{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T06:37:48Z","timestamp":1780641468974,"version":"3.54.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1013626","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:00:00Z","timestamp":1762905600000}}],"reference-count":38,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T00:00:00Z","timestamp":1762128000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF 2303695"],"award-info":[{"award-number":["NSF 2303695"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["NSF 2120200"],"award-info":[{"award-number":["NSF 2120200"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["GM131865"],"award-info":[{"award-number":["GM131865"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["T32-GM145443"],"award-info":[{"award-number":["T32-GM145443"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["T32-GM007267"],"award-info":[{"award-number":["T32-GM007267"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006192","name":"Advanced Scientific Computing Research","doi-asserted-by":"publisher","award":["DE-SC0023452"],"award-info":[{"award-number":["DE-SC0023452"]}],"id":[{"id":"10.13039\/100006192","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate\n                    <jats:italic>in vitro<\/jats:italic>\n                    vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1013626","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T18:40:48Z","timestamp":1762195248000},"page":"e1013626","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8314-2703","authenticated-orcid":true,"given":"Tien","family":"Comlekoglu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. Quetzalc\u00f3atl","family":"Toledo-Mar\u00edn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tina","family":"Comlekoglu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Douglas W.","family":"DeSimone","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shayn M.","family":"Peirce","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Geoffrey","family":"Fox","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3634-190X","authenticated-orcid":true,"given":"James A.","family":"Glazier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2025,11,3]]},"reference":[{"issue":"1","key":"pcbi.1013626.ref001","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.ydbio.2005.10.003","article-title":"Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling","volume":"289","author":"RMH Merks","year":"2006","journal-title":"Dev Biol."},{"key":"pcbi.1013626.ref002","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.91924.3","article-title":"Agent-based model demonstrates the impact of nonlinear, complex interactions between cytokinces on muscle regeneration","volume":"13","author":"M Haase","year":"2024","journal-title":"Elife."},{"issue":"8","key":"pcbi.1013626.ref003","doi-asserted-by":"crossref","DOI":"10.1242\/bio.060615","article-title":"Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm","volume":"13","author":"T Comlekoglu","year":"2024","journal-title":"Biol Open."},{"key":"pcbi.1013626.ref004","doi-asserted-by":"crossref","first-page":"100210","DOI":"10.1016\/j.crtox.2024.100210","article-title":"A computational dynamic systems model for in silico prediction of neural tube closure defects","volume":"8","author":"JH Berkhout","year":"2024","journal-title":"Curr Res Toxicol."},{"issue":"4","key":"pcbi.1013626.ref005","doi-asserted-by":"crossref","first-page":"102317","DOI":"10.1016\/j.isci.2021.102317","article-title":"A mechanical model of early somite segmentation","volume":"24","author":"P Adhyapok","year":"2021","journal-title":"iScience."},{"key":"pcbi.1013626.ref006","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.cpc.2007.03.007","article-title":"A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis","volume":"176","author":"N Chen","year":"2007","journal-title":"Comput Phys Commun."},{"key":"pcbi.1013626.ref007","doi-asserted-by":"crossref","unstructured":"Wright SA, Plimpton SJ, Swiler TP. Potts-model grain growth simulations: parallel algorithms and applications. Albuquerque, NM (United States): Sandia National Lab.. 1997. https:\/\/www.osti.gov\/biblio\/522745","DOI":"10.2172\/522745"},{"key":"pcbi.1013626.ref008","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1142\/S0129626405002155","article-title":"An efficient parallel algorithm to evolve simulations of the cellular potts model","volume":"15","author":"\u00c9 Gusatto","year":"2005","journal-title":"Parallel Process Lett."},{"key":"pcbi.1013626.ref009","unstructured":"Farimani AB, Gomes J, Pande VS. Deep learning the physics of transport phenomena. 