metabolized drugs. Here, we examine the impact of adding serum or albumin into hepatocyte and microsomal incubations on the predictability of in vivo hepatic clearance. The addition of protein into hepatocyte incubations has been reported to improve the predictability for high clearance (extraction ratio) drugs and highly protein-bound drugs. Analyzing published data for 60 different drugs and 97 experimental comparisons (with 17 drugs being investigated from two to seven) we confirmed the marked underprediction of clearance. However, we could not validate any relevant improved predictability within twofold by the addition of serum to hepatocyte incubations or albumin to microsomal incubations. This was the case when investigating all measurements, or when subdividing analyses by extraction ratio, degree of protein binding, Biopharmaceutics Drug Disposition Classification System class, examining Extended Clearance Classification System class 1B drugs only, or drug charge. Manipulating characteristics of small data sets of like compounds and adding scaling factors can appear to yield good predictability, but the carryover of these methods to alternate drug classes and different laboratories is not evident. Improvement in predictability of poorly soluble compounds is greater than that for soluble compounds, but not to a meaningful extent. Overall, we cannot confirm that protein addition improves in vitro-in vivo extrapolation predictability to any clinically meaningful degree when considering all drugs and different subsets. SIGNIFICANCE STATEMENT: The addition of protein into microsomal or hepatocyte incubations has been widely proposed to improve hepatic clearance predictions. To date, studies examining this phenomenon have not included appropriate negative controls where predictability is achieved without protein addition and have been conducted with small data sets of similar compounds that don't apply to alternate drug classes. Here, an extensive analysis of published data for 60 drugs and 97 experimental comparisons couldn't validate any relevant clinically improved clearance predictability with protein addition.

International Society for the Study of Xenobiotics (ISSX) New Investigator Group Committee 2019-2020 concluding remarks.

The International Society for the Study of Xenobiotics (ISSX) New Investigators Group has assembled a global team of emerging scientists to collaboratively compose a series of articles whose topics span the broad field of drug metabolism and will guide both new and established investigators alike. The New Investigator Group Committee members are proud to have provided such an opportunity to many promising early-career scientists from across the globe, and would like to acknowledge each contributor for their efforts.

Recent advances in computational metabolite structure predictions and altered metabolic pathways assessment to inform drug development processes.

Many drug candidates fail during preclinical and clinical trials due to variable or unexpected metabolism which may lead to variability in drug efficacy or adverse drug reactions. The drug metabolism field aims to address this important issue from many angles which range from the study of drug-drug interactions, pharmacogenomics, computational metabolic modeling, and others. This manuscript aims to provide brief but comprehensive manuscript summaries highlighting the conclusions and scientific importance of seven exceptional manuscripts published in recent years within the field of drug metabolism. Two main topics within the field are reviewed: novel computational metabolic modeling approaches which provide complex outputs beyond site of metabolism predictions, and experimental approaches designed to discern the impacts of interindividual variability and species differences on drug metabolism. The computational approaches discussed provide novel outputs in metabolite structure and formation likelihood and/or extend beyond the saturated field of drug phase I metabolism, while the experimental metabolic pathways assessments aim to highlight the impacts of genetic polymorphisms and clinical animal model metabolic differences on human metabolism and subsequent health outcomes.

Pharmacogenomics in the era of next generation sequencing - from byte to bedside.

Pharmacogenetic research has resulted in the identification of a multitude of genetic variants that impact drug response or toxicity. These polymorphisms are mostly common and have been included as actionable information in the labels of numerous drugs. In addition to common variants, recent advances in Next Generation Sequencing (NGS) technologies have resulted in the identification of a plethora of rare and population-specific pharmacogenetic variations with unclear functional consequences that are not accessible by conventional forward genetics strategies. In this review, we discuss how comprehensive sequencing information can be translated into personalized pharmacogenomic advice in the age of NGS. Specifically, we provide an update of the functional impacts of rare pharmacogenetic variability and how this information can be leveraged to improve pharmacogenetic guidance. Furthermore, we critically discuss the current status of implementation of pharmacogenetic testing across drug development and layers of care. We identify major gaps and provide perspectives on how these can be minimized to optimize the utilization of NGS data for personalized clinical decision-support.

Recent developments in predicting CYP-independent metabolism.

