Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems Under Selective Saturation. III. Solution by Projection Operators

Abstract

A general method of solving equations governing the transient response of heterogeneous spin systems to continuous and pulsed RF saturation using the projection-operator technique is outlined. An effective rate equation is derived in which there is natural separation of relaxation and source terms. Our previously derived implicit solution to the coupled Bloch equations is reformulated using this more general approach, which avoids some of the restrictive assumptions made earlier. With this formulation, we provide an analytical and explicit solution to the full set of coupled Bloch equations with no additional assumptions or restrictive conditions attached limiting their general validity. The results obtained with this new method of solution are compared with the results previously obtained by the Laplace-transform technique for heat-denatured albumin.