Evaluation of the accuracy and angular resolution of q-ball imaging

Advances in Fetal Brain Imaging

Over the last 20 years, there have been remarkable developments in fetal brain MR imaging analysis methods. This article delves into the specifics of structural imaging, diffusion imaging, functional MR imaging, and spectroscopy, highlighting the latest advancements in motion correction, fetal brain development atlases, and the challenges and innovations. Furthermore, this article explores the clinical applications of these advanced imaging techniques in comprehending and diagnosing fetal brain development and abnormalities.

Improving delineation of the corticospinal tract in the monkey brain scanned with conventional DTI by using a compressed sensing based algorithm

Background

The corticospinal tract (CST) is a major tract for motor function. It can be impaired by stroke. Its degeneration is associated with stroke outcome. Diffusion tensor imaging (DTI) tractography plays an important role in assessing fiber bundle integrity. However, it is limited in detecting crossing fibers in the brain. The crossing fiber angular resolution of intra-voxel structure (CFARI) algorithm shows potential to resolve complex fibers in the brain. The objective of the present study was to improve delineation of CST pathways in monkey brains scanned by conventional DTI.

Methods

Healthy rhesus monkeys were scanned by diffusion MRI with 128 diffusion encoding directions to evaluate the CFARI algorithm. Four monkeys with ischemic occlusion were also scanned with DTI (b = 1000 s/mm², 30 diffusion directions) at 6, 48, and 96 hours post stroke. CST fibers were reconstructed with DTI and CFARI-based tractography and evaluated. A two-way repeated MANOVA was used to determine significances of changes in DTI indices, tract number, and volumes of the CST between hemispheres or post-stroke time points.

Results

CFARI algorithm revealed substantially more fibers originated from the ventral premotor cortex in healthy and stroke monkey brains than DTI tractography. In addition, CFARI showed better sensitivity in detecting CST abnormality than DTI tractography following stroke.

Conclusion

CFARI significantly improved delineation of the CST in the brain scanned by DTI with 30 gradient directions. It showed better sensitivity in detecting abnormity of the CST following stroke. Preliminary results suggest that CFARI could facilitate prediction of function outcomes after stroke.

Tractography methods and findings in brain tumors and traumatic brain injury

White matter fiber tracking using diffusion magnetic resonance imaging (dMRI) provides a noninvasive approach to map brain connections, but improving anatomical accuracy has been a significant challenge since the birth of tractography methods. Utilizing tractography in brain studies therefore requires understanding of its technical limitations to avoid shortcomings and pitfalls. This review explores tractography limitations and how different white matter pathways pose different challenges to fiber tracking methodologies. We summarize the pros and cons of commonly-used methods, aiming to inform how tractography and its related analysis may lead to questionable results. Extending these experiences, we review the clinical utilization of tractography in patients with brain tumors and traumatic brain injury, starting from tensor-based tractography to more advanced methods. We discuss current limitations and highlight novel approaches in the context of these two conditions to inform future tractography developments.

A critical review of connectome validation studies

Diffusion MRI tractography is the most widely used macroscale method for mapping connectomes in vivo. However, tractography is prone to various errors and biases, and thus tractography-derived connectomes require careful validation. Here, we critically review studies that have developed or utilized phantoms and tracer maps to validate tractography-derived connectomes, either quantitatively or qualitatively. We identify key factors impacting connectome reconstruction accuracy, including streamline seeding, propagation and filtering methods, and consider the strengths and limitations of state-of-the-art connectome phantoms and associated validation studies. These studies demonstrate the inherent limitations of current fiber orientation models and tractography algorithms and their impact on connectome reconstruction accuracy. Reconstructing connectomes with both high sensitivity and high specificity is challenging, given that some tractography methods can generate an abundance of spurious connections, while others can overlook genuine fiber bundles. We argue that streamline filtering can minimize spurious connections and potentially improve the biological plausibility of connectomes derived from tractography. We find that algorithmic choices such as the tractography seeding methodology, angular threshold, and streamline propagation method can substantially impact connectome reconstruction accuracy. Hence, careful application of tractography is necessary to reconstruct accurate connectomes. Improvements in diffusion MRI acquisition techniques will not necessarily overcome current tractography limitations without accompanying modeling and algorithmic advances.

