A comprehensive approach for correcting voxel-wise b-value errors in diffusion MRI

Nonlinear Gradient Field Mapping Using a Spherical Grid Phantom for 3 and 7 Tesla MR Imaging Systems Equipped with High-performance Gradient Coils

Recent high-performance gradient coils are fabricated mainly at the expense of spatial linearity. In this study, we measured the spatial nonlinearity of the magnetic field generated by the gradient coils of two MRI systems with high-performance gradient coils. The nonlinearity of the gradient fields was measured using 3D gradient echo sequences and a spherical phantom with a built-in lattice structure. The spatial variation of the gradient field was approximated to the 3rd order polynomials. The coefficients of the polynomials were calculated using the steepest descent method. The geometric distortion of the acquired 3D MR images was corrected using the polynomials and compared with the 3D images corrected using the harmonic functions provided by the MRI venders. As a result, it was found that the nonlinearity correction formulae provided by the vendors were insufficient and needed to be verified or corrected using a geometric phantom such as used in this study.

Long-Term Stability of Gradient Characteristics Warrants Model-Based Correction of Diffusion Weighting Bias

The study aims to test the long-term stability of gradient characteristics for model-based correction of diffusion weighting (DW) bias in an apparent diffusion coefficient (ADC) for multisite imaging trials. Single spin echo (SSE) DWI of a long-tube ice-water phantom was acquired quarterly on six MR scanners over two years for individual diffusion gradient channels, along with B0 mapping, as a function of right-left (RL) and superior-inferior (SI) offsets from the isocenter. Additional double spin-echo (DSE) DWI was performed on two systems. The offset dependences of derived ADC were fit to 4th-order polynomials. Chronic shim gradients were measured from spatial derivatives of B0 maps along the tube direction. Gradient nonlinearity (GNL) was modeled using vendor-provided gradient field descriptions. Deviations were quantified by root-mean-square differences (RMSD), normalized to reference ice-water ADC, between the model and reference (RMSDREF), measurement and model (RMSDEXP), and temporal measurement variations (RMSDTMP). Average RMSDREF was 4.9 ± 3.2 (%RL) and –14.8 ± 3.8 (%SI), and threefold larger than RMSDEXP. RMSDTMP was close to measurement errors (~3%). GNL-induced bias across gradient systems varied up to 20%, while deviation from the model accounted at most for 6.5%, and temporal variation for less than 3% of ADC reproducibility error. Higher SSE RMSDEXP = 7.5–11% was reduced to 2.5–4.8% by DSE, consistent with the eddy current origin. Measured chronic shim gradients below 0.1 mT/m had a minor contribution to ADC bias. The demonstrated long-term stability of spatial ADC profiles and consistency with system GNL models justifies retrospective and prospective DW bias correction based on system gradient design models. Residual errors due to eddy currents and shim gradients should be corrected independent of GNL.

Evaluating diffusion dispersion across an extended range of b-values and frequencies: Exploiting gap-filled OGSE shapes, strong gradients, and spiral readouts

Purpose

To address the long echo times and relatively weak diffusion sensitization that typically limit oscillating gradient spin‐echo (OGSE) experiments, an OGSE implementation combining spiral readouts, gap‐filled oscillating gradient shapes providing stronger diffusion encoding, and a high‐performance gradient system is developed here and utilized to investigate the tradeoff between b‐value and maximum OGSE frequency in measurements of diffusion dispersion (i.e., the frequency dependence of diffusivity) in the in vivo human brain. In addition, to assess the effects of the marginal flow sensitivity introduced by these OGSE waveforms, flow‐compensated variants are devised for experimental comparison.

Methods

Using DTI sequences, OGSE acquisitions were performed on three volunteers at b‐values of 300, 500, and 1000 s/mm² and frequencies up to 125, 100, and 75 Hz, respectively; scans were performed for gap‐filled oscillating gradient shapes with and without flow sensitivity. Pulsed gradient spin‐echo DTI acquisitions were also performed at each b‐value. Upon reconstruction, mean diffusivity (MD) maps and maps of the diffusion dispersion rate were computed.

Results

The power law diffusion dispersion model was found to fit best to MD measurements acquired at b = 1000 s/mm² despite the associated reduction of the spectral range; this observation was consistent with Monte Carlo simulations. Furthermore, diffusion dispersion rates without flow sensitivity were slightly higher than flow‐sensitive measurements.

