{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T08:49:58Z","timestamp":1785919798457,"version":"3.56.0"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T00:00:00Z","timestamp":1785801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Pharmaceuticals"],"abstract":"<jats:p>Background\/Objectives: Poly(lactide-co-glycolide) (PLGA) microspheres support long-acting drug delivery, but their release profiles are difficult to predict because burst release, diffusion, polymer degradation, and formulation-dependent effects interact across multiple time scales. This study aimed to develop a continuous-time model that combines accurate release prediction with physically admissible trajectories and release-component attribution. Methods: MC-NODE encodes ten drug, polymer, and formulation descriptors, decomposes the non-negative release rate into burst, diffusion, degradation-associated late-stage, and neural-residual components, and applies a formulation-dependent plateau through a semi-analytical state map. The model was evaluated on a literature-curated dataset containing 321 in vitro release curves, 4913 observations, 89 drugs, and 113 publications using DOI-grouped five-fold cross-validation, complementary extrapolation and sparse-sampling protocols, synthetic mechanism-recovery experiments, and retrospective orthogonal consistency analysis. Results: MC-NODE achieved an RMSE of 0.094\u00b10.005 and an R2 of 0.854\u00b10.018, with all 321 out-of-fold trajectories satisfying monotonicity and range criteria. It recovered synthetic contribution labels more accurately than the ablated variants. The degradation-associated late-stage contribution showed positive associations with experimental degradation, molecular-weight loss, pore-evolution, and mass-loss indicators, while the diffusion contribution was positively associated with an experimental diffusion indicator. Dominant-process agreement was 83.3%, and matched external or out-of-fold trajectories achieved an RMSE of 0.108\u00b10.020. Under drug-grouped, chemical-cluster, and alternative sparse-sampling evaluations, MC-NODE retained the lowest absolute trajectory-level errors among the compared models. Conclusions: MC-NODE improves formulation-level PLGA release prediction while preserving continuous, monotonic, and bounded trajectories. Its component outputs provide experimentally supported, model-attributed summaries for comparative formulation analysis.<\/jats:p>","DOI":"10.3390\/ph19081227","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T15:08:09Z","timestamp":1785856089000},"page":"1227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["MC-NODE: A Mechanism-Decomposed Neural Differential Model for PLGA Microsphere Drug Release Prediction and Attribution"],"prefix":"10.3390","volume":"19","author":[{"given":"Zi\u2019an","family":"Tang","sequence":"first","affiliation":[{"name":"Department of Pharmaceutics, UCL School of Pharmacy, University College London, London WC1N 1AX, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Li","sequence":"additional","affiliation":[{"name":"Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianfu","family":"Li","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0501-2824","authenticated-orcid":false,"given":"Feng","family":"Xue","sequence":"additional","affiliation":[{"name":"Graduate School of Information, Production and Systems, Waseda University, Kitakyushu 808-0135, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.3390\/polym3031377","article-title":"Poly Lactic-co-Glycolic Acid (PLGA) as Biodegradable Controlled Drug Delivery Carrier","volume":"3","author":"Makadia","year":"2011","journal-title":"Polymers"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ijpharm.2011.05.049","article-title":"The Mechanisms of Drug Release in Poly(lactic-co-glycolic acid)-Based Drug Delivery Systems\u2014A Review","volume":"415","author":"Fredenberg","year":"2011","journal-title":"Int. J. Pharm."},{"key":"ref_3","first-page":"100440","article-title":"Release Mechanisms of PLGA-Based Drug Delivery Systems: A Review","volume":"10","author":"Siepmann","year":"2025","journal-title":"Int. J. Pharm. X"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Al Hagbani, T., Vishwa, B., Abu Lila, A.S., Alotaibi, H.F., Khafagy, E.S., Moin, A., and Gowda, D.V. (2022). Pulmonary Targeting of Levofloxacin Using Microsphere-Based Dry Powder Inhalation. Pharmaceuticals, 15.","DOI":"10.3390\/ph15050560"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Seon, S., Li, Y., Lee, S., Jeon, Y.S., Kang, D.S., and Ryu, D.J. (2024). Self-Assembled PLGA-Pluronic F127 Microsphere for Sustained Drug Release for Osteoarthritis. Pharmaceuticals, 17.","DOI":"10.3390\/ph17040471"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1038\/s41597-025-04621-9","article-title":"A Dataset on Formulation Parameters and Characteristics of Drug-Loaded PLGA Microparticles","volume":"12","author":"Bao","year":"2025","journal-title":"Sci. Data"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"213100","DOI":"10.1016\/j.bioadv.2022.213100","article-title":"Bottom-Up Design of Hydrogels for Programmable Drug Release","volume":"141","author":"Owh","year":"2022","journal-title":"Biomater. Adv."