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 used 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 on its variance. The technique can be used 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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GENERAL SCIENTIFIC SUMMARY Introduction and background. Many materials are essentially mixtures of different substances. For example, in porous media a fluid occupies the vacant regions of the underlying solid host. A common food like milk is characterized by fat globules in water. Many physical characteristics of such heterogeneous media are determined by the distribution of pore or droplet sizes. We can measure features of pores by probing the incessant motion of water molecules within them via magnetic resonance (MR).
Main results. We present and validate a framework for measuring different statistical features of the pore size distribution. The method utilizes theoretical relationships between an array of measured MR signals and these features. A new numerical method is described for accurately computing them from MR data. The technique is validated via experiments performed on glass microcapillaries.
Wider implications. Using the developed framework, it is possible to measure new and useful features of porous media ranging from biological tissue (such as nerves) to synthetic and naturally occurring materials (such as emulsions, many food products, and so on). As such, the technique could be employed in the diagnosis and monitoring of many diseases of the nervous system. It could also be used to assess the quality of food processing.
Figure. Experimental data points are depicted by symbols and the lines represent the continuous representation of the signal decay (bottom). The predicted and estimated values for the mean and standard deviation of the inner diameter distributions (top).