In this work, discrepancies between recent theories for susceptibility-induced T 2 -shortening and classical results, namely outer sphere theory and diffusion through local fields with random gradients, are considered. These discrepancies are assigned to the use of unrestricted diffusion in the new theories. Key words: susceptibility; T 2 -shortening; gradients; diffusion; CPMG sequence T 2 -shortening caused by proton diffusion within field inhomogeneities created by magnetized spheres has long been known to be governed by the outer sphere theory, provided the motional averaging condition is satisfied (1). A recent theory has considerably improved our theoretical knowledge by accounting for echo refocusing (2). However, this new theory does not yield an exact agreement with the "classical" results obtained without echo pulses (1) when increasing the echo time up to an infinite limit, especially if one considers the numerical constants appearing in the equations. This question was briefly addressed in two footnotes in Ref. 3; the present note is aimed at making this point more explicit.
LONG ECHO LIMITThe outer sphere theory describes the loss of phase coherence induced by diffusion within field inhomogeneities created by a random distribution of spherical dipoles (1,3):where v is the volume fraction occupied by the spheres, ⌬ r is the mean square angular frequency shift at the surface of the sphere (⌬ r ϭ (4/5) 1/2 ␥B eq ϭ (4/5) 1/2 ␥ /r 3 , ␥ being the proton gyromagnetic ratio, the particle magnetic moment, r the particle radius, and B eq its equatorial magnetic field), and D ϭ r 2 /D is the diffusion time, with D the water diffusion coefficient. J( D