Using the wild bootstrap to quantify uncertainty in diffusion tensor imaging

Deep learning microstructure estimation of developing brains from diffusion MRI: A newborn and fetal study

Diffusion-weighted magnetic resonance imaging (dMRI) is widely used to assess the brain white matter. Fiber orientation distribution functions (FODs) are a common way of representing the orientation and density of white matter fibers. However, with standard FOD computation methods, accurate estimation requires a large number of measurements that usually cannot be acquired for newborns and fetuses. We propose to overcome this limitation by using a deep learning method to map as few as six diffusion-weighted measurements to the target FOD. To train the model, we use the FODs computed using multi-shell high angular resolution measurements as target. Extensive quantitative evaluations show that the new deep learning method, using significantly fewer measurements, achieves comparable or superior results than standard methods such as Constrained Spherical Deconvolution and two state-of-the-art deep learning methods. For voxels with one and two fibers, respectively, our method shows an agreement rate in terms of the number of fibers of 77.5% and 22.2%, which is 3% and 5.4% higher than other deep learning methods, and an angular error of 10° and 20°, which is 6° and 5° lower than other deep learning methods. To determine baselines for assessing the performance of our method, we compute agreement metrics using densely sampled newborn data. Moreover, we demonstrate the generalizability of the new deep learning method across scanners, acquisition protocols, and anatomy on two clinical external datasets of newborns and fetuses. We validate fetal FODs, successfully estimated for the first time with deep learning, using post-mortem histological data. Our results show the advantage of deep learning in computing the fiber orientation density for the developing brain from in-vivo dMRI measurements that are often very limited due to constrained acquisition times. Our findings also highlight the intrinsic limitations of dMRI for probing the developing brain microstructure.

Fast and robust quantification of uncertainty in non-linear diffusion MRI models

Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.

Deep learning microstructure estimation of developing brains from diffusion MRI: a newborn and fetal study

Diffusion-weighted magnetic resonance imaging (dMRI) is widely used to assess the brain white matter. Fiber orientation distribution functions (FODs) are a common way of representing the orientation and density of white matter fibers. However, with standard FOD computation methods, accurate estimation of FODs requires a large number of measurements that usually cannot be acquired for newborns and fetuses. We propose to overcome this limitation by using a deep learning method to map as few as six diffusion-weighted measurements to the target FOD. To train the model, we use the FODs computed using multi-shell high angular resolution measurements as target. Extensive quantitative evaluations show that the new deep learning method, using significantly fewer measurements, achieves comparable or superior results to standard methods such as Constrained Spherical Deconvolution. We demonstrate the generalizability of the new deep learning method across scanners, acquisition protocols, and anatomy on two clinical datasets of newborns and fetuses. Additionally, we compute agreement metrics within the HARDI newborn dataset, and validate fetal FODs with post-mortem histological data. The results of this study show the advantage of deep learning in inferring the microstructure of the developing brain from in-vivo dMRI measurements that are often very limited due to subject motion and limited acquisition times, but also highlight the intrinsic limitations of dMRI in the analysis of the developing brain microstructure. These findings, therefore, advocate for the need for improved methods that are tailored to studying the early development of human brain.

Incorporating outlier information into diffusion-weighted MRI modeling for robust microstructural imaging and structural brain connectivity analyses

The white matter structures of the human brain can be represented using diffusion-weighted MRI tractography. Unfortunately, tractography is prone to find false-positive streamlines causing a severe decline in its specificity and limiting its feasibility in accurate structural brain connectivity analyses. Filtering algorithms have been proposed to reduce the number of invalid streamlines but the currently available filtering algorithms are not suitable to process data that contains motion artefacts which are typical in clinical research. We augmented the Convex Optimization Modelling for Microstructure Informed Tractography (COMMIT) algorithm to adjust for these signals drop-out motion artefacts. We demonstrate with comprehensive Monte-Carlo whole brain simulations and in vivo infant data that our robust algorithm is capable of properly filtering tractography reconstructions despite these artefacts. We evaluated the results using parametric and non-parametric statistics and our results demonstrate that if not accounted for, motion artefacts can have severe adverse effects in human brain structural connectivity analyses as well as in microstructural property mappings. In conclusion, the usage of robust filtering methods to mitigate motion related errors in tractogram filtering is highly beneficial, especially in clinical studies with uncooperative patient groups such as infants. With our presented robust augmentation and open-source implementation, robust tractogram filtering is readily available.