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Omidian, H., and Wilson, R.L. (2025). PLGA Implants for Controlled Drug Delivery and Regenerative Medicine: Advances, Challenges, and Clinical Potential. Pharmaceuticals, 18.","DOI":"10.3390\/ph18050631"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gupta, R., Chen, Y., Sarkar, M., and Xie, H. (2022). Surfactant Mediated Accelerated and Discriminatory In Vitro Drug Release Method for PLGA Nanoparticles of Poorly Water-Soluble Drug. Pharmaceuticals, 15.","DOI":"10.3390\/ph15121489"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1038\/s41467-022-35343-w","article-title":"Machine Learning Models to Accelerate the Design of Polymeric Long-Acting Injectables","volume":"14","author":"Bannigan","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4838","DOI":"10.1038\/s41467-023-40459-8","article-title":"Applied Machine Learning as a Driver for Polymeric Biomaterials Design","volume":"14","author":"McDonald","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"109756","DOI":"10.1016\/j.compbiomed.2025.109756","article-title":"Utilizing Machine Learning for Predicting Drug Release from Polymeric Drug Delivery Systems","volume":"188","author":"Aghajanpour","year":"2025","journal-title":"Comput. Biol. Med."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"124905","DOI":"10.1016\/j.ijpharm.2024.124905","article-title":"Optimising the Production of PLGA Nanoparticles by Combining Design of Experiment and Machine Learning","volume":"667","author":"Seegobin","year":"2024","journal-title":"Int. J. Pharm."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1038\/s41597-025-05520-9","article-title":"A Formulation Dataset of Poly(lactide-co-glycolide) Nanoparticles for Small Molecule Delivery","volume":"12","author":"Goren","year":"2025","journal-title":"Sci. Data"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e2501190","DOI":"10.1002\/adhm.202501190","article-title":"Lymphoid and CXCR4 Cell Targeted Lipid Nanoparticles Facilitate HIV-1 Proviral DNA Excision","volume":"14","author":"Panja","year":"2025","journal-title":"Adv. Healthc. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s43452-026-01434-4","article-title":"Multi-Objective Design Method of Concrete Mix Ratio Based on Machine Learning: Forward Prediction and Reverse Design","volume":"26","author":"Yang","year":"2026","journal-title":"Arch. Civ. Mech. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4218","DOI":"10.1038\/s41598-024-82728-6","article-title":"Machine Learning Integrated with In Vitro Experiments for Study of Drug Release from PLGA Nanoparticles","volume":"15","author":"Sun","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Song, Y., Bashyal, S., Cho, H.J., Woo, M.R., Kim, J.O., and Hwang, D. (2026). Interpretable Two-Stage Machine Learning for Early and Full Drug Release Prediction in PLGA Microspheres. Pharmaceuticals, 19.","DOI":"10.3390\/ph19050767"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.jconrel.2024.08.010","article-title":"Machine Learning of Raman Spectra Predicts Drug Release from Polysaccharide Coatings for Targeted Colonic Delivery","volume":"374","author":"Abdalla","year":"2024","journal-title":"J. Control. Release"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1208\/s12248-025-01101-1","article-title":"Machine Learning Predicts Drug Release Profiles and Kinetic Parameters Based on Tablets\u2019 Formulations","volume":"27","author":"Protopapa","year":"2025","journal-title":"AAPS J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"114602","DOI":"10.1016\/j.jconrel.2026.114602","article-title":"Automated Active Learning to Optimize Hydrogel Drug Release Profiles","volume":"391","author":"Cheong","year":"2026","journal-title":"J. Control. Release"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1080\/01969722.2025.2521831","article-title":"Wavelet-Enhanced Sequence-to-Sequence Modeling with Attention Mechanism for Short-Term Wind Power Forecasting","volume":"57","author":"Karaca","year":"2026","journal-title":"Cybern. Syst."},{"key":"ref_23","unstructured":"Chen, R.T.Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. (2018). Neural Ordinary Differential Equations. Proceedings of the Advances in Neural Information Processing Systems, Curran Associates, Inc."