General orientation transform for the estimation of fiber orientations in white matter tissues

Abstract

The orientation distribution function (ODF), which is obtained from the radial integral of the probability density function weighted by r n (r is the radial length), has been used to estimate fiber orientations of white matter tissues. Currently, there is no general expression of the ODF that is suitable for any n value in the HARDI methods. Theory and methods:A novel methodology is proposed to calculate the ODF for any n > −1 through the Taylor series expansion and a generalized expression for −1 < n < 4 is provided. Then a series of single-shell HARDI methods, termed the general orientation transform (GOT), is developed based on the obtained expression. By combining complementary GOTs, a composite estimator is obtained and further optimized via constrained optimization to take full advantage of individual merits. The final optimized HARDI method is termed the combined GOT with constrained optimization (coGOT). The proposed method is compared with other commonly used HARDI methods on the simulated data, the physical phantom data, the ISMRM 2015 Tractography challenge data, and in vivo HCP datasets.Results: coGOT can resolve crossing fibers with higher resolution, performs better robustness, generates fewer spurious lobes in glyphs, and thus provides distinct improvement in the tractography. The evaluations show coGOT's superior capability in reconstructing the fiber orientations from dMRI signals.Conclusions: Generalization of the ODF allows us to obtain a wide range of HARDI estimators to select suitable candidates for composite formulation. The optimized estimator coGOT has great potential for studying neural architecture and serving as fiber tracking tools. K E Y W O R D S orientation distribution function (ODF), high angular resolution diffusion imaging (HARDI), general orientation transform(GOT), combined GOT with constrained optimization(coGOT) Diwei Shi and Sisi Li contributed equally to this work.

Three‐dimensional diffusion MRI using simultaneous multislab with blipped‐CAIPI in a 4D k‐space framework

“…36 Fiber orientation distribution function (ODF) was estimated using the combined general orientation transform with constrained optimization method. 43…”

“…Fractional anisotropy (FA) and mean diffusivity were calculated using the FSL's dtifit function 36 . Fiber orientation distribution function (ODF) was estimated using the combined general orientation transform with constrained optimization method 43 …”

Improved reconstruction of crossing fibers in the mouse optic pathways with orientation distribution function fingerprinting

“…Contemporary reconstruction methods including constrained spherical deconvolution (CSD), 3,15 Diffusion Spectrum Imaging (DSI), 16,17 Generalized Q‐sampling Imaging (GQI), 18 Orientation Probability Density Transform, 19 Mean Apparent Propagator MRI, 20 or General Orientation Transform 21 offer improved angular precision in brain tractography. In this work, we aimed to obtain more accurate reconstruction of rodent optic pathways by incorporating a dictionary‐based technique called Orientation Distribution Function Fingerprinting (ODF‐FP) 22,23 …”