{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:55:58Z","timestamp":1787021758398,"version":"build-2736575974"},"reference-count":61,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T00:00:00Z","timestamp":1681344000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007421","name":"University of the Philippines","doi-asserted-by":"publisher","award":["UP-OIL-COOPERATE"],"award-info":[{"award-number":["UP-OIL-COOPERATE"]}],"id":[{"id":"10.13039\/501100007421","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006733","name":"Commission on Higher Education","doi-asserted-by":"publisher","award":["Faculty Development Program - II (CHED-FDP-II)"],"award-info":[{"award-number":["Faculty Development Program - II (CHED-FDP-II)"]}],"id":[{"id":"10.13039\/501100006733","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010446","name":"Institute for Basic Science","doi-asserted-by":"crossref","award":["IBS-R029-C3"],"award-info":[{"award-number":["IBS-R029-C3"]}],"id":[{"id":"10.13039\/501100010446","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    Anovulation refers to a menstrual cycle characterized by the absence of ovulation. Exogenous hormones such as synthetic progesterone and estrogen have been used to attain this state to achieve contraception. However, large doses are associated with adverse effects such as increased risk for thrombosis and myocardial infarction. This study utilizes optimal control theory on a modified menstrual cycle model to determine the minimum total exogenous estrogen\/progesterone dose, and timing of administration to induce anovulation. The mathematical model correctly predicts the mean daily levels of pituitary hormones\n                    <jats:italic>LH<\/jats:italic>\n                    and\n                    <jats:italic>FSH<\/jats:italic>\n                    , and ovarian hormones\n                    <jats:italic>E<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    ,\n                    <jats:italic>P<\/jats:italic>\n                    <jats:sub>4<\/jats:sub>\n                    , and\n                    <jats:italic>Inh<\/jats:italic>\n                    throughout a normal menstrual cycle and reflects the reduction in these hormone levels caused by exogenous estrogen and\/or progesterone. Results show that it is possible to reduce the total dose by 92% in estrogen monotherapy, 43% in progesterone monotherapy, and that it is most effective to deliver the estrogen contraceptive in the mid follicular phase. Finally, we show that by combining estrogen and progesterone the dose can be lowered even more. These results may give clinicians insights into optimal formulations and schedule of therapy that can suppress ovulation.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1010073","type":"journal-article","created":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T13:26:57Z","timestamp":1681392417000},"page":"e1010073","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":9,"title":["Toward an optimal contraception dosing strategy"],"prefix":"10.1371","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4134-9845","authenticated-orcid":true,"given":"Brenda Lyn A.","family":"Gavina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5418-4579","authenticated-orcid":true,"given":"Aurelio A.","family":"de los Reyes V","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2694-0044","authenticated-orcid":true,"given":"Mette S.","family":"Olufsen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6898-5796","authenticated-orcid":true,"given":"Suzanne","family":"Lenhart","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johnny T.","family":"Ottesen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2023,4,13]]},"reference":[{"key":"pcbi.1010073.ref001","volume-title":"Women, Hormones and the Menstrual Cycle: Herbal and Medical Solutions from Adolescence to Menopause","author":"R Trickey","year":"1998"},{"issue":"3","key":"pcbi.1010073.ref002","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.anireprosci.2010.08.030","article-title":"The normal menstrual cycle in women","volume":"124","author":"M Mihm","year":"2011","journal-title":"Anim Reprod Sci"},{"key":"pcbi.1010073.ref003","volume-title":"Clinical gynecologic endocrinology and infertility","author":"L Speroff","year":"2011","edition":"8"},{"issue":"3","key":"pcbi.1010073.ref004","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1111\/tog.12665","article-title":"WHO type 1 anovulation: an update on diagnosis, management and implications for long-term health","volume":"22","author":"V Talaulikar","year":"2020","journal-title":"Obstet Gynecol"},{"key":"pcbi.1010073.ref005","first-page":"429","article-title":"A model for the production of ovarian hormones during the menstrual cycle","volume":"21","author":"J Selgrade","year":"1999","journal-title":"Fields Inst Commun"},{"key":"pcbi.1010073.ref006","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1289\/ehp.00108s5873","article-title":"A model of gonadotropin regulation during the menstrual cycle in women: qualitative features","volume":"108","author":"P Schlosser","year":"2000","journal-title":"Environ Health Perspect"},{"key":"pcbi.1010073.ref007","unstructured":"Harris L. Differential equation models for the hormonal regulation of the menstrual cycle [Ph.D. thesis]. North Carolina State University; 2002."