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

Structural Development of Speech Networks in Young Children at Risk for Speech Disorder

Characterizing the structural development of the neural speech network in early childhood is important for understanding speech acquisition. To investigate speech in the developing brain, 94 children aged 4-7-years-old at risk for early speech disorder were scanned using diffusion weighted imaging (DWI) magnetic resonance imaging (MRI). Additionally, each child completed the Syllable Repetition Task (SRT), a validated measure of phoneme articulation. The DWI data were modeled using multi-compartment restriction spectrum imaging (RSI) to measure restricted and hindered diffusion properties in both grey and white matter. Consequently, we analyzed the diffusion data using both whole brain analysis, and automated fiber quantification (AFQ) analysis to establish tract profiles for each of six fiber pathways thought to be important for supporting speech development. In the whole brain analysis, we found that SRT performance was associated with restricted diffusion in bilateral inferior frontal gyrus ( pars opercularis ), right pre-supplementary/ supplementary motor area (pre-SMA/SMA), and bilateral cerebellar grey matter ( p < .005). Age moderated these associations in left pars opercularis and frontal aslant tract (FAT). However, in both cases only the cerebellar findings survived a cluster correction. We also found associations between SRT performance and restricted diffusion in cortical association fiber pathways, especially left FAT, and in the cerebellar peduncles. Analyses using automatic fiber quantification (AFQ) highlighted differences in high and low performing children along specific tract profiles, most notably in left but not right FAT. These findings suggest that individual differences in speech performance are reflected in structural gray and white matter differences as measured by restricted and hindered diffusion metrics, and offer important insights into developing brain networks supporting speech in very young children.

Nonlinear Gradient Field Estimation in Diffusion MRI Tensor Simulation

Gradient nonlinearities not only induce spatial distortion in magnetic resonance imaging (MRI), but also introduce discrepancies between intended and acquired diffusion sensitization in diffusion weighted (DW) MRI. Advances in scanner performance have increased the importance of correcting gradient nonlinearities. The most common approaches for gradient nonlinear field estimations rely on phantom calibration field maps which are not always feasible, especially on retrospective data. Here, we derive a quadratic minimization problem for the complete gradient nonlinear field (L(r)). This approach starts with corrupt diffusion signal and estimates the L(r) in two scenarios: (1) the true diffusion tensor known and (2) the true diffusion tensor unknown (i.e., diffusion tensor is estimated). We show the validity of this mathematical approach, both theoretically and through tensor simulation. The estimated field is assessed through diffusion tensor metrics: mean diffusivity (MD), fractional anisotropy (FA), and principal eigenvector (V1). In simulation with 300 diffusion tensors, the study shows the mathematical model is not ill-posed and remains stable. We find when the true diffusion tensor is known (1) the change in determinant of the estimated L(r) field and the true field is near zero and (2) the median difference in estimated L(r) corrected diffusion metrics to true values is near zero. We find the results of L(r) estimation are dependent on the level of L(r) corruption. This work provides an approach to estimate gradient field without the need for additional calibration scans. To the best of our knowledge, the mathematical derivation presented here is novel.

Evaluation of Mean Shift, ComBat, and CycleGAN for Harmonizing Brain Connectivity Matrices Across Sites

Connectivity matrices derived from diffusion MRI (dMRI) provide an interpretable and generalizable way of understanding the human brain connectome. However, dMRI suffers from inter-site and between-scanner variation, which impedes analysis across datasets to improve robustness and reproducibility of results. To evaluate different harmonization approaches on connectivity matrices, we compared graph measures derived from these matrices before and after applying three harmonization techniques: mean shift, ComBat, and CycleGAN. The sample comprises 168 age-matched, sex-matched normal subjects from two studies: the Vanderbilt Memory and Aging Project (VMAP) and the Biomarkers of Cognitive Decline Among Normal Individuals (BIOCARD). First, we plotted the graph measures and used coefficient of variation (CoV) and the Mann-Whitney U test to evaluate different methods' effectiveness in removing site effects on the matrices and the derived graph measures. ComBat effectively eliminated site effects for global efficiency and modularity and outperformed the other two methods. However, all methods exhibited poor performance when harmonizing average betweenness centrality. Second, we tested whether our harmonization methods preserved correlations between age and graph measures. All methods except for CycleGAN in one direction improved correlations between age and global efficiency and between age and modularity from insignificant to significant with p-values less than 0.05.

