1990 Problem A: Brain Drug Problem

Researchers on brain disorders test the effect so the new medical drugs – for example, dopamine against Parkinson’s disease – with intracerebral injections. To this end, they must estimate the size and shape of the spatial distribution of the drug after the injection, in order to estimate accurately the region of the brain that the drug has affected.

The research data consists of the measurements of the amounts of drug in each of 50 cylindrical tissue samples.  Each cylinder has length 0.76mm and diameter 0.66mm.  The centers of the parallel cylinders lie on a gird with mesh 1mm x 0.76mm x 1mm, so that the cylinders touch one another on their circular bases but not along their sides, as shown in the accompanying figure.  The injection was made near the center of the cylinder with the highest cont.  Naturally, one expects that there is drug also between the cylinders and outside the region covered by the samples.

Estimate the distribution in the region affected by the drug.

One unit represents a scintillation count, or 4.753 x 10^-3 mole of dopamine.  For example, the table shows that the middle rear cylinder contains 28353 units.