A Systematic Review of Published Physiologically-based Kinetic Models and an Assessment of their Chemical Space Coverage

A brief review on models for birds exposed to chemicals

"A Who's Who of pesticides is therefore of concern to us all. If we are going to live so intimately with these chemicals eating and drinking them, taking them into the very marrow of our bones - we had better know something about their nature and their power."-Rachel Carson, Silent Spring. In her day, Rachel Carson was right: plant protection products (PPP), like all the other chemical substances that humans increasingly release into the environment without further precaution, are among our worst enemies today (Bruhl and Zaller, 2019; Naidu et al., 2021; Tang et al., 2021; Topping et al., 2020). All compartments of the biosphere, air, soil and water, are potential reservoirs within which all species that live there are impaired. Birds are particularly concerned: PPP are recognized as a factor in the decline of their abundance and diversity predominantly in agricultural landscapes. Due to the restrictions on vertebrates testing, in silico-based approaches are an ideal choice alternative given input data are available. This is where the problem lies as we will illustrate in this paper. We performed an extensive literature search covering a long period of time, a wide diversity of bird species, a large range of chemical substances, and as many model types as possible to encompass all our future need to improve environmental risk assessment of chemicals for birds. In the end, we show that poultry species exposed to pesticides are the most studied at the individual level with physiologically based toxicokinetic models. To go beyond, with more species, more chemical types, over several levels of biological organization, we show that observed data are crucially missing (Gilbert, 2011). As a consequence, improving existing models or developing new ones could be like climbing Everest if no additional data can be gathered, especially on chemical effects and toxicodynamic aspects.

Advancing PFAS risk assessment: Integrative approaches using agent-based modelling and physiologically-based kinetic for environmental and health safety

Per- and polyfluoroalkyl substances (PFAS), ubiquitous in a myriad of consumer and industrial products, and depending on the doses of exposure represent a hazard to both environmental and public health, owing to their persistent, mobile, and bio accumulative properties. These substances exhibit long half-lives in humans and can induce potential immunotoxic effects at low exposure levels, sparking growing concerns. While the European Food Safety Authority (EFSA) has assessed the risk to human health related to the presence of PFAS in food, in which a reduced antibody response to vaccination in infants was considered as the most critical human health effect, a comprehensive grasp of the molecular mechanisms spearheading PFAS-induced immunotoxicity is yet to be attained. Leveraging modern computational tools, including the Agent-Based Model (ABM) Universal Immune System Simulator (UISS) and Physiologically Based Kinetic (PBK) models, a deeper insight into the complex mechanisms of PFAS was sought. The adapted UISS serves as a vital tool in chemical risk assessments, simulating the host immune system's reactions to diverse stimuli and monitoring biological entities within specific adverse health contexts. In tandem, PBK models unravelling PFAS' biokinetics within the body i.e. absorption, distribution, metabolism, and elimination, facilitating the development of time-concentration profiles from birth to 75 years at varied dosage levels, thereby enhancing UISS-TOX's predictive abilities. The integrated use of these computational frameworks shows promises in leveraging new scientific evidence to support risk assessments of PFAS. This innovative approach not only allowed to bridge existing data gaps but also unveiled complex mechanisms and the identification of unanticipated dynamics, potentially guiding more informed risk assessments, regulatory decisions, and associated risk mitigations measures for the future.

Computational Tools to Facilitate Early Warning of New Emerging Risk Chemicals

Innovative tools suitable for chemical risk assessment are being developed in numerous domains, such as non-target chemical analysis, omics, and computational approaches. These methods will also be critical components in an efficient early warning system (EWS) for the identification of potentially hazardous chemicals. Much knowledge is missing for current use chemicals and thus computational methodologies complemented with fast screening techniques will be critical. This paper reviews current computational tools, emphasizing those that are accessible and suitable for the screening of new and emerging risk chemicals (NERCs). The initial step in a computational EWS is an automatic and systematic search for NERCs in literature and database sources including grey literature, patents, experimental data, and various inventories. This step aims at reaching curated molecular structure data along with existing exposure and hazard data. Next, a parallel assessment of exposure and effects will be performed, which will input information into the weighting of an overall hazard score and, finally, the identification of a potential NERC. Several challenges are identified and discussed, such as the integration and scoring of several types of hazard data, ranging from chemical fate and distribution to subtle impacts in specific species and tissues. To conclude, there are many computational systems, and these can be used as a basis for an integrated computational EWS workflow that identifies NERCs automatically.

Making PBPK models more reproducible in practice

Systems biology aims to understand living organisms through mathematically modeling their behaviors at different organizational levels, ranging from molecules to populations. Modeling involves several steps, from determining the model purpose to developing the mathematical model, implementing it computationally, simulating the model's behavior, evaluating, and refining the model. Importantly, model simulation results must be reproducible, ensuring that other researchers can obtain the same results after writing the code de novo and/or using different software tools. Guidelines to increase model reproducibility have been published. However, reproducibility remains a major challenge in this field. In this paper, we tackle this challenge for physiologically-based pharmacokinetic (PBPK) models, which represent the pharmacokinetics of chemicals following exposure in humans or animals. We summarize recommendations for PBPK model reporting that should apply during model development and implementation, in order to ensure model reproducibility and comprehensibility. We make a proposal aiming to harmonize abbreviations used in PBPK models. To illustrate these recommendations, we present an original and reproducible PBPK model code in MATLAB, alongside an example of MATLAB code converted to Systems Biology Markup Language format using MOCCASIN. As directions for future improvement, more tools to convert computational PBPK models from different software platforms into standard formats would increase the interoperability of these models. The application of other systems biology standards to PBPK models is encouraged. This work is the result of an interdisciplinary collaboration involving the ELIXIR systems biology community. More interdisciplinary collaborations like this would facilitate further harmonization and application of good modeling practices in different systems biology fields.

Preface to the special issue of Food and Chemical Toxicology on "New approach methodologies and machine learning in food safety and chemical risk assessment: Development of reproducible, open-source, and user-friendly tools for exposure, toxicokinetic, and toxicity assessments in the 21st century"

This Special Issue contains articles on applications of various new approach methodologies (NAMs) in the field of toxicology and risk assessment. These NAMs include in vitro high-throughput screening, quantitative structure-activity relationship (QSAR) modeling, physiologically based pharmacokinetic (PBPK) modeling, network toxicology analysis, molecular docking simulation, omics, machine learning, deep learning, and "template-and-anchor" multiscale computational modeling. These in vitro and in silico approaches complement each other and can be integrated together to support different applications of toxicology, including food safety assessment, dietary exposure assessment, chemical toxicity potency screening and ranking, chemical toxicity prediction, chemical toxicokinetic simulation, and to investigate the potential mechanisms of toxicities, as introduced further in selected articles in this Special Issue.

Physiologically based kinetic (PBK) modeling of propiconazole using a machine learning-enhanced read-across approach for interspecies extrapolation

A significant challenge in the traditional human health risk assessment of agrochemicals is the uncertainty in quantifying the interspecies differences between animal models and humans. To work toward a more accurate and animal-free risk determination, new approaches such as physiologically based kinetic (PBK) modeling have been used to perform dosimetry extrapolation from animals to humans. However, the regulatory use and acceptance of PBK modeling is limited for chemicals that lack in vivo animal pharmacokinetic (PK) data, given the inability to evaluate models. To address these challenges, this study developed PBK models in the absence of in vivo PK data for the fungicide propiconazole, an activator of constitutive androstane receptor (CAR)/pregnane X receptor (PXR). A fit-for-purpose read-across approach was integrated with hierarchical clustering - an unsupervised machine learning algorithm, to bridge the knowledge gap. The integration allowed the incorporation of a broad spectrum of attributes for analog consideration, and enabled the analog selection in a simple, reproducible, and objective manner. The applicability was evaluated and demonstrated using penconazole (source) and three pseudo-unknown target chemicals (epoxiconazole, tebuconazole and triadimefon). Applying this machine learning-enhanced read-across approach, difenoconazole was selected as the most appropriate analog for propiconazole. A mouse PBK model was developed and evaluated for difenoconazole (source), with the mode of action of CAR/PXR activation incorporated to simulate the in vivo autoinduction of metabolism. The difenoconazole mouse model then served as a template for constructing the propiconazole mouse model. A parallelogram approach was subsequently applied to develop the propiconazole rat and human models, enabling a quantitative assessment of interspecies differences in dosimetry. This integrated approach represents a substantial advancement toward refining risk assessment of propiconazole within the framework of animal alternative safety assessment strategies.