Conclusion

The presented OGSE implementation provided an improved depiction of diffusion dispersion and demonstrated the advantages of measuring dispersion at higher b‐values rather than higher frequencies within the regimes employed in this study.

What's New and What's Next in Diffusion MRI Preprocessing

Diffusion MRI (dMRI) provides invaluable information for the study of tissue microstructure and brain connectivity, but suffers from a range of imaging artifacts that greatly challenge the analysis of results and their interpretability if not appropriately accounted for. This review will cover dMRI artifacts and preprocessing steps, some of which have not typically been considered in existing pipelines or reviews, or have only gained attention in recent years: brain/skull extraction, B-matrix incompatibilities w.r.t the imaging data, signal drift, Gibbs ringing, noise distribution bias, denoising, between- and within-volumes motion, eddy currents, outliers, susceptibility distortions, EPI Nyquist ghosts, gradient deviations, B₁ bias fields, and spatial normalization. The focus will be on “what’s new” since the notable advances prior to and brought by the Human Connectome Project (HCP), as presented in the predecessing issue on “Mapping the Connectome” in 2013. In addition to the development of novel strategies for dMRI preprocessing, exciting progress has been made in the availability of open source tools and reproducible pipelines, databases and simulation tools for the evaluation of preprocessing steps, and automated quality control frameworks, amongst others. Finally, this review will consider practical considerations and our view on “what’s next” in dMRI preprocessing.

Mapping gradient nonlinearity and miscalibration using diffusion-weighted MR images of a uniform isotropic phantom

PURPOSE

To use diffusion measurements to map the spatial dependence of the magnetic field produced by the gradient coils of an MRI scanner with sufficient accuracy to correct errors in quantitative diffusion MRI (DMRI) caused by gradient nonlinearity and gradient amplifier miscalibration.

THEORY AND METHODS

The field produced by the gradient coils is expanded in regular solid harmonics. The expansion coefficients are found by fitting a model to a minimum set of diffusion-weighted images of an isotropic diffusion phantom. The accuracy of the resulting gradient coil field maps is evaluated by using them to compute corrected b-matrices that are then used to process a multi-shell diffusion tensor imaging (DTI) dataset with 32 diffusion directions per shell.

RESULTS

The method substantially reduces both the spatial inhomogeneity of the computed mean diffusivities (MD) and the computed values of the fractional anisotropy (FA), as well as virtually eliminating any artifactual directional bias in the tensor field secondary to gradient nonlinearity. When a small scaling miscalibration was purposely introduced in the x, y, and z, the method accurately detected the amount of miscalibration on each gradient axis.

CONCLUSION

The method presented detects and corrects the effects of gradient nonlinearity and gradient gain miscalibration using a simple isotropic diffusion phantom. The correction would improve the accuracy of DMRI measurements in the brain and other organs for both DTI and higher order diffusion analysis. In particular, it would allow calibration of MRI systems, improving data harmony in multicenter studies.

Empirical validation of gradient field models for an accurate ADC measured on clinical 3T MR systems in body oncologic applications

PURPOSE

To empirically corroborate vendor-provided gradient nonlinearity (GNL) characteristics and demonstrate efficient GNL bias correction for human brain apparent diffusion coefficient (ADC) across 3T MR systems and spatial locations.

METHODS

Spatial distortion vector fields (DVF) were mapped in 3D using a surface fiducial array phantom for individual gradient channels on three 3T MR platforms from different vendors. Measured DVF were converted into empirical 3D GNL tensors and compared with their theoretical counterparts derived from vendor-provided spherical harmonic (SPH) coefficients. To illustrate spatial impact of GNL on ADC, diffusion weighted imaging using three orthogonal gradient directions was performed on a volunteer brain positioned at isocenter (as a reference) and offset superiorly by 10-17 cm (>10% predicted GNL bias). The SPH tensor-based GNL correction was applied to individual DWI gradient directions, and derived ADC was compared with low-bias reference for human brain white matter (WM) ROIs.

