On the existence of an unambiguous solution in factor analysis of dynamic studies

Abstract

Achievement of an unambiguous solution in factor analysis of dynamic radionuclide studies depends on constraints reflecting the known properties of factors. The constraints should be tight enough to prevent ambiguity but sufficiently general in order to ensure the data-based derivation of factors. In dynamic scintigraphy, the non-negativity of factors is their essential property which is implied by the physical nature of measured quantities. Considering factors as the images of compartments in the distribution space of a radiopharmaceutical (i.e. performing the factor analysis in the spatial domain), a powerful additional constraint can be applied. This constraint is based on the presence of segments in the image matrix where the subtotal number of compartments is projected. Using this constraint, the existence of physiologically related unique solution in factor analysis can be proved providing the number of factors is chosen properly.