Geodesic Uncertainty in Diffusion MRI

We study theoretical and operational issues of geodesic tractography, a geometric methodology for retrieving biologically plausible neural fibers in the brain from diffusion weighted magnetic resonance imaging. The premise is that true positives are geodesics in a suitably constructed metric space, but unlike traditional first order methods these are not a priori constrained to connect nongeneric points on subdimensional manifolds, such as the characteristics in traditional streamline methods. By virtue of the Hopf-Rinow theorem geodesic tractography furnishes a huge amount of redundancy, ensuring the a priori existence of at least one tentative fiber between any two points and permitting additional tractometric and data-extrinsic constraints for (fuzzy or crisp) classification of true and false positives. In our feasibility study we consider a hybrid paradigm that unifies existing ideas on tractography, combining deterministic and probabilistic elements in a way naturally supported by metric geometry. Particular attention is paid to an analytical prediction of geodesic deviation on numerically computed geodesics, a ‘tidal’ effect induced by small perturbations resulting from data noise. Taking these effects into account clarifies the inherent uncertainty of geodesics, while simultaneosuly offering a dimensionality reduction of the tractography problem.

Diffusion MRI and anatomic tracing in the same brain reveal common failure modes of tractography

Anatomic tracing is recognized as a critical source of knowledge on brain circuitry that can be used to assess the accuracy of diffusion MRI (dMRI) tractography. However, most prior studies that have performed such assessments have used dMRI and tracer data from different brains and/or have been limited in the scope of dMRI analysis methods allowed by the data. In this work, we perform a quantitative, voxel-wise comparison of dMRI tractography and anatomic tracing data in the same macaque brain. An ex vivo dMRI acquisition with high angular resolution and high maximum b-value allows us to compare a range of q-space sampling, orientation reconstruction, and tractography strategies. The availability of tracing in the same brain allows us to localize the sources of tractography errors and to identify axonal configurations that lead to such errors consistently, across dMRI acquisition and analysis strategies. We find that these common failure modes involve geometries such as branching or turning, which cannot be modeled well by crossing fibers. We also find that the default thresholds that are commonly used in tractography correspond to rather conservative, low-sensitivity operating points. While deterministic tractography tends to have higher sensitivity than probabilistic tractography in that very conservative threshold regime, the latter outperforms the former as the threshold is relaxed to avoid missing true anatomical connections. On the other hand, the q-space sampling scheme and maximum b-value have less of an impact on accuracy. Finally, using scans from a set of additional macaque brains, we show that there is enough inter-individual variability to warrant caution when dMRI and tracer data come from different animals, as is often the case in the tractography validation literature. Taken together, our results provide insights on the limitations of current tractography methods and on the critical role that anatomic tracing can play in identifying potential avenues for improvement.

Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND's accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.

Using the Wild Bootstrap to Quantify Uncertainty in Mean Apparent Propagator MRI

Purpose: Estimation of uncertainty of MAP-MRI metrics is an important topic, for several reasons. Bootstrap derived uncertainty, such as the standard deviation, provides valuable information, and can be incorporated in MAP-MRI studies to provide more extensive insight. Methods: In this paper, the uncertainty of different MAP-MRI metrics was quantified by estimating the empirical distributions using the wild bootstrap. We applied the wild bootstrap to both phantom data and human brain data, and obtain empirical distributions for the MAP-MRI metrics return-to-origin probability (RTOP), non-Gaussianity (NG), and propagator anisotropy (PA). Results: We demonstrated the impact of diffusion acquisition scheme (number of shells and number of measurements per shell) on the uncertainty of MAP-MRI metrics. We demonstrated how the uncertainty of these metrics can be used to improve group analyses, and to compare different preprocessing pipelines. We demonstrated that with uncertainty considered, the results for a group analysis can be different. Conclusion: Bootstrap derived uncertain measures provide additional information to the MAP-MRI derived metrics, and should be incorporated in ongoing and future MAP-MRI studies to provide more extensive insight.

