{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:42:32Z","timestamp":1785426152551,"version":"3.56.0"},"reference-count":38,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T00:00:00Z","timestamp":1779235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100032397","name":"Atlantic Technological University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100032397","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/0458dap48","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100025294","name":"Research Ireland","doi-asserted-by":"crossref","award":["21\/FFP-A\/9152"],"award-info":[{"award-number":["21\/FFP-A\/9152"]}],"id":[{"id":"10.13039\/501100025294","id-type":"DOI","asserted-by":"crossref"}]},{"award":["21\/FFP-A\/9152"],"award-info":[{"award-number":["21\/FFP-A\/9152"]}],"id":[{"id":"https:\/\/ror.org\/010t7sr36","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>The microstructure of semicrystalline bioresorbable polymers is central to their biomedical performance because the crystalline content influences both the mechanical stability and the degradation behaviour. Experimental studies have shown that crystallinity evolves concurrently with mass loss during enzymatic degradation. However, most existing models represent the material as a single homogeneous structure, preventing them from capturing this microstructural evolution or the state-selective mechanisms that drive it. We present a one-dimensional partial differential equation model for the enzymatic degradation of thin films, which treats the crystalline and amorphous states as distinct reactive components. Calibrated to poly(\u03b5-caprolactone) (PCL) degraded by Candida antarctica lipase in vitro, the model accurately reproduces both the observed weight-loss profile and the concurrent decline in crystallinity. Parameter uncertainty analysis indicates that while there are varying degrees of confidence in individual parameter values, the overall model predictive uncertainty is well constrained. Parameter sensitivity analysis shows that the amorphous catalytic rate (the rate at which the enzyme degrades the amorphous region) is the dominant driver of degradation dynamics. The identified model parameters are used to explore the role of film thickness on the rates of mass and crystallinity loss. It was found that thin films remain largely reaction-limited, whereas thicker specimens become increasingly transport-influenced, with slower degradation and delayed structural evolution in the material interior. The model provides a useful tool to explore the effect of changing PCL film thickness on degradation rate and crystallinity-related properties without extensive experimentation.<\/jats:p>","DOI":"10.3390\/polym18101248","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T14:12:54Z","timestamp":1779286374000},"page":"1248","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Reaction\u2013Diffusion Model for Capturing Mass Loss and Microstructure Evolution in Enzymatic Degradation of Poly(\u03b5-Caprolactone) Films"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7725-7926","authenticated-orcid":false,"given":"Nanshin","family":"Nansak","sequence":"first","affiliation":[{"name":"Centre for Mathematical Modelling and Intelligent Systems for Health and Environment, Atlantic Technological University, F91 YW50 Sligo, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8798-7455","authenticated-orcid":false,"given":"Leo","family":"Creedon","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Modelling and Intelligent Systems for Health and Environment, Atlantic Technological University, F91 YW50 Sligo, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-7877-0880","authenticated-orcid":false,"given":"Denis","family":"O\u2019Mahoney","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Modelling and Intelligent Systems for Health and Environment, Atlantic Technological University, F91 YW50 Sligo, Ireland"},{"name":"Department of Mechanical Engineering, Atlantic Technological University, H91 T8NW Galway, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0446-3101","authenticated-orcid":false,"given":"Ramen","family":"Ghosh","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Modelling and Intelligent Systems for Health and Environment, Atlantic Technological University, F91 YW50 Sligo, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1434-1215","authenticated-orcid":false,"given":"Marion","family":"McAfee","sequence":"additional","affiliation":[{"name":"Centre for Mathematical Modelling and Intelligent Systems for Health and Environment, Atlantic Technological University, F91 YW50 Sligo, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"126654","DOI":"10.1016\/j.ijbiomac.2023.126654","article-title":"Bioresorbable films of polycaprolactone blended with poly(lactic acid) or poly(lactic-co-glycolic acid)","volume":"248","author":"Dodda","year":"2023","journal-title":"Int. J. Biol. Macromol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1080\/09205063.2017.1394711","article-title":"PCL and PCL-based materials in biomedical applications","volume":"29","author":"Malikmammadov","year":"2018","journal-title":"J. Biomater. Sci. Polym. Ed."