Radial q‐space sampling for DSI

Abstract

Purpose Diffusion Spectrum Imaging (DSI) has been shown to be an effective tool for non-invasively depicting the anatomical details of brain microstructure. Existing implementations of DSI sample the diffusion encoding space using a rectangular grid. Here we present a different implementation of DSI whereby a radially symmetric q-space sampling scheme for DSI (RDSI) is used to improve the angular resolution and accuracy of the reconstructed Orientation Distribution Functions (ODF). Methods Q-space is sampled by acquiring several q-space samples along a number of radial lines. Each of these radial lines in q-space is analytically connected to a value of the ODF at the same angular location by the Fourier slice theorem. Results Computer simulations and in vivo brain results demonstrate that RDSI correctly estimates the ODF when moderately high b-values (4000 s/mm2) and number of q-space samples (236) are used. Conclusion The nominal angular resolution of RDSI depends on the number of radial lines used in the sampling scheme, and only weakly on the maximum b-value. In addition, the radial analytical reconstruction reduces truncation artifacts which affect Cartesian reconstructions. Hence, a radial acquisition of q-space can be favorable for DSI.

A theoretical signal processing framework for linear diffusion MRI: Implications for parameter estimation and experiment design

“…In the modern q-space literature, it is relatively rare for authors to discuss fundamental sampling theory concepts like the Nyquist rate , aliasing , and resolution , even though such concepts should be fundamental for Fourier-based EAP reconstruction methods like diffusion spectrum imaging (DSI) (Wedeen et al, 2005) and radial DSI (Baete et al, 2016). When these concepts are discussed, they are frequently examined empirically rather than theoretically (Lacerda et al, 2016; Tian et al, 2016), and popular methods for DSI sampling design are often based on extensive empirical testing (Kuo et al, 2008, 2013) instead of leveraging well-established insights from sampling theory.…”

Accelerated radial diffusion spectrum imaging using a multi‐echo stimulated echo diffusion sequence

“…Whereas the conventional rectangular acquisition of q‐space samples in DSI uses a three‐dimensional Fourier Transform to reconstruct the probability density function (PDF) from q‐space, radially sampled DSI benefits from the geometry of its sampling scheme. That is, the three‐dimensional Fourier Transform is rewritten using the Fourier slice theorem to the one‐dimensional radial Fourier Transform of a three‐dimensional Radon transform . In this reconstruction, both q‐space and the PDF are sampled on radial grids, and the ODF can be easily calculated without interpolation.…”

“…From these ODFs, the PDF is integrated radially outward, weighted by the square of the displacement L . The preservation of radial geometry has the advantage that every radial line in q‐space generates a value of the ODF at the same angular location in the spatial domain . Hence, the nominal angular resolution is mainly determined by the number of lines intersecting the unit sphere and not by the largest q‐space value sampled .…”

“…Q‐space was sampled according to the recently proposed radial q‐space sampling scheme [Fig. b, ] as discussed above. For this sampling scheme 236 samples were acquired on 59 radial lines N l , evenly distributed on a radius 4 half sphere.…”

Model‐based denoising in diffusion‐weighted imaging using generalized spherical deconvolution

“…Two popular approaches are diffusion kurtosis imaging (DKI) and neurite orientation dispersion and density imaging (NODDI) . Moreover, multiple b‐values are required for the model‐free determination of the 3D probability distribution, as in diffusion spectrum imaging (DSI) .…”