{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:10Z","timestamp":1760149750260,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Portuguese Foundation for Science and Technology (FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia)","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020","UIDP\/04106\/2020","2022.03091.PTDC"],"award-info":[{"award-number":["UIDB\/04106\/2020","UIDP\/04106\/2020","2022.03091.PTDC"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"national funds (OE)","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020","UIDP\/04106\/2020","2022.03091.PTDC"],"award-info":[{"award-number":["UIDB\/04106\/2020","UIDP\/04106\/2020","2022.03091.PTDC"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of anesthesia relies on a pharmacokinetic\/pharmacodynamic (PK\/PD) model proposed by Bailey and Haddad in 2005 to regulate the infusion of propofol. In order to evaluate our approach and compare it with existing results in the literature, we examine a minimum-time problem for anesthetizing a patient. By applying the Pontryagin minimum principle, we introduce the shooting method as a means to solve the problem at hand. Additionally, we conducted numerical simulations using the MATLAB computing environment. We solve the time-optimal control problem using our newly proposed analytical method and discover that the optimal continuous infusion rate of the anesthetic and the minimum required time for transition from the awake state to an anesthetized state exhibit similarity between the two methods. However, the advantage of our new analytic method lies in its independence from unknown initial conditions for the adjoint variables.<\/jats:p>","DOI":"10.3390\/axioms12090867","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T08:01:30Z","timestamp":1694160090000},"page":"867","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2042-7226","authenticated-orcid":false,"given":"Mohamed A.","family":"Zaitri","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"},{"name":"Department of Mathematics, University of Djelfa, Djelfa 17000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7238-546X","authenticated-orcid":false,"given":"Cristiana J.","family":"Silva","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"},{"name":"Department of Mathematics, ISCTE\u2014Instituto Universit\u00e1rio de Lisboa, 1649-026 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"},{"name":"Research Center in Exact Sciences (CICE), Faculty of Sciences and Technology (FCT), University of Cape Verde (Uni-CV), Praia 7943-010, Cape Verde"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Evers, A.S., Maze, M., and Kharasch, E.D. (2011). Anesthetic Pharmacology: Basic Principles and Clinical Practice, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511781933"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1016\/j.jvs.2006.06.035","article-title":"The effects of the type of anesthesia on outcomes of lower extremity infrainguinal bypass","volume":"44","author":"Singh","year":"2006","journal-title":"J. Vasc. 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