A heuristic function for modelling scintillation pulses and other phenomena of interest in medical imaging

There are recurring phenomena in medical imaging, which benefit from robust, descriptive mathematical models. These models serve, for instance, in pulse characterization, relative comparison, mathematical convolution/deconvolution, parametric and Monte Carlo simulation, and circuit design. As a rule, these phenomena share a signal rise which is somewhat exponential in shape, which succumbs to a competing decay described by one, or more, exponential functions. It is proposed that this behavior may be well represented by the logistic function: 1/(1+exp(-x)), a special case of the sigmoidal function, in combination with an appropriate number of exponential decays. This has been tested with scintillation light data acquired in Bollinger-Thomas experiments, and with arterial blood samples in tracer kinetic modelling of C11-choline prostate imaging data, typically yielding fits with R² values greater than 99.5%.