As lead optimization efforts have successfully reduced metabolic liabilities due to cytochrome P450 (CYP)-mediated metabolism, there has been an increase in the frequency of involvement of non-CYP enzymes in the metabolism of investigational compounds. Although there have been numerous notable advancements in the characterization of non-CYP enzymes with respect to their localization, reaction mechanisms, species differences and identification of typical substrates, accurate prediction of non-CYP-mediated clearance, with a particular emphasis with the difficulties in accounting for any extrahepatic contributions, remains a challenge. The current manuscript comprehensively summarizes the recent advancements in the prediction of drug metabolism and the in vitro to in vitro extrapolation of clearance for substrates of non-CYP drug metabolizing enzymes.

Analyzing Potential Intestinal Transporter Drug-Drug Interactions: Reevaluating Ticagrelor Interaction Studies.

PURPOSE: Previous studies evaluating ticagrelor drug-drug interactions have not differentiated intestinal versus systemic mechanisms, which we do here. METHODS: Using recently published methodologies from our laboratory to differentiate metabolic- from transporter-mediated drug-drug interactions, a critical evaluation of five published ticagrelor drug-drug interactions was carried out to investigate the purported clinical significance of enzymes and transporters in ticagrelor disposition. RESULTS: The suggested CYP3A4 inhibitors, ketoconazole and diltiazem, displayed unchanged mean absorption time (MAT) and time of maximum concentration (Tmax) values as was expected, i.e., the interactions were mainly mediated by metabolic enzymes. The potential CYP3A4/P-gp inhibitor cyclosporine also showed an unchanged MAT value. Further analysis assuming there was no P-gp effect suggested that the increased AUC and unchanged t1/2 for ticagrelor after cyclosporine administration were attributed to the inhibition of intestinal CYP3A4 rather than P-gp. Rifampin, an inducer of CYP3As after multiple dosing, unexpectedly showed decreased MAT and Tmax values, which cannot be completely explained. In contrast, grapefruit juice, an intestinal CYP3A/P-gp/OATP inhibitor, significantly increased MAT and Tmax values for ticagrelor, which may be due to activation of P-gp or inhibition of OATPs expressed in intestine. CONCLUSIONS: This study provides new insight into the role of transporter pathways in ticagrelor intestinal absorption by examining potential MAT and Tmax changes mediated by drug-drug interactions.

Investigating Intestinal Transporter Involvement in Rivaroxaban Disposition through Examination of Changes in Absorption.

PURPOSE: The involvement of the intestinally expressed xenobiotic transporters P-glycoprotein (P-gp) and Breast Cancer Resistance Protein (BCRP) have been implicated in rivaroxaban disposition based on in vitro studies, similar to what had previously been proposed for apixaban. We recently showed that these efflux transporters were not clinically relevant for apixaban disposition and examine here their relevance for this second Factor Xa inhibitor. METHODS: Using recently published methodologies to discern metabolic- from transporter- mediated drug interactions, a critical evaluation was undertaken of 9 rivaroxaban studies reporting 12 DDIs, one study of food effects and one study of hepatic function. RESULTS: Rationale examination of these clinical studies using basic pharmacokinetic theory finds little support for the clinical significance of intestinal efflux transporters in rivaroxaban disposition. Drug-drug interactions are most likely adequately predicted based on the level of CYP 3A metabolism. CONCLUSION: These analyses indicate that inhibition of efflux transporters appears to have negligible, clinically insignificant effects on the rivaroxaban absorption process, which is consistent with the concern that predictions based on in vitro measures may not translate to a clinically relevant interaction in vivo. We emphasize the need to evaluate gastric emptying, dissolution and other processes related to absorption when using MAT changes to indicate efflux transporter inhibition.

Advances in the study of drug metabolism - symposium report of the 12th Meeting of the International Society for the Study of Xenobiotics (ISSX).

