Abstract
Background
Dermal absorption of chemicals represents an important route of exposure in pharmaceutical, occupational, and environmental settings. Thousands of chemicals with little toxicity or toxicokinetic (TK) data are in use. However, in many cases, in vitro bioactivity data are available. While it is not feasible to collect in vivo TK data, TK may be estimated using high-throughput methods.
Objective
This study developed a generalized physiologically-based TK (PBTK) dermal exposure model for in vitro-in vivo extrapolation (IVIVE). This model estimates dermal exposures that result in systemic concentrations comparable to those associated with in vitro bioactivity.
Methods
The PBTK model simulated dermal exposures for 22 unique exposure scenarios across 12 chemicals with published in vivo concentration time course TK data. Two different methods for estimating chemical- and vehicle-specific skin permeability were evaluated: Potts-Guy [1] and Surrey [2]. Root mean squared log10 errors (RMSLE) were calculated on a per-chemical and method basis.
Results
Given only 12 chemicals with in vivo TK data to permit evaluation, a single, optimal method for predicting dermal permeability could not be identified. IVIVE was performed separately using both permeability methods to calculate administered equivalent doses (AEDs) relevant to potential occupational exposure for 561 chemicals with in vitro bioactivity data. AEDs were defined here as parts per million (ppm) solution concentrations that would result in bioactive plasma concentrations after eight hours of submerged hands. The Potts-Guy method indicated that AED concentrations were not achievable for many chemicals.
Significance
The new dermal PBTK model works with a pre-existing database of more than one thousand compounds including industrial chemicals and pesticides. Regardless of method, IVIVE indicated that dermal exposures can lead to bioactive plasma concentrations for only a small fraction of the chemicals with in vitro bioactivity data examined. Gloves might be recommended for handling those chemicals.
Impact statement
Rapid estimation of risk posed by chemicals through dermal contact is an important need for occupational settings. A generic PBTK model was developed to characterize dermal absorption using chemical-specific in vitro data for metabolism and protein binding and physico-chemical properties. The model was evaluated using in vivo toxicokinetic data for multiple chemicals. The data were equivocal with respect to different dermal absorption assumptions. The new model allows for conversion of in vitro chemical bioactivity data from high-throughput toxicity screening to solution concentrations that would result in bioactive plasma concentrations in occupationally relevant conditions.

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Data availability
R package “httk”, including R scripts, data files, and C code, is freely distributed via the Comprehensive R Archive Network (CRAN – https://cran.r-project.org/). The “httk” codebase is provided in a public GitHub repository (https://github.com/USEPA/CompTox-ExpoCast-httk). A change log describing revisions is available at: https://cran.r-project.org/web/packages/httk/news/news.html.
References
Potts RO, Guy RH. Predicting skin permeability. Pharm Res. 1992;9:663–9.
Chen L, Han L, Saib O, Lian G. In silico prediction of percutaneous absorption and disposition kinetics of chemicals. Pharm Res. 2015;32:1779–93.
Fisher HA, Evans MV, Bunge AL, Hubal EAC, Vallero DA. A compartment model to predict in vitro finite dose absorption of chemicals by human skin. Chemosphere. 2024;349:140689.
OECD TG 428: Skin absorption: in vitro Method. OECD Guidelines for the Testing of Chemicals, Section 2004; 4.
Hoang K. Dermal exposure assessment: principles and applications. US Environmental Protection Agency, Office of Health and Environmental Assessment, Washington, DC. EPA/600/8-91, 1992.
Anissimov YG, Jepps OG, Dancik Y, Roberts MS. Mathematical and pharmacokinetic modelling of epidermal and dermal transport processes. Adv Drug Deliv Rev. 2013;65:169–90.
Selzer D, Neumann D, Schaefer UF. Mathematical models for dermal drug absorption. Expert Opin Drug Metab Toxicol. 2015;11:1567–83.
Bell SM, Chang X, Wambaugh JF, Allen DG, Bartels M, Brouwer KLR, et al. In vitro to in vivo extrapolation for high throughput prioritization and decision making. Toxicol Vitr. 2018;47:213–27.
