https://www.nature.com/articles/s41598-019-50654-7 (2019)

In this paper, the authors built a compartmental model of lead pharmacokinetics, specifically investigating lead’s relationship with calcium and means of neurotoxicity. Competition between lead and calcium is closely related to the toxicity of lead, as well as its storage and mobilization in bone and retention and excretion. The competition is present at the blood brain barrier, and thus is especially pertinent to neurotoxicity. Understanding how lead is absorbed, how/where it targets in the body, and age dependency in toxicity can help improve treatment and prevention methods. Their model focuses on neurological impacts of lead toxicity, uses more current knowledge about molecular pharmacology, and translates molecular mechanisms into a mathematical model.  By using a more complex model, they were able to describe and potentially explain nonlinear phenomena. 

In this section, we will summarize the general findings of the paper, but mainly focus on why it is useful to model the lead-calcium dynamic in this way and how modeling is used to illuminate how lead acts on the body (specifically neurologically). The authors state that they use “traditional phase space methods, parameter sensitivity analysis and bifurcation theory to study the transitions in the system’s behavior in response to various physiological parameters” so we plan to look into these methods so we can understand the choices the authors made in this paper. However, since we are not experts on mathematical modelling, we will probably focus more on how the overall pharmacokinetic model works and what it tells us about the molecular mechanisms of lead toxicity.