The 12th International Society for the Study of Xenobiotics (ISSX) meeting, held in Portland, OR, USA from July 28 to 31, 2019, was attended by diverse members of the pharmaceutical sciences community. The ISSX New Investigators Group provides learning and professional growth opportunities for student and early career members of ISSX. To share meeting content with those who were unable to attend, the ISSX New Investigators herein elected to highlight the "Advances in the Study of Drug Metabolism" symposium, as it engaged attendees with diverse backgrounds. This session covered a wide range of current topics in drug metabolism research including predicting sites and routes of metabolism, metabolite identification, ligand docking, and medicinal and natural products chemistry, and highlighted approaches complemented by computational modeling. In silico tools have been increasingly applied in both academic and industrial settings, alongside traditional and evolving in vitro techniques, to strengthen and streamline pharmaceutical research. Approaches such as quantum mechanics simulations facilitate understanding of reaction energetics toward prediction of routes and sites of drug metabolism. Furthermore, in tandem with crystallographic and orthogonal wet lab techniques for structural validation of drug metabolizing enzymes, in silico models can aid understanding of substrate recognition by particular enzymes, identify metabolic soft spots and predict toxic metabolites for improved molecular design. Of note, integration of chemical synthesis and biosynthesis using natural products remains an important approach for identifying new chemical scaffolds in drug discovery. These subjects, compiled by the symposium organizers, presenters, and the ISSX New Investigators Group, are discussed in this review.

Are There Any Experimental Perfusion Data that Preferentially Support the Dispersion and Parallel-Tube Models over the Well-Stirred Model of Organ Elimination?

In reviewing previously published isolated perfused rat liver studies, we find no experimental data for high-clearance metabolized drugs that reasonably or unambiguously support preference for the dispersion and parallel-tube models versus the well-stirred model of organ elimination when only entering and exiting drug concentrations are available. It is likely that the investigators cited here may have been influenced by: 1) the unphysiologic aspects of the well-stirred model, which may have led them to undervalue the studies that directly test the various hepatic disposition models for high-clearance drugs (for which model differences are the greatest); 2) experimental assumptions made in the last century, which are no longer valid today, related to the predictability of in vivo outcomes from in vitro measures of drug elimination and the influence of albumin in hepatic drug uptake; and 3) a lack of critical review of previously reported experimental studies, resulting in inappropriate interpretation of the available experimental data. The number of papers investigating the theoretical aspects of the dispersion, parallel-tube, and well-stirred models of hepatic elimination greatly outnumber the papers that actually examine the experimental evidence available to substantiate these models. When all experimental studies that measure organ elimination using entering and exiting drug concentrations at steady state are critically reviewed, the simple but unphysiologic well-stirred model is the only model that can describe all trustworthy published available data. SIGNIFICANCE STATEMENT: Although the dispersion model of hepatic elimination more adequately reflects physiologic reality, there are no convincing experimental data that unambiguously favor this model. The well-stirred model can describe all well-designed perfusion studies with high-clearance drugs and nondrug substrates, but the field has not recognized this because of hesitation to accept a nonphysiologic model and flawed attempts to utilize in vitro-in vivo extrapolation approaches.

Intestinal Efflux Transporters P-gp and BCRP Are Not Clinically Relevant in Apixaban Disposition.

PURPOSE: The involvement of the intestinally expressed xenobiotic transporters P-glycoprotein (P-gp) and Breast Cancer Resistance Protein (BCRP) have been implicated in apixaban disposition based on in vitro studies. Recommendations against co-administration of apixaban with inhibitors of these efflux transporters can be found throughout the literature as well as in the apixaban FDA label. However, the clinical relevance of such findings is questionable due to the high permeability and high solubility characteristics of apixaban. METHODS: Using recently published methodologies to discern metabolic- from transporter- mediated drug-drug interactions, a critical evaluation of all published apixaban drug-drug interaction studies was conducted to investigate the purported clinical significance of efflux transporters in apixaban disposition. RESULTS: Rational examination of these clinical studies using basic pharmacokinetic theory does not support the clinical significance of intestinal efflux transporters in apixaban disposition. Further, there is little evidence that efflux transporters are clinically significant determinants of systemic clearance. CONCLUSIONS: Inhibition or induction of intestinal CYP3A4 can account for exposure changes of apixaban in all clinically significant drug-drug interactions, and lack of intestinal CYP3A4 inhibition can explain all studies with no exposure changes, regardless of the potential for these perpetrators to inhibit intestinal or systemic efflux transporters.

Challenging the Relevance of Unbound Tissue-to-Blood Partition Coefficient (Kpuu) on Prediction of Drug-Drug Interactions.