Interspecies scaling of toxicity reference values in human health versus ecological risk assessments: A critical review

Risk assessments that focus on anthropogenic chemicals in environmental media-whether considering human health or ecological effects-often rely on toxicity data from experimentally studied species to estimate safe exposures for species that lack similar data. Current default extrapolation approaches used in both human health risk assessments and ecological risk assessments (ERAs) account for differences in body weight between the test organisms and the species of interest, but the two default approaches differ in important ways. Human health risk assessments currently employ a default based on body weight raised to the three-quarters power. Ecological risk assessments for wildlife (i.e., mammals and birds) are typically based directly on body weight, as measured in the test organism and receptor species. This review describes differences in the experimental data underlying these default practices and discusses the many factors that affect interspecies variability in chemical exposures. The interplay of these different factors can lead to substantial departures from default expectations. Alternative methodologies for conducting more accurate interspecies extrapolations in ERAs for wildlife are discussed, including tissue-based toxicity reference values, physiologically based toxicokinetic and/or toxicodynamic modeling, chemical read-across, and a system of categorical defaults based on route of exposure and toxic mode of action. Integr Environ Assess Manag 2024;20:749-764. © 2023 SETAC.

Human biomonitoring and toxicokinetics as key building blocks for next generation risk assessment

Human health risk assessment is historically built upon animal testing, often following Organisation for Economic Co-operation and Development (OECD) test guidelines and exposure assessments. Using combinations of human relevant in vitro models, chemical analysis and computational (in silico) approaches bring advantages compared to animal studies. These include a greater focus on the human species and on molecular mechanisms and kinetics, identification of Adverse Outcome Pathways and downstream Key Events as well as the possibility of addressing susceptible populations and additional endpoints. Much of the advancement and progress made in the Next Generation Risk Assessment (NGRA) have been primarily focused on new approach methodologies (NAMs) and physiologically based kinetic (PBK) modelling without incorporating human biomonitoring (HBM). The integration of toxicokinetics (TK) and PBK modelling is an essential component of NGRA. PBK models are essential for describing in quantitative terms the TK processes with a focus on the effective dose at the expected target site. Furthermore, the need for PBK models is amplified by the increasing scientific and regulatory interest in aggregate and cumulative exposure as well as interactions of chemicals in mixtures. Since incorporating HBM data strengthens approaches and reduces uncertainties in risk assessment, here we elaborate on the integrated use of TK, PBK modelling and HBM in chemical risk assessment highlighting opportunities as well as challenges and limitations. Examples are provided where HBM and TK/PBK modelling can be used in both exposure assessment and hazard characterization shifting from external exposure and animal dose/response assays to animal-free, internal exposure-based NGRA.

PBPK Modeling as an Alternative Method of Interspecies Extrapolation that Reduces the Use of Animals: A Systematic Review

INTRODUCTION

Physiologically based pharmacokinetic (PBPK) modeling is a computational approach that simulates the anatomical structure of the studied species and presents the organs and tissues as compartments interconnected by arterial and venous blood flows.

AIM

The aim of this systematic review was to analyze the published articles focused on the development of PBPK models for interspecies extrapolation in the disposition of drugs and health risk assessment, presenting to this modeling an alternative to reduce the use of animals.

METHODS

For this purpose, a systematic search was performed in PubMed using the following search terms: "PBPK" and "Interspecies extrapolation". The revision was performed according to PRISMA guidelines.

RESULTS

In the analysis of the articles, it was found that rats and mice are the most commonly used animal models in the PBPK models; however, most of the physiological and physicochemical information used in the reviewed studies were obtained from previous publications. Additionally, most of the PBPK models were developed to extrapolate pharmacokinetic parameters to humans and the main application of the models was for toxicity testing.

CONCLUSION

PBPK modeling is an alternative that allows the integration of in vitro and in silico data as well as parameters reported in the literature to predict the pharmacokinetics of chemical substances, reducing in large quantity the use of animals that are required in traditional studies.

New approach methodologies in human regulatory toxicology - Not if, but how and when!

