System Identification of Cortisol Secretion: Characterizing Pulsatile Dynamics OF TECHNOLOGy by Rose Taj Faghih JUN 1 0 2014 B.S., Electrical Engineering (2008) University of Maryland, College Park LIBRARIES S.M., Electrical Engineering and Computer Science (2010), Massachusetts Institute of Technology Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2014 @ Massachusetts Institute of Technology 2014. All rights reserved. Signature redacted Author ........... ............................. Department of Electrical Engineering and Computer Science Signature redacted May 14,2014 Certified by........ .................................... Emery N. Brown Edward Hood Taplin Professor of Medical Engineering Professor of Computational Neuroscience Thesis Supervisor Certified by Si onRtIIm mdRctE~d Munther A. Dahleh Professor of Electrical Engineering and Computer Science Professor of Engineering Systems Division Thesis Supervisor b Signature redacted,; A cce;pte d Uy .... ....... 4, ..... ...... .. .... S/Prdsar Leslie A. Kolodziejski Chair, Department Committee on Graduate Students System Identification of Cortisol Secretion: Characterizing Pulsatile Dynamics by Rose Taj Faghih Submitted to the Department of Electrical Engineering and Computer Science on May 14, 2014, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Cortisol controls the body's metabolism and response to inflammation and stress. Cortisol is released in pulses from the adrenal glands in response to pulses of adreno- corticotropic hormone (ACTH) released from the anterior pituitary; in return, cortisol has a negative feedback effect on ACTH release. Modeling cortisol secretion and the interactions between ACTH and cortisol allows for quantifying normal and abnormal physiology and can potentially be used for diagnosis and optimal treatment of some cortisol disorders. Due to noise, modeling these interactions using concurrent data from serum ACTH and cortisol levels is challenging. First, using serum cortisol lev- els, we model cortisol secretion from the adrenal glands by representing the sparse pulses of cortisol using an impulse train. We formulate an optimization problem and successfully recover infusion and clearance rates as well as physiologically plausible cortisol pulses. Then, for serum ACTH and cortisol levels, we model ACTH and cortisol secretion by representing the sparse ACTH pulses using an impulse train. By considering a multi-rate system, we formulate another optimization problem and suc- cessfully recover model parameters as well as physiologically plausible ACTH pulses. We solve both optimization problems under the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, and recover the timing and amplitudes of the pulses using compressed sensing, and employ generalized cross validation for de- termining the number of pulses. In all our studies mentioned above, the datasets we use consist of ACTH and cortisol levels sampled at 10-minute intervals from 10 healthy women. Finally, we present a mathematical characterization of pulsatile cor- tisol secretion. We hypothesize that there is a controller in the anterior pituitary that leads to pulsatile release of cortisol, and propose a mathematical formulation for such controller. Our proposed controller achieves impulse control, and the obtained impulses and plasma cortisol levels exhibit cortisol circadian and ultradian rhythms that are in agreement with experimental data. 3 Thesis Supervisor: Emery N. Brown Title: Edward Hood Taplin Professor of Medical Engineering Professor of Computational Neuroscience Thesis Supervisor: Munther A. Dahleh Title: Professor of Electrical Engineering and Computer Science Professor of Engineering Systems Division 4 5 .A a 4)L 'Woudtthat 6eing (existence) fiad a tongue, that it might remove the vei(s from existent beings! O'6reath of (phenomenaf) existence, whatsoeverywords thou ma-gst utter, know that therefirg thou hast 6ound anotherveiCupon it. e Mat na-wi of Jacaraddin %uiti TransCation and Commentanj, Nichoson 6 TIo my beI~vedyarents andtn- CoveC-g 6rotir 7 Acknowledgments I am greatly indebted to my advisors Professor Emery N. Brown and Professor Munther A. Dahleh as this thesis would not have been possible without their guidance, depth of knowledge, understanding, ideas, unwavering support, patience, invaluable advice, and precious feedback. Working under the supervision of these brilliant minds and goodhearted souls, and having them as my role models, has truly been a great honor and privilege for me. I am very lucky that I could benefit from the light of their wisdom in my academic and personal life, and I hope to benefit from their wisdom even