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109701","DOI":"10.1016\/j.eurpolymj.2020.109701","article-title":"The role of polycaprolactone-triol (PCL-T) in biomedical applications: A state-of-the-art review","volume":"131","author":"Abrisham","year":"2020","journal-title":"Eur. Polym. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1038\/s41578-019-0150-z","article-title":"Design of biodegradable, implantable devices towards clinical translation","volume":"5","author":"Li","year":"2020","journal-title":"Nat. Rev. Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2347","DOI":"10.1021\/acsabm.6c00009","article-title":"Dual-Enzyme Responsive Polymeric Micelles with Cascade Targeting and Caspase-3 Activated Drug Release for Tumor-Specific Chemotherapy","volume":"9","author":"Liu","year":"2026","journal-title":"ACS Appl. Bio Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106686","DOI":"10.1016\/j.reactfunctpolym.2026.106686","article-title":"Stimuli-responsive polysaccharide nanoplatforms for targeted cancer therapy","volume":"222","author":"Rana","year":"2026","journal-title":"React. Funct. Polym."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/s00253-006-0488-1","article-title":"Biodegradability and biodegradation of poly (lactide)","volume":"72","author":"Tokiwa","year":"2006","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Riccio, J., Presotto, L., Bahiri, S., Doniza, L., Inverso, D., Sironi, L., Nevo, U., and Chirico, G. (2025). Agent-based modeling of macrophage-fibroblast interactions in the immune response to biomaterials. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0329186"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.polymdegradstab.2014.12.008","article-title":"In vitro enzymatic degradation of the cross-linked poly (\u03b5-caprolactone) implants","volume":"112","author":"Yang","year":"2015","journal-title":"Polym. Degrad. Stab."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1002\/polb.21889","article-title":"Morphological changes of annealed poly-\u03b5-caprolactone by enzymatic degradation with lipase","volume":"48","author":"Sekosan","year":"2010","journal-title":"J. Polym. Sci. Part Polym. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.ijbiomac.2016.11.040","article-title":"Lactobacillus sps. lipase mediated poly (\u03b5-caprolactone) degradation","volume":"95","author":"Khan","year":"2017","journal-title":"Int. J. Biol. Macromol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.ibiod.2014.11.017","article-title":"Degradation of poly (\u03b5-caprolactone) by a thermophilic bacterium Ralstonia sp. strain MRL-TL isolated from hot spring","volume":"98","author":"Shah","year":"2015","journal-title":"Int. Biodeterior. Biodegrad."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2300296","DOI":"10.1002\/mabi.202300296","article-title":"Probing the Effects of Antimicrobial-Lysozyme Derivatization on Enzymatic Degradation of Poly (\u03b5-caprolactone) Film and Fiber","volume":"23","author":"Maroju","year":"2023","journal-title":"Macromol. Biosci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"179066","DOI":"10.1016\/j.scitotenv.2025.179066","article-title":"Enzymatic biodegradation of Poly (\u03b5-Caprolactone)(PCL) by a thermostable cutinase from a mesophilic bacteria Mycobacterium marinum","volume":"972","author":"Ravi","year":"2025","journal-title":"Sci. Total Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2844","DOI":"10.1021\/acsomega.8b02642","article-title":"Enzyme-embedded degradation of poly (\u03b5-caprolactone) using lipase-derived from probiotic lactobacillus plantarum","volume":"4","author":"Khan","year":"2019","journal-title":"ACS Omega"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.ijbiomac.2019.12.105","article-title":"Enzymatic hydrolysis of polyester: Degradation of poly (\u03b5-caprolactone) by Candida antarctica lipase and Fusarium solani cutinase","volume":"144","author":"Shi","year":"2020","journal-title":"Int. J. Biol. Macromol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2947","DOI":"10.1007\/s10924-020-01826-4","article-title":"Biodegradation of polycaprolactone (PCL) with different molecular weights by Candida antarctica lipase","volume":"28","author":"Ma","year":"2020","journal-title":"J. Polym. Environ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1016\/j.apsusc.2014.06.082","article-title":"Ex vivo evaluation of biodegradable poly (\u03b5-caprolactone) films in digestive fluids","volume":"313","author":"Chang","year":"2014","journal-title":"Appl. Surf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0141-3910(96)00208-X","article-title":"Enzymatic degradation of poly (\u03b5-caprolactone) film in phosphate buffer solution containing lipases","volume":"56","author":"Gan","year":"1997","journal-title":"Polym. Degrad. Stab."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Li, L., Lin, X., Bao, J., Xia, H., and Li, F. (2022). Two Extracellular poly (\u03b5-caprolactone)-degrading enzymes from Pseudomonas hydrolytica sp. DSWY01T: Purification, characterization, and gene analysis. Front. Bioeng. Biotechnol., 10.","DOI":"10.3389\/fbioe.2022.835847"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/0141-8130(93)90054-P","article-title":"Kinetics and mechanism of heterogeneous hydrolysis of poly [(R)-3-hydroxybutyrate] film by PHA depolymerases","volume":"15","author":"Mukai","year":"1993","journal-title":"Int. J. Biol. Macromol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0141-3910(94)00114-N","article-title":"Development of a mathematical model describing the enzymatic degradation of biomedical polyurethanes. 