Exchange-induced relaxation in the presence of a fictitious field

•A theory of exchange-induced relaxation in the presence of a fictitious field was derived.•The method can be generalized for description of relaxation in the rotating frames of rank n⩾3.•The derived expressions provide a means to analyze data from MRI experiments with the RAFFn method. In the present study we derive a solution for two site fast exchange-induced relaxation in the presence of a fictitious magnetic field as generated by amplitude and frequency modulated RF pulses. This solution provides a means to analyze data obtained from relaxation experiments with the method called RAFFn (Relaxation Along a Fictitious Field of rank n), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (rank n). The RAFF2 technique is relevant to MRI relaxation methods that provide good contrast enhancement for tumor detection. The relaxation equations for n=2 are derived for the fast exchange regime using density matrix formalism. The method of derivation can be further extended to obtain solutions for n>2.