Microscopic susceptibility anisotropy imaging

Abstract

Purpose: The gradient-echo MR signal in brain white matter depends on the orientation of the fibers with respect to the external magnetic field. To map microstructure-specific magnetic susceptibility in orientationally heterogeneous material, it is thus imperative to regress out unwanted orientation effects.

Methods: This work introduces a novel framework, referred to as microscopic susceptibility anisotropy imaging, that disentangles the 2 principal effects conflated in gradient-echo measurements, (a) the susceptibility properties of tissue microenvironments, especially the myelin microstructure, and (b) the axon orientation distribution relative to the magnetic field. Specifically, we utilize information about the orientational tissue structure inferred from diffusion MRI data to factor out the $B_0$ -direction dependence of the frequency difference signal.

Results: A human pilot study at 3 T demonstrates proxy maps of microscopic susceptibility anisotropy unconfounded by fiber crossings and orientation dispersion as well as magnetic field direction. The developed technique requires only a dual-echo gradient-echo scan acquired at 1 or 2 head orientations with respect to the magnetic field and a 2-shell diffusion protocol achievable on standard scanners within practical scan times.

Conclusions: The quantitative recovery of microscopic susceptibility features in the presence of orientational heterogeneity potentially improves the assessment of microstructural tissue integrity.

Keywords: brain white matter; gradient-echo MR imaging; microscopic frequency shift; orientational tissue heterogeneity; spherical mean technique (SMT).

Figure 1

The gradient‐echo measurements were carried out at 3 different head orientations (downwards, standard, upwards) with respect to the external magnetic field. The rotation axis of the head inside the MRI scanner was left‐right; the angle between upward and downward head position was $59.8^{\circ }$ in this instance

Figure 2

Frequency difference mapping, ¹⁷ , ¹⁸ shown for 3 echo times at a single magnetic field direction in various axial planes, demonstrates that the gradient‐echo frequency shift contrast is largely due to its dependence on echo time and the orientational heterogeneity of brain white matter. For comparison, the bottom row depicts the DTI color‐encoded principal direction. Left (L), right (R)

Figure 3

Spherical Mean Technique (SMT) ²⁰ , ²¹ for microscopic diffusion anisotropy mapping. (a) Estimation of microscopic diffusion features, such as microscopic fractional anisotropy and intra‐axonal volume fraction, unconfounded by fiber crossings and orientation dispersion. (b) Quantitative recovery of the axon orientation distribution using spherical deconvolution with a spatially varying impulse response function, showing the crossing of the callosal fibers and the pyramidal tract in the centrum semiovale. (c) Probabilistic tractography, ⁴⁸ visualized with MRtrix3, revealing the complex architecture of the fiber pathways in the individual human brain

Figure 4

Maps of the microscopic frequency shift ${\omega }_{A,t_0}(t)/(2\pi )$ obtained from gradient‐echo measurements with different numbers of magnetic field directions at echo time t = 40.5 ms. For comparison, the fourth row shows the macroscopic frequency shift for a single $B_0$‐direction before factoring out orientational heterogeneity. The 2 arrows point to white matter regions with fiber bundles predominantly running parallel (left) and perpendicular to the external magnetic field in standard head orientation

Figure 5

Time dependence of the microscopic frequency shift ${\omega }_{A,t_0}(t)/(2\pi )$, here estimated from 3 magnetic field directions at various echo times. The bottom section maps the DTI color‐encoded principal direction, showing the orientational heterogeneity in brain white matter. The 2 arrows indicate the pyramidal tract (left) and the superior longitudinal fasciculus, which are largely oriented parallel and perpendicular to the main magnetic field in standard head position, respectively

Figure 6

Microscopic anisotropy mapping both in diffusion and susceptibility MRI. An important observation is that all these microscopic feature maps are relatively homogeneous in brain white matter because the confounding effects due to fiber crossings and orientation dispersion as well as magnetic field and diffusion gradient direction have been factored out. For comparison, the bottom row shows the orientation dispersion entropy that quantifies the orientational tissue heterogeneity ²⁰

Figure 7

The box plots (with 1.5‐times the interquartile range) show, from left to right, the macroscopic frequency shift and orientation distribution weighting for the gradient‐echo measurement in standard head position as well as the microscopic frequency shift, after regressing out the effects of fiber crossings and orientation dispersion, in various white matter regions for 3 healthy adults. The dots depict the median of individual subjects. Posterior limb of internal capsule (PLIC), superior longitudinal fasciculus (SLF), superior corona radiata (SCR), corpus callosum (CC); prefix: left (l), right (r)

Figure 8

Noise amplification effect in microscopic susceptibility anisotropy imaging. The right panel maps the amplification factor for different sets of magnetic field directions at echo time of 40.5 ms. The acquisition of multiple head orientations with respect to the $B_0$‐direction (especially in upward and downward position) significantly reduces noise amplification in brain regions where otherwise the fiber pathways predominantly run parallel to the external magnetic field