The predominantly animal-centric approach of chemical safety assessment has increasingly come under pressure. Society is questioning overall performance, sustainability, continued relevance for human health risk assessment and ethics of this system, demanding a change of paradigm. At the same time, the scientific toolbox used for risk assessment is continuously enriched by the development of "New Approach Methodologies" (NAMs). While this term does not define the age or the state of readiness of the innovation, it covers a wide range of methods, including quantitative structure-activity relationship (QSAR) predictions, high-throughput screening (HTS) bioassays, omics applications, cell cultures, organoids, microphysiological systems (MPS), machine learning models and artificial intelligence (AI). In addition to promising faster and more efficient toxicity testing, NAMs have the potential to fundamentally transform today's regulatory work by allowing more human-relevant decision-making in terms of both hazard and exposure assessment. Yet, several obstacles hamper a broader application of NAMs in current regulatory risk assessment. Constraints in addressing repeated-dose toxicity, with particular reference to the chronic toxicity, and hesitance from relevant stakeholders, are major challenges for the implementation of NAMs in a broader context. Moreover, issues regarding predictivity, reproducibility and quantification need to be addressed and regulatory and legislative frameworks need to be adapted to NAMs. The conceptual perspective presented here has its focus on hazard assessment and is grounded on the main findings and conclusions from a symposium and workshop held in Berlin in November 2021. It intends to provide further insights into how NAMs can be gradually integrated into chemical risk assessment aimed at protection of human health, until eventually the current paradigm is replaced by an animal-free "Next Generation Risk Assessment" (NGRA).

Risk assessment in the 21st century: where are we heading?

Reliance on animal tests for chemical safety assessment is increasingly being challenged, not only because of ethical reasons, but also because they procrastinate regulatory decisions and because of concerns over the transferability of results to humans. New approach methodologies (NAMs) need to be fit for purpose and new thinking is required to reconsider chemical legislation, validation of NAMs and opportunities to move away from animal tests. This article summarizes the presentations from a symposium at the 2022 Annual Congress of the British Toxicology Society on the topic of the future of chemical risk assessment in the 21st century. The symposium included three case-studies where NAMs have been used in safety assessments. The first case illustrated how read-across augmented with some in vitro tests could be used reliably to perform the risk assessment of analogues lacking data. The second case showed how specific bioactivity assays could identify an NAM point of departure (PoD) and how this could be translated through physiologically based kinetic modelling in an in vivo PoD for the risk assessment. The third case showed how adverse-outcome pathway (AOP) information, including molecular-initiating event and key events with their underlying data, established for certain chemicals could be used to produce an in silico model that is able to associate chemical features of an unstudied substance with specific AOPs or AOP networks. The manuscript presents the discussions that took place regarding the limitations and benefits of these new approaches, and what are the barriers and the opportunities for their increased use in regulatory decision making.

An Overview of Physiologically-Based Pharmacokinetic Models for Forensic Science

A physiologically-based pharmacokinetic (PBPK) model represents the structural components of the body with physiologically relevant compartments connected via blood flow rates described by mathematical equations to determine drug disposition. PBPK models are used in the pharmaceutical sector for drug development, precision medicine, and the chemical industry to predict safe levels of exposure during the registration of chemical substances. However, one area of application where PBPK models have been scarcely used is forensic science. In this review, we give an overview of PBPK models successfully developed for several illicit drugs and environmental chemicals that could be applied for forensic interpretation, highlighting the gaps, uncertainties, and limitations.

In-Depth Analysis of Physiologically Based Pharmacokinetic (PBPK) Modeling Utilization in Different Application Fields Using Text Mining Tools

In the past decade, only a small number of papers have elaborated on the application of physiologically based pharmacokinetic (PBPK) modeling across different areas. In this review, an in-depth analysis of the distribution of PBPK modeling in relation to its application in various research topics and model validation was conducted by text mining tools. Orange 3.32.0, an open-source data mining program was used for text mining. PubMed was used for data retrieval, and the collected articles were analyzed by several widgets. A total of 2699 articles related to PBPK modeling met the predefined criteria. The number of publications per year has been rising steadily. Regarding the application areas, the results revealed that 26% of the publications described the use of PBPK modeling in early drug development, risk assessment and toxicity assessment, followed by absorption/formulation modeling (25%), prediction of drug-disease interactions (20%), drug-drug interactions (DDIs) (17%) and pediatric drug development (12%). Furthermore, the analysis showed that only 12% of the publications mentioned model validation, of which 51% referred to literature-based validation and 26% to experimentally validated models. The obtained results present a valuable review of the state-of-the-art regarding PBPK modeling applications in drug discovery and development and related fields.

