Can In Vitro-In Vivo Extrapolation Be Successful? Recognizing the Incorrect Clearance Assumptions

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.

Are all measures of liver Kpuu a function of FH, as determined following oral dosing, or have we made a critical error in defining hepatic drug clearance?

Here we present, utilizing universally accepted relationships for hepatic clearance at steady state, that for all models of hepatic elimination the ratio of unbound liver drug concentration to unbound systemic blood concentration, Kpuu, is a function of or related to the hepatic bioavailability for that drug, FH. According to the derivation for the well-stirred model, Kpuu can never exceed unity, can frequently be a function of hepatic blood flow, and is equivalent to the value of FH as determined following oral dosing. For the parallel tube model, Kpuu will not equal FH but will be a function of FH and will also never be a value greater than 1. When hepatic clearance is rate limited by basolateral transporters, Kpuu will be less than 1, and less than FH. We believe that such outcomes are highly unlikely, and that the error arises from a basic assumption concerning hepatic clearance that leads to the mechanistic models of hepatic elimination, the well-stirred, parallel tube and dispersion models. That basic assumption is that the steady-state systemic concentration multiplied by the hepatic systemic clearance is equal to the product of the average unbound liver steady-state concentration and the intrinsic hepatic clearance (Css · CL = CH,u · CLint). Calculations of Kpuu and FH based on present methods of analysis provide a strong argument as to why this universally accepted relationship is not correct. Alternatively, we have shown in recent publications that hepatic clearance may be adequately determined based on Kirchhoff's Laws where no assumption of the above equality concerning hepatic intrinsic clearance is required, and where Kpuu is independent of hepatic extraction ratio and FH.

Uridine 5'-Diphospho-glucuronosyltransferase 1A3 (UGT1A3) Prediction of Hepatic Clearance of Organic Anion Transporting Polypeptide 1B3 (OATP1B3) Substrate Telmisartan by Glucuronidation Using In Vitro-In Vivo Extrapolation (IVIVE)

BACKGROUND AND OBJECTIVE

The prediction of pharmacokinetic parameters for drugs metabolised by cytochrome P450 enzymes has been the subject of active research for many years, while the application of in vitro-in vivo extrapolation (IVIVE) techniques for non-cytochrome P450 enzymes has not been thoroughly evaluated. There is still no established quantitative method for predicting hepatic clearance of drugs metabolised by uridine 5'-diphospho-glucuronosyltransferases (UGTs), not to mention those which undergo hepatic uptake. The objective of the study was to predict the human hepatic clearance for telmisartan based on in vitro metabolic stability and hepatic uptake results.

METHODS

Telmisartan was examined in liver systems, allowing to estimate intrinsic clearance (CLint, in vitro) based on the substrate disappearance rate with the use of liquid chromatography tandem mass spectrometry (LC-MS/MS) technique. Obtained CLint, in vitro values were corrected for corresponding unbound fractions. Prediction of human hepatic clearance was made from scaled unbound CLint, in vitro data with the use of the well-stirred model, and finally referenced to the literature value of observed clearance in humans, allowing determination of the essential scaling factors.

RESULTS

The in vitro scaled CLint, in vitro by UGT1A3 was assessed using three systems, human hepatocytes, liver microsomes, and recombinant enzymes. Obtained values were scaled and hepatic metabolism clearance was predicted, resulting in significant clearance underprediction. Utilization of the extended clearance concept (ECC) and hepatic uptake improved prediction of hepatic metabolism clearance. The scaling factors for hepatocytes, assessing the in vitro-in vivo difference, changed from sixfold difference to only twofold difference with the application of the ECC.

CONCLUSIONS

The study showed that taking into consideration hepatic uptake of a drug allows us to obtain satisfactory scaling factors, hence enabling the prediction of in vivo hepatic glucuronidation from in vitro data.

Introducing the Dynamic Well-Stirred Model for Predicting Hepatic Clearance and Extraction Ratio

