The orientation dependence of the gradient-echo MR signal in brain white matter conflates two principal effects, (i) the susceptibility properties of tissue microenvironments, especially the myelin microstructure, and (ii) the axon orientation distribution with respect to the external magnetic field. This work introduces a clinically feasible MRI method based on gradient-echo and diffusion measurements, which we refer to as microscopic susceptibility anisotropy imaging, that disentangles both effects, hence enabling us to estimate microscopic susceptibility anisotropy unconfounded by fibre crossings and orientation dispersion as well as magnetic field direction.
It has been challenging to map microscopic susceptibility features in orientationally heterogeneous tissue such as brain white matter since the gradient-echo signal depends on the axon orientation relative to the magnetic field1–3. Last year, an ex-vivo study using monkey brain demonstrated that the Spherical Mean Technique (SMT)4 is capable of factoring out the orientation dependence. However, this requires a dense sampling of magnetic field directions and thus is not clinically viable. In this work, we use information about the directional tissue structure inferred from diffusion MRI to remove the confounding effect of the axon orientation distribution and show the first microscopic susceptibility anisotropy maps in humans.
Microdomain population model. The gradient-echo signal is produced by a large population of microdomains, e.g. (myelinated) axon segments, which may have a complex orientation distribution p. Here we adopt a phenomenological approach and describe, at echo time t, the effective frequency shift of a single microdomain as
$$$(1)\qquad\delta\omega(\theta;t)=\omega_\mathrm{A}(t)\sin^2(\theta)$$$
with respect to a typically short reference time5–7. θ denotes the angle between the microdomain orientation u and magnetic field direction B0, ωA(t) is a time-dependent index of microscopic susceptibility anisotropy quantifying the frequency shift when a small axon segment is oriented perpendicular to B0. The spherical convolution of p with the microscopic signal shift yields the macroscopic (i.e. voxel-scale) signal shift
$$$(2)\qquad\delta E(B_0;t)=\int_{S^2}\exp(i\omega_\mathrm{A}(t)(1-\langle B_0,u\rangle^2)\,t)p(u)\,du$$$
observed in gradient-echo MR measurements. The microscopic frequency anisotropy ωA(t) can then be estimated using Equation (2) once we have knowledge of the axon orientation distribution p, which may be obtained from diffusion imaging.
Protocol design. We conducted a human pilot study with a healthy male volunteer (aged 45 years) after written informed consent had been obtained. The multi-modal dataset was acquired on a 3T Siemens Prisma system equipped with a 32-channel head coil. A 3D flow-compensated gradient-echo scan (flip angle 22°, TR = 58 ms, 1.4 mm isotropic, GRAPPA/2) measured a train of 12 gradient echoes (TE1 = 5.8 ms, ESP = 4 ms) at three different head orientations (Figure 1). In addition, a diffusion EPI scan (TR = 4.9 s, TE = 79 ms, 1.5 mm isotropic, SMS/3, twice with signal readout reversed) was performed with two b-shells of 1000 and 3000 s/mm2 and 90 evenly distributed gradient directions each.
Data preprocessing. The three gradient-echo scans were first co-registered. After phase unwrapping8, we computed the frequency difference signal with respect to the first gradient echo5,6, which eliminated time-independent frequency shifts and non-local susceptibility effects, and subsequently subtracted the background field, which was recovered using second-order total generalised variation regularisation9. Following diffusion data preprocessing, we estimated the axon orientation distribution p through spherical deconvolution with a spatially varying impulse response function, which was obtained with the Spherical Mean Technique (SMT), a recently introduced method for microscopic diffusion anisotropy mapping10,11.
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