2017. https:\/\/arxiv.org\/abs\/1709.02432"},{"issue":"3","key":"pcbi.1013626.ref010","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1007\/s10973-020-09875-6","article-title":"Using deep learning to learn physics of conduction heat transfer","volume":"146","author":"M Edalatifar","year":"2020","journal-title":"J Therm Anal Calorim."},{"issue":"4","key":"pcbi.1013626.ref011","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1021\/acs.jctc.0c01343","article-title":"TorchMD: a deep learning framework for molecular simulations","volume":"17","author":"S Doerr","year":"2021","journal-title":"J Chem Theory Comput."},{"issue":"1","key":"pcbi.1013626.ref012","doi-asserted-by":"crossref","first-page":"3894","DOI":"10.1038\/s41598-020-60853-2","article-title":"Reaction diffusion system prediction based on convolutional neural network","volume":"10","author":"A Li","year":"2020","journal-title":"Sci Rep."},{"key":"pcbi.1013626.ref013","doi-asserted-by":"crossref","unstructured":"Fox G, Jha S. Learning everywhere: a taxonomy for the integration of machine learning and simulations. In: 2019 15th International Conference on eScience (eScience). 2019. p. 439\u201348. https:\/\/doi.org\/10.1109\/escience.2019.00057","DOI":"10.1109\/eScience.2019.00057"},{"key":"pcbi.1013626.ref014","doi-asserted-by":"crossref","first-page":"667828","DOI":"10.3389\/fphys.2021.667828","article-title":"Deep learning approaches to surrogates for solving the diffusion equation for mechanistic real-world simulations","volume":"12","author":"JQ Toledo-Mar\u00edn","year":"2021","journal-title":"Front Physiol."},{"key":"pcbi.1013626.ref015","unstructured":"Toledo-Marin JQ, Glazier JA, Fox G. Analyzing the performance of deep encoder-decoder networks as surrogates for a diffusion equation. 2023. https:\/\/arxiv.org\/abs\/2302.03786"},{"key":"pcbi.1013626.ref016","doi-asserted-by":"crossref","unstructured":"Ronneberger O, Fischer P, Brox T. U-net: convolutional networks for biomedical image segmentation. 2015. https:\/\/arxiv.org\/abs\/1505.04597","DOI":"10.1007\/978-3-319-24574-4_28"},{"issue":"1","key":"pcbi.1013626.ref017","doi-asserted-by":"crossref","first-page":"14888","DOI":"10.1038\/s41598-022-18646-2","article-title":"A comparison of deep learning U-net architectures for posterior segment OCT retinal layer segmentation","volume":"12","author":"J Kugelman","year":"2022","journal-title":"Sci Rep."},{"issue":"2","key":"pcbi.1013626.ref018","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/S1076-6332(03)00671-8","article-title":"Statistical validation of image segmentation quality based on a spatial overlap index","volume":"11","author":"KH Zou","year":"2004","journal-title":"Acad Radiol."},{"issue":"1","key":"pcbi.1013626.ref019","doi-asserted-by":"crossref","first-page":"8242","DOI":"10.1038\/s41598-020-64803-w","article-title":"Evaluating white matter lesion segmentations with refined S\u00f8rensen-Dice analysis","volume":"10","author":"A Carass","year":"2020","journal-title":"Sci Rep."},{"issue":"2","key":"pcbi.1013626.ref020","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1177\/21925682231200783","article-title":"An automatized deep segmentation and classification model for lumbar disk degeneration and clarification of its impact on clinical decisions","volume":"15","author":"Z Soydan","year":"2025","journal-title":"Global Spine J."},{"issue":"7","key":"pcbi.1013626.ref021","doi-asserted-by":"crossref","first-page":"5097","DOI":"10.1007\/s00330-023-09421-6","article-title":"Automatic segmentation and radiomic texture analysis for osteoporosis screening using chest low-dose computed tomography","volume":"33","author":"Y-C Chen","year":"2023","journal-title":"Eur Radiol."},{"key":"pcbi.1013626.ref022","doi-asserted-by":"crossref","unstructured":"Rubner Y, Tomasi C, Guibas LJ. A metric for distributions with applications to image databases. In: Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271); 1998. p. 59\u201366.","DOI":"10.1109\/ICCV.1998.710701"},{"issue":"2","key":"pcbi.1013626.ref023","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1023\/A:1026543900054","article-title":"The earth mover\u2019s distance as a metric for image retrieval","volume":"40","author":"Y Rubner","year":"2000","journal-title":"International Journal of Computer Vision."},{"key":"pcbi.1013626.ref024","doi-asserted-by":"crossref","unstructured":"Zhang C, Cai Y, Lin G, Shen C. DeepEMD: differentiable earth mover\u2019s distance for few-shot learning; 2023. https:\/\/arxiv.org\/abs\/2003.06777.","DOI":"10.1109\/TPAMI.2022.3217373"},{"issue":"8","key":"pcbi.1013626.ref025","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1093\/emboj\/cdg176","article-title":"Modeling the early stages of vascular network assembly","volume":"22","author":"G Serini","year":"2003","journal-title":"EMBO J."