The well-stirred model (WSM) incorporating the fraction of unbound drug (fu) to account for the effect of plasma binding on intrinsic clearance has been widely used for predicting hepatic clearance under the assumption that drug protein binding reaches equilibrium instantaneously. Our theoretical analysis reveals that the effect of protein binding on intrinsic clearance is better accounted for with the dynamic free fraction (fD), a measure of drug protein binding affinity, which leads to a putative dynamic well-stirred model (dWSM) without the instantaneous equilibrium assumption. Using recombinant CYP3A4 as the in vitro clearance system, we demonstrate that the binding effect of albumin on the intrinsic clearance of both highly bound midazolam and highly free verapamil is fully corrected by their corresponding fD values, respectively. On the other hand, fu only corrects the binding effect of albumin on the intrinsic clearance of verapamil, and yields severe over-correction of the intrinsic clearance of midazolam. The results suggest that the traditional WSM is suitable for highly free drugs like verapamil but not necessarily for highly bound drugs such as midazolam due to the violation of the instantaneous equilibrium assumption or under-estimating the true free drug concentration. In comparison, the dWSM incorporating fD holds true as long as drug elimination follows steady-state kinetics, and hence, it is more broadly applicable to drugs with different protein binding characteristics. Here we demonstrate with 36 diverse drugs, that the dWSM significantly improves the accuracy of predicting human hepatic clearance and liver extraction ratio from in vitro microsomal clearance data, highlighting the importance of drug plasma protein binding kinetics in addressing the under-prediction of hepatic clearance by the WSM.

Empirical scaling factor for predicting human pharmacokinetic profiles of disproportionate metabolites using the Css-MRTpo method and chimeric mice with humanised livers

Predicting plasma concentration-time profiles of disproportionate metabolites in humans is crucial for evaluating metabolites according to the Safety Testing guidelines. We evaluated Css-MRTpo, an empirical method, using chimeric mice with humanised livers capable of generating human-disproportionate metabolites. Azilsartan and AZ-M2 were administered to humanised chimeric mice, and pharmacokinetic parameters were obtained. Pharmacokinetic data for DS-1971a and DS-M1 in humanised chimeric mice were obtained from the literature. The human plasma concentration-time profiles of these compounds were simulated using the Css-MRTpo method. Azilsartan, DS-1971a, and PF-04937319 produced human disproportionate metabolites, AZ-M2, DS-M1, and PF-M1, respectively. The predicted human pharmacokinetic profiles of PF-04937319 and PF-M1 were obtained from a previous study, and their outcomes were re-evaluated. Our findings revealed that the plasma concentrations of the three metabolites were unexpectedly underpredicted, whereas the three unchanged drugs were reasonably predicted. Further, the introduction of the empirical scaling factor of 3, obtained from six model compounds, improved the predictability of metabolites, suggesting the potential usefulness of the Css-MRTpo method in combination with humanised chimeric mice for predicting the pharmacokinetic profiles of disproportionate metabolites at the early stage of new drug development.

Drug Design and Success of Prospective Mouse In Vitro-In Vivo Extrapolation (IVIVE) for Predictions of Plasma Clearance (CLp) from Hepatocyte Intrinsic Clearance (CLint)

Hepatocyte intrinsic clearance (CL_int) and methods of in vitro-in vivo extrapolation (IVIVE) are often used to predict plasma clearance (CL_p) in drug discovery. While the prediction success of this approach is dependent on the chemotype, specific molecular properties and drug design features that govern these outcomes are poorly understood. To address this challenge, we investigated the success of prospective mouse CL_p IVIVE across 2142 chemically diverse compounds. Dilution scaling, which assumes that the free fraction in hepatocyte incubations (f_u,inc) is governed by binding to the 10% of serum in the incubation medium, was used as our default CL_p IVIVE approach. Results show that predictions of CL_p are better for smaller (molecular weight (MW) < 500 Da), less polar (total polar surface area (TPSA) < 100 Ų, hydrogen bond donor (HBD) ≤1, hydrogen bond acceptor (HBA) ≤ 6), lipophilic (log D > 3), and neutral compounds, with low HBD count playing the key role. If compounds are classified according to their chemical space, predictions were good for compounds resembling central nervous system (CNS) drugs [average absolute fold error (AAFE) of 2.05, average fold error (AFE) of 0.90], moderate for classical druglike compounds (according to Lipinski, Veber, and Ghose guidelines; AAFE of 2.55; AFE of 0.68), and poor for nonclassical "beyond the rule of 5" compounds (AAFE of 3.31; AFE of 0.41). From the perspective of measured druglike properties, predictions of CL_p were better for compounds with moderate-to-high hepatocyte CL_int (>10 μL/min/10⁶ cells), high passive cellular permeability (P_app > 100 nm/s), and moderate observed CL_p (5-50 mL/min/kg). Influences of plasma protein binding (f_u,p) and P-glycoprotein (Pgp) apical efflux ratio (AP-ER) were less pronounced. If the extended clearance classification system (ECCS) is applied, predictions were good for class 2 (P_app > 50 nm/s; neutral or basic; AAFE of 2.35; AFE of 0.70) and acceptable for class 1A compounds (AAFE of 2.98; AFE of 0.70). Classes 1B, 3 A/B, and 4 showed poor outcomes (AAFE > 3.80; AFE < 0.60). Functional groups trending toward weaker CL_p IVIVE were esters, carbamates, sulfonamides, carboxylic acids, ketones, primary and secondary amines, primary alcohols, oxetanes, and compounds liable to aldehyde oxidase metabolism, likely due to multifactorial reasons. Multivariate analysis showed that multiple properties are relevant, combining together to define the overall success of CL_p IVIVE. Our results indicate that the current practice of prospective CL_p IVIVE is suitable only for CNS-like compounds and well-behaved classical druglike space (e.g., high permeability or ECCS class 2) without challenging functional groups. Unfortunately, based on existing mouse data, prospective CL_p IVIVE for complex and nonclassical chemotypes is poor and hardly better than random guessing. This is likely due to complexities such as extrahepatic metabolism and transporter-mediated disposition which are poorly captured by this methodology. With small-molecule drug discovery increasingly evolving toward nonclassical and complex chemotypes, existing CL_p IVIVE methodology will require improvement. While empirical correction factors may bridge the gap in the near future, improved and new in vitro assays, data integration models, and machine learning (ML) methods are increasingly needed to address this challenge and reduce the number of nonclinical pharmacokinetic (PK) studies.