RESULTS

Empiric and predicted GNL errors were comparable for all three studied 3T MR systems, with <1.0% differences in the median and width of spatial histograms for individual GNL tensor elements. Median (±width) of ADC (10-3mm2/s) histograms measured at isocenter in WM reference ROIs from three MR systems were: 0.73 ± 0.11, 0.71 ± 0.14, 0.74 ± 0.17, and at off-isocenters (before versus after GNL correction) were respectively 0.63 ± 0.14 versus 0.72 ± 0.11, 0.53 ± 0.16 versus 0.74 ± 0.18, and 0.65 ± 0.16 versus 0.76 ± 0.18.

CONCLUSION

The phantom-based spatial distortion measurements validated vendor-provided gradient fields, and accurate WM ADC was recovered regardless of spatial locations and clinical MR platforms using system-specific tensor-based GNL correction for routine DWI.

Effects of Sex and Age on Fat Fraction, Diffusion-Weighted Image Signal Intensity and Apparent Diffusion Coefficient in the Bone Marrow of Asymptomatic Individuals: A Cross-Sectional Whole-Body MRI Study

We aimed to describe the relationships between the relative fat fraction (%FF), muscle-normalized diffusion-weighted (DW) image signal intensity and water apparent diffusion coefficient (ADC), sex and age for normal bone marrow, in the normal population. Our retrospective cohort consisted of 100 asymptomatic individuals, equally divided by sex and 10-year age groups, who underwent whole-body MRI at 1.5 T for early cancer detection. Semi-automated segmentation of global bone marrow volume was performed using the DW images and the resulting segmentation masks were projected onto the ADC and %FF maps for extraction of parameter values. Differences in the parameter values between sexes at age ranges were assessed using the Mann–Whitney and Kruskal–Wallis tests. The Spearman correlation coefficient r was used to assess the relationship of each imaging parameter with age, and of %FF with ADC and normalized DW signal intensity values. The average %FF of normal bone marrow was 65.6 ± 7.2%, while nSI_b50, nSI_b900 and ADC were 1.7 ± 0.5, 3.2 ± 0.9 and 422 ± 67 μm²/s, respectively. The bone marrow %FF values increased with age in both sexes (r = 0.63 and r = 0.64, respectively, p < 0.001). Values of nSI_b50 and nSI_b900 were higher in younger women compared to men of the same age groups (p < 0.017), but this difference decreased with age. In our cohort of asymptomatic individuals, the values of bone marrow relative %FF, normalized DW image signal intensity and ADC indicate higher cellularity in premenopausal women, with increasing bone marrow fat with aging in both sexes.

Empirical field mapping for gradient nonlinearity correction of multi-site diffusion weighted MRI

BACKGROUND

Achieving inter-site / inter-scanner reproducibility of diffusion weighted magnetic resonance imaging (DW-MRI) metrics has been challenging given differences in acquisition protocols, analysis models, and hardware factors.

PURPOSE

Magnetic field gradients impart scanner-dependent spatial variations in the applied diffusion weighting that can be corrected if the gradient nonlinearities are known. However, retrieving manufacturer nonlinearity specifications is not well supported and may introduce errors in interpretation of units or coordinate systems. We propose an empirical approach to mapping the gradient nonlinearities with sequences that are supported across the major scanner vendors.

STUDY TYPE

Prospective observational study.

SUBJECTS

A spherical isotropic diffusion phantom, and a single human control volunteer.

FIELD STRENGTH/SEQUENCE

3 T (two scanners). Stejskal-Tanner spin echo sequence with b-values of 1000, 2000 s/mm² with 12, 32, and 384 diffusion gradient directions per shell.

ASSESSMENT

We compare the proposed correction with the prior approach using manufacturer specifications against typical diffusion pre-processing pipelines (i.e., ignoring spatial gradient nonlinearities). In phantom data, we evaluate metrics against the ground truth. In human and phantom data, we evaluate reproducibility across scans, sessions, and hardware.

STATISTICAL TESTS

Wilcoxon rank-sum test between uncorrected and corrected data.

RESULTS

In phantom data, our correction method reduces variation in mean diffusivity across sessions over uncorrected data (p < 0.05). In human data, we show that this method can also reduce variation in mean diffusivity across scanners (p < 0.05).

CONCLUSION

Our method is relatively simple, fast, and can be applied retroactively. We advocate incorporating voxel-specific b-value and b-vector maps should be incorporated in DW-MRI harmonization preprocessing pipelines to improve quantitative accuracy of measured diffusion parameters.