Evaluation of Mean Shift, ComBat, and CycleGAN for Harmonizing Brain Connectivity Matrices Across Sites

Connectivity matrices derived from diffusion MRI (dMRI) provide an interpretable and generalizable way of understanding the human brain connectome. However, dMRI suffers from inter-site and between-scanner variation, which impedes analysis across datasets to improve robustness and reproducibility of results. To evaluate different harmonization approaches on connectivity matrices, we compared graph measures derived from these matrices before and after applying three harmonization techniques: mean shift, ComBat, and CycleGAN. The sample comprises 168 age-matched, sex-matched normal subjects from two studies: the Vanderbilt Memory and Aging Project (VMAP) and the Biomarkers of Cognitive Decline Among Normal Individuals (BIOCARD). First, we plotted the graph measures and used coefficient of variation (CoV) and the Mann-Whitney U test to evaluate different methods' effectiveness in removing site effects on the matrices and the derived graph measures. ComBat effectively eliminated site effects for global efficiency and modularity and outperformed the other two methods. However, all methods exhibited poor performance when harmonizing average betweenness centrality. Second, we tested whether our harmonization methods preserved correlations between age and graph measures. All methods except for CycleGAN in one direction improved correlations between age and global efficiency and between age and modularity from insignificant to significant with p-values less than 0.05.

Frequency-dependent diffusion kurtosis imaging in the human brain using an oscillating gradient spin echo sequence and a high-performance head-only gradient

Measuring the time/frequency dependence of diffusion MRI is a promising approach to distinguish between the effects of different tissue microenvironments, such as membrane restriction, tissue heterogeneity, and compartmental water exchange. In this study, we measure the frequency dependence of diffusivity (D) and kurtosis (K) with oscillating gradient diffusion encoding waveforms and a diffusion kurtosis imaging (DKI) model in human brains using a high-performance, head-only MAGNUS gradient system, with a combination of b-values, oscillating frequencies (f), and echo time that has not been achieved in human studies before. Frequency dependence of diffusivity and kurtosis are observed in both global and local white matter (WM) and gray matter (GM) regions and characterized with a power-law model ∼Λ*fθ. The frequency dependences of diffusivity and kurtosis (including changes between fmin and fmax, Λ, and θ) vary over different WM and GM regions, indicating potential microstructural differences between regions. A trend of decreasing kurtosis over frequency in the short-time limit is successfully captured for in vivo human brains. The effects of gradient nonlinearity (GNL) on frequency-dependent diffusivity and kurtosis measurements are investigated and corrected. Our results show that the GNL has prominent scaling effects on the measured diffusivity values (3.5∼5.5% difference in the global WM and 6∼8% difference in the global cortex) and subsequently affects the corresponding power-law parameters (Λ, θ) while having a marginal influence on the measured kurtosis values (<0.05% difference) and power-law parameters (Λ, θ). This study expands previous OGSE studies and further demonstrates the translatability of frequency-dependent diffusivity and kurtosis measurements to human brains, which may provide new opportunities to probe human brain microstructure in health and disease.

Efficient approximate signal reconstruction for correction of gradient nonlinearities in diffusion-weighted imaging

In diffusion weighted MRI (DW-MRI), hardware nonlinearities lead to spatial variations in the orientation and magnitude of diffusion weighting. While the correction of these spatial distortions has been well established for analyses of DW-MRI, the existing voxel-wise empirical correction for gradient nonlinearities requires reimplementation of existing models, as the resultant gradients vary by voxel. Herein, we propose a two-step signal approximation after voxel-wise correction of gradient nonlinearity effects in DW-MRI. The proposed technique (1) scales the diffusion signal and (2) resamples the gradient orientations. This results in uniform gradients across the corrected image and provides the key advantage of seamless integration into current diffusion workflows. We investigated the validity of our technique by fitting a multi-compartment neurite orientation dispersion and density imaging (NODDI) model to the empirical correction and proposed approximation in five subjects from the MASiVar pediatric dataset. We evaluated intra-cellular volume fraction (iVF), CSF volume fraction (cVF), and orientation dispersion index (ODI) from NODDI. The Cohen's d of iVF, cVF and ODI between the techniques was <0.2 indicating the proposed technique does not exhibit significant differences from the voxel-wise correction technique. Our two-step signal approximation is an efficient representation of the voxel-wise gradient table correction. Using this approximation, correction of gradient nonlinearities can be easily incorporated into existing diffusion preprocessing pipelines and is implemented in "PreQual: An automated pipeline for integrated preprocessing and quality assurance of diffusion weighted MRI images".

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.