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.

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

Clearances are important parameters in pharmacokinetic (PK) models. All clearances in PK models are either process clearances that include diffusion, transport, and metabolism clearances or system clearances that include organ and systemic clearance. Clearance and volume of distribution are two independent parameters that characterize drug disposition in both individual compartments and systems of compartments. In this minireview, we show that systemic and organ clearances are net clearances that can be easily derived by partition analysis. When drugs are eliminated from the central compartment by first-order processes, systemic clearance is constant. When drugs are eliminated from a peripheral compartment, instantaneous systemic clearance will vary with time. However, average clearance and clearance at steady state will be constant and will equal dose divided by area under the curve. We show that peripheral elimination will not have a large impact on most pharmacokinetic analyses and that standard models of organ and systemic clearance are useful and appropriate. SIGNIFICANCE STATEMENT: There are two basic kinds of clearances used in pharmacokinetic models, process and system clearances. We show that organ and systemic clearances are net clearances with blood or plasma as the driving concentration. For linear pharmacokinetics, clearance is constant for elimination from the central compartment but varies with time for peripheral elimination. Despite the different kinds of clearance parameters and models, standard clearance models and concepts remain valid.

Plasma Protein-Mediated Uptake and Contradictions to the Free Drug Hypothesis: A Critical Review

According to the free drug hypothesis (FDH), only free, unbound drug is available to interact with biological targets. This hypothesis is the fundamental principle that continues to explain the vast majority of all pharmacokinetic and pharmacodynamic processes. Under the FDH, the free drug concentration at the target site is considered the driver of pharmacodynamic activity and pharmacokinetic processes. However, deviations from the FDH are observed in hepatic uptake and clearance predictions, where observed unbound intrinsic hepatic clearance (CL_int,u) is larger than expected. Such deviations are commonly observed when plasma proteins are present and form the basis of the so-called plasma protein-mediated uptake effect (PMUE). This review will discuss the basis of plasma protein binding as it pertains to hepatic clearance based on the FDH, as well as several hypotheses that may explain the underlying mechanisms of PMUE. Notably, some, but not all, potential mechanisms remained aligned with the FDH. Finally, we will outline possible experimental strategies to elucidate PMUE mechanisms. Understanding the mechanisms of PMUE and its potential contribution to clearance underprediction is vital to improving the drug development process.

Simplifying the Extended Clearance Concept Classification System (EC3S) to Guide Clearance Prediction in Drug Discovery

PURPOSE

The Extended Clearance Concept Classification System was established as a development-stage tool to provide a framework for identifying fundamental mechanism(s) governing drug disposition in humans. In the present study, the applicability of the EC3S in drug discovery has been investigated. In its current format, the EC3S relies on low-throughput hepatocyte uptake data, which are not frequently generated in a discovery setting.

METHODS

A relationship between hepatocyte uptake clearance and MDCK permeability was first established along with intrinsic clearance from human liver microsomes. The performance of this approach was examined by categorizing 64 drugs into EC3S classes and comparing the predicted major elimination pathway(s) to that observed in humans. As an extension of the work, the ability of the simplified EC3S to predict human systemic clearance based on intrinsic clearance generated using in-vitro metabolic systems was evaluated.