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).

Diffusion MRI in the brain - Theory and concepts

Over the past two decades, diffusion MRI has become an essential tool in neuroimaging investigations. This is due to its sensitivity to the motion of water molecules as they diffuse through the microstructural environment, allowing diffusion MRI to be used as a 'probe' of tissue microstructure. Furthermore, this sensitivity is strongly direction-dependent, notably in brain white matter, due to the alignment of structures that restrict or hinder the motion of water molecules, notably axonal membranes. This provides a means of inferring the orientation of fibres in vivo, and by use of appropriate fibre-tracking algorithms, of delineating the path of white matter tracts in the brain. The ability to perform so-called tractography in humans in vivo non-invasively is unique to diffusion MRI, and is now used in applications such as neurosurgery planning and more broadly within investigations of brain connectomics. This review describes the theory and concepts of diffusion MRI and describes its most important areas of application in the brain, with a strong focus on tractography.

In-vivo probabilistic atlas of human thalamic nuclei based on diffusion- weighted magnetic resonance imaging

The thalamic nuclei are involved in many neurodegenerative diseases and therefore, their identification is of key importance in numerous clinical treatments. Automated segmentation of thalamic subparts is currently achieved by exploring diffusion-weighted magnetic resonance imaging (DW-MRI), but in absence of such data, atlas-based segmentation can be used as an alternative. Currently, there is a limited number of available digital atlases of the thalamus. Moreover, all atlases are created using a few subjects only, thus are prone to errors due to the inter-subject variability of the thalamic morphology. In this work, we present a probabilistic atlas of anatomical subparts of the thalamus built upon a relatively large dataset where the individual thalamic parcellation was done by employing a recently proposed automatic diffusion-based clustering method. Our analyses, comparing the segmentation performance between the atlas-based and the clustering method, demonstrate the ability of the provided atlas to substitute the automated diffusion-based subdivision in the individual space when the DW-MRI is not available.

Tracking and validation techniques for topographically organized tractography

Topographic regularity of axonal connections is commonly understood as the preservation of spatial relationships between nearby neurons and is a fundamental structural property of the brain. In particular the retinotopic mapping of the visual pathway can even be quantitatively computed. Inspired from this previously untapped anatomical knowledge, we propose a novel tractography method that preserves both topographic and geometric regularity. We make use of parameterized curves with Frenet-Serret frame and introduce a highly flexible mechanism for controlling geometric regularity. At the same time, we incorporate a novel local data support term in order to account for topographic organization. Unifying geometry with topographic regularity, we develop a Bayesian framework for generating highly organized streamlines that accurately follow neuroanatomy. We additionally propose two novel validation techniques to quantify topographic regularity. In our experiments, we studied the results of our approach with respect to connectivity, reproducibility and topographic regularity aspects. We present both qualitative and quantitative comparisons of our technique against three algorithms from MRtrix3. We show that our method successfully generates highly organized fiber tracks while capturing bundle anatomy that are geometrically challenging for other approaches.