European Union Regulation (EC) No 1223/2009 of the European Parliament and of the Council of 30 November 2009 on cosmetic products. Official J European Union 2009;342:59.
Lynch C, Sakamuru S, Ooka M, Huang R, Klumpp-Thomas C, Shinn P, et al. High-throughput screening to advance in vitro toxicology: accomplishments, challenges, and future directions. Annu Rev Pharm Toxicol. 2024;64:191–209.
Rotroff DM, Wetmore BA, Dix DJ, Ferguson SS, Clewell HJ, Houck KA, et al. Incorporating human dosimetry and exposure into high-throughput in vitro toxicity screening. Toxicol. Sci. 2010;117:348–58.
Tan Y-M, Liao KH, Conolly RB, Blount BC, Mason AM, Clewell HJ. Use of a physiologically based pharmacokinetic model to identify exposures consistent with human biomonitoring data for chloroform. J Toxicol Environ Health, Part A. 2006;69:1727–56.
Wambaugh JF, Bare JC, Carignan CC, Dionisio KL, Dodson RE, Jolliet O, et al. New approach methodologies for exposure science. Curr Opin Toxicol. 2019;15:76–92.
Tan Y-M, Liao KH, Clewell HJ. Reverse dosimetry: interpreting trihalomethanes biomonitoring data using physiologically based pharmacokinetic modeling. J Expos Sci Environ Epidemiol. 2007;17:591–603.
Pearce RG, Setzer RW, Strope CL, Sipes NS, Wambaugh JF. httk: R package for high-throughput toxicokinetics. J Stat Softw. 2017;79:1–26.
Spracklin DK, Chen D, Bergman AJ, Callegari E, Obach RS. Mini-review: comprehensive drug disposition knowledge generated in the modern human radiolabeled ADME Study. CPT: Pharmacomet Syst Pharm. 2020;9:428–34.
Lancia P, Louazzani M, Gros L, Ginestar J, Fioravanzo E, Baleydier A. Overview of in silico tools to evaluate human health toxicity, ecotoxicity, and toxicokinetic profiles in the hazard assessment of chemicals used in cosmetics. Chem Res Toxicol. 2025; https://doi.org/10.1021/acs.chemrestox.4c00534.
Hu M, Zhang Z, Zhang Y, Zhan M, Qu W, He G, et al. Development of human dermal PBPK models for the bisphenols BPA, BPS, BPF, and BPAF with parallel-layered skin compartment: Basing on dermal administration studies in humans. Sci Total Environ. 2023;868:161639.
Aljallal MA, Chaudhry Q, Price NR. Assessment of performance of the profilers provided in the OECD QSAR toolbox for category formation of chemicals. Sci Rep. 2024;14:18330.
Shah M, Patel M, Shah M, Patel M, Prajapati M. Computational transformation in drug discovery: A comprehensive study on molecular docking and quantitative structure activity relationship (QSAR). Intell Pharm. 2024;2:589–95.
Flynn G. Physicochemical determinants of skin absorption. In T.E. Gerrity and C.J. Henry, Principles of route-to-route extrapolation for risk assessment.1990;93–127 New York; Elsevier.
Brown TN, Armitage JM, Egeghy P, Kircanski I, Arnot JA. Dermal permeation data and models for the prioritization and screening-level exposure assessment of organic chemicals. Environ Int. 2016;94:424–35.
Card ML, Gomez-Alvarez V, Lee W-H, Lynch DG, Orentas NS, Lee MT, et al. History of EPI Suite™ and future perspectives on chemical property estimation in US Toxic Substances Control Act new chemical risk assessments. Environ Sci: Process Impacts. 2017;19:203–12.
Kundu S, Singh A, Samanta S, Mishra R, Mishra R, Chattopadhyay D. Evaluation of selected quantitative structure permeability relationship (QSPR) based mathematical models for the prediction of skin permeability of Camellia sinensis (tea) compounds: Selection of QSPR model for screening tea compounds. Ind J Physiol Allied Sci. 2023;75 https://doi.org/10.55184/ijpas.v75i03.143.
Isaacs KK, Glen WG, Egeghy P, Goldsmith M-R, Smith L, Vallero D, et al. SHEDS-HT: an integrated probabilistic exposure model for prioritizing exposures to chemicals with near-field and dietary sources. Environ Sci Technol. 2014;48:12750–9.