Mapping the impact of nonlinear gradient fields with noise on diffusion MRI

In diffusion MRI, gradient nonlinearities cause spatial variations in the magnitude and direction of diffusion gradients. Studies have shown artifacts from these distortions can results in biased diffusion tensor information and tractography. Here, we investigate the impact of gradient nonlinearity correction in the presence of noise. We introduced empirically derived gradient nonlinear fields at different signal-to-noise ratio (SNR) levels in two experiments: tensor field simulation and simulation of the brain. For each experiment, this work compares two techniques empirically: voxel-wise gradient table correction and approximate correction by scaling the signal directly. The impact was assessed through diffusion metrics including mean diffusivity (MD), fractional anisotropy (FA), axial diffusivity (AD), radial diffusivity (RD), and principal eigen vector (V1). The study shows (1) the correction of gradient nonlinearities will not lead to substantively incorrect estimation of diffusion metrics in a linear system, (2) gradient nonlinearity correction does not interact adversely with noise, (3) nonlinearity correction suppresses the impact of nonlinearities in typical SNR data, (4) for SNR below 30, the performance of both the gradient nonlinearity correction techniques were similar, and (5) larger impacts are seen in regions where the gradient nonlinearities are distinct. Thus, this study suggests that there were greater beneficial effects than adverse effects due to the correction of nonlinearities. Additionally, correction of nonlinearities is recommended when region of interests are in areas with pronounced nonlinearities.

Evaluation of Apparent Diffusion Coefficient Repeatability and Reproducibility for Preclinical MRIs Using Standardized Procedures and a Diffusion-Weighted Imaging Phantom

Relevant to co-clinical trials, the goal of this work was to assess repeatability, reproducibility, and bias of the apparent diffusion coefficient (ADC) for preclinical MRIs using standardized procedures for comparison to performance of clinical MRIs. A temperature-controlled phantom provided an absolute reference standard to measure spatial uniformity of these performance metrics. Seven institutions participated in the study, wherein diffusion-weighted imaging (DWI) data were acquired over multiple days on 10 preclinical scanners, from 3 vendors, at 6 field strengths. Centralized versus site-based analysis was compared to illustrate incremental variance due to processing workflow. At magnet isocenter, short-term (intra-exam) and long-term (multiday) repeatability were excellent at within-system coefficient of variance, wCV [±CI] = 0.73% [0.54%, 1.12%] and 1.26% [0.94%, 1.89%], respectively. The cross-system reproducibility coefficient, RDC [±CI] = 0.188 [0.129, 0.343] µm2/ms, corresponded to 17% [12%, 31%] relative to the reference standard. Absolute bias at isocenter was low (within 4%) for 8 of 10 systems, whereas two high-bias (>10%) scanners were primary contributors to the relatively high RDC. Significant additional variance (>2%) due to site-specific analysis was observed for 2 of 10 systems. Base-level technical bias, repeatability, reproducibility, and spatial uniformity patterns were consistent with human MRIs (scaled for bore size). Well-calibrated preclinical MRI systems are capable of highly repeatable and reproducible ADC measurements.

Diffusion-Weighted Imaging of the Abdomen: Correction for Gradient Nonlinearity Bias in Apparent Diffusion Coefficient

BACKGROUND

Gradient nonlinearity (GNL) introduces spatial nonuniformity bias in apparent diffusion coefficient (ADC) measurements, especially at large offsets from the magnet isocenter.

PURPOSE

To investigate the effects of GNL in abdominal ADC measurements and to develop an ADC bias correction procedure.

STUDY TYPE

Retrospective.

PHANTOM/POPULATION

Two homemade ultrapure water phantoms/25 patients with histologically confirmed pancreatic ductal adenocarcinoma (PDAC).

FIELD STRENGTH/SEQUENCE

A 3.0 T/diffusion-weighted imaging (DWI) with single-shot echo-planar imaging sequence.

ASSESSMENT

ADC bias was computed in the three orthogonal directions at different offset locations. The spatial-dependent correctors of ADC bias were generated from the ADCs of phantom 1. The ADCs were estimated before and after corrections for the phantom 1 with both the proposed approach and the theoretical GNL correction method. For the patients, ADCs were measured in abdominal tissues including left and right liver lobes, PDAC, spleen, bilateral kidneys, and bilateral paraspinal muscles.

STATISTICAL TEST

Friedman tests and Wilcoxon tests.

RESULTS

The ADC bias measured by phantom 1 was 9.7% and 12.6% higher in the right-left and anterior-posterior directions and 9.2% lower in the superior-inferior direction at the 150 mm offsets from the magnetic isocenter. The corrected vs. the uncorrected ADCs measurements (median: 2.20 × 10^-3  mm² /sec for both the proposed method and the theoretical GNL method vs. 2.31 × 10^-3  mm² /sec, respectively) and their relative ADC errors (0.014, 0.016, and 0.054, respectively) were lower in the phantom 1. The relative ADC errors substantially decreased after correction in the phantom 2 (median: 0.048 and -0.008, respectively). The ADCs of all the abdominal tissues were lower after correction except for the left liver lobes (P = 0.13).

DATA CONCLUSION

GNL bias in abdominal ADC can be measured by a DWI phantom. The proposed correction procedure was successfully applied for the bias correction in abdominal ADC.

EVIDENCE LEVEL

3.

TECHNICAL EFFICACY

Stage 1.

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.