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Bennett Allan Landman¹, Jonathan Andrew David Farrell¹, ², Seth A. Smith², ³, Peter C. van Zijl, ²³, Jerry L. Prince¹

¹Johns Hopkins University, Baltimore, Maryland, USA; ²Kennedy Krieger Institute, Baltimore, Maryland, USA; ³Johns Hopkins University School of Medicine, Baltimore, Maryland, USA

Q-space imaging is an emerging diffusion weighted MR imaging technique that shows great promise in classifying changes in tissue microstructure. Unlike diffusion tensor imaging, q-space imaging identifies the molecular diffusion probability density function without the need to assume a Gaussian distribution. Traditional analysis techniques use limited diffusion models (e.g., bi-exponential) to regularize noisy data and do not properly account for the properties of Rician noise. We present a robust M-estimator for diffusion probability density functions based on maximum likelihood. In simulation and in vivo spinal cord, the method improves reliability of the estimated probability functions and increases tissue contrast. 

Yu-Chien Wu¹, ², Aaron S. Field, ²³, Andrew L. Alexander, ²³

¹University of Wisconsin-Madison, Madison , Wisconsin, USA; ²Madison, Wisconsin, USA; ³University of Wisconsin-Madison, Madison, Wisconsin, USA

The distribution of water diffusion in biological tissues may be estimated by a 3D Fourier Transform (FT) of diffusion-weighted measurements in q-space. In this study, methods for estimating diffusion spectrum measures (the zero-displacement probability, the mean-squared displacement, and the orientation distribution function) directly from the q-space signals are described. These methods were evaluated using both computer simulations and hybrid diffusion imaging (HYDI) measurements on a human brain.  This new direct computation approach reduces HYDI data processing time and image artifacts arising from 3D FT and regridding interpolation. In addition, it is less sensitive to the noise and q-space truncation effects.

Evren Ozarslan¹, Cheng Guan Koay, Peter J. Basser

¹National Institutes of Health, Bethesda, Maryland, USA

Dependence of the diffusion-weighted MR signal on the diffusion gradient strength was represented as a series of eigenfunctions of the simple harmonic oscillator Hamiltonian. This formulation made it possible to rapidly estimate the ensemble average propagator and potentially useful descriptors such as its moments and return-to-origin probability. The proposed technique has significant advantages over the previously employed biexponential curve fitting and cumulant expansion methods. Unlike these approaches,  the simple harmonic oscillator based method is linear, and capable of approximating complicated signal profiles such as non-monotonic patterns due to diffraction-like effects.

Xiaohong Joe Zhou¹, ², Osama Abdullah², Dumitru Baleanu³, Richard L. Magin²

¹University of Illinois Medical Center, Chicago, Illinois, USA; ²University of Illinois at Chicago, Chicago, Illinois, USA; ³Cankaya University, Ankara, Turkey

It is well known that diffusion-induced MR signal loss deviates from mono-exponential decay, especially at high b-values.  We demonstrate that the anomalous diffusion behavior can be characterized by extending the Bloch-Torrey equation through application of the operators of fractional calculus. Theoretical analyses and experimental results have shown that a model for anomalous diffusion can be established by directly solving the fractionalized Bloch-Torrey equation in time and space.  Using this mathematical tool, we may extend the applications of diffusion imaging beyond simply evaluating apparent diffusion coefficients and stretched exponential constant α, and eventually reveal new parameters related to tissue micro-environment.

Edward Sai Kam Hui¹, ², Liqun Qi², Matthew M. Cheung¹, Kyle H. Cheng¹, Joseph A. Helpern³, Jens H. Jensen³, Ed X. Wu¹

¹The University of Hong Kong, Pokfulam, Hong Kong; ²The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong; ³New York University School of Medicine, New York, USA

Orthogonal transformation of diffusion kurtosis tensor is implemented to obtain axial (K_//) and radial kurtosis (K_^) which measures kurtosis parallel and perpendicular, respectively, to principal diffusion direction, which could potentially yield extra information regarding diffusion environment in brain tissue. In vivo and ex vivo experiments were performed on normal adult SD rat brains. It was found that fixation has more effect on the intrinsic structure parallel than perpendicular to nerves as depicted by more increase in K_// than increase in K_^ suggesting that directional kurtoses has excellent sensitivity to changes in diffusion environments, and gains superiority to mean kurtosis (MK).

Chunlei Liu¹, Sarah Charlotte Mang², Michael E. Moseley¹

¹Stanford University, Stanford, California , USA; ²University of Tuebingen, Tuebingen, Germany

The higher order tensor (HOT) model by Liu et al proposes to quantitatively characterize general diffusion processes using a series of diffusion tensors with increasing orders. Each order of these tensors offers a well defined physical interpretation, with the second order tensor meaning the second order cumulant (covariance matrix), the third order tensor meaning the third order cumulant (skewness tensor), and the fourth order tensor meaning the fourth order cumulant (kurtosis tensor). We present a very first in vivo implementation of generalized diffusion tensor imaging (GDTI) with HOT and propose a set of techniques to generate higher order diffusion contrast.

Chun-Hung Yeh¹, Jacques-Donald Tournier², ³, Kuan-Hung Cho¹, Ching-Po Lin¹, Fernando Calamante², ³, Alan Connelly², ³

¹Institute of Neuroscience, National Yang-Ming University, Taipei, Taiwan; ²Brain Research Institute, Melbourne, Australia; ³Department of Medicine, University of Melbourne, Melbourne, Australia

In the q-space formalism, the short gradient pulse approximation is preferable to determine spin displacement. However, we propose that the application of a longer £_ which is clinically achievable is theoretically beneficial for resolving fibre orientations, as it enhances both the DW signal and the contrast between the DW directions. We thus investigate the relationship between £_ and the DW signal measured as a function of orientation using both simulated and experimental data. The results show that prolonging £_ preferentially enhances the transverse DW signal. This effect is advantageous for estimating fiber orientations and hence for fiber-tracking applications.

Fang-Cheng Yeh¹, Van J. Wedeen², Wen-Yih Isaac Tseng, ¹³

¹National Taiwan University College of Medicine, Taipei, Taiwan; ²Harvard Medical School, Charlestown, Massachusetts, USA; ³National Taiwan University Hospital, Taipei, Taiwan

A recursive decomposition algorithm for resolving intra-voxel fiber directions in diffusion spectrum imaging (DSI) and q-ball imaging (QBI) is presented. The proposed algorithm recursively decomposes orientation distribution function (ODF) and obtains fiber directions.

Shahrum Nedjati-Gilani¹, Geoff J M Parker², Daniel C. Alexander¹

¹University College London, London, UK; ²University of Manchester, Manchester, UK

We present an algorithm that uses regularized super-resolution to find fibre populations and their respective orientations and volume fractions accurately from a sub-voxel scale in a 3D diffusion MRI acquisition. We can use our method to recover fibre configurations such as bending, fanning, and partial volume effects.

Xin Hong¹, Lori Rose Arlinghaus¹, Adam W. Anderson¹

¹Vanderbilt University, Nashville, Tennessee, USA

In this study an algorithm is developed to transform the Fiber Orientation Distribution (FOD) function based on HARDI data, which takes into account not only translation, but also rotation, scaling, and shearing effects of the spatial transformation. The algorithm is tested using both numerical phantom and in vivo human data. This technique makes it possible to compare the intra-voxel fiber distribution between subjects, which will be helpful in various clinical studies of white matter diseases.