Evans MV, Moxon TE, Lian G, Deacon BN, Chen T, Adams LD, et al. A regression analysis using simple descriptors for multiple dermal datasets: Going from individual membranes to the full skin. J Appl Toxicol. 2023;43:940–50.
Mitragotri S, Anissimov YG, Bunge AL, Frasch HF, Guy RH, Hadgraft J, et al. Mathematical models of skin permeability: An overview. Int J Pharm. 2011;418:115–29.
Sayre RR, Wambaugh JF, Grulke CM. Database of pharmacokinetic time-series data and parameters for 144 environmental chemicals. Sci Data. 2020;7;122.
Davidson-Fritz SE, Ring CL, Evans MV, Schacht CM, Chang X, Breen M, et al. Enabling transparent toxicokinetic modeling for public health risk assessment. PLOS ONE. 2025;20:e0321321.
Breen M, Ring CL, Kreutz A, Goldsmith M-R, Wambaugh JF. High-throughput PBTK models for in vitro to in vivo extrapolation. Expert Opin Drug Metab Toxicol. 2021;17:903–21.
Dawson DE, Ingle BL, Phillips KA, Nichols JW, Wambaugh JF, Tornero-Velez R. Designing QSARs for Parameters of High-Throughput Toxicokinetic Models Using Open-Source Descriptors. Environ Sci Technol. 2021;55:6505–17.
Sipes NS, Wambaugh JF, Pearce R, Auerbach SS, Wetmore BA, Hsieh J-H, et al. An Intuitive Approach for Predicting Potential Human Health Risk with the Tox21 10k Library. Environ Sci Technol. 2017;51:10786–96.
Wang L, Chen L, Lian G, Han L. Determination of partition and binding properties of solutes to stratum corneum. Int J Pharm. 2010;398:114–22.
Kruse P, Ring C, Feshuk M, Brown J, Thunes C. ctxR: Utilities for Interacting with the ‘CTX’APIs. R package version 2024;1.
Linakis MW, Sayre RR, Pearce RG, Sfeir MA, Sipes NS, Pangburn HA, et al. Development and Evaluation of a High Throughput Inhalation Model for Organic Chemicals. J Expos Sci Environ Epidemiol. 2020;30:866–77.
Wang Y-H. Confidence Assessment of the Simcyp Time-Based Approach and a Static Mathematical Model in Predicting Clinical Drug-Drug Interactions for Mechanism-Based CYP3A Inhibitors. Drug Metab Disposit. 2010;38:1094–104.
Wambaugh JF, Wetmore BA, Pearce R, Strope C, Goldsmith R, Sluka JP, et al. Toxicokinetic triage for environmental chemicals. Toxicol Sci. 2015;147:55–67.
Wambaugh JF, Hughes MF, Ring CL, MacMillan DK, Ford J, Fennell TR, et al. Evaluating in vitro-in vivo extrapolation of toxicokinetics. Toxicol Sci. 2018;163:152–69.
Geci R, Gadaleta D, de Lomana MG, Ortega-Vallbona R, Colombo E, Serrano-Candelas E, et al. Systematic evaluation of high-throughput PBK modelling strategies for the prediction of intravenous and oral pharmacokinetics in humans. Arch Toxicol 2024; https://doi.org/10.1007/s00204-024-03764-9.
Paul Friedman K, Gagne M, Loo L-H, Karamertzanis P, Netzeva T, Sobanski T, et al. Utility of in vitro bioactivity as a lower bound estimate of in vivo adverse effect levels and in risk-based prioritization. Toxicol Sci. 2020;173:202–25.
Paul Friedman K, Thomas RS, Wambaugh JF, Harrill JA, Judson RS, Shafer TJ, et al. Integration of new approach methods for the assessment of data poor chemicals. Toxicol Sci. 2025;205:74–105.
Anderson SE, Meade BJ. Potential health effects associated with dermal exposure to occupational chemicals. Environ Health Insights. 2014;8s1:EHI.S15258.
Mattie DR, Grabau JH, McDougal JN. Significance of the Dermal Route of Exposure to Risk Assessment. Risk Anal. 1994;14:277–84.