Diffusion MRI tractography for neurosurgery: the basics, current state, technical reliability and challenges

Diffusion magnetic resonance imaging (dMRI) tractography is currently the only imaging technique that allows for non-invasive delineation and visualisation of white matter (WM) tractsin vivo,prompting rapid advances in related fields of brain MRI research in recent years. One of its major clinical applications is for pre-surgical planning and intraoperative image guidance in neurosurgery, where knowledge about the location of WM tracts nearby the surgical target can be helpful to guide surgical resection and optimise post-surgical outcomes. Surgical injuries to these WM tracts can lead to permanent neurological and functional deficits, making the accuracy of tractography reconstructions paramount. The quality of dMRI tractography is influenced by many modifiable factors, ranging from MRI data acquisition through to the post-processing of tractography output, with the potential of error propagation based on decisions made at each and subsequent processing steps. Research over the last 25 years has significantly improved the anatomical accuracy of tractography. An updated review about tractography methodology in the context of neurosurgery is now timely given the thriving research activities in dMRI, to ensure more appropriate applications in the clinical neurosurgical realm. This article aims to review the dMRI physics, and tractography methodologies, highlighting recent advances to provide the key concepts of tractography-informed neurosurgery, with a focus on the general considerations, the current state of practice, technical challenges, potential advances, and future demands to this field.

In-vivo diffusion MRI protocol optimization for the chimpanzee brain and examination of aging effects on the primate optic nerve at 3T

BACKGROUND

Diffusion MRI (dMRI) data acquisition protocols are well-established on modern high-field clinical scanners for human studies. However, these protocols are not suitable for the chimpanzee (or other large-brained mammals) because of its substantial difference in head geometry and brain volume compared with humans. Therefore, an optimal dMRI data acquisition protocol dedicated to chimpanzee neuroimaging is needed.

METHODS

A multi-shot (4 segments) double spin-echo echo-planar imaging (MS-EPI) sequence and a single-shot double spin-echo EPI (SS-EPI) sequence were optimized separately for in vivo dMRI data acquisition of chimpanzees using a clinical 3T scanner. Correction for severe susceptibility-induced image distortion and signal drop-off of the chimpanzee brain was performed and evaluated using FSL software. DTI indices in different brain regions and probabilistic tractography were compared. A separate DTI data set from n=34 chimpanzees (13 to 56 years old) was collected using the optimal protocol. Age-related changes in diffusivity indices of optic nerve fibers were evaluated.

RESULTS

The SS-EPI sequence acquired dMRI data of the chimpanzee brain with approximately doubled the SNR as the MS-EPI sequence given the same scan time. The quality of white matter fiber tracking from the SS-EPI data was much higher than that from MS-EPI data. However, quantitative analysis of DTI indices showed no difference in most ROIs between the SS-EPI and MS-EPI sequences. The progressive evolution of diffusivity indices of optic nerves indicated mild changes in fiber bundles of chimpanzees aged 40 years and above.

CONCLUSION

The single-shot EPI-based acquisition protocol provided better image quality of dMRI for chimpanzee brains and is recommended for in vivo dMRI study or clinical diagnosis of chimpanzees (or other large animals) using a clinical scanner. Also, the tendency of FA decrease or diffusivity increase in the optic nerve of aged chimpanzees was seen but did not show significant age-related changes, suggesting aging may have less impact on optic nerve fiber integrity of chimpanzees, in contrast to previous results for both macaque monkeys and humans.

Optimization of graph construction can significantly increase the power of structural brain network studies

Structural brain networks derived from diffusion magnetic resonance imaging data have been used extensively to describe the human brain, and graph theory has allowed quantification of their network properties. Schemes used to construct the graphs that represent the structural brain networks differ in the metrics they use as edge weights and the algorithms they use to define the network topologies. In this work, twenty graph construction schemes were considered. The schemes use the number of streamlines, the fractional anisotropy, the mean diffusivity or other attributes of the tracts to define the edge weights, and either an absolute threshold or a data-driven algorithm to define the graph topology. The test-retest data of the Human Connectome Project were used to compare the reproducibility of the graphs and their various attributes (edges, topologies, graph theoretical metrics) derived through those schemes, for diffusion images acquired with three different diffusion weightings. The impact of the scheme on the statistical power of the study and on the number of participants required to detect a difference between populations or an effect of an intervention was also calculated. The reproducibility of the graphs and their attributes depended heavily on the graph construction scheme. Graph reproducibility was higher for schemes that used thresholding to define the graph topology, while data-driven schemes performed better at topology reproducibility (mean similarities of 0.962 and 0.984 respectively, for graphs derived from diffusion images with b=2000 s/mm²). Additionally, schemes that used thresholding resulted in better reproducibility for local graph theoretical metrics (intra-class correlation coefficients (ICC) of the order of 0.8), compared to data-driven schemes. Thresholded and data-driven schemes resulted in high (0.86 or higher) ICCs only for schemes that use exclusively the number of streamlines to construct the graphs. Crucially, the number of participants required to detect a difference between populations or an effect of an intervention could change by a factor of two or more depending on the scheme used, affecting the power of studies to reveal the effects of interest.