more in the years to come. They have been immensely encouraging and great sources of enthusiasm, inspiration, and positive energy. While guiding me with my research, they have always given me freedom to explore research areas and approaches for tackling problems independently to improve my abilities to think deeply and crit- ically to grow as an independent researcher. They have also provided me with the opportunity to collaborate with researchers from different backgrounds to work on an interdisciplinary research project. I would like to express my gratitude to my committee member Professor George Verghese for helpful conversations, insightful suggestions and invaluable advice. I was very fortunate that I could benefit from his support, kindness, and wisdom. He is enormously devoted to students and spent many hours of his precious time giving me great feedback and advice on my research. I am grateful to our collaborators Dr. Elizabeth Klerman and Dr. Gail Adler for providing us with ACTH and cortisol data, which made this research possible. I am also grateful to them for providing me with feedback on Chapters 2 and 3 of this the- sis, particularly the discussions concerning the physiological aspects of this research. They have read multiple drafts of these chapters, providing me with great feedback and comments on improving these chapters. From our interactions, I have learned 8 how to bridge the communication gap between electrical engineering and physiology and communicate with medical doctors. I would like to thank Professor Ketan Savla for mentoring me during my masters and early stages of my PhD when he was a research scientist at MIT. I have learned a lot from Ketan through our collaborations and his kind mentorship; I am grateful for his invaluable advice that has been crucial for me to grow as a researcher. I was very fortunate to be the head teaching assistant for Professor Babak Ayazi- far, Professor Dimitri Bertsekas, Professor Jeff Shapiro, and Dr. Ligong Wang for 6.041/6.431: Probabilistic Systems Analysis and Applied Probability. I learned a lot from them and their teaching styles. Babak inspires me with his art of teaching; I am indebted to him for the invaluable lessons I learned from him regarding teaching skills. Babak and Dimitri also provided me with great advice on what it takes to manage a big and diverse class of graduate and undergraduate students. I am grateful to my academic advisor Professor Muriel Medard for her kind advice throughout my graduate studies. I would like to thank Professor Terry Orlando for his support and advice. I would also like to thank all the professors at the Laboratory for Information and Decision Systems (LIDS) for creating an intellectually stimulat- ing environment in the lab. I would like to express my gratitude to my undergraduate professors who had a great influence on my academic career. I would like to thank Dr. Donald Day for introduc- ing me to undergraduate research by nominating me for my first research experience as an undergraduate at Drexel University. I would like to thank Professor Thomas Antonsen, Professor Edward Ott and Professor Michelle Girvan for co-supervising my second research experience as an undergraduate at the University of Maryland. I would like to specially thank Professor Antonsen for being a great mentor, spending a lot of his precious time providing me with advice, which has been crucial to my academic career. I would like to also thank Professor Gilmer Blankenship, Professor Rama Chellappa, Professor Christopher Davis, Professor Satyandra Gupta, Professor William Levine, and Professor Edo Waks for their advice and support during my undergraduate studies. 9 I would like to thank Sheri Leone and Albert Carter for being super helpful and friendly, as well as their wonderful administrative work. I would like to specially thank Sheri for her friendship. I would like to thank Brian Jones for tech support. I would also like to thank Debbie Wright, Jenifer Donovan, and Janet Fischer for administrative support. My EECS friends and labmates in LIDS and Neuroscience Statistics Research Lab- oratory (NSRL) have been an important part of my life as a graduate student. I would like to specially thank my lovely EECS friends Audrey Fan, Shreya Saxena, Christina Lee, and Ermin Wei for their friendship and all the enjoyable moments over the years. Working on interdisciplinary research, I had the opportunity to be a member of two amazing laboratories and benefit from the stimulating environments and mentorship of my labmates in both labs. This has exposed me to a wide variety of philosophies and has provided me with a unique opportunity