Heavy metal never tasted so good: A mathematical model of cadmium exposure from dark chocolate consumption

Abstract

Ingested heavy metals are known to cause adverse health effects, such as reproductive harm and cancer. Unfortunately, many foods consumed today, such as chocolate, baby food, fruit juice, rice, fish, and many more contain trace amounts of heavy metals, including lead, cadmium, and arsenic. Mathematical modeling can simulate how consuming contaminated foods leads to accumulation of harmful compounds in the human body and also provides a tool to determine the impact of consumption changes. As part of the SIMIODE Challenge Using Differential Equations Modeling (SCUDEM) competition, we developed a simple mathematical model to investigate heavy metal accumulation from dark chocolate. Our model included half-life based decay of the metals, a Fourier transform of sales data to account for consumption, and parameters to simulate various concentrations of contaminants present in dark chocolate. The model developed for the competition had inaccuracies, so we began the iterative process of developing a more complex mathematical model. Each iteration showed that, heavy metals-specifically cadmium-accumulate to concerning levels over time and can ultimately contribute to negative health effects. This paper details the evolution of our model, and illustrates the importance of iteratively changing the process in mathematical modeling.