Mapping connectomes with diffusion MRI: deterministic or probabilistic tractography?

PURPOSE

Human connectomics necessitates high-throughput, whole-brain reconstruction of multiple white matter fiber bundles. Scaling up tractography to meet these high-throughput demands yields new fiber tracking challenges, such as minimizing spurious connections and controlling for gyral biases. The aim of this study is to determine which of the two broadest classes of tractography algorithms-deterministic or probabilistic-is most suited to mapping connectomes.

METHODS

This study develops numerical connectome phantoms that feature realistic network topologies and that are matched to the fiber complexity of in vivo diffusion MRI (dMRI) data. The phantoms are utilized to evaluate the performance of tensor-based and multi-fiber implementations of deterministic and probabilistic tractography.

RESULTS

For connectome phantoms that are representative of the fiber complexity of in vivo dMRI, multi-fiber deterministic tractography yields the most accurate connectome reconstructions (F-measure = 0.35). Probabilistic algorithms are hampered by an abundance of false-positive connections, leading to lower specificity (F = 0.19). While omitting connections with the fewest number of streamlines (thresholding) improves the performance of probabilistic algorithms (F = 0.38), multi-fiber deterministic tractography remains optimal when it benefits from thresholding (F = 0.42).

CONCLUSIONS

Multi-fiber deterministic tractography is well suited to connectome mapping, while connectome thresholding is essential when using probabilistic algorithms.

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.

Empirical consideration of the effects of acquisition parameters and analysis model on clinically feasible q-ball imaging

Q-ball imaging (QBI) is a popular high angular resolution diffusion imaging (HARDI) technique used to study brain architecture in vivo. Simulation and phantom-based studies suggest that QBI results are affected by the b-value, the number of diffusion weighting directions, and the signal-to-noise ratio (SNR). However, optimal acquisition schemes for QBI in clinical settings are largely undetermined given empirical (observed) imaging considerations. In this study, we acquire a HARDI dataset at five b-values with 11 repetitions on a single subject to investigate the effects of acquisition scheme and subsequent analysis models on the accuracy and precision of measures of tissue composition and fiber orientation derived from clinically feasible QBI at 3T. Clinical feasibility entails short scan protocols - less than 5minutes in the current study - resulting in lower SNR, lower b-values, and fewer diffusion directions than are typical in most QBI protocols with research applications, where time constraints are less prevalent. In agreement with previous studies, we find that the b-value and number of diffusion directions impact the magnitude and variation of QBI indices in both white matter and gray matter regions; however, QBI indices are most heavily dependent on the maximum order of the spherical harmonic (SH) series used to represent the diffusion orientation distribution function (ODF). Specifically, to ensure numerical stability and reduce the occurrence of false peaks and inflated anisotropy, we recommend oversampling by at least 8-12 more diffusion directions than the number of estimated coefficients for a given SH order. In addition, in an equal scan time comparison of QBI accuracy, we find that increasing the directional resolution of the HARDI dataset is preferable to repeating observations; however, our results indicate that as few as 32 directions at a low b-value (1000s/mm2) captures most of the angular information in the q-ball ODF. Our findings provide guidance for determining an optimal acquisition scheme for QBI in the low SNR and low scan time regime, and suggest that care must be taken when choosing the basis functions used to represent the QBI ODF.

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.

