Nuclear medicine and mathematics.

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently used in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: they are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new "allies" of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking.