The Role of Leptin and Ghrelin in Food Intake and Body Composition Changes: A mathematical model

Abstract

This works explores the physiological functions of leptin, including its secretion, effects on appetite, carbohydrate and lipid metabolism, and its interaction with ghrelin. In addition, the reciprocal interactions between ghrelin and leptin are of growing clinical interest. We detail a possible mathematical model describing the dynamics of key energy substrates, regulatory hormones, appetite, and fat mass over daily and weekly timescales. The model incorporates physiological responses to three mixed meals (breakfast, lunch, dinner), represented in the present case by difference-of-exponential influx functions. The size of these meal pulses is modulated by appetite, which is dynamically regulated by ghrelin and leptin concentrations. The model links the net energy balance, derived from nutrient absorption rates and estimated energy expenditure, to changes in body fat mass. The system is formulated as fifteen coupled nonlinear algebraic and ordinary differential equations (ODEs), including state variables for appetite, gut glucose and lipid contents, glycemia, lipidemia, insulinemia, plasma ghrelin and leptin concentrations, and fat mass. We aim to develop a mathematical model which could be employed for effective weight management interventions tailored to individuals by considering not only energy balance and food choices but also hormone interactions especially ghrelin and leptin.