Q-Space Diffusion Weighted MRI Analyzed with Maximizing Rician
Likelihood Improves Reliability and Tissue Contrast
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.
Computation of Diffusion Function Measures in Q-Space Using Magnetic
Resonance Hybrid Diffusion Imaging
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.
Simple Harmonic Oscillator Based Estimation and Reconstruction for
One-Dimensional Q-Space MR
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.
Analysis of High B-Value Diffusion Images Using Fractional Order
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.
Towards Better Understanding of Brain Tissue Using Directional
Kurtoses by Orthogonal Transformation of Diffusion Kurtosis Tensor D (KDT)
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).
In Vivo Higher-Order Contrast Measured with Generalized
Diffusion Tensor Imaging Using Higher-Order Tensors
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.
Effect of Diffusion Gradient Pulse Duration on Fibre Orientation
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.
A Recursive Algorithm to Decompose Orientation Distribution Function
and Resolve Intra-Voxel Fiber Directions
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.
Regularized Super-Resolution for Diffusion MRI
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.
Spatial Normalization of the Fiber Orientation
Distribution Based on High Angular Resolution Diffusion Imaging Data
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.