Leptin augmented model to include the role of obesity in insulin-glucose regulatory system for T2DM subjects

Leptin is a fat cell-derived hormone involved in satiety and body weight regulation. It also plays a critical regulatory role in the insulin-glucose regulatory system by modulating glucose metabolism and energy homeostasis. However, existing insulin-glucose models often fail to consider the impact of body weight indicators mainly body mass index (BMI) and plasma leptin. To address this limitation, we propose augmenting the ordinary differential equations (ODE) of the Oral Minimal Model (OMM) with an additional equation, incorporating leptin as well as supplementary terms and parameters. By estimating the model parameters, the model behaviour is aligned with the observed data of glucose, insulin and leptin for individuals with type 2 diabetes mellitus (T2DM). Based on model behaviour, revised indices formulated from Oral Glucose Tolerance Test (OGTT) data by including BMI and fasting leptin values are found to have a better correlation with existing indices. Additionally, parameter sensitivity analysis is performed to investigate the influence of the model parameters on the observed variables. Validation of the augmented model with clinical data (without leptin) demonstrates a superior fit to glucose and insulin data compared to the base model. This model emphasizes the intricate associations between leptin, glucose, and insulin concentrations with a potential for developing targeted interventions and therapies for T2DM. Notably, this manuscript introduces the first ODE-based model that incorporates leptin and BMI in the insulin-glucose pathway.