A new approach to MR trabecular bone characterization is presented. This method probes the diffusion of spins through internal magnetic field gradients due to the susceptibility contrast between the bone and water (or marrow) phases. The resulting spin magnetization decay encodes properties of the underlying structure. This method, termed decay due to diffusion in the internal field (DDIF), is well established as a probe of pore size and structure. In the present work its application is shown for in vitro experiments on excised bovine tibiae samples. A comparison with pulsed field gradient (PFG) measurement of restricted diffusion shows a strong correlation of DDIF with the surface-to-volume ratio (SVR) of bones. Calculation of the internal magnetic field within the bone structure also supports this interpretation. These NMR measurements compare well with the image analysis from microscopic computed tomography (CT). The SVR is not accessible in the clinically standard densitometry measurements, and provides vital information on bone strength and therefore on its fracture risk. The DDIF and PFG methods derive this information from a straightforward pulse sequence that does not employ either high ap- Osteoporosis is a disorder of the skeleton in which bone strength is abnormally weak and susceptible to fractures from minor trauma. Therapeutic treatment of osteoporosis is under intense development. Current diagnostics of osteoporosis using dual X-ray measurement of bone density do not entirely predict fracture risk, because the internal bone structure, apart from the bone density, contributes significantly to the mechanical strength and thus fracture risk (1,2). Such bone structure is routinely characterized by microscopic computed tomography (CT) with resolution down to 10 m for small samples. However, it is not available for in vivo examination due to the high radiation dose. Recent efforts to achieve high-resolution 3D images of the trabecular architecture using magnetic resonance imaging (MRI) are very promising. However, it is difficult to drastically improve its resolution far beyond the current levels (ϳ100 m) in clinical implementation, primarily due to the clinically allowed MRI scan time.This article describes a different approach to the characterization of bone architecture compared to the highresolution imaging approach. An NMR technique is used that is well-established in inorganic porous media to obtain statistical properties of the trabecular structure. This technique, referred to as decay from diffusion in an internal field (DDIF), can obtain pore-structure characteristics (such as the pore-size distribution (3)) at a resolution of about 1 m. In vitro DDIF data on bovine trabecular bone samples show a clear correlation with bone strength. This trend correlates well with measurements of the surface-tovolume ratio (SVR) using a pulsed field gradient (PFG), demonstrating the DDIF is also sensitive to the SVR of bones. This interpretation is further understood via theoretical calculations of the interna...

Trabecular bone structure is known to play a crucial role in the overall strength, and thus fracture risk, of such areas of the skeleton as the vertebrae, spine, femur, tibiae, or radius. Several MR methods devoted to probing this structure depend upon the susceptibility difference between the solid bone matrix and the intervening fluid/marrow/fat, usually in the context of a linewidth (1/T(2)') measurement or mapping technique. A recently demonstrated new approach to this system involves using internal gradients to encode diffusion weighting, and extracting structural information (e.g., surface-to-volume ratio) from the resulting signal decay. This contrast method has been demonstrated in bulk measurements on cleaned, water-saturated bovine trabecular bone samples. In the present work, microscopic imaging (0.156 mm in-plane resolution) is performed in order to spatially resolve this contrast on the trabecular level, and confirm its interpretation for the bulk measurements. It is found that the local rate of decay due to diffusion in the internal field (DDIF) is maximal close to the trabecular surfaces. The overall decay rate in a lower resolution scan probes the abundance of these surfaces, and provides contrast beyond that found in conventional proton density weighted or T(1)-weighted imaging. Furthermore, a microscopic calculation of internal field distributions shows a qualitative distinction between the structural sensitivities of DDIF and T(2)'. DDIF contrast is highly localized around trabecular walls than is the internal field itself, making it a less sensitive but more specific measure of such important properties as trabecular number.

In this article, the authors demonstrate a rapid NMR method to measure a full three-dimensional diffusion tensor. This method is based on a multiple modulation multiple echo sequence and utilizes static and pulsed magnetic field gradients to measure diffusion along multiple directions simultaneously. The pulse sequence was optimized using a well-known linear inversion metric (condition number) and successfully tested on both isotropic (water) and anisotropic (asparagus) diffusion systems.

The structure factor provides a fundamental characterization of porous and granular materials as it is the key for solid crystals via measurements of x-ray and neutron scattering. Here, we demonstrate that the structure factor of the granular and porous media can be approximated by the pair correlation function of the inhomogeneous internal magnetic field, which arises from the susceptibility difference between the pore filling liquid and the solid matrix. In-depth understanding of the internal field is likely to contribute to further development of techniques to study porous and granular media. DOI: 10.1103/PhysRevLett.100.025501 PACS numbers: 76.60.Jx, 61.05.Qr, 61.43.Gt, 75.75.+a Sand piles, rocks, and colloids share a common structure element that they are examples of materials formed by aggregation of granular particles in another medium. Their physical properties are critically dependent on the grain-grain interactions and the structure of the grain arrangement [1][2][3]. Details of the packing are important for the presence of heterogeneous force causing jamming [4,5], unique acoustic properties [6], and clustering [1]. It was found that the spatial correlation functions of the electromagnetic fields in such porous media can be useful to predict fluid flow and structure factor. For example, twodimensional images have been used to construct the spatial correlation functions of porous media and to infer material properties [7][8][9][10], and it was shown that correlation length of electric field is similar to the hydraulic radius [11]. In biomedical imaging, magnetic field correlation was examined for a potential quantitative assessment of iron in brain [12]. It was shown that the magnetic field correlation function is closely related to the structure factor of the pore space [13,14]. Thus it is desirable to devise an experimental method to directly measure the correlation function of the electromagnetic field in such media.In this Letter, we present a NMR method to measure the spatial magnetic correlation function in model porous materials. When a granular sample is placed in a uniform magnetic field, the solid grain and the interstitial material are magnetized differently due to a susceptibility contrast, producing an inhomogeneous magnetic field in the pore space -often called internal field. We use nuclear spins to probe the magnetic field difference between two positions by the following method. First, we employ pulsed field gradient (PFG) NMR to select spins by their translational diffusion displacement. For this experiment, the effect of the internal field is nullified. Then, we perform a similar experiment but with the internal field effect. The field difference between the two positions causes a signal decay that is related to the magnetic field correlation at that displacement. We show that the method is robust for different grain sizes, diffusion, encoding times, and displacement resolution and reliably obtains surface-to-volume ratio (SVR).Conventional translation diffusion measurements ofte...

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