[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82088-en":3,"doc-seo-82088-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82088,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",7,"Healthcare","Model Predictive Controller to Regulate Cortisol Levels in Individuals With Adrenal Insufficiency","A model predictive controller (MPC) is developed to support physicians prescribing cortisol replacement therapy for patients with adrenal insufficiency (AI), also called hypocortisolism. The work proposes a mathematical HPA-axis model that integrates the endogenous circadian rhythm and simulates primary and secondary AI. Using open-loop simulations with fixed hydrocortisone dosing, a feasible non-optimal replacement strategy is identified. MPC is then introduced to compute optimal daily cortisol dosing while rigorously enforcing dosage constraints.","arXiv :2607 .08902v1 [ q-bio .QM] 9 Jul 2026  \nModel Predictive Controller to Regulate Cortisol Levels in Individuals With Adrenal Insufficiency  \nRenuka Joshi 1*, Nayana Saha 1 , Vittal Srinivasan 1 ,  \nStanislaw H. Z˙ak 1 , Cary N. Mariash2  \n1* Elmore Family School of Electrical and Computer Engineering, Purdue University, 610 Purdue Mall, West Lafayette, 47906, Indiana,  \nUnited States.  \n2 Division of Endocrinology, Indiana University School of Medicine, 340 West 10th Street, Indianapolis, 46202, Indiana, United States.  \n*Corresponding author(s). E-mail(s): [joshi278@purdue.edu](joshi278@purdue.edu) ; Contributing authors: [saha80@purdue.edu](saha80@purdue.edu) ; [srini133@purdue.edu](srini133@purdue.edu) ;  \n[zak@purdue.edu](zak@purdue.edu) ; [cmariash@iu.edu](cmariash@iu.edu) ;  \nAbstract  \nA model predictive controller (MPC) is used to construct a virtual assistant to aida physician in prescribing cortisol replacement therapy for patients with adrenal insufficiency (AI) . AI, also known as hypocortisolism, is a condition that occurs due to a low concentration of cortisol. This hormonal imbalance significantly impacts the individual’s ability to regulate stress, metabolism, and immune responses. Thus, it is essential to maintain cortisol levels within a healthy range. The production of cortisol is governed by the hypothalamus-pituitary-adrenal (HPA) axis, a part of the endocrine system. In this paper, a novel mathematical model of the HPA axis is proposed that incorporates the endogenous circadian rhythm. This model simulates two conditions of hypocortisolism: primary and secondary AI. Adrenal insufficiency cannot be cured, but it can be treated with cortisol replacement therapy. The standard practice is to prescribe a therapeutic dose of hydrocortisone (HC) . To evaluate the accuracy of the proposed HPA axis model, an open-loop cortisol replacement strategy with a fixed dosage is used to simulate both primary and secondary AI. The simulation results show that, analytically, it is possible to arrive at a fixed working cortisol replacement strategy. However, this strategy, though effective, is not optimal. To obtain optimal cortisol replacement strategies, an MPC is proposed. An important feature of  \n1  \nMPC is that constraints on allowable cortisol replacement dosages can be rigorously addressed. This controller can serve as a virtual assistant to physicians in prescribing daily cortisol replacement therapy.  \nKeywords: Endocrine system, Hypothalamus-Pituitary-Adrenal (HPA) axis, mathematical modeling of HPA axis, circadian rhythm, primary adrenal insufficiency, secondary adrenal insufficiency, Model Predictive Control (MPC) .  \n1 Introduction  \nHypocortisolism, also known as adrenal insufficiency (AI), occurs when the adrenal glands do not produce a sufficient amount of the cortisol hormone. Cortisol is crucial in regulating stress, metabolism, and immune responses. A significant challenge in diagnosing AI is that its symptoms develop gradually over time. Such symptoms include fatigue, low blood pressure, hypoglycemia, muscle weakness, and reduced body immunity to infections. In addition, there are psychological effects such as depression, anxiety, and reduced resilience to stress. Chronic stress is a primary factor contributing to the dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis. This hormonal imbalance is related to conditions such as Addison’s disease and hypothalamic-pituitary (HP) disorder, which are modeled in this paper. The cycle of chronic stress and cortisol deficiency continues to weaken the ability to cope with external stress. Research on the effects of stress-related hypocortisolemic disorders can lead to early detection and targeted therapies. Therefore, it is essential to address this condition to reduce its physical, psychological, and social impacts by advancing the understanding of stress-related health disorders.  \nThe HPA axis, shown in Fig. 1, regulates stress and immune system","cbCaigFc7K1FwAUQ","https://ap.wps.com/l/cbCaigFc7K1FwAUQ","pdf",6215629,1,25,"English","en",105,"# Abstract\n# Introduction\n## Hypocortisolism and clinical motivation\n## HPA axis dynamics and hormones\n## Circadian rhythm and feedback loops\n## Literature review","[{\"question\":\"What condition does the paper focus on, and why is cortisol regulation important?\",\"answer\":\"The paper focuses on adrenal insufficiency (AI), where cortisol concentrations are too low. Cortisol is crucial for stress regulation, metabolism, immune responses, and overall homeostasis.\"},{\"question\":\"How does the proposed HPA-axis model incorporate circadian behavior?\",\"answer\":\"It introduces a mathematical model of the HPA axis that incorporates the endogenous circadian rhythm, allowing simulation of diurnal cortisol variations through circadian-driven dynamics and feedback loops.\"},{\"question\":\"Why is MPC proposed instead of using a fixed-dose open-loop strategy?\",\"answer\":\"Open-loop simulations with fixed hydrocortisone dosing yield a working but non-optimal strategy. MPC is proposed to obtain optimal cortisol replacement decisions and to handle dosing constraints rigorously.\"}]",1784178152,63,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"model-predictive-controller-to-regulate-cortisol-levels-in-individuals-with-adrenal-insufficiency","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/healthcare/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/model-predictive-controller-to-regulate-cortisol-levels-in-individuals-with-adrenal-insufficiency/82088/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What condition does the paper focus on, and why is cortisol regulation important?","Question",{"text":74,"@type":75},"The paper focuses on adrenal insufficiency (AI), where cortisol concentrations are too low. Cortisol is crucial for stress regulation, metabolism, immune responses, and overall homeostasis.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the proposed HPA-axis model incorporate circadian behavior?",{"text":79,"@type":75},"It introduces a mathematical model of the HPA axis that incorporates the endogenous circadian rhythm, allowing simulation of diurnal cortisol variations through circadian-driven dynamics and feedback loops.",{"name":81,"@type":72,"acceptedAnswer":82},"Why is MPC proposed instead of using a fixed-dose open-loop strategy?",{"text":83,"@type":75},"Open-loop simulations with fixed hydrocortisone dosing yield a working but non-optimal strategy. 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