{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T02:03:40Z","timestamp":1784167420832,"version":"3.55.0"},"reference-count":51,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Membranes"],"abstract":"<jats:p>Microfluidic diffusion systems provide a powerful in vitro platform for evaluating transdermal drug delivery (TDD), yet their predictive capability is often constrained by limited experimental datasets and nonlinear transport behavior across membrane\u2014device configurations. This study integrates machine learning (ML) with microfluidic experimentation to develop accurate and generalizable surrogate models for cumulative drug permeation under different hydrodynamic and membrane conditions. This work presents an ML-augmented microfluidic TDD framework for predicting cumulative drug permeation from small experimental datasets. Caffeine cream permeation was examined across twelve device\u2014membrane configurations (sMDC, mMDC, and LiveBox2 paired with PET, CA, rat skin, and alginate) at three perfusion flow rates. For each configuration, SVR, MLP, RFR, GBR, XGB, and KNN models were trained and cross-validated using only 33 experimental measurements. SVR showed the strongest overall performance among the evaluated models, achieving test R2 values typically above 0.97 and RMSE values of &lt;1\u20133 \u00b5g\/cm2, accurately capturing the nonlinear time-flow-cumulative mass behavior of TDD profiles. A domain-bounded Gaussian-noise augmentation strategy was used to increase local sampling density while keeping augmented values within the experimentally observed time and cumulative-mass ranges. Polynomial equations were obtained from the predictions of SVR to capture the interaction between inputs and outputs. The trained SVR surrogates were then used for automated steady-state identification and surrogate-based operating-point selection, revealing the dependence of the selected flow rate on membrane permeability and device geometry. Alginate consistently delivered the highest steady-state cumulative mass across all systems (up to ~448 \u00b5g\/cm2), establishing it as the most efficient TDD membrane among those evaluated. Finally, compact third-degree polynomial equations were derived from the SVR predictions, enabling explicit analytical prediction and rapid design-space exploration. Overall, these ML-derived models and analytical equations provide a fast, low-cost tool for predictive design, enabling rapid microfluidic system evaluation and operating-condition selection, and significantly accelerating the development and screening of next-generation TDD platforms.<\/jats:p>","DOI":"10.3390\/membranes16070239","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T01:05:07Z","timestamp":1784163907000},"page":"239","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Machine Learning\u2013Driven Surrogate Modeling and Operating-Point Selection for a Microfluidic Diffusion-Membrane Platform for Transdermal Drug Delivery"],"prefix":"10.3390","volume":"16","author":[{"given":"Tara","family":"Torabi","sequence":"first","affiliation":[{"name":"Chemical Engineering Department, Urmia University of Technology, Urmia 5716617165, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahsa Jafar","family":"Harasy","sequence":"additional","affiliation":[{"name":"Computer Engineering Department, Urmia University, Urmia 5716617165, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jafar","family":"Tahmoresnezhad","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology and Computer Engineering, Urmia University of Technology, Urmia 5716617165, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samira","family":"Malekmohammadi","sequence":"additional","affiliation":[{"name":"Henry Royce Institute, University of Manchester, Manchester M13 9PL, UK"},{"name":"Department of Materials, School of Natural Sciences, University of Manchester, Manchester M13 9PL, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5316-0989","authenticated-orcid":false,"given":"Adolfo","family":"Iulianelli","sequence":"additional","affiliation":[{"name":"Institute of Membrane Technology of the National Research Council (CNR-ITM), Via P. Bucci 17C, 87036 Rende, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7724-0737","authenticated-orcid":false,"given":"Kamran","family":"Ghasemzadeh","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Edinburgh, Edinburgh EH9 3JW, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1038\/s41551-021-00698-w","article-title":"The evolution of commercial drug delivery technologies","volume":"5","author":"Vargason","year":"2021","journal-title":"Nat. Biomed. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"181","DOI":"10.4103\/jmss.JMSS_53_18","article-title":"A review of controlled drug delivery systems based on cells and cell membranes","volume":"9","author":"Zargar","year":"2019","journal-title":"J. Med. Signals Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.addr.2017.08.009","article-title":"Device-assisted transdermal drug delivery","volume":"127","author":"Lee","year":"2018","journal-title":"Adv. Drug Deliv. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mishra, B., and Bonde, G.V. (2020). Transdermal drug delivery. Controlled Drug Delivery Systems, CRC Press.","DOI":"10.1201\/9780429197833-14"},{"key":"ref_5","first-page":"244","article-title":"An updated review on transdermal drug delivery systems","volume":"8","author":"Mali","year":"2015","journal-title":"Skin"},{"key":"ref_6","first-page":"7","article-title":"Transdermal drug delivery system: Formulation, development and evaluation\u2014An overview","volume":"6","author":"Bathe","year":"2015","journal-title":"Drug Deliv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1002\/adhm.201500040","article-title":"Microfluidic organ-on-a-chip technology for advancement of drug development and toxicology","volume":"4","author":"Caplin","year":"2015","journal-title":"Adv. Healthc. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Niculescu, A.-G., Chircov, C., B\u00eerc\u0103, A.C., and Grumezescu, A.M. (2021). Fabrication and applications of microfluidic devices: A review. Int. J. Mol. Sci., 22.","DOI":"10.3390\/ijms22042011"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.dmpk.2017.11.003","article-title":"Organ\/body-on-a-chip based on microfluidic technology for drug discovery","volume":"33","author":"Kimura","year":"2018","journal-title":"Drug Metab. Pharmacokinet."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1039\/C8LC00827B","article-title":"Personalised organs-on-chips: Functional testing for precision medicine","volume":"19","author":"Mummery","year":"2019","journal-title":"Lab A Chip"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1038\/nature13118","article-title":"The present and future role of microfluidics in biomedical research","volume":"507","author":"Sackmann","year":"2014","journal-title":"Nature"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.bios.2014.07.029","article-title":"Advantages and challenges of microfluidic cell culture in polydimethylsiloxane devices","volume":"63","author":"Halldorsson","year":"2015","journal-title":"Biosens. Bioelectron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1038\/nbt.2989","article-title":"Microfluidic organs-on-chips","volume":"32","author":"Bhatia","year":"2014","journal-title":"Nat. Biotechnol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jconrel.2024.06.045","article-title":"Machine learning in drug delivery","volume":"373","author":"Gormley","year":"2024","journal-title":"J. Control. Release"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"122818","DOI":"10.1016\/j.ijpharm.2023.122818","article-title":"Machine learning in additive manufacturing & Microfluidics for smarter and safer drug delivery systems","volume":"636","author":"Dedeloudi","year":"2023","journal-title":"Int. J. Pharm."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hathout, R.M. (2021). Machine learning methods in drug delivery. Applications of Artificial Intelligence in Process Systems Engineering, Elsevier.","DOI":"10.1016\/B978-0-12-821092-5.00007-3"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kocsis, D., Dhinakaran, S., Pandey, D., Laki, A.J., Laki, M., Sztankovics, D., Lengyel, M., Vr\u00e1bel, J., Naszlady, M.B., and Sebesty\u00e9n, A. (2024). Fluid Dynamics Optimization of Microfluidic Diffusion Systems for Assessment of Transdermal Drug Delivery: An Experimental and Simulation Study. Sci. Pharm., 92.","DOI":"10.3390\/scipharm92020035"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.ijpharm.2015.05.050","article-title":"Topical and transdermal delivery of caffeine","volume":"490","author":"Luo","year":"2015","journal-title":"Int. J. Pharm."},{"key":"ref_19","unstructured":"Huang, Y., Zhai, J., and Boukouvala, F. (2023). 33rd European Symposium on Computer Aided Process Engineering, Elsevier."