Derivation of Fiber Orientations From Oblique Views Through Human Brain Sections in 3D-Polarized Light Imaging

3D-Polarized Light Imaging (3D-PLI) enables high-resolution three-dimensional mapping of the nerve fiber architecture in unstained histological brain sections based on the intrinsic birefringence of myelinated nerve fibers. The interpretation of the measured birefringent signals comes with conjointly measured information about the local fiber birefringence strength and the fiber orientation. In this study, we present a novel approach to disentangle both parameters from each other based on a weighted least squares routine (ROFL) applied to oblique polarimetric 3D-PLI measurements. This approach was compared to a previously described analytical method on simulated and experimental data obtained from a post mortem human brain. Analysis of the simulations revealed in case of ROFL a distinctly increased level of confidence to determine steep and flat fiber orientations with respect to the brain sectioning plane. Based on analysis of histological sections of a human brain dataset, it was demonstrated that ROFL provides a coherent characterization of cortical, subcortical, and white matter regions in terms of fiber orientation and birefringence strength, within and across sections. Oblique measurements combined with ROFL analysis opens up new ways to determine physical brain tissue properties by means of 3D-PLI microscopy.

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.

Bayesian uncertainty quantification in linear models for diffusion MRI

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.

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.

Probabilistic tractography using Lasso bootstrap

Diffusion magnetic resonance imaging (dMRI) can be used for noninvasive imaging of white matter tracts. Using fiber tracking, which propagates fiber streamlines according to fiber orientations (FOs) computed from dMRI, white matter tracts can be reconstructed for investigation of brain diseases and the brain connectome. Because of image noise, probabilistic tractography has been proposed to characterize uncertainties in FO estimation. Bootstrap provides a nonparametric approach to the estimation of FO uncertainties and residual bootstrap has been used for developing probabilistic tractography. However, recently developed models have incorporated sparsity regularization to reduce the required number of gradient directions to resolve crossing FOs, and the residual bootstrap used in previous methods is not applicable to these models. In this work, we propose a probabilistic tractography algorithm named Lasso bootstrap tractography (LBT) for the models that incorporate sparsity. Using a fixed tensor basis and a sparsity assumption, diffusion signals are modeled using a Lasso formulation. With the residuals from the Lasso model, a distribution of diffusion signals is obtained according to a modified Lasso bootstrap strategy. FOs are then estimated from the synthesized diffusion signals by an algorithm that improves FO estimation by enforcing spatial consistency of FOs. Finally, streamlining fiber tracking is performed with the computed FOs. The LBT algorithm was evaluated on simulated and real dMRI data both qualitatively and quantitatively. Results demonstrate that LBT outperforms state-of-the-art algorithms.

Robust thalamic nuclei segmentation method based on local diffusion magnetic resonance properties

The thalamus is an essential relay station in the cortical–subcortical connections. It is characterized by a complex anatomical architecture composed of numerous small nuclei, which mediate the involvement of the thalamus in a wide range of neurological functions. We present a novel framework for segmenting the thalamic nuclei, which explores the orientation distribution functions (ODFs) from diffusion magnetic resonance images at 3 T. The differentiation of the complex intra-thalamic microstructure is improved by using the spherical harmonic (SH) representation of the ODFs, which provides full angular characterization of the diffusion process in each voxel. The clustering was performed using the k-means algorithm initialized in a data-driven manner. The method was tested on 35 healthy volunteers and our results show a robust, reproducible and accurate segmentation of the thalamus in seven nuclei groups. Six of them closely matched the anatomy and were labeled as anterior, ventral anterior, medio-dorsal, ventral latero-ventral, ventral latero-dorsal and pulvinar, while the seventh cluster included the centro-lateral and the latero-posterior nuclei. Results were evaluated both qualitatively, by comparing the segmented nuclei to the histological atlas of Morel, and quantitatively, by measuring the clusters’ extent and the clusters’ spatial distribution across subjects and hemispheres. We also showed the robustness of our approach across different sequences and scanners, as well as intra-subject reproducibility of the segmented clusters using additional two scan–rescan datasets. We also observed an overlap between the path of the main long-connection tracts passing through the thalamus and the spatial distribution of the nuclei identified with our clustering algorithm. Our approach, based on SH representations of the ODFs, outperforms the one based on angular differences between the principle diffusion directions, which is considered so far as state-of-the-art method. Our findings show an anatomically reliable segmentation of the main groups of thalamic nuclei that could be of potential use in many clinical applications.

