Comparison of gradient encoding directions for higher order tensor diffusion data

On the down-sampling of diffusion MRI data along the angular dimension

BACKGROUND

It has been established that the diffusion gradient directions in diffusion MRI should be uniformly distributed in 3D spherical space, so that orientation-dependent diffusion properties (e.g., fractional anisotropy or FA) can be properly quantified. Sometimes the acquired data need to be down-sampled along the angular dimension before computing diffusion properties (e.g., to exclude data points corrupted by motion artifact; to harmonize data obtained with different protocols). It is important to quantitatively assess the impact of data down-sampling on measurement of diffusion properties.

MATERIALS AND METHODS

Here we report 1) a numerical procedure for down-sampling diffusion MRI (e.g., for data harmonization), and 2) a spatial uniformity index of diffusion directions, aiming to predict the quality of the chosen down-sampling schemes (e.g., from data harmonization; or rejection of motion corrupted data points). We quantitatively evaluated human diffusion MRI data, which were down-sampled from 64 or 60 diffusion gradient directions to 30 directions, in terms of their 1) FA value accuracy (using fully-sampled data as the ground truth), 2) FA fitting residuals, and 3) spatial uniformity indices.

RESULTS

Our experimental data show that the proposed spatial uniformity index is correlated with errors in FA obtained from down-sampled diffusion MRI data. The FA fitting residuals that are typically used to assess diffusion MRI quality are not correlated with either FA errors or spatial uniformity index.

CONCLUSIONS

These results suggest that the spatial uniformity index could be more valuable in assessing quality of down-sampled diffusion MRI data, as compared with FA fitting residual measures. We expect that our implemented software procedure should prove valuable for 1) guiding data harmonization for multi-site diffusion MRI studies, and 2) assessing the impact of rejecting motion corrupted data points on the accuracy of diffusion measures.

A systematic evaluation of intraoperative white matter tract shift in pediatric epilepsy surgery using high-field MRI and probabilistic high angular resolution diffusion imaging tractography

OBJECTIVE Characterization of intraoperative white matter tract (WMT) shift has the potential to compensate for neuronavigation inaccuracies using preoperative brain imaging. This study aimed to quantify and characterize intraoperative WMT shift from the global hemispheric to the regional tract-based scale and to investigate the impact of intraoperative factors (IOFs). METHODS High angular resolution diffusion imaging (HARDI) diffusion-weighted data were acquired over 5 consecutive perioperative time points (MR₁ to MR₅) in 16 epilepsy patients (8 male; mean age 9.8 years, range 3.8-15.8 years) using diagnostic and intraoperative 3-T MRI scanners. MR₁ was the preoperative planning scan. MR₂ was the first intraoperative scan acquired with the patient's head fixed in the surgical position. MR₃ was the second intraoperative scan acquired following craniotomy and durotomy, prior to lesion resection. MR₄ was the last intraoperative scan acquired following lesion resection, prior to wound closure. MR₅ was a postoperative scan acquired at the 3-month follow-up visit. Ten association WMT/WMT segments and 1 projection WMT were generated via a probabilistic tractography algorithm from each MRI scan. Image registration was performed through pairwise MRI alignments using the skull segmentation. The MR₁ and MR₂ pairing represented the first surgical stage. The MR₂ and MR₃ pairing represented the second surgical stage. The MR₃ and MR₄ (or MR₅) pairing represented the third surgical stage. The WMT shift was quantified by measuring displacements between a pair of WMT centerlines. Linear mixed-effects regression analyses were carried out for 6 IOFs: head rotation, craniotomy size, durotomy size, resected lesion volume, presence of brain edema, and CSF loss via ventricular penetration. RESULTS The average WMT shift in the operative hemisphere was 2.37 mm (range 1.92-3.03 mm) during the first surgical stage, 2.19 mm (range 1.90-3.65 mm) during the second surgical stage, and 2.92 mm (range 2.19-4.32 mm) during the third surgical stage. Greater WMT shift occurred in the operative than the nonoperative hemisphere, in the WMTs adjacent to the surgical lesion rather than those remote to it, and in the superficial rather than the deep segment of the pyramidal tract. Durotomy size and resection size were significant, independent IOFs affecting WMT shift. The presence of brain edema was a marginally significant IOF. Craniotomy size, degree of head rotation, and ventricular penetration were not significant IOFs affecting WMT shift. CONCLUSIONS WMT shift occurs noticeably in tracts adjacent to the surgical lesions, and those motor tracts superficially placed in the operative hemisphere. Intraoperative probabilistic HARDI tractography following craniotomy, durotomy, and lesion resection may compensate for intraoperative WMT shift and improve neuronavigation accuracy.

Q-ball imaging models: comparison between high and low angular resolution diffusion-weighted MRI protocols for investigation of brain white matter integrity

INTRODUCTION

Q-ball imaging (QBI) is one of the typical data models for quantifying white matter (WM) anisotropy in diffusion-weighted MRI (DwMRI) studies. Brain and spinal investigation by high angular resolution DwMRI (high angular resolution imaging (HARDI)) protocols exhibits higher angular resolution in diffusion imaging compared to low angular resolution models, although with longer acquisition times. We aimed to assess the difference between QBI-derived anisotropy values from high and low angular resolution DwMRI protocols and their potential advantages or shortcomings in neuroradiology.

METHODS

Brain DwMRI data sets were acquired in seven healthy volunteers using both HARDI (b = 3000 s/mm(2), 54 gradient directions) and low angular resolution (b = 1000 s/mm(2), 32 gradient directions) acquisition schemes. For both sequences, tract of interest tractography and generalized fractional anisotropy (GFA) measures were extracted by using QBI model and were compared between the two data sets.

