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

Purpose: The orientation distribution function (ODF), which is obtained from the radial integral of the probability density function weighted by (Formula presented.) ((Formula presented.) 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 (Formula presented.) through the Taylor series expansion and a generalized expression for (Formula presented.) 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.