RESULTS

The assessment enabled the use of MDCK permeability and unscaled unbound intrinsic clearance to generate cut-off criteria to categorize compounds into four EC3S classes: Class 12ab, 2cd, 34ab, and 34cd, with major elimination mechanism(s) assigned to each class. The predictivity analysis suggested that systemic clearance could generally be predicted within threefold for EC3S class 12ab and 34ab compounds. For classes 2cd and 34cd, systemic clearance was poorly predicted using in-vitro systems explored in this study.

CONCLUSION

Collectively, our simplified classification approach is expected to facilitate the identification of mechanism(s) involved in drug elimination, faster resolution of in-vitro to in-vivo disconnects, and better design of mechanistic pharmacokinetic studies in drug discovery.

Fast Methods for Drug Approval: Research Perspectives for Pandemic Preparedness

Public heath emergencies such as the outbreak of novel infectious diseases represent a major challenge for drug regulatory bodies, practitioners, and scientific communities. In such critical situations drug regulators and public health practitioners base their decisions on evidence generated and synthesised by scientists. The urgency and novelty of the situation create high levels of uncertainty concerning the safety and effectiveness of drugs. One key tool to mitigate such emergencies is pandemic preparedness. There seems to be, however, a lack of scholarly work on methodology for assessments of new or existing drugs during a pandemic. Issues related to risk attitudes, evidence production and evidence synthesis for drug approval require closer attention. This manuscript, therefore, engages in a conceptual analysis of relevant issues of drug assessment during a pandemic. To this end, we rely in our analysis on recent discussions in the philosophy of science and the philosophy of medicine. Important unanswered foundational questions are identified and possible ways to answer them are considered. Similar problems often have similar solutions, hence studying similar situations can provide important clues. We consider drug assessments of orphan drugs and drug assessments during endemics as similar to drug assessment during a pandemic. Furthermore, other scientific fields which cannot carry out controlled experiments may guide the methodology to draw defeasible causal inferences from imperfect data. Future contributions on methodologies for addressing the issues raised here will indeed have great potential to improve pandemic preparedness.

Large-scale perfused tissues via synthetic 3D soft microfluidics

The vascularization of engineered tissues and organoids has remained a major unresolved challenge in regenerative medicine. While multiple approaches have been developed to vascularize in vitro tissues, it has thus far not been possible to generate sufficiently dense networks of small-scale vessels to perfuse large de novo tissues. Here, we achieve the perfusion of multi-mm3 tissue constructs by generating networks of synthetic capillary-scale 3D vessels. Our 3D soft microfluidic strategy is uniquely enabled by a 3D-printable 2-photon-polymerizable hydrogel formulation, which allows for precise microvessel printing at scales below the diffusion limit of living tissues. We demonstrate that these large-scale engineered tissues are viable, proliferative and exhibit complex morphogenesis during long-term in-vitro culture, while avoiding hypoxia and necrosis. We show by scRNAseq and immunohistochemistry that neural differentiation is significantly accelerated in perfused neural constructs. Additionally, we illustrate the versatility of this platform by demonstrating long-term perfusion of developing neural and liver tissue. This fully synthetic vascularization platform opens the door to the generation of human tissue models at unprecedented scale and complexity.

Review of the application of Kirchhoff's Laws of series and parallel flows to pharmacology: Defining organ clearance

Dosing rate decisions for drugs and changes in dosing in a patient due to disease states, drug interactions and pharmacogenomics are all based on clearance, a measure of the body's ability to eliminate drug. The primary organs of elimination are the liver and the kidney. Clearance for each of these organs is a summative composition of biologic processes. In 1857, Gustav Kirchhoff first developed his laws to describe the "motion of electricity in conductors... [and] ...in wires", recognizing that summative processes occur either in parallel or in series. Since then, Kirchhoff's Laws have also been applied to heat transfer, diffusion and drag force on falling objects, but not to pharmacology. Although not previously recognized, renal clearance always follow Kirchhoff's Laws, as does hepatic clearance for drugs where basolateral transporters are not clinically relevant. However, when basolateral transporters are clinically relevant, we demonstrate that the present accepted approach is inconsistent with recognized drug disposition processes. However, this clearance relationship can be easily corrected using Kirchhoff's Laws. The purpose of this review is to demonstrate that Kirchhoff's Laws, which define how to approach rate processes that occur in parallel versus processes that occur in series, can be applicable to pharmacology in addition to the over 160-year recognition of their use in physical sciences. We anticipate that the application to clearance will be only the first of many such pharmacological analyses.

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.