},{"issue":"1","key":"pcbi.1010073.ref008","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1006\/bulm.2002.0326","article-title":"Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle","volume":"65","author":"L Clark","year":"2003","journal-title":"Bull Math BIol"},{"key":"pcbi.1010073.ref009","unstructured":"Pasteur RI. A multiple inhibin model of the human menstrual cycle [Ph.D. thesis]. 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Mathematical modeling and simulation of the female menstrual cycle [Ph.D. thesis]. Freie Universit\u00e4t Berlin, Germany; 2009."},{"key":"pcbi.1010073.ref019","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.jtbi.2012.11.020","article-title":"A mathematical model of the human menstrual cycle for the administration of GnRH analogues","volume":"321","author":"S R\u00f6blitz","year":"2013","journal-title":"J Theor Biol"},{"key":"pcbi.1010073.ref020","unstructured":"United Nations. Contraceptive Use by Method 2019. 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University of New Mexico; 2019."},{"issue":"12","key":"pcbi.1010073.ref034","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0243386","article-title":"Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer","volume":"15","author":"J Cunningham","year":"2020","journal-title":"PLOS One"},{"key":"pcbi.1010073.ref035","volume-title":"Control Applications for Biomedical Engineering Systems","author":"AT Azar","year":"2020"},{"issue":"1","key":"pcbi.1010073.ref036","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10479-009-0563-y","article-title":"Optimal control of dosage decisions in controlled ovarian hyperstimulation","volume":"178","author":"M He","year":"2010","journal-title":"Annals of Operations Research"},{"issue":"1","key":"pcbi.1010073.ref037","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/S0015-0282(01)01824-6","article-title":"Ovarian function during and after treatment with the new progestagen Org 30659","volume":"76","author":"A Obruca","year":"2001","journal-title":"Fertil steril"},{"issue":"5","key":"pcbi.1010073.ref038","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1002\/uog.10114","article-title":"Quantifying effect of combined oral contraceptive pill on functional ovarian reserve as measured by serum anti-m\u00fcllerian hormone and small antral follicle count using three-dimensional ultrasound","volume":"39","author":"S Deb","year":"2012","journal-title":"Ultrasound Obstetr Gynecol"},{"issue":"6410","key":"pcbi.1010073.ref039","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1136\/bmj.288.6410.7","article-title":"Interpretation of single progesterone measurement in diagnosis of anovulation and defective luteal phase: observations on analysis of the normal range","volume":"288","author":"N Wathen","year":"1984","journal-title":"BMJ"},{"issue":"4","key":"pcbi.1010073.ref040","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.3945\/ajcn.2009.27990","article-title":"Effect of daily fiber intake on reproductive function: the BioCycle study","volume":"90","author":"BioCycle Study Group","year":"2009","journal-title":"Am J Clin Nutr"},{"issue":"5","key":"pcbi.1010073.ref041","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1016\/S0002-9378(99)70120-1","article-title":"The mechanism of action of hormonal contraceptives and intrauterine contraceptive devices","volume":"181","author":"R Rivera","year":"1999","journal-title":"AJOG"},{"issue":"5","key":"pcbi.1010073.ref042","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1586\/eog.11.48","article-title":"Currently available combined oral contraception","volume":"6","author":"T Kimble","year":"2011","journal-title":"Expert Rev Obstet Gynecol"},{"issue":"2","key":"pcbi.1010073.ref043","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1530\/jrf.0.0700615","article-title":"Effect of enucleation of the corpus luteum at different stages of the luteal phase of the human menstrual cycle on subsequent follicular development","volume":"70","author":"D Baird","year":"1984","journal-title":"Reproduction"},{"issue":"6","key":"pcbi.1010073.ref044","first-page":"743","article-title":"Oral steroid contraception","volume":"11","author":"L Sech","year":"2015","journal-title":"Women\u2019s Health"},{"key":"pcbi.1010073.ref045","unstructured":"Bormann I. DigitizeIt; 2021. ver. 2.5. Available from: https:\/\/www.digitizeit.xyz\/."