Propagation of lead in the human body

Lead is a toxin that has well known side effects including fatigue, muscle pain, impaired kidney function, lower IQs for children, and brittle bones. Lead can be absorbed into the body through paint, air, water, and various other consumer products. Once ingested, blood transports lead throughout the body. The vast majority of lead absorbed in the body accumulates in the bone. Here we explore a three-compartment nonlinear ODE model for lead in blood, cortical bone, and trabecular bone. Thereafter, we compare the ODE results with a PDE model in which it is assumed that lead slowly diffuses through the bone. Numerical solutions of the model ODE equations suggest that in order to have results which are consistent with experimental data, one should assume nonlinear interactions between the blood and cortical bone, but linear interactions between the blood and trabecular bone. On the other hand, we find that the PDE model we use does not provide for a good comparison with the data. We briefly touch upon some possible reasons for this discrepancy, and ways in which the model could be improved.