A deep learning approach to estimation of subject-level bias and variance in high angular resolution diffusion imaging

The ability to evaluate empirical diffusion MRI acquisitions for quality and to correct the resulting imaging metrics allows for improved inference and increased replicability. Previous work has shown promise for estimation of bias and variance of generalized fractional anisotropy (GFA) but comes at the price of computational complexity. This paper aims to provide methods for estimating GFA, bias of GFA and standard deviation of GFA quickly and accurately. In order to provide a method for bias and variance estimation that can return results faster than the previously studied statistical techniques, three deep, fully-connected neural networks are developed for GFA, bias of GFA, and standard deviation of GFA. The results of these networks are compared to the observed values of the metrics as well as those fit from the statistical techniques (i.e. Simulation Extrapolation (SIMEX) for bias estimation and wild bootstrap for variance estimation). Our GFA network provides predictions that are closer to the true GFA values than a Q-ball fit of the observed data (root-mean-square error (RMSE) 0.0077 vs 0.0082, p < .001). The bias network also shows statistically significant improvement in comparison to the SIMEX-estimated error of GFA (RMSE 0.0071 vs. 0.01, p < .001).

Evaluation of inter-site bias and variance in diffusion-weighted MRI

An understanding of the bias and variance of diffusion weighted magnetic resonance imaging (DW-MRI) acquisitions across scanners, study sites, or over time is essential for the incorporation of multiple data sources into a single clinical study. Studies that combine samples from various sites may be introducing confounding due to site-specific artifacts and patterns. Differences in bias and variance across sites may render the scans incomparable, and, without correction, any inferences obtained from these data are misleading. We present an analysis of the bias and variance of scans of the same subjects across different sites and evaluate their impact on statistical analyses. In previous work, we presented a simulation extrapolation (SIMEX) technique for bias estimation as well as a wild bootstrap technique for variance estimation in metrics obtained from a Q-ball imaging (QBI) reconstruction of empirical high angular resolution diffusion imaging (HARDI) data. We now apply those techniques to data acquired from 5 healthy volunteers on 3 independent scanners under closely matched acquisition protocols. The bias and variance of GFA measurements were estimated on a voxel-wise basis for each scan and compared across study sites to identify site-specific differences. Further, we provide model recommendations that can be used to determine the extent of the impact of bias and variance as well as aspects of the analysis to account for these differences. We include a decision tree to help researchers determine if model adjustments are necessary based on the bias and variance results.

SHARD: Spherical Harmonic-based Robust Outlier Detection for HARDI Methods

High Angular Resolution Diffusion Imaging (HARDI) models are used to capture complex intra-voxel microarchitectures. The magnetic resonance imaging sequences that are sensitized to diffusion are often highly accelerated and prone to motion, physiologic, and imaging artifacts. In diffusion tensor imaging, robust statistical approaches have been shown to greatly reduce these adverse factors without human intervention. Similar approaches would be possible with HARDI methods, but robust versions of each distinct HARDI approach would be necessary. To avoid the computational and pragmatic burdens of creating individual robust HARDI analysis variants, we propose a robust outlier imputation model to mitigate outliers prior to traditional HARDI analysis. This model uses a weighted spherical harmonic fit of diffusion weighted magnetic resonance imaging scans to estimate the values which had been corrupted during acquisition to restore them. Briefly, spherical harmonics of 6th order were used to generate basis function which were weighted by diffusion signal for detection of outliers. For validation, a single healthy volunteer was scanned for a single session comprising of two scans one without head movement and the other with deliberate head movement at a b-value of 3000 s/mm2 with 64 diffusion weighted directions with a single b0 (5 averages) per scan. The deliberate motion from the volunteer created natural artifacts in the acquisition of one of the scans. The imputation model shows reduction in root mean squared error of the raw signal intensities and improvement for the HARDI method Q-ball in terms of the Angular Correlation Coefficient. The results reveal that there is quantitative and qualitative improvement. The proposed model can be used as general pre-processing model before implementing any HARDI model in general to restore the artifacts which are created because of the outlier diffusion signal in certain gradient volumes.

Empirical single sample quantification of bias and variance in Q-ball imaging

PURPOSE

The bias and variance of high angular resolution diffusion imaging methods have not been thoroughly explored in the literature and may benefit from the simulation extrapolation (SIMEX) and bootstrap techniques to estimate bias and variance of high angular resolution diffusion imaging metrics.

METHODS

The SIMEX approach is well established in the statistics literature and uses simulation of increasingly noisy data to extrapolate back to a hypothetical case with no noise. The bias of calculated metrics can then be computed by subtracting the SIMEX estimate from the original pointwise measurement. The SIMEX technique has been studied in the context of diffusion imaging to accurately capture the bias in fractional anisotropy measurements in DTI. Herein, we extend the application of SIMEX and bootstrap approaches to characterize bias and variance in metrics obtained from a Q-ball imaging reconstruction of high angular resolution diffusion imaging data.