PURPOSE: To examine the theoretical/practical utility of the liver-to-blood partition coefficient (Kpuu) for predicting drug-drug interactions (DDIs), and compare the Kpuu-approach to the extended clearance concept AUCR-approach. METHODS: The Kpuu relationship was derived from first principles. Theoretical simulations investigated the impact of changes in a single hepatic-disposition process on unbound systemic (AUCB,u) and hepatic exposure (AUCH,u) versus Kpuu. Practical aspects regarding Kpuu utilization were examined by predicting the magnitude of DDI between ketoconazole and midazolam employing published ketoconazole Kpuu values. RESULTS: The Kpuu hepatic-disposition relationship is based on the well-stirred model. Simulations emphasize that changes in influx/efflux intrinsic clearances result in Kpuu changes, however AUCH,u remains unchanged. Although incorporation of Kpuu is believed to improve DDI-predictions, utilizing published ketoconazole Kpuu values resulted in prediction errors for a midazolam DDI. CONCLUSIONS: There is limited benefit in using Kpuu for DDI-predictions as the AUCR-based approach can reasonably predict DDIs without measurement of intracellular drug concentrations, a difficult task hindered by experimental variability. Further, Kpuu changes can mislead as they may not correlate with changes in AUCB,u or AUCH,u. The well-stirred model basis of Kpuu when applied to hepatic-disposition implies that nuances of intracellular drug distribution are not considered by the Kpuu model.

Understanding drug-drug interaction and pharmacogenomic changes in pharmacokinetics for metabolized drugs.

Here we characterize and summarize the pharmacokinetic changes for metabolized drugs when drug-drug interactions and pharmacogenomic variance are observed. Following multiple dosing to steady-state, oral systemic concentration-time curves appear to follow a one-compartment body model, with a shorter rate limiting half-life, often significantly shorter than the single dose terminal half-life. This simplified disposition model at steady-state allows comparisons of measurable parameters (i.e., area under the curve, half-life, maximum concentration and time to maximum concentration) following drug interaction or pharmacogenomic variant studies to be utilized to characterize whether a drug is low versus high hepatic extraction ratio, even without intravenous dosing. The characteristics of drugs based on the ratios of area under the curve, maximum concentration and half-life are identified with recognition that volume of distribution is essentially unchanged for drug interaction and pharmacogenomic variant studies where only metabolic outcomes are changed and transporters are not significantly involved. Comparison of maximum concentration changes following single dose interaction and pharmacogenomic variance studies may also identify the significance of intestinal first pass changes. The irrelevance of protein binding changes on pharmacodynamic outcomes following oral and intravenous dosing of low hepatic extraction ratio drugs, versus its relevance for high hepatic extraction ratio drugs is re-emphasized.

The Extended Clearance Concept Following Oral and Intravenous Dosing: Theory and Critical Analyses.

PURPOSE: To derive the theoretical basis for the extended clearance model of organ elimination following both oral and IV dosing, and critically analyze the approaches previously taken. METHODS: We derived from first principles the theoretical basis for the extended clearance concept of organ elimination following both oral and IV dosing and critically analyzed previous approaches. RESULTS: We point out a number of critical characteristics that have either been misinterpreted or not clearly presented in previously published treatments. First, the extended clearance concept is derived based on the well-stirred model. It is not appropriate to use alternative models of hepatic clearance. In analyzing equations, clearance terms are all intrinsic clearances, not total drug clearances. Flow and protein binding parameters should reflect blood measurements, not plasma values. In calculating the AUCR-factor following oral dosing, the AUC terms do not include flow parameters. We propose that calculations of AUCR may be a more useful approach to evaluate drug-drug and pharmacogenomic interactions than evaluating rate-determining steps. Through analyses of cerivastatin and fluvastatin interactions with cyclosporine we emphasize the need to characterize volume of distribution changes resulting from transporter inhibition/induction that can affect rate constants in PBPK models. Finally, we note that for oral doses, prediction of systemic and intrahepatic drug-drug interactions do not require knowledge of fu,H or Kp,uu for substrates/victims. CONCLUSIONS: The extended clearance concept is a powerful tool to evaluate drug-drug interactions, pharmacogenomic and disease state variance but evaluating the AUCR-factor may provide a more valuable approach than characterizing rate-determining steps.

