Transverse NMR Relaxation as a Probe of Mesoscopic Structure

Transverse NMR relaxation in a macroscopic sample is shown to be extremely sensitive to the structure of mesoscopic magnetic susceptibility variations. Such a sensitivity is proposed as a novel kind of contrast in the NMR measurements. For suspensions of arbitrary-shaped paramagnetic objects, the transverse relaxation is found in the case of a small dephasing effect of an individual object. Strong relaxation rate dependence on the objects’ shape agrees with experiments on whole blood. Demonstrated structure sensitivity is a generic effect that arises in NMR relaxation in porous media, biological systems, as well as in kinetics of diffusion limited reactions.

Figure 1

Second order processes for $f(t)$. Left: FID relaxation. Circles, wavy lines, and crosses stand for $-i\delta \omega$, $Y(\mathbf{k})$, and $\tilde{v}(\mathbf{k})$ respectively. Solid lines represent free propagators ${\eta }^{(0)}(\mathbf{k},\tau )$ in time intervals between interactions. External momenta are set to zero due to Eq. (3). Right: CPMG relaxation. Each section represents a free propagator ${\eta }^{(0)}$ in the interval $\Delta t$ between successive refocusing pulses. Complex conjugation on every other interval $\Delta t$ is indicated with the filled circle. Equation (12) is obtained as a sum of all such configurations.

Figure 2

Mesoscopic relaxivity $r_2=f(\tau )/\tau$ for ${\alpha }^2=15/2\pi$. Left: objects are spheres, $t=t_E$ for the SE, $t=\Delta t$ for the CPMG. Right: shape effect: disks vs spheres. CPMG relaxivity $r_2(\Delta t/t_D=1)$, objects are disks with height-to-radius ratio $c$, and spheres of the same volume.

Figure 3

Theory (lines) vs experiments (symbols). Left: relaxation rate $R_2=-(\ln s)/t$ for the FID (boxes) and SE (circles) as a function of the particle diameter. Filled and hollow symbols correspond to measured and Monte Carlo simulated relaxation rates [16]. Right: CPMG relaxation rate for the human blood samples [6] for $B_0=1.41,1.18,0.94,0.71\mathrm{T}$ (from top to bottom). Experimental errors are 10%–20% [6]. Following our discussion after Eq. (8), theory agrees with experiment for small $\alpha$ and overestimates it for $\alpha \simeq 1$.