DTI Image Registration under Probabilistic Fiber Bundles Tractography Learning

Diffusion Tensor Imaging (DTI) image registration is an essential step for diffusion tensor image analysis. Most of the fiber bundle based registration algorithms use deterministic fiber tracking technique to get the white matter fiber bundles, which will be affected by the noise and volume. In order to overcome the above problem, we proposed a Diffusion Tensor Imaging image registration method under probabilistic fiber bundles tractography learning. Probabilistic tractography technique can more reasonably trace to the structure of the nerve fibers. The residual error estimation step in active sample selection learning is improved by modifying the residual error model using finite sample set. The calculated deformation field is then registered on the DTI images. The results of our proposed registration method are compared with 6 state-of-the-art DTI image registration methods under visualization and 3 quantitative evaluation standards. The experimental results show that our proposed method has a good comprehensive performance.

Resolving Fine Cardiac Structures in Rats with High-Resolution Diffusion Tensor Imaging

Cardiac architecture is fundamental to cardiac function and can be assessed non-invasively with diffusion tensor imaging (DTI). Here, we aimed to overcome technical challenges in ex vivo DTI in order to extract fine anatomical details and to provide novel insights in the 3D structure of the heart. An integrated set of methods was implemented in ex vivo rat hearts, including dynamic receiver gain adjustment, gradient system scaling calibration, prospective adjustment of diffusion gradients, and interleaving of diffusion-weighted and non-diffusion-weighted scans. Together, these methods enhanced SNR and spatial resolution, minimised orientation bias in diffusion-weighting, and reduced temperature variation, enabling detection of tissue structures such as cell alignment in atria, valves and vessels at an unprecedented level of detail. Improved confidence in eigenvector reproducibility enabled tracking of myolaminar structures as a basis for segmentation of functional groups of cardiomyocytes. Ex vivo DTI facilitates acquisition of high quality structural data that complements readily available in vivo cardiac functional and anatomical MRI. The improvements presented here will facilitate next generation virtual models integrating micro-structural and electro-mechanical properties of the heart.

Mapping cardiac microstructure of rabbit heart in different mechanical states by high resolution diffusion tensor imaging: A proof-of-principle study

Myocardial microstructure and its macroscopic materialisation are fundamental to the function of the heart. Despite this importance, characterisation of cellular features at the organ level remains challenging, and a unifying description of the structure of the heart is still outstanding. Here, we optimised diffusion tensor imaging data to acquire high quality data in ex vivo rabbit hearts in slack and contractured states, approximating diastolic and systolic conditions. The data were analysed with a suite of methods that focused on different aspects of the myocardium. In the slack heart, we observed a similar transmural gradient in helix angle of the primary eigenvector of up to 23.6°/mm in the left ventricle and 24.2°/mm in the right ventricle. In the contractured heart, the same transmural gradient remained largely linear, but was offset by up to +49.9° in the left ventricle. In the right ventricle, there was an increase in the transmural gradient to 31.2°/mm and an offset of up to +39.0°. The application of tractography based on each eigenvector enabled visualisation of streamlines that depict cardiomyocyte and sheetlet organisation over large distances. We observed multiple V- and N-shaped sheetlet arrangements throughout the myocardium, and insertion of sheetlets at the intersection of the left and right ventricle. This study integrates several complementary techniques to visualise and quantify the heart's microstructure, projecting parameter representations across different length scales. This represents a step towards a more comprehensive characterisation of myocardial microstructure at the whole organ level.

Choosing the polarity of the phase-encoding direction in diffusion MRI: Does it matter for group analysis?