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"126327","DOI":"10.1016\/j.neucom.2023.126327","article-title":"Deep neural networks in the cloud: Review, applications, challenges and research directions","volume":"545","author":"Chan","year":"2023","journal-title":"Neurocomputing"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107556","DOI":"10.1016\/j.comnet.2020.107556","article-title":"Towards artificial intelligence enabled 6G: State of the art, challenges, and opportunities","volume":"183","author":"Zhang","year":"2020","journal-title":"Comput. Netw."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"108766","DOI":"10.1016\/j.asoc.2022.108766","article-title":"Multi-layer perceptron classification method of medical data based on biogeography-based optimization algorithm with probability distributions","volume":"121","author":"Li","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"123139","DOI":"10.1016\/j.renene.2025.123139","article-title":"Optimization of sustainable biogas valorization to hydrogen via tri-reforming process in packed bed membrane reactor: An integrated CFD-ML digital twin approach","volume":"249","author":"Torabi","year":"2025","journal-title":"Renew. Energy"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Heddam, S., Kim, S., Mehr, A.D., Zounemat-Kermani, M., Elbeltagi, A., Malik, A., and Kisi, O. (2022). A long short-term memory deep learning approach for river water temperature prediction. Current Trends and Advances in Computer-Aided Intelligent Environmental Data Engineering, Elsevier.","DOI":"10.1016\/B978-0-323-85597-6.00015-X"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"109060","DOI":"10.1016\/j.compchemeng.2025.109060","article-title":"Stochastic Algorithm-Based Optimization using Artificial Intelligence\/Machine Learning Models for Sorption Enhanced Steam Methane Reformer Reactor","volume":"196","author":"Bishnu","year":"2025","journal-title":"Comput. Chem. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Afzaal, H., Farooque, A.A., Esau, T.J., Schumann, A.W., Zaman, Q.U., Abbas, F., and Bos, M. (2023). Artificial neural modeling for precision agricultural water management practices. Precision Agriculture, Elsevier.","DOI":"10.1016\/B978-0-443-18953-1.00005-2"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Khandelwal, K., and Dalai, A.K. (2024). Prediction of individual gas yields of supercritical water gasification of lignocellulosic biomass by machine learning models. Molecules, 29.","DOI":"10.3390\/molecules29102337"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107538","DOI":"10.1016\/j.asoc.2021.107538","article-title":"Prediction and analysis of train arrival delay based on XGBoost and Bayesian optimization","volume":"109","author":"Shi","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_29","unstructured":"Cunningham, P., Cord, M., and Delany, S.J. (2008). Supervised learning. Machine Learning Techniques for Multimedia: Case Studies on Organization and Retrieval, Springer."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/s41524-018-0081-z","article-title":"A strategy to apply machine learning to small datasets in materials science","volume":"4","author":"Zhang","year":"2018","journal-title":"npj Comput. Mater."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"054901","DOI":"10.1063\/5.0012285","article-title":"Small data materials design with machine learning: When the average model knows best","volume":"128","author":"Vanpoucke","year":"2020","journal-title":"J. Appl. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"112701","DOI":"10.1016\/j.compositesb.2025.112701","article-title":"Tackling data scarcity in machine learning-based CFRP drilling performance prediction through a broad learning system with virtual sample generation (BLS-VSG)","volume":"305","author":"Ge","year":"2025","journal-title":"Compos. Part B Eng."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Izonin, I., Tkachenko, R., Berezsky, O., Krak, I., Kov\u00e1\u010d, M., and Fedorchuk, M. (2024). Improvement of the ANN-based prediction technology for extremely small biomedical data analysis. Technologies, 12.","DOI":"10.3390\/technologies12070112"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Vabalas, A., Gowen, E., Poliakoff, E., and Casson, A.J. (2019). Machine learning algorithm validation with a limited sample size. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0224365"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"126510","DOI":"10.1016\/j.jhydrol.2021.126510","article-title":"An integrated approach based on Gaussian noises-based data augmentation method and AdaBoost model to predict faecal coliforms in rivers with small dataset","volume":"599","author":"Bilali","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2372497","DOI":"10.1080\/09500839.2024.2372497","article-title":"Prediction of material toughness using ensemble learning and data augmentation","volume":"104","author":"Smyrnov","year":"2024","journal-title":"Philos. Mag. Lett."