Empirical models of transverse relaxation for spherical magnetic perturbers

Ferromagnetic or superparamagnetic particles as MRI contrast agent present many advantages for bringing about soft tissue contrast as compared to single-ion complexes. The classic microscopic outersphere theory that works successfully for small molecules in understanding the transverse relaxation rate 1/T2 is not valid for these larger and stronger magnetic spheres. We categorize the relaxation behavior of the tissue-sphere system for ferromagnetic spherical perturbers in five diffusion regimes. Over the entire range of perturber size a general understanding of the relaxation mechanisms is described in terms of basic physical features of the system, and, through empiric models, the imaging sequences of spin echo and gradient echo. The models are verified with results of our spectroscopic measurements as well as simulations and experiments in the literature. Normalized models, obtained through proper scaling of the sphere radius and the relaxation rate, can be used to quantitatively estimate 1/T2 for various combinations of the variables. Effects of diffusion upon image contrast and effects of sphere size change upon relaxation with their possible applications in microvascular dilatation and other areas are then discussed.