Modelling Vitamin D Concentration Dynamics in the Human Body Using Partial Differential Equation

Abstract

Vitamin D is important for bone health, the immune system, regulating metabolic processes, and maintaining the calcium and phosphate balance. Many people, however, encounter vitamin D deficiencies, which can be attributed to insufficient sun exposure, a lack of vitamin D-rich food, and certain health issues. Most existing models have used ordinary differential equations (ODEs) to model vitamin D dynamics. The problem with the existing models, however, is that the models assume a uniform distribution, which does not account for the differing spatial levels of vitamin D in various body compartments. This research focuses on vitamin D dynamics in sunlight exposure, supplementation, and body mass index (BMI), and aims to apply it to an existing partial differential equation (PDE) model. The model is built using the Crank-Nicolson finite difference method to solve the equations and is validated with a synthetic dataset of 1000 people. The model shows that sunlight exposure and vitamin D supplementation positively contribute to serum 25-hydroxyvitamin D (25(OH)D) levels, and negatively impact it is BMI. Unlike traditional ODE models, the PDE model does a better job of mimicking the distribution, conversion, and destruction of vitamin D in principal body compartments. The study shows that, for simulating the dynamics of vitamin D, the PDE approach has more biological realism, which may be applied to future studies of vitamin D metabolism and public health.