},{"issue":"5","key":"pcbi.1010073.ref046","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1095\/biolreprod36.5.1247","article-title":"The effects of progesterone on follicular growth in the rabbit ovary","volume":"36","author":"S Setty","year":"1987","journal-title":"Biol Reprod"},{"issue":"6","key":"pcbi.1010073.ref047","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1210\/endo-117-6-2443","article-title":"Progesterone inhibits basal production of follicle-stimulating hormone in ovine pituitary cell culture","volume":"117","author":"S Batra","year":"1985","journal-title":"Endocrinology"},{"issue":"1","key":"pcbi.1010073.ref048","doi-asserted-by":"crossref","first-page":"275","DOI":"10.3934\/jimo.2014.10.275","article-title":"The control parameterization method for nonlinear optimal control: a survey","volume":"10","author":"Q Lin","year":"2014","journal-title":"J Ind Manag Optim"},{"key":"pcbi.1010073.ref049","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011418","volume-title":"Optimal control applied to biological models","author":"S Lenhart","year":"2007"},{"key":"pcbi.1010073.ref050","doi-asserted-by":"crossref","DOI":"10.1002\/9781118122631","volume-title":"Optimal control","author":"FL Lewis","year":"2012","edition":"3"},{"key":"pcbi.1010073.ref051","unstructured":"Digirolamo C. Applications of GPOPS-II to optimal control problems with delays [Ph.D. thesis]. North Carolina State University; 2020."},{"issue":"3","key":"pcbi.1010073.ref052","first-page":"386","article-title":"Occurrence and function of corpora lutea during different forms of oral contraception","volume":"57","author":"E \u00d8stergaard","year":"1968","journal-title":"Acta Endocrinol"},{"key":"pcbi.1010073.ref053","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1090\/conm\/410\/07725","article-title":"Optimal therapy regimen for treatment-resistant mutations of HIV","volume":"410","author":"G Weiqing","year":"2006","journal-title":"Contemp Math"},{"issue":"13","key":"pcbi.1010073.ref054","doi-asserted-by":"crossref","first-page":"5813","DOI":"10.1073\/pnas.92.13.5813","article-title":"Estradiol and the inhibition of hypothalamic gonadotropin-releasing hormone pulse generator activity in the rhesus monkey","volume":"92","author":"T Ord\u00f6g","year":"1995","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"suppl_2","key":"pcbi.1010073.ref055","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1093\/humrep\/8.suppl_2.37","article-title":"Electrophysiological approaches to gonadotrophin releasing hormone pulse generator activity in the rhesus monkey","volume":"8","author":"K O\u2019Byrne","year":"1993","journal-title":"Human Reproduction"},{"key":"pcbi.1010073.ref056","article-title":"LH levels may be used as an indicator for the time of antagonist administration in GnRH antagonist protocols\u2014a proof-of-concept study","volume":"10","author":"M Liu","year":"2019","journal-title":"Frontiers in Endocrinology"},{"key":"pcbi.1010073.ref057","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1006527232605","article-title":"The probability of conception on different days of the cycle with respect to ovulation: an overview","volume":"13","author":"A Ferreira-Poblete","year":"1997","journal-title":"Advances in Contraception"},{"issue":"2","key":"pcbi.1010073.ref058","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1002\/sim.4780100207","article-title":"Identifying the fertile phase of the human menstrual cycle","volume":"10","author":"P Royston","year":"1991","journal-title":"Statistics in Medicine"},{"issue":"s1","key":"pcbi.1010073.ref059","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.1365-3016.2006.00765.x","article-title":"Estimation of the day-specific probabilities of conception: current state of the knowledge and the relevance for epidemiological research","volume":"20","author":"CD Lynch","year":"2006","journal-title":"Paediatric and Perinatal Epidemiology"},{"issue":"4","key":"pcbi.1010073.ref060","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1093\/humrep\/des449","article-title":"Day-specific probabilities of conception in fertile cycles resulting in spontaneous pregnancies","volume":"28","author":"JJ Stirnemann","year":"2013","journal-title":"Human Reproduction"},{"issue":"1","key":"pcbi.1010073.ref061","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3168\/jdsc.2020-18816","article-title":"An automated controlled-release device for intravaginal hormone delivery","volume":"1","author":"M Masello","year":"2020","journal-title":"JDS communications"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010073","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,13]],"date-time":"2023-04-13T13:27:57Z","timestamp":1681392477000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010073"}},"subtitle":[],"editor":[{"given":"Krasimira","family":"Tsaneva-Atanasova","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2023,4,13]]},"references-count":61,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4,13]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010073","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2022.04.04.486926","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,13]]}}}