The use of NAMs and omics data in risk assessment

The animal-centric approach so far predominantly employed in risk assessment has been questioned in recent years due to a number of shortcomings regarding performance, consistency, transferability of results, sustainability, costs and ethical reasons. Alternatives to animal testing, collectively termed NAMs, may have the potential to deliver sound, cost-effective, prompt and reliable information, but their regulatory acceptance has not been established yet. The main reasons behind this are mostly related to actual methodological obstacles, with particular reference to addressing complex endpoints such as repeated-dose toxicity, the issue of translating the concept of adversity to NAMs, and doubts of stakeholders about the level of chemical safety ensured by NAMs. With the aim of providing an updated view on major conceptual and methodological developments in the field of toxicology, a symposium and a workshop were organised by the German Federal Institute for Risk Assessment (Bundesinstitut für Risikobewertung, BfR) and Helmholtz Centre for Environmental Research on 15-17 November 2021 in Berlin. The conference, entitled 'Challenges in Public Health Protection in the 21st Century: New Methods, Omics and Novel Concepts in Toxicology' brought together eminent scientists with representatives from industry and regulatory authorities. The organisation, day-to-day operations and the reporting of the event main outcomes in a position paper were the main focus of the present EFSA EU-FORA work programme. Tasks pertaining to 'The use of NAMs and omics data in risk assessment' were implemented under the shared supervision of units 'Testing and Assessment Strategies Pesticides' and 'Effect-based Analytics and Toxicogenomics' of the German Federal Institute for Risk Assessment.

A generic avian physiologically-based kinetic (PBK) model and its application in three bird species

Physiologically-based kinetic (PBK) models are effective tools for designing toxicological studies and conducting extrapolations to inform hazard characterization in risk assessment by filling data gaps and defining safe levels of chemicals. In the present work, a generic avian PBK model for male and female birds was developed using PK-Sim and MoBi from the Open Systems Pharmacology Suite (OSPS). The PBK model includes an ovulation model (egg development) to predict concentrations of chemicals in eggs from dietary exposure. The model was parametrized for chicken (Gallus gallus), bobwhite quail (Colinus virginianus) and mallard duck (Anas platyrhynchos) and was tested with nine chemicals for which in vivo studies were available. Time-concentration profiles of chemicals reaching tissues and egg compartment were simulated and compared to in vivo data. The overall accuracy of the PBK model predictions across the analyzed chemicals was good. Model simulations were found to be in the range of 22-79% within a 3-fold and 41-89% were within 10- fold deviation of the in vivo observed data. However, for some compounds scarcity of in-vivo data and inconsistencies between published studies allowed only a limited goodness of fit evaluation. The generic avian PBK model was developed following a "best practice" workflow describing how to build a PBK model for novel species. The credibility and reproducibility of the avian PBK models were scored by evaluation according to the available guidance documents from WHO (2010), and OECD (2021), to increase applicability, confidence and acceptance of these in silico models in chemical risk assessment.

Towards best use and regulatory acceptance of generic physiologically based kinetic (PBK) models for in vitro-to-in vivo extrapolation (IVIVE) in chemical risk assessment

With an increasing need to incorporate new approach methodologies (NAMs) in chemical risk assessment and the concomitant need to phase out animal testing, the interpretation of in vitro assay readouts for quantitative hazard characterisation becomes more important. Physiologically based kinetic (PBK) models, which simulate the fate of chemicals in tissues of the body, play an essential role in extrapolating in vitro effect concentrations to in vivo bioequivalent exposures. As PBK-based testing approaches evolve, it will become essential to standardise PBK modelling approaches towards a consensus approach that can be used in quantitative in vitro-to-in vivo extrapolation (QIVIVE) studies for regulatory chemical risk assessment based on in vitro assays. Based on results of an ECETOC expert workshop, steps are recommended that can improve regulatory adoption: (1) define context and implementation, taking into consideration model complexity for building fit-for-purpose PBK models, (2) harmonise physiological input parameters and their distribution and define criteria for quality chemical-specific parameters, especially in the absence of in vivo data, (3) apply Good Modelling Practices (GMP) to achieve transparency and design a stepwise approach for PBK model development for risk assessors, (4) evaluate model predictions using alternatives to in vivo PK data including read-across approaches, (5) use case studies to facilitate discussions between modellers and regulators of chemical risk assessment. Proof-of-concepts of generic PBK modelling approaches are published in the scientific literature at an increasing rate. Working on the previously proposed steps is, therefore, needed to gain confidence in PBK modelling approaches for regulatory use.

