Comparison of different methods for predicting customized drug dosage in superovulation stage of in-vitro fertilization

In vitro fertilization (IVF) is one of the highly pursued assisted reproductive technologies worldwide. The IVF procedure is divided into four stages: Superovulation, Egg-retrieval, Insemination/Fertilization and Embryo transfer. Superovulation is the most crucial stage in IVF, since it involves external injection of hormones to stimulate development and maturation of multiple oocytes. The maximum amount of effort and money for IVF procedure goes into superovulation. Although numerous advancements have been made in IVF procedures, little attention has been given to modifying the standard protocols based on a predictive model. Currently, the same protocol is followed for every patient undergoing the IVF superovulation procedure. In reality every patient reponds differently and hence the proposition to modify the amounts of drug administered based on the patient's initial treatment response is a reasonable approach. The modification of drug dose if based on a well developed mathematical model which takes into account the variability in the follicle growth dynamics as well as the desired outcome thus increasing the predictive value of the method. A model for the follicle growth dynamics and number as a function of the injected hormones and patient characteristics has been developed and validated. The modeling basics have been adapted from batch crystallization moment model, since moments are representatives of specific properties like number, shape and size of the particles under consideration. 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 involving follicle growth dynamics and the optimal control theory, optimal dose and frequency of medication customized for each patient is predicted for obtaining the desired result. The optimal control problem is solved by different methods like the maximum principle and dicretized non-linear programming. The problem is solved with and without constraints to check the variation in the dosage amounts and size of follicles at the retrieval time. The results from different approaches are compared. Thus, a systematic comparison of the different methods will help in deciding the best solution strategy for customized drug dosage. It will also provide information about the sensitivity of the model parameters and hence the source of uncertainty in the system.