Research

My research lies at the intersection of optimization theory, control theory, dynamic input recovery, dynamical systems theory, inverse theory, and trajectory optimization. The general goal is to construct methods, techniques, or algorithms to recover the underlying dynamics of an unknown system and/or the underlying dynamics of the control signal driving the system, using a set of partial or complete measurements of the system. Specifically, my current Ph.D. research involved studying the underlying dynamics of the glucose-insulin system in an individual’s body from their continuous glucose monitoring (CGM) trace which essentially is a discrete sequence of measurements of the glucose concentration in the intertitial fluid (ISF) of the individual.

Estimating HbA1c

I have succesfully obtained two methods for estimating HbA1c values for type 2 diabetes (T2D) patients from their CGM trace and the research has been published in Majumdar et al., 2023 ¹. I have also analyzed these methods of HbA1c estimation on CGM traces from type 1 diabetes (T1D) patients. The latter research has been provided in my thesis Majumdar, 2024 ².

Estimating the continuous Blood Glucose Concentration (BG)

I have also developed a method, based on trajectory optimization, to obtain an estimate of the continuous blood glucose concentration (BG) from a patients CGM trace. In this method we assume a simple dynamical system describing the dynamical relationship between BG and ISF. Collocation methods are used to discretize the continuous system and then a suitable set of discrete BG values are obtained which generates discrete ISF values as close as possible to the measured ISF, provided by the CGM trace. This is done by solving a nonlinear programming problem (NLP). The discrete BG value estimates are then suitably interpolated to obtain an estimate of the continuous BG. This research has been provided in my thesis Majumdar, 2024 ².