{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T08:00:15Z","timestamp":1778227215341,"version":"3.51.4"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["FSSF-2023-0016"],"award-info":[{"award-number":["FSSF-2023-0016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In veins, clotting initiation displays a threshold response to flow intensity and injury size. Mathematical models can provide insights into the conditions leading to clot growth initiation under flow for specific subjects. However, it is hard to determine the thrombin generation curves that favor coagulation initiation in a fast manner, especially when considering a wide range of conditions related to flow and injury size. In this work, we propose to address this challenge by using a neural network model trained with the numerical simulations of a validated 2D model for clot formation. Our surrogate model approximates the results of the 2D simulations, reaching an accuracy of 94% on the test dataset. We used the trained artificial neural network to determine the threshold for thrombin generation parameters that alter the coagulation initiation response under varying flow speed and injury size conditions. Our model predictions show that increased levels of the endogenous thrombin potential (ETP) and peak thrombin concentration increase the likelihood of coagulation initiation, while an elevated time to peak decreases coagulation. The lag time has a small effect on coagulation initiation, especially when the injury size is small. Our surrogate model can be considered as a proof-of-concept of a tool that can be deployed to estimate the risk of bleeding in specific patients based on their Thrombin Generation Assay results.<\/jats:p>","DOI":"10.3390\/axioms12090873","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T21:41:12Z","timestamp":1694554872000},"page":"873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Thrombin Generation Thresholds for Coagulation Initiation under Flow"],"prefix":"10.3390","volume":"12","author":[{"given":"Anass","family":"Bouchnita","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA"},{"name":"Bioinformatics Program, The University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-1860-0039","authenticated-orcid":false,"given":"Kanishk","family":"Yadav","sequence":"additional","affiliation":[{"name":"Bioinformatics Program, The University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Pierre","family":"Llored","sequence":"additional","affiliation":[{"name":"Ecole Centrale Casblanca, Ville Verte Bouskoura, Casablanca 20000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8823-3391","authenticated-orcid":false,"given":"Alvaro","family":"Gurovich","sequence":"additional","affiliation":[{"name":"Department of Physical Therapy and Movement Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vitaly","family":"Volpert","sequence":"additional","affiliation":[{"name":"Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France"},{"name":"S.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow 117198, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1161\/ATVBAHA.108.173930","article-title":"Threshold response of initiation of blood coagulation by tissue factor in patterned microfluidic capillaries is controlled by shear rate","volume":"28","author":"Shen","year":"2008","journal-title":"Arterioscler. Thromb. Vasc. Biol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2969","DOI":"10.1529\/biophysj.107.109009","article-title":"Characterization of the threshold response of initiation of blood clotting to stimulus patch size","volume":"93","author":"Kastrup","year":"2007","journal-title":"Biophys. 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