Fiber orientation-dependent white matter contrast in gradient echo MRI

Abstract

Recent studies have shown that there is a direct link between the orientation of the nerve fibers in white matter (WM) and the contrast observed in magnitude and phase images acquired using gradient echo MRI. Understanding the origin of this link is of great interest because it could offer access to a new diagnostic tool for investigating tissue microstructure. Since it has been suggested that myelin is the dominant source of this contrast, creating an accurate model for characterizing the effect of the myelin sheath on the evolution of the NMR signal is an essential step toward fully understanding WM contrast. In this study, we show by comparison of the results of simulations and experiments carried out on human subjects at 7T, that the magnitude and phase of signals acquired from WM in vivo can be accurately characterized by (i) modeling the myelin sheath as a hollow cylinder composed of material having an anisotropic magnetic susceptibility that is described by a tensor with a radially oriented principal axis, and (ii) adopting a two-pool model in which the water in the sheath has a reduced T(2) relaxation time and spin density relative to its surroundings, and also undergoes exchange. The accuracy and intrinsic simplicity of the hollow cylinder model provides a versatile framework for future exploitation of the effect of WM microstructure on gradient echo contrast in clinical MRI.

Fig. 1.

Axial image data illustrating the steps followed in generating a FDM. A frequency map is created from short TE (5 ms) phase data, f_{TE = 5 ms} (A). Another frequency map is formed from long TE (25 ms) phase data, f_{TE = 25 ms} (B). These maps were produced by scaling high-pass-filtered phase images by TE and then setting the average frequency in cerebrospinal fluid to zero. An FDM is then created by subtracting the short TE frequency map from the long TE frequency map, Δf = f_{TE = 25 ms} − f_{TE = 5 ms} (C). DTI fiber orientation map that has been converted into red/green/blue values and weighted by the FA maps (D). The fiber orientation is color-coded such that red is left/right, green is anterior/posterior, and blue is foot/head. Particularly large frequency differences occur in the corpus callosum where the nerve fibers are perpendicular to B₀ (central red region in D).

Fig. 2.

Plots of the average normalized WM magnitude signal against TE, for different fiber orientations relative to B₀, characterized by an angular θ range (A). An expanded segment of the plot is shown with error bars (Inset). The corresponding averaged frequency difference is also shown for each θ range (B). The simulated signal evolution plots for the hollow cylinder model that achieved the lowest residual fit to the data (χ_I + E + χ_A in Table 2) are shown as solid lines in A and B.

Fig. 3.

Schematic of the hollow cylinder model. Nerve fibers are modeled as infinite hollow cylinders oriented at angle, θ, to B₀ (A). A two-pool model is adopted where the cylindrical annulus forms the small pool of myelin water, and the large pool corresponds to the external and internal spaces (B). The susceptibility of the myelin sheath is anisotropic and described by a cylindrically symmetric tensor in which the principal axis is radially oriented (C).

Fig. 4.

Calculated field perturbations due to the hollow cylinder model populated with isotropic susceptibility (A and D), exchange-related field offsets (B and E), and radially oriented anisotropic susceptibility (C and F). The field perturbations are simulated with the cylinder axis (fiber orientation) parallel to B₀, θ = 0° (A–C), and with the cylinder axis perpendicular to B₀, θ = 90° (D–F). The fields are simulated for a g-ratio (r_i/r_o) of 0.8. For ease of comparison, the results are shown for the relevant perturbation (χ_I, E, or χ_A) set equal to 1 ppb.

Fig. 5.

Comparison of estimates of the nonlocal frequency offsets in WM voxels produced by applying the hollow cylinder model to the measured data (A–C) and by simulation of the field perturbation produced by the anatomical arrangement of GM and WM (D–F). Maps were generated for the χ_I + E (A and D), χ_I + χ_A (B and E), and χ_I + E + χ_A (C and F) mechanism combinations using the model parameters that yielded the lowest average difference values. By subtracting the simulated nonlocal offsets (D–F) from the measured offsets (A–C), difference values were formed for each subject.