Merged Group Tractography Evaluation with Selective Automated Group Integrated Tractography

Introduction: Tractography analysis in group-based studies across large populations has been difficult to implement. We propose Selective Automated Group Integrated Tractography (SAGIT), an automated group tractography software platform that incorporates multiple diffusion magnetic resonance imaging (dMRI) practices which will allow great accessibility to group-wise dMRI. We use a merged tractography approach that permits evaluation of tractography datasets at the group level. We also introduce an image normalized overlap score (NOS) that measures the quality of the group tractography results. We deploy SAGIT to evaluate deterministic and probabilistic constrained spherical deconvolution (CST det , CST prob ) tractography, eXtended Streamline Tractography (XST), and diffusion tensor tractography (DTT) in their ability to delineate different neuroanatomy, as well as validating NOS across these different brain regions. Materials and methods: Magnetic resonance sequences were acquired from 42 healthy adults. Anatomical and group registrations were performed using Automated Normalization Tools. Cortical segmentation was performed using FreeSurfer. Four tractography algorithms were used to delineate six sets of neuroanatomy: fornix, facial/vestibular-cochlear cranial nerve complex, vagus nerve, rubral-cerebellar decussation, optic radiation, and auditory radiation. The tracts were generated both with and without region of interest filters. The generated visual reports were then evaluated by five neuroscientists. Results: At a group level, merged tractography demonstrated that different methods have different fiber distribution characteristics. CST prob is prone to false-positives, and thereby suitable in anatomy with strong priors. CST det and XST are more conservative, but have greater difficulty resolving hemispherical decussation and distant crossing projections. DTT consistently shows the worst reproducibility across the anatomies. Linear regression of rater scores against NOS shows significant (p < 0.05) correlation of the two sets of scores in filtered tractography. However, correlations are not significant (p > 0.05) for unfiltered tractography. Conclusion: The tractography results demonstrated reliable and consistent performance of SAGIT across multiple subjects and techniques. Through SAGIT, we quantifiably demonstrated that different algorithms showed different strengths and weaknesses at a group level. While no single algorithm seems to be suitable for all anatomical tasks, it is useful to consider the use of a mix of algorithms for different anatomical segments. SAGIT appears to be a promising group-wise tractography analysis approach for this purpose.

Investigating the capability to resolve complex white matter structures with high b-value diffusion magnetic resonance imaging on the MGH-USC Connectom scanner

One of the major goals of the NIH Blueprint Human Connectome Project was to map and quantify the white matter connections in the brain using diffusion tractography. Given the prevalence of complex white matter structures, the capability of resolving local white matter geometries with multiple crossings in the diffusion magnetic resonance imaging (dMRI) data is critical. Increasing b-value has been suggested for delineation of the finer details of the orientation distribution function (ODF). Although increased gradient strength and duration increase sensitivity to highly restricted intra-axonal water, gradient strength limitations require longer echo times (TE) to accommodate the increased diffusion encoding times needed to achieve a higher b-value, exponentially lowering the signal-to-noise ratio of the acquisition. To mitigate this effect, the MGH-USC Connectom scanner was built with 300 mT/m gradients, which can significantly reduce the TE of high b-value diffusion imaging. Here we report comparisons performed across b-values based on q-ball ODF metrics to investigate whether high b-value diffusion imaging on the Connectom scanner can improve resolving complex white matter structures. The q-ball ODF features became sharper as the b-value increased, with increased power fraction in higher order spherical harmonic series of the ODF and increased peak heights relative to the overall size of the ODF. Crossing structures were detected in an increasingly larger fraction of white matter voxels and the spatial distribution of two-way and three-way crossing structures was largely consistent with known anatomy. Results indicate that dMRI with high diffusion encoding on the Connectom system is a promising tool to better characterize, and ultimately understand, the underlying structural organization and motifs in the human brain.

How does B-value affect HARDI reconstruction using clinical diffusion MRI data?

Background

A number of imaging factors can affect the orientation distribution function (ODF) reconstruction in high angular resolution diffusion imaging (HARDI). The aim of this study was to investigate the effect of the b-value on the HARDI reconstruction and to seek for the appropriate b-value for ODF reconstruction from clinical HARDI data.

Methods

Diffusion MRI data with various b-values were collected on a GE 3T MRI scanner. To reconstruct the diffusion ODF and fiber ODF, decomposition-based spherical polar Fourier imaging and deconvolution-based constrained spherical deconvolution approaches were applied separately. The full width at half maximum (FWHM) of the ODF and the angular difference of the peaks extracted from ODF were measured to investigate the effect of b-value on the ODF reconstruction. Visual inspection of the ODF was used to evaluate the reconstructions.