A State-of-the-Art Review on the Alternatives to Animal Testing for the Safety Assessment of Cosmetics

Almost a decade after the stipulated deadline in the 7th amendment to the EU Cosmetics Directive, which bans the marketing of animal-tested cosmetics in the EU from 2013, animal experimentation for cosmetic-related purposes remains a topic of animated debate. Cosmetic industry continues to be scrutinised for the practice, despite its leading role in funding and adopting innovation in this field. This paper aims to provide a state-of-the-art review of the field on alternative testing methods, also known as New Approach Methodologies (NAMs), with the focus on assessing the safety of cosmetic ingredients and products. It starts with innovation drivers and global regulatory responses, followed by an extensive, endpoint-specific overview of accepted/prospective NAMs. The overview covers main developments in acute toxicity, skin corrosion/irritation, serious eye damage/irritation, skin sensitisation, repeated dose toxicity, reproductive toxicity/endocrine disruption, mutagenicity/genotoxicity, carcinogenicity, photo-induced toxicity, and toxicokinetics. Specific attention was paid to the emerging in silico methodology. This paper also provides a brief overview of the studies on public perception of animal testing in cosmetics. It concludes with a view that educating consumers and inviting them to take part in advocacy could be an effective tool to achieve policy changes, regulatory acceptance, and investment in innovation.

Case study on the impact of the source of metabolism parameters in next generation physiologically based pharmacokinetic models: Implications for occupational exposures to trimethylbenzenes

Physiologically based pharmacokinetic (PBPK) models are a means of making important linkages between exposure assessment and in vitro toxicity. A key constraint on rapid application of PBPK models in risk assessment is traditional reliance on substance-specific in vivo toxicokinetic data to evaluate model quality. Bounding conditions, in silico, in vitro, and chemical read-across approaches have been proposed as alternative sources for metabolic clearance estimates. A case study to test consistency of predictive ability across these approaches was conducted using trimethylbenzenes (TMB) as prototype chemicals. Substantial concordance was found among TMB isomers with respect to accuracy (or inaccuracy) of approaches to estimating metabolism; for example, the bounding conditions never reproduced the human in vivo toxicokinetic data within two-fold. Using only approaches that gave acceptable prediction of in vivo toxicokinetics for the source compound (1,2,4-TMB) substantially narrowed the range of plausible internal doses for a given external dose for occupational, emergency response, and environmental/community health risk assessment scenarios for TMB isomers. Thus, risk assessments developed using the target compound models with a constrained subset of metabolism estimates (determined for source chemical models) can be used with greater confidence that internal dosimetry will be estimated with accuracy sufficient for the purpose at hand.

A Permeability- and Perfusion-based PBPK model for Improved Prediction of Concentration-time Profiles

To improve predictions of concentration‐time (C‐t) profiles of drugs, a new physiologically based pharmacokinetic modeling framework (termed ‘PermQ’) has been developed. This model includes permeability into and out of capillaries, cell membranes, and intracellular lipids. New modeling components include (i) lumping of tissues into compartments based on both blood flow and capillary permeability, and (ii) parameterizing clearances in and out of membranes with apparent permeability and membrane partitioning values. Novel observations include the need for a shallow distribution compartment particularly for bases. C‐t profiles were modeled for 24 drugs (7 acidic, 5 neutral, and 12 basic) using the same experimental inputs for three different models: Rodgers and Rowland (RR), a perfusion‐limited membrane‐based model (K_p,mem), and PermQ. K_p,mem and PermQ can be directly compared since both models have identical tissue partition coefficient parameters. For the 24 molecules used for model development, errors in V_ss and t_1/2 were reduced by 37% and 43%, respectively, with the PermQ model. Errors in C‐t profiles were reduced (increased EOC) by 43%. The improvement was generally greater for bases than for acids and neutrals. Predictions were improved for all 3 models with the use of parameters optimized for the PermQ model. For five drugs in a test set, similar results were observed. These results suggest that prediction of C‐t profiles can be improved by including capillary and cellular permeability components for all tissues.