Diffusion as a Natural Contrast in MR Imaging of Peripheral Artery Disease (PAD) Tissue Changes. A Case Study of the Clinical Application of DTI for a Patient with Chronic Calf Muscles Ischemia

This paper reports a first application of diffusion tensor imaging with corrections by using the B-matrix spatial distribution method (BSD-DTI) for peripheral artery disease (PAD) detected in the changes of diffusion tensor parameters (DTPs). A 76-year-old male was diagnosed as having PAD, since he demonstrated in angiographic images of lower legs severe arterial stenosis and the presence of lateral and peripheral circulation and assigned to the double-blind RCT using mesenchymal stem cells (MSCs) or placebo for the regenerative treatment of implications of ischemic diseases. In order to indicate changes in diffusivity in calf muscles in comparison to a healthy control, a DTI methodology was developed. The main advantage of the applied protocol was decreased scanning time, which was achieved by reducing b-value and number of scans (to 1), while maintaining minimal number of diffusion gradient directions and high resolution. This was possible due to calibration via the BSD method, which reduced systematic errors and allowed quantitative analysis. In the course of PAD, diffusivities were elevated across the calf muscles in posterior compartment and lost their anisotropy. Different character was noticed for anterior compartment, in which diffusivities along and across muscles were decreased without a significant loss of anisotropy. After the intervention involving a series of injections, the improvement of DTPs and tractography was visible, but can be assigned neither to MSCs nor placebo before unblinding.

A comparative study of gradient nonlinearity correction strategies for processing diffusion data obtained with ultra-strong gradient MRI scanners

Purpose

The analysis of diffusion data obtained under large gradient nonlinearities necessitates corrections during data reconstruction and analysis. While two such preprocessing pipelines have been proposed, no comparative studies assessing their performance exist. Furthermore, both pipelines neglect the impact of subject motion during acquisition, which, in the presence of gradient nonlinearities, induces spatio‐temporal B‐matrix variations. Here, spatio‐temporal B‐matrix tracking (STB) is proposed and its performance compared to established pipelines.

Methods

Diffusion tensor MRI (DT‐MRI) was performed using a 300 mT/m gradient system. Data were acquired with volunteers positioned in regions with pronounced gradient nonlinearities, and used to compare the performance of six different processing pipelines, including STB.

Results

Up to 30% errors were observed in DT‐MRI parameter estimates when neglecting gradient nonlinearities. Moreover, the order in which B0 inhomogeneity, eddy current and gradient nonlinearity corrections were performed was found to impact the consistency of parameter estimates significantly. Although, no pipeline emerged as a clear winner, the STB approach seemed to yield the most consistent parameter estimates under large gradient nonlinearities.

Conclusions

Under large gradient nonlinearities, the choice of preprocessing pipeline significantly impacts the estimated diffusion parameters. Motion‐induced spatio‐temporal B‐matrix variations can lead to systematic bias in the parameter estimates, that can be ameliorated using the proposed STB framework.

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A comprehensive approach for correcting voxel-wise b-value errors in diffusion MRI

PURPOSE

In diffusion MRI, the actual b-value played out on the scanner may deviate from the nominal value due to magnetic field imperfections. A simple image-based correction method for this problem is presented.

METHODS

The apparent diffusion constant (ADC) of a water phantom was measured voxel-wise along 64 diffusion directions at b = 1000 s/mm² . The true diffusion constant of water was estimated, considering the phantom temperature. A voxel-wise correction factor, providing an effective b-value including any magnetic field deviations, was determined for each diffusion direction by relating the measured ADC to the true diffusion constant. To test the method, the measured b-value map was used to calculate the corrected voxel-wise ADC for additionally acquired diffusion data sets on the same water phantom and data sets acquired on a small water phantom at three different positions. Diffusion tensor was estimated by applying the measured b-value map to phantom and in vivo data sets.

RESULTS

The b-value-corrected ADC maps of the phantom showed the expected spatial uniformity as well as a marked improvement in consistency across diffusion directions. The b-value correction for the brain data resulted in a 5.8% and 5.5% decrease in mean diffusivity and angular differences of the primary diffusion direction of 2.71° and 0.73° inside gray and white matter, respectively.

CONCLUSION

The actual b-value deviates significantly from its nominal setting, leading to a spatially variable error in the common diffusion outcome measures. The suggested method measures and corrects these artifacts.