Research Projects - BITS Pilani

Prajakta Bedekar

Assistant Professor,
Department of Mathematics

Birla Institute of Technology & Science, Pilani
Hyderabad Campus
Jawahar Nagar, Kapra Mandal
Dist.-Medchal-500 078
Telangana, India

prajakta.b@hyderabad.bits-pilani.ac.in

Research Overview

The overarching theme of my research has been creation, analysis, and numerical validation of mathematical models for problems arising in biology and medicine applied to real-world data. The vast predictive power yielded by explainable mathematical models intrigues and motivates me. My focus is on building mathematical models using tools from partial differential equations (PDEs), probabilistic modelling, and optimal decision theory. Short research project summaries are listed below. For more information, refer to the respective publications or email me.

Take a look at my blog post in SIAM News for a gentle introduction to my work pertaining to time-dependence in antibody measurements for a person in relation to a population.

Cellular Differentiation

Thesis: Mathematical Models of Self-Organized Patterning of human Embryonic Stem Cells (hESCs)
If a spatially confined hESC colony is treated uniformly with BMP4 (Bone Morphogenetic Protein 4), the cells differentiate to form three germ layers: an outer trophectoderm-like ring, an inner ectodermal circle and a ring of mesendoderm. We develop a reaction-diffusion model for the activator-inhibitor cascade including BMP4, Wnt, Nodal and their inhibitors to explain this phenomenon. We use Robin boundary conditions to effectively model the physical realities of the system. Finite Element simulations are used to study these systems numerically. We also present a detailed theoretical proof of the existence and stability of steady state solutions for a specialized activator-inhibitor system, subject to certain sufficient conditions on the data of the problem.

Time-dependent Antibody Kinetics and Prevalence Estimation

Antibody testing can identify past immune events such as infection and vaccinations by quantifying the immune response of an individual. When randomly administered to a fraction of the population, it can be used to extrapolate and estimate information about an entire population. In particular, time plays a complex role while considering antibody measurements, from the personal timeline for an individual to the absolute timeline for a disease. Using tools from probabilistic modelling, graph theory and optimal decision theory I constructed a unique approach to simulate and predict population prevalence of a disease over time and optimally classify a measurement into previously infected/vaccinated or not.

We recently generalized this framework for repeated infections and vaccinations, by using time-inhomogeneous Markov chain framework, where each transition probability changes with time.
Ongoing: exploration of mathematical properties of the general model.

Ongoing: Sperm-egg Interaction for Fertilization Success

The process of fertilization consists of movement of spermatozoa towards an oocyte through the female reproductive system, followed by their interaction and fusion. While the mechanisms of spermatozoa movement through gradients of temperature and chemicals are well studied, not much attention has been accorded to the next steps. To this end, I have been working on modeling of sperm-egg interactions accounting for glycan and enzyme kinetics. This is a part of a larger research project to quantify fertilization success.

So far, we have created a 1-D advection-diffusion-reaction model whose numerical solutions are calculated using operator splitting. We notice that peak of the product complex drifts towards egg, even in the absence of advection. This allows for zona pellucida penetration in the presence of large enough diffusion. Next steps involve constructing a novel probabilistic framework to model inter-spermatozoa competition yielding a meaningful notion of probability of fertilization success.

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Prajakta Bedekar

Research Overview

Cellular Differentiation

Time-dependent Antibody Kinetics and Prevalence Estimation

Ongoing: Sperm-egg Interaction for Fertilization Success

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