Optimal control for predicting customized drug dosage for superovulation stage of in vitro fertilization Kirti M. Yenkie a,b , Urmila Diwekar a,b,n a The Richard and Loan Hill Department of Bioengineering, University of Illinois, Chicago, IL 60607, USA b Center for Uncertain Systems: Tools for Optimization & Management (CUSTOM), Vishwamitra Research Institute, Clarendon Hills, IL 60514, USA HIGHLIGHTS  Mathematical model for superovulation in IVF treatment.  Real world patient data used to validate the model.  The problem of finding optimal drug dosage requirements is formulated as an optimal control problem.  Significant improvement in quantity of eggs of particular size is obtained by optimal control as compared to the dosage used. article info Article history: Received 16 September 2013 Received in revised form 11 February 2014 Accepted 14 April 2014 Available online 18 April 2014 Keywords: Assisted reproductive technology Hormones Follicle growth Medication frequency abstract in vitro fertilization (IVF) is one of the most highly pursued assisted reproductive technologies (ART) worldwide. IVF procedure is divided into four stages: Superovulation, Egg-retrieval, Insemination/Fertilization and Embryo transfer. Among these superovulation is the most crucial stage since it involves external injection of hormones to stimulate development and maturation of multiple follicles or oocytes. Although numerous advancements have been made in IVF procedures, little attention has been given to modifying the existing protocols based on a ‘patient specific’ predictive model. A model for follicle growth and number change as a function of the injected hormones and patient characteristics has been developed and validated for data available on 50 superovulation cycles. The model has 9 patient specific parameters which can be determined from the initial 2 days of observation and can help in projecting the superovulation outcome for the ongoing cycle. Based on this model, the dosage of the hormones to stimulate multiple ovulation or follicle growth is predicted by using the theory of optimal control. The objective of successful superovulation is to obtain maximum number of mature oocytes/follicles within a particular size range. Using the mathematical model of follicle growth dynamics and optimal control theory, optimal dose and frequency of medication customized for each patient (n¼5) is predicted for obtaining the desired result. The results indicate a better final day follicle size distribution when the dosage of the hormones is varied by some amounts as compared to the actual dosage given to the patient in the existing cycles. This ensures a better success rate for the superovulation cycles and reduces the costs of excess medication and daily monitoring. The idea is to provide the medical practitioners with a guideline for planned treatment, for a procedure currently based on trial and error in order to get better success rates. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Around 8–12% couples all over the world suffer from infertility issues at some point in their lives. In certain regions, mostly some developing countries this figure reaches to almost one-third of the total population (Kols et al., 1997), like the countries in sub Saharan Africa where 64% infertility diagnosis in women were due to infections like tubal problems, etc. Exposure to excess heat, pesticides and other harmful chemicals at workplace and drinking water pollutants like arsenic, etc. are the leading causes of infertility in males in developing nations. In most of the developing nations it is argued that health problems like infertility do not make the person ill. However, as per the definition (Grad, 2002) by WHO (World Health Organization) health is a ‘ state of complete physical, mental and social well-being and not merely the absence of disease or infirmity’ . In developing nations like India, there is another prevailing issue of gender inequality which in most cases leads to the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology http://dx.doi.org/10.1016/j.jtbi.2014.04.013 0022-5193/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author at: Center for Uncertain Systems: Tools for Optimization & Management (CUSTOM), Vishwamitra Research Institute, Clarendon Hills, IL 60514, USA. Tel.: þ1 630 886 3047. E-mail address: urmila@vri-custom.org (U. Diwekar). Journal of Theoretical Biology 355 (2014) 219–228