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It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009094","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T17:40:26Z","timestamp":1624902026000},"page":"e1009094","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":37,"title":["Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5503-1934","authenticated-orcid":true,"given":"John T.","family":"Nardini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8658-8666","authenticated-orcid":true,"given":"Bernadette J.","family":"Stolz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4000-6971","authenticated-orcid":true,"given":"Kevin B.","family":"Flores","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1705-7869","authenticated-orcid":true,"given":"Heather A.","family":"Harrington","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1771-5910","authenticated-orcid":true,"given":"Helen M.","family":"Byrne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"issue":"6","key":"pcbi.1009094.ref001","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.3748\/wjg.v9.i6.1144","article-title":"Mechanism and its regulation of tumor-induced angiogenesis","volume":"9","author":"MK Gupta","year":"2003","journal-title":"World Journal of Gastroenterology"},{"issue":"3","key":"pcbi.1009094.ref002","first-page":"231","article-title":"Building blood vessels in development and disease","volume":"20","author":"EJ Kushner","year":"2013","journal-title":"Current Opinion in Hematology"},{"issue":"1","key":"pcbi.1009094.ref003","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1046\/j.1087-0024.2000.00014.x","article-title":"Angiogenesis in wound healing","volume":"5","author":"MG Tonnesen","year":"2000","journal-title":"Journal of Investigative Dermatology Symposium Proceedings"},{"issue":"10","key":"pcbi.1009094.ref004","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1038\/nrc909","article-title":"VEGF and the quest for tumour angiogenesis factors","volume":"2","author":"N Ferrara","year":"2002","journal-title":"Nature Reviews Cancer"},{"key":"pcbi.1009094.ref005","first-page":"331","volume-title":"Advances in Cancer Research","author":"J Folkman","year":"1974"},{"issue":"21","key":"pcbi.1009094.ref006","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1056\/NEJM197111182852108","article-title":"Tumor angiogenesis: therapeutic implications","volume":"285","author":"LM Sherwood","year":"1971","journal-title":"New England Journal of Medicine"},{"issue":"2","key":"pcbi.1009094.ref007","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1084\/jem.133.2.275","article-title":"Isolation of a tumor factor responsible for angiogenesis","volume":"133","author":"J Folkman","year":"1971","journal-title":"The Journal of Experimental Medicine"},{"issue":"3","key":"pcbi.1009094.ref008","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/S0950-3536(05)80188-X","article-title":"2 Endothelial cell proteases: physiological role and regulation","volume":"6","author":"S Menashi","year":"1993","journal-title":"Bailli\u00e8re\u2019s Clinical Haematology"},{"issue":"3","key":"pcbi.1009094.ref009","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/S1040-8428(89)80002-2","article-title":"Tumor-related angiogenesis","volume":"9","author":"N Paweletz","year":"1989","journal-title":"Critical Reviews in Oncology\/Hematology"},{"issue":"6","key":"pcbi.1009094.ref010","doi-asserted-by":"crossref","first-page":"2330","DOI":"10.1083\/jcb.101.6.2330","article-title":"Human endothelial cells are chemotactic to endothelial cell growth factor and heparin","volume":"101","author":"VP Terranova","year":"1985","journal-title":"Journal of Cell Biology"},{"issue":"6","key":"pcbi.1009094.ref011","first-page":"624","article-title":"Mechanisms of neovascularization. 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