},{"key":"ref_24","unstructured":"Rubanova, Y., Chen, R.T.Q., and Duvenaud, D. (2019). Latent Ordinary Differential Equations for Irregularly-Sampled Time Series. Proceedings of the Advances in Neural Information Processing Systems, Curran Associates, Inc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"114577","DOI":"10.1016\/j.ymssp.2026.114577","article-title":"Application of Machine-Vision-Driven Physics-Informed Neural Networks in Pantograph\u2013Catenary System State Detection","volume":"257","author":"Yan","year":"2026","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","first-page":"61929","article-title":"EARTH: Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graph","volume":"Volume 267","author":"Wan","year":"2025","journal-title":"Proceedings of the 42nd International Conference on Machine Learning"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"8905","DOI":"10.1038\/s41467-025-63982-2","article-title":"Scale-Up of Complex Molecular Reaction System by Hybrid Mechanistic Modeling and Deep Transfer Learning","volume":"16","author":"Chen","year":"2025","journal-title":"Nat. Commun."},{"key":"ref_29","unstructured":"Kuleshov, I., Romanenkova, E., Zhuzhel, V.A., Boeva, G., Vorsin, E., and Zaytsev, A. (2026, January 23\u201327). DeNOTS: Stable Deep Neural ODEs for Time Series. Proceedings of the The Fourteenth International Conference on Learning Representations, Rio de Janeiro, Brazil."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"e75815","DOI":"10.1002\/advs.75815","article-title":"Interpretable Machine Learning Framework for Nb\u2013Si Based Alloy Design with Enhanced Fracture Toughness","volume":"13","author":"Chen","year":"2026","journal-title":"Adv. Sci."},{"key":"ref_31","unstructured":"von Bassewitz, J.P., Pervez, A., Fumero, M., Robinson, M.R., Karaletsos, T., and Locatello, F. (2026, January 23\u201327). Learning Explicit Single-Cell Dynamics Using ODE Representations. Proceedings of the The Fourteenth International Conference on Learning Representations, Rio de Janeiro, Brazil."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6901","DOI":"10.1038\/s41467-026-73257-z","article-title":"Inferring Stochastic Dynamics by Biophysical Neural ODE Using Single-Cell Transcriptomics","volume":"17","author":"Dou","year":"2026","journal-title":"Nat. Commun."},{"key":"ref_33","unstructured":"Maddix, D.C., Ma, R., Mahoney, M.W., and Wang, Y. (2026, January 23\u201327). End-to-End Probabilistic Framework for Learning with Hard Constraints. Proceedings of the The Fourteenth International Conference on Learning Representations, Rio de Janeiro, Brazil."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/j.tibtech.2022.09.019","article-title":"Towards Machine Learning for Hydrogel Drug Delivery Systems","volume":"41","author":"Owh","year":"2023","journal-title":"Trends Biotechnol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"108907","DOI":"10.1016\/j.compbiolchem.2026.108907","article-title":"Predicting Curcumin Release Kinetics from Nanocarriers Using a Physics-Informed Machine Learning Framework","volume":"122","author":"Rahdar","year":"2026","journal-title":"Comput. Biol. Chem."},{"key":"ref_36","unstructured":"Wyder, P.M., Goldfeder, J.A., Yermakov, A., Zhao, Y., Riva, S., Williams, J.P., Zoro, D., Rude, A.S., Tomasetto, M., and Germany, J. (2025). Common Task Framework for a Critical Evaluation of Scientific Machine Learning Algorithms. Proceedings of the Advances in Neural Information Processing Systems, Curran Associates, Inc."},{"key":"ref_37","unstructured":"Gorishniy, Y., Rubachev, I., Khrulkov, V., and Babenko, A. (2021). Revisiting Deep Learning Models for Tabular Data. Proceedings of the Advances in Neural Information Processing Systems, Curran Associates, Inc."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.jddst.2015.10.009","article-title":"Importance of PLGA Microparticle Swelling for the Control of Prilocaine Release","volume":"30","author":"Gasmi","year":"2015","journal-title":"J. Drug Deliv. Sci. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.ijpharm.2016.08.032","article-title":"Towards a Better Understanding of the Different Release Phases from PLGA Microparticles: Dexamethasone-Loaded Systems","volume":"514","author":"Gasmi","year":"2016","journal-title":"Int. J. Pharm."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"681","DOI":"10.3109\/02652048.2013.778905","article-title":"Evaluation of the Degradation of Clonidine-Loaded PLGA Microspheres","volume":"30","author":"Gaignaux","year":"2013","journal-title":"J. Microencapsul."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.jconrel.2006.02.015","article-title":"Elevated Temperature Accelerated Release Testing of PLGA Microspheres","volume":"112","author":"Zolnik","year":"2006","journal-title":"J. Control. 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