Results

The FWHM of the ODFs in the corpus callosum, which was chosen as the region of interest (ROI), decreased with increasing b-values. The differences in the FWHM for the diffusion ODF and the fiber ODF between the b-values of 2000 s/mm² and 2500 s/mm² were not significant. The angular differences of the ODF between 2000 s/mm² and 2500 s/mm² were lowest in both single-directional and two-directional situations. The ODFs became sharper and crossing-fiber situations were detected with an increase in b-value. B = 2000 s/mm² and above revealed most of the two-way or three-way crossing-fiber structures.

Conclusions

Considering both the signal-to-noise ratio and the acquisition time, b = 2000 s/mm² is the basic requirement for ODF reconstruction using current HARDI methods on clinical data. This study can provide a useful reference for researchers and clinicians attempting to set appropriate scan protocols for specific HARDI experiments.

Fiber estimation and tractography in diffusion MRI: development of simulated brain images and comparison of multi-fiber analysis methods at clinical b-values

Advances in diffusion-weighted magnetic resonance imaging (DW-MRI) have led to many alternative diffusion sampling strategies and analysis methodologies. A common objective among methods is estimation of white matter fiber orientations within each voxel, as doing so permits in-vivo fiber-tracking and the ability to study brain connectivity and networks. Knowledge of how DW-MRI sampling schemes affect fiber estimation accuracy, tractography and the ability to recover complex white-matter pathways, differences between results due to choice of analysis method, and which method(s) perform optimally for specific data sets, all remain important problems, especially as tractography-based studies become common. In this work, we begin to address these concerns by developing sets of simulated diffusion-weighted brain images which we then use to quantitatively evaluate the performance of six DW-MRI analysis methods in terms of estimated fiber orientation accuracy, false-positive (spurious) and false-negative (missing) fiber rates, and fiber-tracking. The analysis methods studied are: 1) a two-compartment "ball and stick" model (BSM) (Behrens et al., 2003); 2) a non-negativity constrained spherical deconvolution (CSD) approach (Tournier et al., 2007); 3) analytical q-ball imaging (QBI) (Descoteaux et al., 2007); 4) q-ball imaging with Funk-Radon and Cosine Transform (FRACT) (Haldar and Leahy, 2013); 5) q-ball imaging within constant solid angle (CSA) (Aganj et al., 2010); and 6) a generalized Fourier transform approach known as generalized q-sampling imaging (GQI) (Yeh et al., 2010). We investigate these methods using 20, 30, 40, 60, 90 and 120 evenly distributed q-space samples of a single shell, and focus on a signal-to-noise ratio (SNR = 18) and diffusion-weighting (b = 1000 s/mm(2)) common to clinical studies. We found that the BSM and CSD methods consistently yielded the least fiber orientation error and simultaneously greatest detection rate of fibers. Fiber detection rate was found to be the most distinguishing characteristic between the methods, and a significant factor for complete recovery of tractography through complex white-matter pathways. For example, while all methods recovered similar tractography of prominent white matter pathways of limited fiber crossing, CSD (which had the highest fiber detection rate, especially for voxels containing three fibers) recovered the greatest number of fibers and largest fraction of correct tractography for complex three-fiber crossing regions. The synthetic data sets, ground-truth, and tools for quantitative evaluation are publically available on the NITRC website as the project "Simulated DW-MRI Brain Data Sets for Quantitative Evaluation of Estimated Fiber Orientations" at http://www.nitrc.org/projects/sim_dwi_brain.

Determination of the appropriate b value and number of gradient directions for high-angular-resolution diffusion-weighted imaging

High-angular-resolution diffusion-weighted imaging (HARDI) is one of the most common MRI acquisition schemes for use with higher order models of diffusion. However, the optimal b value and number of diffusion-weighted (DW) directions for HARDI are still undetermined, primarily as a result of the large number of available reconstruction methods and corresponding parameters, making it impossible to identify a single criterion by which to assess performance. In this study, we estimate the minimum number of DW directions and optimal b values required for HARDI by focusing on the angular frequency content of the DW signal itself. The spherical harmonic (SH) series provides the spherical analogue of the Fourier series, and can hence be used to examine the angular frequency content of the DW signal. Using high-quality data acquired along 500 directions over a range of b values, we estimate that SH terms above l = 8 are negligible in practice for b values up to 5000 s/mm(2), implying that a minimum of 45 DW directions is sufficient to fully characterise the DW signal. l > 0 SH terms were found to increase as a function of b value, levelling off at b = 3000 s/mm(2), suggesting that this value already provides the highest achievable angular resolution. In practice, it is recommended to acquire more than the minimum of 45 DW directions to avoid issues with imperfections in the uniformity of the DW gradient directions and to meet signal-to-noise requirements of the intended reconstruction method.