},{"issue":"11","key":"pcbi.1013626.ref026","doi-asserted-by":"crossref","first-page":"118101","DOI":"10.1103\/PhysRevLett.90.118101","article-title":"Percolation, morphogenesis, and burgers dynamics in blood vessels formation","volume":"90","author":"A Gamba","year":"2003","journal-title":"Phys Rev Lett."},{"issue":"6","key":"pcbi.1013626.ref027","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1016\/j.bulm.2004.04.004","article-title":"Cell directional persistence [corrected] and chemotaxis in vascular morphogenesis","volume":"66","author":"D Ambrosi","year":"2004","journal-title":"Bull Math Biol."},{"key":"pcbi.1013626.ref028","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/B978-0-12-388403-9.00013-8","article-title":"Multi-scale modeling of tissues using CompuCell3D","volume":"110","author":"MH Swat","year":"2012","journal-title":"Methods Cell Biol."},{"issue":"9","key":"pcbi.1013626.ref029","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1093\/bioinformatics\/btt772","article-title":"Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology","volume":"30","author":"J Starru\u00df","year":"2014","journal-title":"Bioinformatics."},{"issue":"2","key":"pcbi.1013626.ref030","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1005387","article-title":"Comparing individual-based approaches to modelling the self-organization of multicellular tissues","volume":"13","author":"JM Osborne","year":"2017","journal-title":"PLoS Comput Biol."},{"key":"pcbi.1013626.ref031","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.61288","article-title":"Artistoo, a library to build, share, and explore simulations of cells and tissues in the web browser","volume":"10","author":"IM Wortel","year":"2021","journal-title":"Elife."},{"key":"pcbi.1013626.ref032","unstructured":"Sultan S, Devi S, Mueller SN, Textor J. A parallelized cellular Potts model that enables simulations at tissue scale. 2023. https:\/\/arxiv.org\/abs\/2312.09317"},{"issue":"4","key":"pcbi.1013626.ref033","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1016\/j.cpc.2010.12.011","article-title":"Parallelizing the Cellular Potts Model on graphics processing units","volume":"182","author":"JJ Tapia","year":"2011","journal-title":"Computer Physics Communications."},{"issue":"11","key":"pcbi.1013626.ref034","doi-asserted-by":"crossref","first-page":"7327","DOI":"10.1109\/TPAMI.2021.3116668","article-title":"Deep generative modelling: a comparative review of VAEs, GANs, normalizing flows, energy-based and autoregressive models","volume":"44","author":"S Bond-Taylor","year":"2022","journal-title":"IEEE Trans Pattern Anal Mach Intell."},{"key":"pcbi.1013626.ref035","doi-asserted-by":"crossref","unstructured":"Comlekoglu T, Toledo-Mar\u00edn JQ, DeSimone DW, Peirce SM, Fox G, Glazier JA. Generative diffusion model surrogates for mechanistic agent-based biological models. 2025. https:\/\/arxiv.org\/abs\/2505.09630","DOI":"10.1088\/2632-2153\/AE11F8\/v2\/response1"},{"key":"pcbi.1013626.ref036","doi-asserted-by":"crossref","unstructured":"He Y, Yu H, Liu X, Yang Z, Sun W, Anwar S. Deep learning based 3D segmentation: a survey. 2024. https:\/\/arxiv.org\/abs\/2103.05423","DOI":"10.2139\/ssrn.4824679"},{"key":"pcbi.1013626.ref037","doi-asserted-by":"crossref","DOI":"10.7717\/peerj.453","article-title":"scikit-image: image processing in Python","volume":"2","author":"S van der Walt","year":"2014","journal-title":"PeerJ."},{"key":"pcbi.1013626.ref038","doi-asserted-by":"crossref","unstructured":"Comlekoglu T, Toledo-Marin JQ, Comlekoglu T, Peirce S, DeSimone D, Fox G. Surrogate modeling of cellular-potts agent-based models as a segmentation task using the U-Net neural network architecture. 2025. https:\/\/doi.org\/10.5281\/zenodo.15399533","DOI":"10.1371\/journal.pcbi.1013626"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1013626","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:00:00Z","timestamp":1762905600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013626","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T18:42:33Z","timestamp":1762972953000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013626"}},"subtitle":[],"editor":[{"given":"Philip K.","family":"Maini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2025,11,3]]},"references-count":38,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11,3]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1013626","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,3]]}}}