Q‐ball reconstruction of multimodal fiber orientations using the spherical harmonic basis

Abstract

The past decade has seen rapid advances in the development of diffusion MRI techniques that permit for the first time the noninvasive characterization of neural architecture. While the exact biophysical determinants of the diffusion signal have yet to be completely elucidated, it is now generally accepted that microscopic boundaries to diffusion in the brain coincide with the local orientations of white matter (WM) fiber tracts (1). The advent of diffusion tensor imaging (DTI) as a tool for modeling intravoxel diffusion has inspired a number of promising applications in which WM connectivity can be evaluated in both health and disease (2,3). Measures derived from the tensor are now widely used to characterize regional anisotropy and orientation of WM throughout the brain, and more recently have been incorporated into tractography algorithms to allow 3D delineation of fiber pathways (4 -6).A major shortcoming of DTI lies in its inability to accurately characterize diffusion in complex WM, where fiber tracts with different orientations intersect or are otherwise partial volume averaged within a voxel (7-9). This limitation presents a significant obstacle to routine clinical application of DTI. For example, in brain tumor patients, presurgical DTI tractography fails to delineate the course of the pyramidal tract in regions of fiber crossing (10). Although intravoxel diffusion in these areas of complex WM can be more accurately characterized using the qspace formalism (11), long experiment times and heavy gradient demands preclude routine in vivo application of this technique in humans. High angular resolution diffusion imaging (HARDI) represents an alternative approach that strives to improve imaging efficiency by recovering the angular structure of diffusion in lieu of the 3D spindisplacement probability function. Shorter imaging times make HARDI particularly promising for clinical applications, especially when combined with the greater signalto-noise ratios (SNRs) afforded by high-field MR systems (12) and the reduction in single-shot echo-planar image artifacts provided by parallel imaging (12)(13)(14).Several approaches for reconstructing fiber orientations from HARDI data have been proposed, including spherical harmonic modeling of the apparent diffusion coefficient (ADC) profile (15,16), multitensor modeling (17), generalized tensor representations (18,19), circular spectrum mapping (20), q-ball imaging (QBI) (21-24), persistent angular structure (25), and spherical deconvolution (26). Among these techniques, QBI and spherical deconvolution have generated considerable interest due to their linearity and sensitivity to multimodal diffusion. QBI has the additional desirable property of model independence because it does not require ad hoc measurement of a "response function" in order to reconstruct fiber orientations. While the two methods differ significantly in their approach to recovering angular information from the measured diffusion data, both define a continuous function over the sphere that encodes the ...

Hybrid diffusion imaging

“…Overall, the ODF profiles from QBI appeared sharper with fewer artifactual side lobes. The angular resolution may be improved by increasing the number of measurements in the outer shell although the relative improvement appeared to be small in a recently published study (Hess et al, 2006).…”

“…In this study, the QBI-ODF were calculated using the straight Funk-Radon Transform (Tuch et al, 2003;Tuch, 2004), although recent studies by Hess et al (Hess et al, 2006), Özarslan et al (Özarslan et al, 2006) and Khachaturian et al (Khachaturian et al, 2007) describe alternative methods that may improve the accuracy of the ODF profiles further. The latter two approaches utilized diffusion measurements at lower diffusion-weighting to improve the ODF performances.…”

Development and initial evaluation of 7-T q-ball imaging of the human brain

“…The q-ball ODF at each voxel was computed from the HARDI data using spherical harmonic basis functions, using methods we have described in detail previously [19]. Truncating the spherical harmonic series at a low order enables q-ball ODF reconstruction from relatively few diffusion-encoding directional measurements with little noise amplification, but achieving higher angular resolution with larger numbers of directional measurements requires higher harmonic orders in the reconstruction.…”

“…A spherical Gaussian smoothing kernel was applied to the RBF reconstructions, where the width of the kernel σ s was chosen visually to smooth out fluctuations in the ODF [15]. RBF q-ball reconstruction performs less reliably at low spherical sampling densities [19] and therefore was not attempted in the fast acquisition regime at b=3000 s·mm −2 .…”

“…However, all of these HARDI approaches remain SNR-limited even on 3T scanners with parallel imaging capability, because of the need for both high spatial resolution and very strong diffusion-weighting, resulting in long examination times and/or suboptimal discrimination of intravoxel crossing fiber tracts. Indeed, the low SNR of HARDI at 3T has motivated the introduction of different forms of regularization to improve the reliability of fiber orientation determination [19][20][21]. Proposed methods for more fully sampling q-space often require even higher diffusion-weighting factors than is typical for HARDI [22][23][24]; hence, these techniques might derive even greater benefits from better SNR.…”