Diffusion microscopist simulator: a general Monte Carlo simulation system for diffusion magnetic resonance imaging

This article describes the development and application of an integrated, generalized, and efficient Monte Carlo simulation system for diffusion magnetic resonance imaging (dMRI), named Diffusion Microscopist Simulator (DMS). DMS comprises a random walk Monte Carlo simulator and an MR image synthesizer. The former has the capacity to perform large-scale simulations of Brownian dynamics in the virtual environments of neural tissues at various levels of complexity, and the latter is flexible enough to synthesize dMRI datasets from a variety of simulated MRI pulse sequences. The aims of DMS are to give insights into the link between the fundamental diffusion process in biological tissues and the features observed in dMRI, as well as to provide appropriate ground-truth information for the development, optimization, and validation of dMRI acquisition schemes for different applications. The validity, efficiency, and potential applications of DMS are evaluated through four benchmark experiments, including the simulated dMRI of white matter fibers, the multiple scattering diffusion imaging, the biophysical modeling of polar cell membranes, and the high angular resolution diffusion imaging and fiber tractography of complex fiber configurations. We expect that this novel software tool would be substantially advantageous to clarify the interrelationship between dMRI and the microscopic characteristics of brain tissues, and to advance the biophysical modeling and the dMRI methodologies.

Validation of DTI tractography-based measures of primary motor area connectivity in the squirrel monkey brain

Diffusion tensor imaging (DTI) tractography provides noninvasive measures of structural cortico-cortical connectivity of the brain. However, the agreement between DTI-tractography-based measures and histological 'ground truth' has not been quantified. In this study, we reconstructed the 3D density distribution maps (DDM) of fibers labeled with an anatomical tracer, biotinylated dextran amine (BDA), as well as DTI tractography-derived streamlines connecting the primary motor (M1) cortex to other cortical regions in the squirrel monkey brain. We evaluated the agreement in M1-cortical connectivity between the fibers labeled in the brain tissue and DTI streamlines on a regional and voxel-by-voxel basis. We found that DTI tractography is capable of providing inter-regional connectivity comparable to the neuroanatomical connectivity, but is less reliable measuring voxel-to-voxel variations within regions.

Optimal short-time acquisition schemes in high angular resolution diffusion-weighted imaging

This work investigates the possibilities of applying high-angular-resolution-diffusion-imaging- (HARDI-) based methods in a clinical setting by investigating the performance of non-Gaussian diffusion probability density function (PDF) estimation for a range of b-values and diffusion gradient direction tables. It does so at realistic SNR levels achievable in limited time on a high-performance 3T system for the whole human brain in vivo. We use both computational simulations and in vivo brain scans to quantify the angular resolution of two selected reconstruction methods: Q-ball imaging and the diffusion orientation transform. We propose a new analytical solution to the ODF derived from the DOT. Both techniques are analytical decomposition approaches that require identical acquisition and modest postprocessing times and, given the proposed modifications of the DOT, can be analyzed in a similar fashion. We find that an optimal HARDI protocol given a stringent time constraint (<10 min) combines a moderate b-value (around 2000 s/mm²) with a relatively low number of acquired directions (>48). Our findings generalize to other methods and additional improvements in MR acquisition techniques.

Estimation of fiber orientation by filtered q-ball imaging*

We proposed a filtered q-ball imaging (fQBI) method for the reconstruction of fiber orientation distribution function (ODF) together with the quantitative comparison to unfiltered QBI. The filter kernel increases the high angular frequency content that is beneficial for the angular resolution in resolving crossing fibers. Through a series of simulations using Monte-Carlo model, the angular resolution of fQBI was demonstrated better than traditional QBI but the deviation of fiber orientation estimate also becomes larger. The improvement of the angular resolution can also reduce the underestimation of separation angles as well as the bias of fiber orientation estimations. In conclusion, fQBI was demonstrated to improve the angular resolution of QBI in resolving crossing fibers. This improvement will be helpful to precisely reconstruct fiber tract and brain network in applications by QBI.

Uncertainty Visualization in HARDI based on Ensembles of ODFs

In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.

APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER()

Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space [Formula: see text] of 2m(th)-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on [Formula: see text] is usually not straightforward computationally because there is no known analytic description of [Formula: see text] for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone [Formula: see text] for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ(2) (m) ⊂ Ω(2) (m) for m ≥ 1, using the subset [Formula: see text] of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ(2) (m). Finally, we experimentally validate the proposed approach and we present an application for computing 2m(th)-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images.

Quality assessment of high angular resolution diffusion imaging data using bootstrap on Q-ball reconstruction

PURPOSE

To develop a bootstrap method to assess the quality of High Angular Resolution Diffusion Imaging (HARDI) data using Q-Ball imaging (QBI) reconstruction.

MATERIALS AND METHODS

HARDI data were re-shuffled using regular bootstrap with jackknife sampling. For each bootstrap dataset, the diffusion orientation distribution function (ODF) was estimated voxel-wise using QBI reconstruction based on spherical harmonics functions. The reproducibility of the ODF was assessed using the Jensen-Shannon divergence (JSD) and the angular confidence interval was derived for the first and the second ODF maxima. The sensitivity of the bootstrap method was evaluated on a human subject by adding synthetic noise to the data, by acquiring a map of image signal-to-noise ratio (SNR) and by varying the echo time and the b-value.

RESULTS

The JSD was directly linked to the image SNR. The impact of echo times and b-values was reflected by both the JSD and the angular confidence interval, proving the usefulness of the bootstrap method to evaluate specific features of HARDI data.

CONCLUSION

The bootstrap method can effectively assess the quality of HARDI data and can be used to evaluate new hardware and pulse sequences, perform multifiber probabilistic tractography, and provide reliability metrics to support clinical studies.

Estimation of fiber orientation and spin density distribution by diffusion deconvolution

A diffusion deconvolution method is proposed to apply deconvolution to the diffusion orientation distribution function (dODF) and calculate the fiber orientation distribution function (fODF), which is defined as the orientation distribution of the fiber spin density. The dODF can be obtained from q-space imaging methods such as q-ball imaging (QBI), diffusion spectrum imaging (DSI), and generalized q-sampling imaging (GQI), and thus the method can be applied to various diffusion sampling schemes. A phantom study was conducted to compare the angular resolution of the fODF with the dODF, and the in vivo datasets were acquired using single-shell, two-shell, and grid sampling schemes, which were then reconstructed by QBI, GQI, and DSI, respectively. The phantom study showed that the fODF significantly improved the angular resolution over the dODF at 45- and 60-degree crossing angles. The in vivo study showed consistent fODF regardless of the applied sampling schemes and reconstruction methods, and the ability to resolve crossing fibers was improved in reduced sampling condition. The fiber spin density obtained from deconvolution showed a higher contrast-to-noise ratio than the fractional anisotropy (FA) mapping, and further application on tractography showed that the fiber spin density can be used to determine the termination of fiber tracts. In conclusion, the proposed deconvolution method is generally applicable to different q-space imaging methods. The calculated fODF improves the angular resolution and also provides a quantitative index of fiber spin density to refine fiber tracking.

How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 Collapse

Key Words

• high-angular resolution diffusion imaging
• anisotropic scalar
• generalized fractional anisotropy
• tensor
• signal-to-noise ratio
• kullback-leibler divergence

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MESH Headings

• Algorithms
• Anisotropy
• Computer Simulation
• Corpus Callosum/physiology
• Diffusion
• Diffusion Magnetic Resonance Imaging/methods
• Female
• Humans
• Imaging, Three-Dimensional/methods
• Male
• Models, Neurological
• Young Adult

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Grants

• EB007813 NIBIB NIH HHS
• R01 EB007813 NIBIB NIH HHS
• AG020098 NIA NIH HHS
• R56 AG020098 NIA NIH HHS
• HD050735 NICHD NIH HHS
• EB008432 NIBIB NIH HHS
• R01 EB008281-14 NIBIB NIH HHS
• R01 AG020098-09 NIA NIH HHS
• R01 EB008281 NIBIB NIH HHS
• R01 EB007813-04 NIBIB NIH HHS
• R01 HD050735 NICHD NIH HHS
• R01 EB008432 NIBIB NIH HHS
• EB008281 NIBIB NIH HHS
• R01 AG020098 NIA NIH HHS
• R01 EB008432-03 NIBIB NIH HHS

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Affiliation(s)

