1. Modeling the superovulation stage in in-vitro fertilization

Around 80 million people all over the world are suffering from infertility issues. The prevalence of infertility has increased worldwide due to modern lifestyle, postponed childbearing, infections, genetic disorders, etc. Most infertile couples resort to medical procedures like assisted reproductive technology (ART) for treatment. In-vitro fertilization (IVF) is the most common technique in ART. It has four basic stages: superovulation, egg retrieval, insemination/fertilization and embryo transfer. Superovulation is a drug induced method to enable multiple follicle growth to 'oocytes' or 'matured follicles' in a single menstrual cycle. The success of IVF majorly depends upon successful superovulation, defined by the number and uniformly sized high quality oocytes retrieved in a cycle. Hence, modeling of this stage in terms of distribution of oocytes obtained per cycle involving the chemical interactions of the drugs used and the conditions imposed on the patient during the process would provide a basis for predicting the possible outcome.

The superovulation stage involves information regarding the size as well as number of growing follicles with time. This information can be represented in the best way using size distributions. Hence, the analogy between the well-known particulate process of batch crystallization and superovulation has been used for model development. The data from previous superovulation cycles from our collaborative hospital in Nanded, India has been used to fit and validate the model by capturing the effect of externally administered drugs like follicle stimulating hormone (FSH).

First time system analysis approach has been used in modeling superovulation. Batch crystallization modeling basics and analogy has been applied to model superovulation in a womanís body. Variation in protocol depending upon patientís condition, earlier medical history and responsiveness will provide a guideline for treatment initiation to medical practitioners and better success rates could be anticipated as against using the same protocol for every patient.

Figure 1. Schematic diagram of the IVF

2. Customize drug dosage to improve success rate of in-vitro fertilization

The IVF treatment protocols followed by medical practitioners are the same for all patients irrespective of their variable characteristics, referred as 'blanket approach' by Fischel and Jackson. The use of an individualistic approach with more caution can avoid the risks associated with excessive stimulation. The success of superovulation is critical in proceeding with the further stages of the IVF cycle. Also, a major portion of the treatment cost is incurred in superovulation.

The superovulation protocol follow a standard for hormonal dosage and after the initial dose of follicle stimulating hormone (FSH) the patient requires daily testing and monitoring to keep a check on her response and thus modify the dose accordingly. Improper dose may result into life threatening complications like ovarian hyper stimulation syndrome (OHSS) or at times lead to undesirable or no effect in the patient. Repeated ovulations can disrupt the ovarian epithelium resulting in malignant transformations causing epithelial ovarian cancer and excess stimulation can result in early onset of menopause.

The aim of this work is to provide a customized drug dosage prediction strategy based on the model and patientís initial response. Superovulation aims at obtaining oocytes or mature follicles in high number within a specific size range with the aid of external hormones. The mathematical definition for application of optimal control theory is 'minimization of the coefficient of variation in follicle size on the last day of FSH administration by controlling the dosage of FSH with time'. The optimal control problem is solved using the method of maximum principle as well as discretized non-linear programming (NLP). The NLP method provided ease in constraint implementation on follicle size and can be used in cases where there is a possibility of follicles reaching the maximum size constraint. Both the methods provide a better superovulation outcome and in some cases we see a considerable reduction in the amounts of FSH required.

The superovulation protocols which lack individualized treatment variations will get a strong base for better treatment initiation. It will reduce the risks associated with the treatment and will be advantageous to the health and well-being of the patient during and after the treatment completion.

Figure 2. Optimal control vs actual observation for Patient - A