Boeniger MF, Ahlers HW. Federal government regulation of occupational skin exposure in the USA. Int Arch Occup Environ Health. 2003;76:387–99.
McDougal JN, Boeniger MF. Methods for Assessing Risks of Dermal Exposures in the Workplace. Crit Rev Toxicol. 2002;32:291–327.
Gilmour N, Kern PS, Alépée N, Boislève F, Bury D, Clouet E, et al. Development of a next generation risk assessment framework for the evaluation of skin sensitisation of cosmetic ingredients. Regul Toxicol Pharm. 2020;116:104721.
Coecke S, Pelkonen O, Leite SB, Bernauer U, Bessems JG, Bois FY, et al. Toxicokinetics as a key to the integrated toxicity risk assessment based primarily on non-animal approaches. Toxicol Vitr. 2013;27:1570–7.
Thomas RS, Paules RS, Simeonov A, Fitzpatrick SC, Crofton KM, Casey WM, et al. The US Federal Tox21 Program: A strategic and operational plan for continued leadership. Altex. 2018;35:163–8.
Wilm A, Jochen K, Kirchmair J. Computational approaches for skin sensitization prediction. Crit Rev Toxicol. 2018;48:738–60.
Raabe HA, Costin GE, Allen DG, Lowit A, Corvaro M, O'Dell L, et al. Human relevance of in vivo and in vitro skin irritation tests for hazard classification of pesticides. Cutan Ocul Toxicol. 2025;44:1–21.
Reichard JF, Maier MA, Naumann BD, Pecquet AM, Pfister T, Sandhu R, et al. Toxicokinetic and toxicodynamic considerations when deriving health-based exposure limits for pharmaceuticals. Regul Toxicol Pharm. 2016;79:S67–S78.
Wetmore BA, Wambaugh JF, Ferguson SS, Li L, Clewell HJ 3rd, et al. Relative impact of incorporating pharmacokinetics on predicting in vivo hazard and mode of action from high-throughput in vitro toxicity assays. Toxicol Sci. 2013;132:327–46.
Frank CL, Brown JP, Wallace K, Wambaugh JF, Shah I, Shafer TJ. Defining toxicological tipping points in neuronal network development. Toxicol Appl Pharm. 2018;354:81–93.
Food U, Administration D Estimating the maximum safe starting dose in initial clinical trials for therapeutics in adult healthy volunteers. US Food and Drug Administration, 2005. 1–27.
Wetmore BA, Wambaugh JF, Allen B, Ferguson SS, Sochaski MA, Setzer RW, et al. Incorporating high-throughput exposure predictions with Dosimetry-adjusted in vitro bioactivity to inform chemical toxicity testing. Toxicol Sci. 2015;148:121–36.
Wambaugh JF, Schacht CM. Ring CL A Simple Physiologically Based Toxicokinetic Model for Multi-Route In Vitro–In Vivo Extrapolation. Environ Sci Technol Lett. 2025;12:261–8.
National Academies of Sciences E, and Medicine,. Using 21st Century Science to Improve Risk-Related Evaluations. The National Academies Press: Washington, DC, 2017.
U.S. Environmental Protection Agency. U.S. EPA. A Proof-of-Concept Case Study Integrating Publicly Available Information to Screen Candidates for Chemical Prioritization under TSCA. In. Washington, DC, 2021.
Health Canada. Bioactivity Exposure Ratio: Application in Priority Setting and Risk Assessment. In. Ottawa, ON, Canada, 2021.
Cocito C. Antibiotics of the virginiamycin family, inhibitors which contain synergistic components. Microbiol Rev. 1979;43:145–92.
Hengge UR, Ruzicka T, Schwartz RA, Cork MJ. Adverse effects of topical glucocorticosteroids. J Am Acad Dermatol. 2006;54:1–15.
Ozdemir A, Bas VN. Iatrogenic Cushing’s Syndrome Due to Overuse of Topical Steroid in the Diaper Area. J Trop Pediatr. 2014;60:404–6.
