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. 2011 Jan:13:15010.
doi: 10.1088/1367-2630/13/1/015010.

NMR characterization of general compartment size distributions

Evren Ozarslan  1 , Noam Shemesh, Cheng Guan Koay, Yoram Cohen, Peter J Basser
Affiliations

NMR characterization of general compartment size distributions

Evren Ozarslan et al. New J Phys. 2011 Jan.

Abstract

The influence of molecular diffusion on the nuclear magnetic resonance (NMR) signal can be exploited to estimate compartment size distributions in heterogeneous specimens. Theoretical relationships between the NMR signal intensity at long diffusion times and the moments of a general distribution of isolated pores with characteristic shapes (planar, cylindrical or spherical) are established. A numerical method based on expressing a general diffusion-attenuated NMR signal profile in a series of complete orthogonal basis functions is introduced and subsequently employed to estimate the moments of the compartment size distribution. The results on simulated and real data obtained from controlled water-filled microcapillaries demonstrate the power of the approach to create contrast based not only on the mean of the compartment size but also its variance. The technique can be employed to address a variety of problems such as characterizing distributions of droplet sizes in emulsions and of apparent axon diameters in nerve fascicles.

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Figures

Figure 1
Figure 1
The pulsed-field gradient stimulated-echo NMR pulse sequence. The oscillatory shaped radiofrequency pulses rotate the magnetization by 90 degrees. The rectangular pulsed-field gradients encode the displacement of spins.
Figure 2
Figure 2
The left panel shows the beta distributions simulated (inset) and the E(q) profiles calculated for ensembles of cylinders whose radii are distributed according to those density functions. The right panel depicts the corresponding moments where the hollow squares show the analytical values while the moments estimated from the simulated E(q) profiles are depicted with solid diamonds. The black curves and symbols correspond to the beta distribution with positive skewness (α = 3.5, β = 6.5) whereas the red color is used for the negatively skewed distribution (α = 6.5, β = 3.5).
Figure 3
Figure 3
The top panel shows the histograms illustrating the composition of the four different specimens of water-filled microcapillaries. Each color represents one of these specimens. The SD000 specimen contains nothing but the 19 μm tubes. The corresponding real NMR data and the 1D-SHORE fit to them are depicted in the four panels below.
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