Structural anisotropy and internal magnetic fields in trabecular bone: Coupling solution and solid dipolar interactions

Louis-S. Boucharda, Felix W. Wehrlib, Chih-Liang Chinb and Warren S. Warrena, , aDepartment of Chemistry, Princeton University, Princeton, NJ 08544, USAbDepartment of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA Received 19 February 2005; revised 27 April 2005. Available online 13 June 2005.
Abstract
We investigate the use of intermolecular multiple-quantum coherence to probe structural anisotropy in trabecular bone. Despite the low volume fraction of bone, the bone–water interface produces internal magnetic field gradients which modulate the dipolar field, depending on sample orientation, choice of dipolar correlation length, correlation gradient direction, and evolution time. For this system, the probing of internal magnetic field gradients in the liquid phase permits indirect measurements of the solid phase dipolar field. Our results suggest that measurements of volume-averaged signal intensity as a function of gradient strength and three orthogonal directions could be used to non-invasively measure the orientation of structures inside a sample or their degree of anisotropy. The system is modeled as having two phases, solid and liquid (bone and water), which differ in their magnetization density and magnetic susceptibility. A simple calculation using a priori knowledge of the material geometry and distribution of internal magnetic fields verifies the experimental measurements as a function of gradient strength, direction, and sample orientation.
Keywords: Distant dipolar field; Intermolecular multiple-quantum coherence; Porous materials; Trabecular bone; Material anisotropy; Microstructure
PACS: 76.60.Jx

Multiple-quantum vector field imaging by magnetic resonance

Louis-S. Bouchard and Warren S. Warren

Published in J. Magn. Res. 177, 9-21 (2005)

We introduce a method for non-invasively mapping fiber orientation in materials and biological tissues using intermolecular multiple-quantum coherences. The nuclear magnetic dipole field of water molecules is configured by a CRAZED sequence to encode spatial distributions of material heterogeneities. At any given point r in space, we obtain the spherical coordinates of fiber orientation (θ,ϕ) with respect to the external field by comparing three signals G_X, G_Y, and G_Z (modulus), acquired with linear gradients applied along the X, Y, and Z axes, respectively. For homogeneous isotropic materials, a subtraction G_Z − G_X − G_Y gives zero. With anisotropic materials, we find an empirical relationship relating G_Z − G_X − G_Y/(G_X + G_Y + G_Z) to the polar angle θ, while G_X − G_Y/(G_X + G_Y + G_Z) is related to the azimuthal angle ϕ. Experiments in structured media confirm the structural sensitivity. This technique can probe length scales not accessible by conventional MRI and diffusion tensor imaging.