RESULTS

QBI tractography and voxel-wise analyses showed that some WM tracts, such as corpus callosum, inferior longitudinal, and uncinate fasciculi, were reconstructed as one-dominant-direction fiber bundles with both acquisition schemes. In these WM tracts, mean percent different difference in GFA between the two data sets was less than 5%. Contrariwise, multidirectional fiber bundles, such as corticospinal tract and superior longitudinal fasciculus, were more accurately depicted by HARDI acquisition scheme.

CONCLUSION

Our results suggest that the design of optimal DwMRI acquisition protocols for clinical investigation of WM anisotropy by QBI models should consider the specific brain target regions to be explored, inducing researchers to a trade-off choice between angular resolution and acquisition time.

K-Optimal Gradient Encoding Scheme for Fourth-Order Tensor-Based Diffusion Profile Imaging

The design of an optimal gradient encoding scheme (GES) is a fundamental problem in diffusion MRI. It is well studied for the case of second-order tensor imaging (Gaussian diffusion). However, it has not been investigated for the wide range of non-Gaussian diffusion models. The optimal GES is the one that minimizes the variance of the estimated parameters. Such a GES can be realized by minimizing the condition number of the design matrix (K-optimal design). In this paper, we propose a new approach to solve the K-optimal GES design problem for fourth-order tensor-based diffusion profile imaging. The problem is a nonconvex experiment design problem. Using convex relaxation, we reformulate it as a tractable semidefinite programming problem. Solving this problem leads to several theoretical properties of K-optimal design: (i) the odd moments of the K-optimal design must be zero; (ii) the even moments of the K-optimal design are proportional to the total number of measurements; (iii) the K-optimal design is not unique, in general; and (iv) the proposed method can be used to compute the K-optimal design for an arbitrary number of measurements. Our Monte Carlo simulations support the theoretical results and show that, in comparison with existing designs, the K-optimal design leads to the minimum signal deviation.

Optimal diffusion tensor imaging with repeated measurements

Several data acquisition schemes for diffusion MRI have been proposed and explored to date for the reconstruction of the 2nd order tensor. Our main contributions in this paper are: (i) the definition of a new class of sampling schemes based on repeated measurements in every sampling point; (ii) two novel schemes belonging to this class; and (iii) a new reconstruction framework for the second scheme. We also present an evaluation, based on Monte Carlo computer simulations, of the performances of these schemes relative to known optimal sampling schemes for both 2nd and 4th order tensors. The results demonstrate that tensor estimation by the proposed sampling schemes and estimation framework is more accurate and robust.

A review of diffusion tensor magnetic resonance imaging computational methods and software tools

In this work we provide an up-to-date short review of computational magnetic resonance imaging (MRI) and software tools that are widely used to process and analyze diffusion-weighted MRI data. A review of different methods used to acquire, model and analyze diffusion-weighted imaging data (DWI) is first provided with focus on diffusion tensor imaging (DTI). The major preprocessing, processing and post-processing procedures applied to DTI data are discussed. A list of freely available software packages to analyze diffusion MRI data is also provided.

The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional way to do this does not preserve the tensorial structure of the equation, which we consider a weakness in the method. For a physically correct measurement procedure, the condition number of the acquisition scheme, which is a determinant of the noise behavior, needs to be rotationally invariant. The method which traditionally is used to find such schemes, however, is cumbersome and mathematically unsatisfactory. This is considered a second weakness, closely connected to the first. In this paper we present an alternative inversion of the diffusion tensor equation, which does preserve the tensor form, for arbitrary order, and which is named the direct tensor solution (DTS). The DTS is derived under the assumption that the apparent diffusion coefficient in any direction is known, i.e. in the infinite acquisition scheme. Whenever the DTS is valid for a given finite acquisition scheme and for a given order, the condition number is rotationally invariant. The DTS provides a compact, algebraic procedure to check this rotational invariance. We also present a method to construct acquisition schemes, for which the DTS is valid for the measurement of higher-order diffusion tensors. Furthermore, the DTS leads to other mathematical insights, such as tensorial relationships between diffusion tensors of different orders, and a more general understanding of the Platonic Variance Method, which we published before.

In vivo generalized diffusion tensor imaging (GDTI) using higher-order tensors (HOT)

Generalized diffusion tensor imaging (GDTI) using higher-order tensor (HOT) statistics generalizes the technique of diffusion tensor imaging by including the effect of nongaussian diffusion on the signal of MRI. In GDTI-HOT, the effect of nongaussian diffusion is characterized by higher-order tensor statistics (i.e., the cumulant tensors or the moment tensors), such as the covariance matrix (the second-order cumulant tensor), the skewness tensor (the third-order cumulant tensor), and the kurtosis tensor (the fourth-order cumulant tensor). Previously, Monte Carlo simulations have been applied to verify the validity of this technique in reconstructing complicated fiber structures. However, no in vivo implementation of GDTI-HOT has been reported. The primary goal of this study is to establish GDTI-HOT as a feasible in vivo technique for imaging nongaussian diffusion. We show that probability distribution function of the molecular diffusion process can be measured in vivo with GDTI-HOT and be visualized with three-dimensional glyphs. By comparing GDTI-HOT to fiber structures that are revealed by the highest resolution diffusion-weighted imaging (DWI) possible in vivo, we show that the GDTI-HOT can accurately predict multiple fiber orientations within one white matter voxel. Furthermore, through bootstrap analysis we demonstrate that in vivo measurement of HOT elements is reproducible, with a small statistical variation that is similar to that of diffusion tensor imaging.