Quantitative study of the susceptibility difference between trabecular bone and bone marrow: Computer simulations

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Abstract
Inherent differences in tissue magnetic susceptibility produce inhomogeneities in the static magnetic field which give rise to an additional dephasing of the transverse magnetization in gradient‐echo images. The enhanced dephasing of the signal results in an increase of the apparent relaxation rate 1/T and a corresponding decrease in signal intensity. These effects have been used to explain the regional loss of marrow signal intensity in the appendicular skeleton, where in the presence of trabecular bone in the proximal tibia there is an enhanced loss of signal compared to the tibial shaft where there is no trabeculation. It has been postulated that differences in tissue magnetic susceptibility arising due to the marrow‐trabeculae interface give rise to magnetic field inhomogeneities and a reduced T. In this study computer simulations are used to determine whether susceptibility differences comparable to that between trabecular bone and tissue relate to the reduction of tissue T and whether the reduction in T is also related to the concentration and magnitude of susceptibility differences. In addition the effects of the spatial distribution of these particulate discontinuities in susceptibility on the measured relaxation time T are also estimated. This model demonstrates that 1/T increases as the number density and magnitude of such susceptibility differences increase. In a pixel of linear dimension L consisting of material simulating tissue water, the presence of circular point susceptibility differences of dimension 0.001 L with magnetic susceptibility equivalent to trabecular bone, 1/T, increases at a rate of 1.60 × 10−2 s−1 /N for N ranging from 25–2500. Differences in magnetic susceptibility that are less than that between soft tissue and trabecular bone are also modeled and the simulations demonstrate that differences in magnetic susceptibility, much lower than that between trabecular bone and tissue equivalent interfaces, also produce a relaxation rate enhancement in gradient‐echo images. © 1991 Academic Press, Inc.