Stochastic Processes from Batch Crystallization to 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 and is divided into four stages: superovulation, egg retrieval, insemination/fertilization and embryo transfer. The first stage of superovulation is a drug induced method to enable multiple follicle growth to oocytes in a single menstrual cycle. The overall success of IVF is dependent upon the initial success in the superovulation stage, defined by high number of uniformly sized and good quality oocytes/eggs retrieved. The research involves mathematical modeling of this stage in terms of follicle growth and their size distribution as a function of interactions of the hormonal drugs and patient response. The premise for this work has been built by deriving some ideas from the particulate process of batch crystallization, a multi-particle growth phenomena which is correlated to the multi-follicle growth in superovulation. Later, the mathematical model is used to predict the optimal hormonal dosing regime to achieve the targeted follicle size and number using the principles from control theory. The model as well as the clinical data is analyzed for sources of uncertainty and a robust stochastic differential equation (SDE) based model is developed for superovulation. On comparison of the model predictions for the patients which had large deviations in the deterministic model and a growth term (G) value higher than 0.6, the stochastic model provided a better prediction accuracy. This work aims at incorporating individualized treatment variations based on patient’s initial response and hence reducing the risks associated with the treatment. The methodologies developed can act as treatment guidelines for medical practitioners and will prove to be advantageous to the health and well being of the patient during and after the IVF treatment completion.