The effect of diffusion and susceptibility differences on T2 measurements for fluids in porous media and biological tissues

A number of features of T2 measurements for fluids in porous media have shown behavior contrary to that suggested by intuition developed in other areas. For porous media with relatively uniform pore spaces the following have been observed, in each case for certain ranges only of χν (susceptibility difference times frequency), D (diffusion coefficient), a (a pore dimension), porespace shape and distribution, echo-time t for single echoes and half-echo-spacing τ for CPMG): (1) In S(t) for FID (free induction decay, S for signal) with constant slope after an initial period of increasing slope; (2) In Ss(t) for single (subscript s) echoes linear (instead of cubic) in t after an initial period; (3) for CPMG R(τ) = 1T2(τ) − 1T2(τ → 0) linear in τ over a substantial range; (4) slope of R(τ) independent of D and a for this range; (5) slope Rs of In Ss(t) independent of D and a, and (6) Rs(t) and R(τ) at long times linear (instead of quadratic) in χν. These features appear to be compatible with the assumption of a truncated Cauchy-Lorentz distribution of the local magnetic fields due to susceptibility differences. The statistics of repeated sampling of local fields in different parts of the porespace during diffusion lead to a suppression, after a short time, of the effects of diffusion on the FID decay rate and the single-echo decay rate over significant ranges of the parameters. Data are presented to extend the range of parameters studied previously.