Notorious for degrading diffusion MRI data quality are so-called susceptibility-induced off-resonance fields, which cause non-linear geometric image deformations. While acquiring additional data to correct for these distortions alleviates the adverse effects of this artifact drastically - e.g., by reversing the polarity of the phase-encoding (PE) direction - this strategy is often not an option due to scan time constraints. Especially in a clinical context, where patient comfort and safety are of paramount importance, acquisition specifications are preferred that minimize scan time, typically resulting in data obtained with only one PE direction. In this work, we investigated whether choosing a different polarity of the PE direction would affect the outcome of a specific clinical research study. To address this methodological question, fractional anisotropy (FA) estimates of FreeSurfer brain regions were obtained in civilian and combat controls, remitted posttraumatic stress disorder (PTSD) patients, and persistent PTSD patients before and after trauma-focused therapy and were compared between diffusion MRI data sets acquired with different polarities of the PE direction (posterior-to-anterior, PA and anterior-to-posterior, AP). Our results demonstrate that regional FA estimates differ on average in the order of 5% between AP and PA PE data. In addition, when comparing FA estimates between different subject groups for specific cingulum subdivisions, the conclusions for AP and PA PE data were not in agreement. These findings increase our understanding of how one of the most pronounced data artifacts in diffusion MRI can impact group analyses and should encourage users to be more cautious when interpreting and reporting study outcomes derived from data acquired along a single PE direction.

Extensive Direct Subcortical Cerebellum-Basal Ganglia Connections in Human Brain as Revealed by Constrained Spherical Deconvolution Tractography

The connections between the cerebellum and basal ganglia were assumed to occur at the level of neocortex. However evidences from animal data have challenged this old perspective showing extensive subcortical pathways linking the cerebellum with the basal ganglia. Here we tested the hypothesis if these connections also exist between the cerebellum and basal ganglia in the human brain by using diffusion magnetic resonance imaging and tractography. Fifteen healthy subjects were analyzed by using constrained spherical deconvolution technique obtained with a 3T magnetic resonance imaging scanner. We found extensive connections running between the subthalamic nucleus and cerebellar cortex and, as novel result, we demonstrated a direct route linking the dentate nucleus to the internal globus pallidus as well as to the substantia nigra. These findings may open a new scenario on the interpretation of basal ganglia disorders.

Insight from uncertainty: bootstrap-derived diffusion metrics differentially predict memory function among older adults

Diffusion tensor imaging suffers from an intrinsic low signal-to-noise ratio. Bootstrap algorithms have been introduced to provide a non-parametric method to estimate the uncertainty of the measured diffusion parameters. To quantify the variability of the principal diffusion direction, bootstrap-derived metrics such as the cone of uncertainty have been proposed. However, bootstrap-derived metrics are not independent of the underlying diffusion profile. A higher mean diffusivity causes a smaller signal-to-noise ratio and, thus, increases the measurement uncertainty. Moreover, the goodness of the tensor model, which relies strongly on the complexity of the underlying diffusion profile, influences bootstrap-derived metrics as well. The presented simulations clearly depict the cone of uncertainty as a function of the underlying diffusion profile. Since the relationship of the cone of uncertainty and common diffusion parameters, such as the mean diffusivity and the fractional anisotropy, is not linear, the cone of uncertainty has a different sensitivity. In vivo analysis of the fornix reveals the cone of uncertainty to be a predictor of memory function among older adults. No significant correlation occurs with the common diffusion parameters. The present work not only demonstrates the cone of uncertainty as a function of the actual diffusion profile, but also discloses the cone of uncertainty as a sensitive predictor of memory function. Future studies should incorporate bootstrap-derived metrics to provide more comprehensive analysis.