Inhibitory Effects of Trapping Agents of Sulfur Drug Reactive Intermediates against Major Human Cytochrome P450 Isoforms.

In some cases, the formation of reactive species from the metabolism of xenobiotics has been linked to toxicity and therefore it is imperative to detect potential bioactivation for candidate drugs during drug discovery. Reactive species can covalently bind to trapping agents in in vitro incubations of compound with human liver microsomes (HLM) fortified with ß-nicotinamide adenine dinucleotide phosphate (NADPH), resulting in a stable conjugate of trapping agent and reactive species, thereby facilitating analytical detection and providing evidence of short-lived reactive metabolites. Since reactive metabolites are typically generated by cytochrome P450 (CYP) oxidation, it is important to ensure high concentrations of trapping agents are not inhibiting the activities of CYP isoforms. Here we assessed the inhibitory properties of fourteen trapping agents against the major human CYP isoforms (CYP1A2, 2C9, 2C19, 2D6 and 3A). Based on our findings, eleven trapping agents displayed inhibition, three of which had IC50 values less than 1 mM (2-mercaptoethanol, N-methylmaleimide and N-ethylmaleimide (NEM)). Three trapping agents (dimedone, N-acetyl-lysine and arsenite) did not inhibit CYP isoforms at concentrations tested. To illustrate effects of CYP inhibition by trapping agents on reactive intermediate trapping, an example drug (ticlopidine) and trapping agent (NEM) were chosen for further studies. For the same amount of ticlopidine (1 µM), increasing concentrations of the trapping agent NEM (0.007-40 mM) resulted in a bell-shaped response curve of NEM-trapped ticlopidine S-oxide (TSO-NEM), due to CYP inhibition by NEM. Thus, trapping studies should be designed to include several concentrations of trapping agent to ensure optimal trapping of reactive metabolites.

A novel reaction mediated by human aldehyde oxidase: amide hydrolysis of GDC-0834.

GDC-0834, a Bruton's tyrosine kinase inhibitor investigated as a potential treatment of rheumatoid arthritis, was previously reported to be extensively metabolized by amide hydrolysis such that no measurable levels of this compound were detected in human circulation after oral administration. In vitro studies in human liver cytosol determined that GDC-0834 (R)-N-(3-(6-(4-(1,4-dimethyl-3-oxopiperazin-2-yl)phenylamino)-4-methyl-5-oxo- 4,5-dihydropyrazin-2-yl)-2-methylphenyl)-4,5,6,7-tetrahydrobenzo[b] thiophene-2-carboxamide) was rapidly hydrolyzed with a CLint of 0.511 ml/min per milligram of protein. Aldehyde oxidase (AO) and carboxylesterase (CES) were putatively identified as the enzymes responsible after cytosolic fractionation and mass spectrometry-proteomics analysis of the enzymatically active fractions. Results were confirmed by a series of kinetic experiments with inhibitors of AO, CES, and xanthine oxidase (XO), which implicated AO and CES, but not XO, as mediating GDC-0834 amide hydrolysis. Further supporting the interaction between GDC-0834 and AO, GDC-0834 was shown to be a potent reversible inhibitor of six known AO substrates with IC50 values ranging from 0.86 to 1.87 µM. Additionally, in silico modeling studies suggest that GDC-0834 is capable of binding in the active site of AO with the amide bond of GDC-0834 near the molybdenum cofactor (MoCo), orientated in such a way to enable potential nucleophilic attack on the carbonyl of the amide bond by the hydroxyl of MoCo. Together, the in vitro and in silico results suggest the involvement of AO in the amide hydrolysis of GDC-0834.

1-Aminobenzotriazole coincubated with (S)-warfarin results in potent inactivation of CYP2C9.

