Distribution of Dopamine in the Brain

We construct a three-dimensional unsteady-state mass transport model to predict the behavior of dopamine levels in the brain. The model is based on the principles of molecular diffusion, first-order decay, and instantaneous point-source input. We exhibit an analytical solution to the governing partial differential equation. We apply the given data on distribution of dopamine, in the brain of a laboratory subject subsequent to an intracerebral injection, to calibrate the parameters of the model. We use two-dimensional curve-fitting and a fivedimensional gridsearch optimization routine. We then use a numerical integration scheme to sum the model concentrations over space so that they could be compared directly to the data values.