Zhang S, Jin R, Liu W, Zhao Y, Zhu G, Chen C, et al. Widespread p-Phenylenediamine Derivatives in Indoor and Outdoor Dust: Occurrence, Fate, and Exposure. Environ Sci Technol Lett. 2024;11:1075–81.
Matsumoto M, Yamaguchi M, Yoshida Y, Senuma M, Takashima H, Kawamura T, et al. An antioxidant, N,N′-diphenyl-p-phenylenediamine (DPPD), affects labor and delivery in rats: A 28-day repeated dose test and reproduction/developmental toxicity test. Food Chem Toxicol. 2013;56:290–6.
Fang L, Fang C, Di S, Yu Y, Wang C, Wang X, et al. Oral exposure to tire rubber-derived contaminant 6PPD and 6PPD-quinone induce hepatotoxicity in mice. Sci Total Environ. 2023;869:161836.
Zhang Y, Yan L, Wang L, Zhang H, Chen J, Geng N. A nation-wide study for the occurrence of PPD antioxidants and 6PPD-quinone in road dusts of China. Sci Total Environ. 2024;922:171393.
Ewa B, Danuta M-Š. Polycyclic aromatic hydrocarbons and PAH-related DNA adducts. J Appl Genet. 2017;58:321–30.
Väänänen V, Hämeilä M, Kalliokoski P, Nykyri E, Heikkilä P. Dermal Exposure to Polycyclic Aromatic Hydrocarbons among Road Pavers. Ann Occup Hyg. 2005;49:167–78.
Ke Y, Huang L, Xia J, Xu X, Liu H, Li YR. Comparative study of oxidative stress biomarkers in urine of cooks exposed to three types of cooking-related particles. Toxicol Lett. 2016;255:36–42.
Fent KW, Eisenberg J, Snawder J, Sammons D, Pleil JD, Stiegel MA, et al. Systemic Exposure to PAHs and Benzene in Firefighters Suppressing Controlled Structure Fires. Ann Occup Hyg. 2014;58:830–45.
Luo K, Zeng D, Kang Y, Lin X, Sun N, Li C, et al. Dermal bioaccessibility and absorption of polycyclic aromatic hydrocarbons (PAHs) in indoor dust and its implication in risk assessment. Environ Pollut. 2020;264:114829.
Li N, Mu Y, Liu Z, Deng Y, Guo Y, Zhang X, et al. Assessment of interaction between maternal polycyclic aromatic hydrocarbons exposure and genetic polymorphisms on the risk of congenital heart diseases. Sci Rep. 2018;8:3075.
Korsh J, Shen A, Aliano K, Davenport T. Polycyclic Aromatic Hydrocarbons and Breast Cancer: A Review of the Literature. Breast Care. 2015;10:316–8.
>Therachiyil L, Hussein OJ, Uddin S, Korashy HM. Regulation of the aryl hydrocarbon receptor in cancer and cancer stem cells of gynecological malignancies: An update on signaling pathways. Semin Cancer Biol. 2022;86:1186–202.
Gowdy JM, Ulsamer AG, Drage JS, Fujikura T, Cockran W, Fisch RO, et al. Hexachlorophene Lesions in Newborn Infants. Am J Dis Child. 1976;130:247–50.
Kenyon EM, Eklund C, Leavens T, Pegram RA. Development and application of a human PBPK model for bromodichloromethane to investigate the impacts of multi-route exposure. J Appl Toxicol. 2016;36:1095–111.
Poet TS, Charles T, HJ A, Bartels MJ. Chlorpyrifos PBPK/PD model for multiple routes of exposure. Xenobiotica. 2014;44:868–81.
McMullin TS, Yang Y, Campbell J, Clewell HJ, Plotzke K, Andersen ME. Development of an integrated multi-species and multi-dose route PBPK model for volatile methyl siloxanes – D4 and D5. Regul Toxicol Pharm. 2016;74:S1–S13.
Roy A, Weisel CP, Gallo MA, Georgopoulos PG. Studies of multiroute exposure/dose reconstruction using physiologically based pharmacokinetic Models1. Toxicol Ind Health. 1996;12:153–63.
Jongeneelen FJ, ten, Berge WFA. generic, cross-chemical predictive PBTK model with multiple entry routes running as application in MS Excel; design of the model and comparison of predictions with experimental results. Ann Occup Hyg. 2011;55:841–64.
