Dispersion of relaxation rates in the rotating frame under the action of spin-locking pulses and diffusion in inhomogeneous magnetic fields

Abstract

A method is described for characterizing magnetically inhomogeneous media and the spatial scales of intrinsic susceptibility variations within samples. The rate of spin-lattice relaxation in the rotating frame, R1ρ , is affected by diffusion effects to a degree that depends on the magnitude of an applied spin-locking field. Appropriate analysis of the dispersion of R1ρ with locking field may be used to characterize susceptibility variations in inhomogeneous tissues. The contribution of diffusion to R1ρ is quantified by an analytic expression derived by analyzing of the effects of diffusion through periodic variations of magnetic susceptibility and is used to predict the effects of inhomogeneities in simple phantoms. The theory is further applied to imaging to derive parametric images that portray the dimensions of susceptibility inhomogeneities independent of their magnitude. Significant dispersion of R1ρ with locking field was predicted and measured experimentally for suspensions of microspheres ranging from 1 to 90 μm in diameter. For scales of practical interest, these dispersion effects occur at much lower locking fields than the range in which chemical exchange effects cause similar dispersion. There is good agreement between theory and experiment, and the method has potential for quantitative tissue characterization and functional imaging.