1. Background, rationale and model formulation","volume":"47","author":"Duguay","year":"1995","journal-title":"Polym. Degrad. Stab."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/S0032-3861(96)00530-7","article-title":"Heterogeneous kinetics of the enzymatic degradation of poly (\u03b2-hydroxyalkanoates)","volume":"38","author":"Timmins","year":"1997","journal-title":"Polymer"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"031001","DOI":"10.1103\/PhysRevApplied.9.031001","article-title":"Localized enzymatic degradation of polymers: Physics and scaling laws","volume":"9","author":"Vernerey","year":"2018","journal-title":"Phys. Rev. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"109074","DOI":"10.1016\/j.polymertesting.2025.109074","article-title":"Modeling product inhibition in enzymatic degradation of Polylactic Acid (PLA)","volume":"154","author":"Nansak","year":"2025","journal-title":"Polym. Test."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.ijbiomac.2018.01.104","article-title":"Enzymatic degradation of poly-[(R)-3-hydroxybutyrate]: Mechanism, kinetics, consequences","volume":"112","author":"Dohovits","year":"2018","journal-title":"Int. J. Biol. Macromol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.polymertesting.2012.10.011","article-title":"A comparative analysis of mass losses of some aliphatic polyesters upon enzymatic degradation","volume":"32","author":"Richert","year":"2013","journal-title":"Polym. Test."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"111799","DOI":"10.1016\/j.indcrop.2019.111799","article-title":"Enzymatic degradation of PLA\/cellulose nanocrystal composites","volume":"141","author":"Hegyesi","year":"2019","journal-title":"Ind. Crops Prod."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"110678","DOI":"10.1016\/j.colsurfb.2019.110678","article-title":"Controlled degradation of poly-\u03b5-caprolactone for resorbable scaffolds","volume":"186","author":"Hegyesi","year":"2020","journal-title":"Colloids Surf. Biointerfaces"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6348","DOI":"10.1016\/j.polymer.2007.08.054","article-title":"In situ investigations on enzymatic degradation of poly (\u03b5-caprolactone)","volume":"48","author":"Hou","year":"2007","journal-title":"Polymer"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3393","DOI":"10.1016\/j.biomaterials.2008.04.042","article-title":"A phenomenological model for the degradation of biodegradable polymers","volume":"29","author":"Wang","year":"2008","journal-title":"Biomaterials"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"034108","DOI":"10.1088\/1748-6041\/3\/3\/034108","article-title":"Dynamics of in vitro polymer degradation of polycaprolactone-based scaffolds: Accelerated versus simulated physiological conditions","volume":"3","author":"Lam","year":"2008","journal-title":"Biomed. Mater."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.actbio.2017.11.023","article-title":"A model for hydrolytic degradation and erosion of biodegradable polymers","volume":"66","author":"Sevim","year":"2018","journal-title":"Acta Biomater."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"109298","DOI":"10.1016\/j.polymdegradstab.2020.109298","article-title":"Modeling temporal and spatial changes during hydrolytic degradation and erosion in biodegradable polymers","volume":"180","author":"Shockley","year":"2020","journal-title":"Polym. Degrad. Stab."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"e433","DOI":"10.7717\/peerj.433","article-title":"Prediction uncertainty assessment of a systems biology model requires a sample of the full probability distribution of its parameters","volume":"2","author":"Stigter","year":"2014","journal-title":"PeerJ"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"106279","DOI":"10.1016\/j.isci.2023.106279","article-title":"Designing supramolecular self-assembly nanomaterials as stimuli-responsive drug delivery platforms for cancer therapy","volume":"26","author":"Liu","year":"2023","journal-title":"Iscience"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1002\/psp4.6","article-title":"Sobol sensitivity analysis: A tool to guide the development and evaluation of systems pharmacology models","volume":"4","author":"Zhang","year":"2015","journal-title":"CPT Pharmacometr. Syst. Pharmacol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1016\/j.ijbiomac.2022.04.121","article-title":"Quantitative analysis of factors determining the enzymatic degradation of poly (lactic acid)","volume":"209","author":"Cui","year":"2022","journal-title":"Int. J. Biol. Macromol."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/10\/1248\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T04:23:10Z","timestamp":1779510190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/10\/1248"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,20]]},"references-count":38,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["polym18101248"],"URL":"https:\/\/doi.org\/10.3390\/polym18101248","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,20]]}}}