Liang Zhan Laboratory of Neuro Imaging, Department of Neurology, UCLA School of Medicine, 635 Charles E. Young Drive South, Suite 225E, Los Angeles, CA 90095-7332, USA
Alex D Leow
Neda Jahanshad
Ming-Chang Chiang
Marina Barysheva
Agatha D Lee
Arthur W Toga
Katie L McMahon
Greig I de Zubicaray
Margaret J Wright
Paul M Thompson

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Quantitative histological validation of diffusion MRI fiber orientation distributions in the rat brain

Diffusion MRI (dMRI) is widely used to measure microstructural features of brain white matter, but commonly used dMRI measures have limited capacity to resolve the orientation structure of complex fiber architectures. While several promising new approaches have been proposed, direct quantitative validation of these methods against relevant histological architectures remains missing. In this study, we quantitatively compare neuronal fiber orientation distributions (FODs) derived from ex vivo dMRI data against histological measurements of rat brain myeloarchitecture using manual recordings of individual myelin stained fiber orientations. We show that accurate FOD estimates can be obtained from dMRI data, even in regions with complex architectures of crossing fibers with an intrinsic orientation error of approximately 5-6 degrees in these regions. The reported findings have implications for both clinical and research studies based on dMRI FOD measures, and provide an important biological benchmark for improved FOD reconstruction and fiber tracking methods.

Probabilistic topography of human corpus callosum using cytoarchitectural parcellation and high angular resolution diffusion imaging tractography

The function of the corpus callosum (CC) is to distribute perceptual, motor, cognitive, learned, and voluntary information between the two hemispheres of the brain. Accurate parcellation of the CC according to fiber composition and fiber connection is of upmost important. In this work, population-based probabilistic connection topographies of the CC, in the standard Montreal Neurological Institute (MNI) space, are estimated by incorporating anatomical cytoarchitectural parcellation with high angular resolution diffusion imaging (HARDI) tractography. First, callosal fibers are extracted using multiple fiber assignment by continuous tracking algorithm based on q-ball imaging (QBI), on 12 healthy and young subjects. Then, the fiber tracts are aligned in the standard MNI coordinate system based on a tract-based transformation scheme. Next, twenty-eight Brodmann's areas on the surface of cortical cortex are registered to the MNI space to parcellate the aligned callosal fibers. Finally, the population-based topological subdivisions of the midsagittal CC to each cortical target are then mapped. And the resulting subdivisions of the CC that connect to the frontal and somatosensory associated cortex are also showed. To our knowledge, it is the first topographic subdivisions of the CC done using HARDI tractography and cytoarchitectonic information. In conclusion, this sophisticated topography of the CC may serve as a landmark to further understand the correlations between the CC, brain intercommunication, and functional cytoarchitectures.

Variability of homotopic and heterotopic callosal connectivity in partial agenesis of the corpus callosum: a 3T diffusion tensor imaging and Q-ball tractography study

BACKGROUND AND PURPOSE

Little is known about the anatomic connectivity of callosal axons in individuals with partial agenesis of the corpus callosum (pAgCC). We used tractography based on both diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI) to investigate interhemispheric white matter connectivity in pAgCC.

MATERIALS AND METHODS

DTI and HARDI were performed at 3T on 6 individuals with pAgCC and 8 control subjects. For HARDI analysis, a Q-ball reconstruction method capable of visualizing multiple intravoxel fiber orientations was used. In both DTI and HARDI, whole-brain 3D fiber tractography was performed by using deterministic streamline algorithms. Callosal fibers were then segmented to identify separately connections between homologous cortical regions (homotopic fibers) and nonhomologous regions (heterotopic fibers) by using manually drawn regions of interest.

RESULTS

In control individuals, we observed densely connected homotopic fibers. However, in individuals with pAgCC, we identified not only homotopic connections but also heterotopic connections in 4 of 6 subjects. Furthermore, the observed homotopic connections in pAgCC did not necessarily correlate with the position or size of the residual callosum. The nature of homotopic and heterotopic connectivity varied considerably among subjects with pAgCC, and HARDI recovered more callosal fibers than DTI.

CONCLUSION

Individuals with pAgCC demonstrate a remarkable diversity of callosal connectivity, including a number of heterotopic tracts that are absent in healthy subjects. The patterns of their callosal connections cannot be predicted from the appearance of their callosal fragments on conventional MR imaging. More tracts and more extensive fibers within tracts are recovered with HARDI than with DTI.