  Lead is a naturally-occurring element. It has been known to man for a long
time, and it is one of the longest established poisons. The current consensus
is that no level of lead exposure should be deemed "safe." New evidence
regarding the blood levels at which morbidities occur has prompted the CDC to
reduce the screening guideline of 10 $\mu$g/dl to 2 $\mu$g/dl. Measurable
cognitive decline (reduced IQ, academic deficits) have been found to occur at
levels below 10mg/dl.
  Knowledge of lead pharmacology allows us to better understand its absorption
and metabolization, mechanisms that produce its medical consequences. Based
upon an original and very simplified compartmental model of Rabinowitz (1973)
with only three major compartments (blood, bone and soft tissue), extensive
biophysical models sprouted over the following two decades. However, none of
these models have been specifically designed to use new knowledge of lead
molecular dynamics to understand its deleterious effects on the brain. We build
and analyze a compartmental model of lead pharmacokinetics, focused
specifically on addressing neurotoxicity. We 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.
  We conclude that modeling the complex interaction of lead and calcium along
their dynamic trajectory may successfully explain counter-intuitive effects on
systemic function and neural behavior which could not be addressed by existing
linear models. Our results encourage further efforts towards using nonlinear
phenomenology in conjunction with empirically driven system parameters, to
obtain a biophysical model able to provide clinical assessments and
predictions.
