Modelling a multi-crystal detector block for PET

A simple mathematical model describes the performance of a modular detector ''block'' which is a key component in an advanced, high-resolution PET Scanner. Each block contains 32 small bismuth germanate (BGO) crystals coupled to four photomultiplier tubes (PMTs) through a coded light pipe. AT each PMT cathode the charge released for 511 keV coincidence events may be characterized as Poisson random variables in which the variance grows as the mean of the observed current. Given the light from BGO, one must; arrange the best coding - the distribution of light to the four PMTs, specify an optimum decoding scheme for choosing the correct crystal location from a noisy ensemble of PMT currents, and estimate the average probability of error. The statistical fluctuation or ''noise'' becomes decoupled from the ''signal'' and can be regarded as independent, additive components with zero mean and unit variance. Moreover, the envelope of the transformed noise distribution approximates very closely a normal (Gaussian) distribution with variance = 1. Specifying the coding and decoding strategy becomes a problem of signalling through a channel corrupted by additive, white, Gaussian noise; a classic problem long since solved within the context of Communication Engineering using geometry: i.e. distance, volume, angle,more » inner product, etc., in a linear space of higher dimension.« less