1-Aminobenzotriazole (ABT) is a nonselective, mechanism-based inactivator of cytochrome P450 (P450) and a useful tool compound to discern P450- from non-P450-mediated metabolism. ABT effectively inactivates major human P450 isoforms, with the notable exception of CYP2C9. Here we propose that ABT preferentially binds to the warfarin-binding pocket in the CYP2C9 active-site cavity; thus, ABT bioactivation and subsequent inactivation is not favored. Therefore, coincubation with (S)-warfarin would result in displacement of ABT from the warfarin-binding pocket and subsequent binding to the active site, converting ABT into a potent inactivator of CYP2C9. To test this hypothesis, in vitro studies were conducted using various coincubation combinations of ABT and (S)-warfarin or diclofenac to modulate the effectiveness of CYP2C9 inactivation by ABT. Coincubation of ABT with (S)-warfarin (diclofenac probe substrate) resulted in potent inactivation, whereas weak inactivation was observed following coincubation of ABT with diclofenac [(S)-warfarin probe substrate]. The kinetic parameters of time-dependent inhibition of ABT for CYP2C9 in the absence and presence of (S)-warfarin (20 µM) were 0.0826 and 0.273 min(-1) for kinact and 3.49 and 0.157 mM for KI, respectively. In addition, a 73.4-fold shift was observed in the in vitro potency (kinact/KI ratio), with an increase from 23.7 ml/min/mmol (ABT alone) to 1740 ml/min/mmol [ABT with (S)-warfarin (20 µM)]. These findings were supported by in silico structural modeling, which showed ABT preferentially binding to the warfarin-binding pocket and the displacement of ABT to the active site in the presence of (S)-warfarin.

The potential of developing high hepatic clearance drugs via controlled release: Lessons from Kirchhoff's Laws.

When a new molecular entity is predicted to exhibit high clearance in humans, pharmaceutical sponsors almost universally search for similar acting back-up compounds that will demonstrate low clearance. Here we show that, except for oral dosing, there can be marked advantages to developing and commercializing controlled release formulations of high clearance drugs, the expertise of readers of this journal. Our recent publications demonstrate that the universally held pharmacokinetic principle that drug delivery rate has no effect on measured drug clearance is not correct. Rather, we show that if clearance from the drug delivery site is markedly less than the iv bolus clearance of a drug, the in vivo drug clearance can be the drug delivery clearance controlled by the designed dosage form. This approach will be especially advantageous for high hepatic clearance drugs. These advantages include not being concerned with: a) saturable nonlinear kinetics, b) significant pharmacogenomic differences, c) drug-drug induction mechanisms, and d) in many cases drug-drug inhibition interactions. This is due to the ability of a drug sponsor to design clearance, independent of the pharmacokinetic characteristics for high clearance compounds, where clearance from the dosage form becomes the drug clearance from the patient. Recognition of this principle, as described here, results from our development of the use of Kirchhoff's Laws from physics to derive rate-defining clearance and rate constant elimination processes independent of differential equation derivations. The key message for readers of this journal is that high clearance drugs are potentially drugable through formulation design and should not be outright disregarded, since for such drugs the dose-corrected area under the curve can be increased if the release rate from the injection site is controlled and slow resulting in drug clearance from the body controlled by clearance from the dosage form. The concepts presented here describe previously unrecognized advantages of controlled release formulations.

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.

The Uses and Advantages of Kirchhoff's Laws vs. Differential Equations in Pharmacology, Pharmacokinetics, and (Even) Chemistry.

In chemistry, rate processes are defined in terms of rate constants, with units of time-1, and are derived by differential equations from amounts. In contrast, when considering drug concentrations in biological systems, particularly in humans, rate processes must be defined in terms of clearance, with units of volume/time, since biological volumes, which are highly dependent on drug partition into biological tissues, cannot be easily determined. In pharmacology, pharmacokinetics, and in making drug dosing decisions, drug clearance and changes in drug clearance are paramount. Clearance is defined as the amount of drug eliminated or moved divided by the exposure driving that elimination or movement. Historically, all clearance derivations in pharmacology and pharmacokinetics have been based on the use of differential equations in terms of rate constants and amounts, which are then converted into clearance equations when multiplied/divided by a hypothesized volume of distribution. Here, we show that except for iv bolus dosing, multiple volumes may be relevant. We have recently shown that clearance relationships, as well as rate constant relationships, may be derived independent of differential equations using Kirchhoff's Laws from physics. Kirchhoff's Laws may be simply translated to recognize that when two or more rate-defining processes operate in parallel, the total value of the overall reaction parameter is equal to the sum of those rate-defining processes. In contrast, when two or more rate-defining processes operate in series, the inverse of the total reaction parameter is equal to the sum of the inverse of those rate-defining steps.