Effects of nongaussian diffusion on "isotropic diffusion measurements'': an ex-vivo microimaging and simulation study

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.Comment: 26 pages, 9 figures. Appearing in J. Magn. Reso

Director Field Analysis to Explore Local White Matter Geometric Structure in diffusion MRI

International audienceIn diffusion MRI, a tensor field or a spherical function field, e.g., an Orientation Distribution Function (ODF) field, are estimated from measured diffusion weighted images. In this paper, inspired by microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter from the estimated tensor field or spherical function field. 1) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in each voxel; 2) We estimate a local orthogonal coordinate frame in each voxel with anisotropic diffusion; 3) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to quantitatively describe orientational distortion (splay, bend, and twist) in diffusion MRI. The proposed scalar indices are useful to detect local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions

Fast Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors

High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex fiber configurations, albeit at the cost of long acquisition times. We propose a method to recover intra-voxel fiber configurations at high spatio-angular resolution relying on a kq-space under-sampling scheme to enable accelerated acquisitions. The inverse problem for reconstruction of the fiber orientation distribution (FOD) is regularized by a structured sparsity prior promoting simultaneously voxelwise sparsity and spatial smoothness of fiber orientation. Prior knowledge of the spatial distribution of white matter, gray matter and cerebrospinal fluid is also assumed. A minimization problem is formulated and solved via a forward-backward convex optimization algorithmic structure. Simulations and real data analysis suggest that accurate FOD mapping can be achieved from severe kq-space under-sampling regimes, potentially enabling high spatio-angular dMRI in the clinical setting.Comment: 10 pages, 5 figures, Supplementary Material

Maxwell-compensated design of asymmetric gradient waveforms for tensor-valued diffusion encoding

Purpose: Asymmetric gradient waveforms are attractive for diffusion encoding due to their superior efficiency, however, the asymmetry may cause a residual gradient moment at the end of the encoding. Depending on the experiment setup, this residual moment may cause significant signal bias and image artifacts. The purpose of this study was to develop an asymmetric gradient waveform design for tensor-valued diffusion encoding that is not affected by concomitant gradient. Methods: The Maxwell index was proposed as a scalar invariant that captures the effect of concomitant gradients and was constrained in the numerical optimization to 100 (mT/m)$^2$ms to yield Maxwell-compensated waveforms. The efficacy of this design was tested in an oil phantom, and in a healthy human brain. For reference, waveforms from literature were included in the analysis. Simulations were performed to investigate if the design was valid for a wide range of experiments and if it could predict the signal bias. Results: Maxwell-compensated waveforms showed no signal bias in oil or in the brain. By contrast, several waveforms from literature showed gross signal bias. In the brain, the bias was large enough to markedly affect both signal and parameter maps, and the bias could be accurately predicted by theory. Conclusion: Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient tensor-valued encoding with concomitant gradients that have a negligible effect on the signal. This waveform design is especially relevant in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition and large/oblique FOVs

Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE, which is enough to solve the degeneracy in the NODDIDA model parameter estimation.Comment: 22 pages, 7 figure