Khalidi H, Onasanwo A, Islam B, Jo H, Fisher C, Aidley R, et al. SimRFlow: An R-based workflow for automated high-throughput PBPK simulation with the Simcyp® simulator. Front Pharmacol 2022;13;929200.
Armitage JM, Hughes L, Sangion A, Arnot JA. Development and intercomparison of single and multicompartment physiologically-based toxicokinetic models: Implications for model selection and tiered modeling frameworks. Environ Int. 2021;154:106557.
ten Berge W. A simple dermal absorption model: Derivation and application. Chemosphere. 2009;75:1440–5.
Ellison CA, Tankersley KO, Obringer CM, Carr GJ, Manwaring J, Rothe H, et al. Partition coefficient and diffusion coefficient determinations of 50 compounds in human intact skin, isolated skin layers and isolated stratum corneum lipids. Toxicol Vitr. 2020;69:104990.
Robertson K, Rees JL. Variation in epidermal morphology in human skin at different body sites as measured by reflectance confocal microscopy. Acta Derm-Venereol. 2010;90:368–73.
Wegner SH, Pinto CL, Ring CL, Wambaugh JF. High-throughput screening tools facilitate calculation of a combined exposure-bioactivity index for chemicals with endocrine activity. Environ Int. 2020;137:105470.
Wambaugh JF, Wetmore BA, Ring CL, Nicolas CI, Pearce R, Honda G, et al. Assessing toxicokinetic uncertainty and variability in risk prioritization. Toxicol Sci. 2019;172:235–51.
Varshavsky JR, Rayasam SDG, Sass JB, Axelrad DA, Cranor CF, Hattis D, et al. Current practice and recommendations for advancing how human variability and susceptibility are considered in chemical risk assessment. Environ Health. 2023;21:133.
Koman PD, Singla V, Lam J, Woodruff TJ. Population susceptibility: A vital consideration in chemical risk evaluation under the Lautenberg Toxic Substances Control Act. PLoS Biol. 2019;17:e3000372.
Chiu WA, White P. Steady-State Solutions to PBPK Models and Their Applications to Risk Assessment I: Route-to-Route Extrapolation of Volatile Chemicals. Risk Anal. 2006;26:769–80.
Acknowledgements
This document has been reviewed in accordance with U.S. Environmental Protection Agency policy and approved for publication. We thank EPA internal reviewers Dr. Peter Egeghy, Dr. Michael Devito, and Dr. Alison Harrill for their helpful comments.
Funding
The United States Environmental Protection Agency (U.S. EPA) through its Office of Research and Development (ORD) funded the research described here. ORD scientists contributed to the research described here. This project was supported by appointments to the Internship/Research Participation Program at ORD and administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the United States Department of Energy and U.S. EPA.
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Annabel Meade: led development of model and initial data analysis, Celia Schacht: led writing and revision of manuscript and revised analysis, Marina V Evans: contributed to development of analysis writing initial draft, model development, Alex George: contributed to model development and data analysis, Rachael Cogbill: contributed to model development, Risa Sayre: contributed to data extraction, John Wambaugh: provided project management and funding and contributed to development of analysis and writing and revision of manuscript.
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The chemical-specific in vitro measurements are based on previously published experiments using human primary cells. In the previously published studies, the vendors providing the cells had obtained relevant consent. ThermoFisher states that “Yes, we comply with country-specific legal and ethical standards for procurement of human liver tissue, including the global ICH Guidelines, and the US’s HIPAA, Uniform Anatomical Gift Act, National Organ Transplant Act, and Hospital Internal Review Board (IRB) approval processes.” The chemical-specific in vivo data measurements are from experiments that have been curated from the literature [28]. The names of the IRB’s used by the vendors in the literature studies are not available.
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Meade, A., Schacht, C.M., Evans, M.V. et al. Incorporating a dermal absorption route into high throughput toxicokinetic modeling. J Expo Sci Environ Epidemiol (2026). https://doi.org/10.1038/s41370-026-00881-8
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DOI: https://doi.org/10.1038/s41370-026-00881-8