},{"key":"ref_37","unstructured":"Liu, D., Kababji, S.E., Mitsakakis, N., Pilgram, L., Walters, T., Clemons, M., Pond, G., El-Hussuna, A., and Eman, K. (2025). Synthetic data generation for augmenting small samples. arXiv."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.ijhydene.2024.04.283","article-title":"Enhancing hydrogen production prediction from biomass gasification via data augmentation and explainable AI: A comparative analysis","volume":"68","author":"Ukwuoma","year":"2024","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"103086","DOI":"10.1016\/j.csite.2023.103086","article-title":"Computational simulation of mass transfer in membranes using hybrid machine learning models and computational fluid dynamics","volume":"47","author":"Liu","year":"2023","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Suthaharan, S. (2016). Support vector machine. Machine Learning Models and Algorithms for Big Data Classification: Thinking with Examples for Effective Learning, Springer.","DOI":"10.1007\/978-1-4899-7641-3"},{"key":"ref_41","first-page":"203","article-title":"Support vector regression","volume":"11","author":"Basak","year":"2007","journal-title":"Neural Inf. Process. -Lett. Rev."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"123965","DOI":"10.1016\/j.jhazmat.2020.123965","article-title":"Prediction and evaluation of plasma arc reforming of naphthalene using a hybrid machine learning model","volume":"404","author":"Wang","year":"2021","journal-title":"J. Hazard. Mater."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.rser.2019.04.002","article-title":"Hybrid machine intelligent SVR variants for wind forecasting and ramp events","volume":"108","author":"Dhiman","year":"2019","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"17260","DOI":"10.1016\/j.ijhydene.2019.02.108","article-title":"Hydrogen production via biomass gasification, and modeling by supervised machine learning algorithms","volume":"44","author":"Ozbas","year":"2019","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"e623","DOI":"10.7717\/peerj-cs.623","article-title":"The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation","volume":"7","author":"Chicco","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"102521","DOI":"10.1016\/j.jwpe.2021.102521","article-title":"Modeling nutrient removal by membrane bioreactor at a sewage treatment plant using machine learning models","volume":"46","author":"Yaqub","year":"2022","journal-title":"J. Water Process Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"156009","DOI":"10.1016\/j.scitotenv.2022.156009","article-title":"Enhanced understanding of osmotic membrane bioreactors through machine learning modeling of water flux and salinity","volume":"838","author":"Chang","year":"2022","journal-title":"Sci. Total Environ."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Khan, M.S.H. (2025). Standard deviation. International Encyclopedia of Statistical Science, Springer.","DOI":"10.1007\/978-3-662-69359-9_593"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1214\/ss\/1032280214","article-title":"Bootstrap confidence intervals","volume":"11","author":"DiCiccio","year":"1996","journal-title":"Stat. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/j.cherd.2022.10.001","article-title":"CFD simulation and optimization of an energy-efficient direct contact membrane distillation (DCMD) desalination system","volume":"188","author":"Zare","year":"2022","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_51","unstructured":"Myers, R.H., Montgomery, D.C., and Anderson-Cook, C.M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons."}],"container-title":["Membranes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-0375\/16\/7\/239\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T01:21:34Z","timestamp":1784164894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-0375\/16\/7\/239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,15]]},"references-count":51,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["membranes16070239"],"URL":"https:\/\/doi.org\/10.3390\/membranes16070239","relation":{},"ISSN":["2077-0375"],"issn-type":[{"value":"2077-0375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,15]]}}}