RESULTS

The results demonstrate that SIMEX and bootstrap approaches provide consistent estimates of the bias and variance of generalized fractional anisotropy, respectively. The RMSE for the generalized fractional anisotropy estimates shows a 7% decrease in white matter and an 8% decrease in gray matter when compared with the observed generalized fractional anisotropy estimates. On average, the bootstrap technique results in SD estimates that are approximately 97% of the true variation in white matter, and 86% in gray matter.

CONCLUSION

Both SIMEX and bootstrap methods are flexible, estimate population characteristics based on single scans, and may be extended for bias and variance estimation on a variety of high angular resolution diffusion imaging metrics.

Empirical estimation of intravoxel structure with persistent angular structure and Q-ball models of diffusion weighted MRI

The diffusion tensor model is nonspecific in regions where micrometer structural patterns are inconsistent at the millimeter scale (i.e., brain regions with pathways that cross, bend, branch, fan, etc.). Numerous models have been proposed to represent crossing fibers and complex intravoxel structure from in vivo diffusion weighted magnetic resonance imaging (e.g., high angular resolution diffusion imaging-HARDI). Here, we present an empirical comparison of two HARDI approaches-persistent angular structure MRI (PAS-MRI) and Q-ball-using a newly acquired reproducibility dataset. Briefly, a single subject was scanned 11 times with 96 diffusion weighted directions and 10 reference volumes for each of two [Formula: see text] values (1000 and [Formula: see text] for a total of 2144 volumes). Empirical reproducibility of intravoxel fiber fractions (number/strength of peaks), angular orientation, and fractional anisotropy was compared with metrics from a traditional tensor analysis approach, focusing on [Formula: see text] values of 1000 and [Formula: see text]. PAS-MRI is shown to be more reproducible than Q-ball and offers advantages at low [Formula: see text] values. However, there are substantial and biologically meaningful differences between the intravoxel structures estimated both in terms of analysis method as well as by [Formula: see text] value. The two methods suggest a fundamentally different microarchitecture of the human brain; therefore, it is premature to perform meta-analysis or combine results across HARDI studies using a different analysis model or acquisition sequences.

Comparison of Multi-Fiber Reproducibility of PAS-MRI and Q-ball With Empirical Multiple b-Value HARDI

Crossing fibers are prevalent in human brains and a subject of intense interest for neuroscience. Diffusion tensor imaging (DTI) can resolve tissue orientation but is blind to crossing fibers. Many advanced diffusion-weighted magnetic resolution imaging (MRI) approaches have been presented to extract crossing-fibers from high angular resolution diffusion imaging (HARDI), but the relative sensitivity and specificity of approaches remains unclear. Here, we examine two leading approaches (PAS and q-ball) in the context of a large-scale, single subject reproducibility study. A single healthy individual was scanned 11 times with 96 diffusion weighted directions and 10 reference volumes for each of five b-values (1000, 1500, 2000, 2500, 3000 s/mm2) for a total of 5830 volumes (over the course of three sessions). We examined the reproducibility of the number of fibers per voxel, volume fraction, and crossing-fiber angles. For each method, we determined the minimum resolvable angle for each acquisition. Reproducibility of fiber counts per voxel was generally high (~80% consensus for PAS and ~70% for q-ball), but there was substantial bias between individual repetitions and model estimated with all data (~10% lower consensus for PAS and ~15% lower for q-ball). Both PAS and q-ball predominantly discovered fibers crossing at near 90 degrees, but reproducibility was higher for PAS across most measures. Within voxels with low anisotropy, q-ball finds more intra-voxel structure; meanwhile, PAS resolves multiple fibers at greater than 75 degrees for more voxels. These results can inform researchers when deciding between HARDI approaches or interpreting findings across studies.

Effects of b-Value and Number of Gradient Directions on Diffusion MRI Measures Obtained with Q-ball Imaging

High-angular-resolution diffusion-weighted imaging (HARDI) MRI acquisitions have become common for use with higher order models of diffusion. Despite successes in resolving complex fiber configurations and probing microstructural properties of brain tissue, there is no common consensus on the optimal b-value and number of diffusion directions to use for these HARDI methods. While this question has been addressed by analysis of the diffusion-weighted signal directly, it is unclear how this translates to the information and metrics derived from the HARDI models themselves. Using a high angular resolution data set acquired at a range of b-values, and repeated 11 times on a single subject, we study how the b-value and number of diffusion directions impacts the reproducibility and precision of metrics derived from Q-ball imaging, a popular HARDI technique. We find that Q-ball metrics associated with tissue microstructure and white matter fiber orientation are sensitive to both the number of diffusion directions and the spherical harmonic representation of the Q-ball, and often are biased when under sampled. These results can advise researchers on appropriate acquisition and processing schemes, particularly when it comes to optimizing the number of diffusion directions needed for metrics derived from Q-ball imaging.