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1990 MCM A: The Brain-Drug Problem

Researchers on brain disorders test the effects of new medical drugs (e.g., dopamine against Parkinson’s disease) with intracerebral injections. To this end, they must estimate the size and the shape of the spatial distribution of the drug after the injection to estimate accurately the region of the brain that the drug has affected.

The research data consist of the measurements of the amounts of drug in each of 50 cylindrical tissue samples (Figure A.9 and Table A.2). Each cylinder has length 0.76 mm and diameter 0.66 mm. The centers of the parallel cylinders lie on a grid with mesh 1 0:76 1 mm 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 scintillation count. Naturally, one expects that there is drug also between the cylinders and outside the region covered by the sample.

Estimate the distribution in the region affected by the drug. One unit represents a scintillation count, or 4:753 1013 mole of dopamine. For example, the table shows that the middle rear cylinder contains 28,353 units.

 

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