The influence of molecular order and microstructure on the R2* and the magnetic susceptibility tensor

In this work, we demonstrate that in the presence of ordered sub-voxel structure such as tubular organization, biomaterials with molecular isotropy exhibits only apparent R2* anisotropy, while biomaterials with molecular anisotropy exhibit both apparent R2* and susceptibility anisotropy by means of susceptibility tensor imaging (STI). To this end, R2* and STI from gradient echo magnitude and phase data were examined in phantoms made from carbon fiber and Gadolinium (Gd) solutions with and without intrinsic molecular order and sub-voxel structure as well as in the in vivo brain. Confidence in the tensor reconstructions was evaluated with a wild bootstrap analysis. Carbon fiber showed both apparent anisotropy in R2* and anisotropy in STI, while the Gd filled capillary tubes only showed apparent anisotropy on R2*. Similarly, white matter showed anisotropic R2* and magnetic susceptibility with higher confidence, while the cerebral veins displayed only strong apparent R2* tensor anisotropy. Ordered sub-voxel tissue microstructure leads to apparent R2* anisotropy, which can be found in both white matter tracts and cerebral veins. However, additional molecular anisotropy is required for magnetic susceptibility anisotropy, which can be found in white matter tracts but not in cerebral veins.

Open Environment for Multimodal Interactive Connectivity Visualization and Analysis

Brain connectivity investigations are becoming increasingly multimodal and they present challenges for quantitatively characterizing and interactively visualizing data. In this study, we present a new set of network-based software tools for combining functional and anatomical connectivity from magnetic resonance imaging (MRI) data. The computational tools are available as part of Functional and Tractographic Connectivity Analysis Toolbox (FATCAT), a toolbox that interfaces with Analysis of Functional NeuroImages (AFNI) and SUrface MApping (SUMA) for interactive queries and visualization. This includes a novel, tractographic mini-probabilistic approach to improve streamline tracking in networks. We show how one obtains more robust tracking results for determining white matter connections by utilizing the uncertainty of the estimated diffusion tensor imaging (DTI) parameters and a few Monte Carlo iterations. This allows for thresholding based on the number of connections between target pairs to reduce the presence of tracts likely due to noise. To assist users in combining data, we describe an interface for navigating and performing queries in two-dimensional and three-dimensional data defined over voxel, surface, tract, and graph domains. These varied types of information can be visualized simultaneously and the queries performed interactively using SUMA and AFNI. The methods have been designed to increase the user's ability to visualize and combine functional MRI and DTI modalities, particularly in the context of single-subject inferences (e.g., in deep brain stimulation studies). Finally, we present a multivariate framework for statistically modeling network-based features in group analysis, which can be implemented for both functional and structural studies.

Prospective acceleration of diffusion tensor imaging with compressed sensing using adaptive dictionaries

PURPOSE

Diffusion MRI requires acquisition of multiple diffusion-weighted images, resulting in long scan times. Here, we investigate combining compressed sensing and a fast imaging sequence to dramatically reduce acquisition times in cardiac diffusion MRI.

METHODS

Fully sampled and prospectively undersampled diffusion tensor imaging data were acquired in five rat hearts at acceleration factors of between two and six using a fast spin echo (FSE) sequence. Images were reconstructed using a compressed sensing framework, enforcing sparsity by means of decomposition by adaptive dictionaries. A tensor was fit to the reconstructed images and fiber tractography was performed.

RESULTS

Acceleration factors of up to six were achieved, with a modest increase in root mean square error of mean apparent diffusion coefficient (ADC), fractional anisotropy (FA), and helix angle. At an acceleration factor of six, mean values of ADC and FA were within 2.5% and 5% of the ground truth, respectively. Marginal differences were observed in the fiber tracts.

CONCLUSION

We developed a new k-space sampling strategy for acquiring prospectively undersampled diffusion-weighted data, and validated a novel compressed sensing reconstruction algorithm based on adaptive dictionaries. The k-space undersampling and FSE acquisition each reduced acquisition times by up to 6× and 8×, respectively, as compared to fully sampled spin echo imaging. Magn Reson Med 76:248-258, 2016. © 2015 Wiley Periodicals, Inc.

Vanderbilt University Institute of Imaging Science Center for Computational Imaging XNAT: A multimodal data archive and processing environment

The Vanderbilt University Institute for Imaging Science (VUIIS) Center for Computational Imaging (CCI) has developed a database built on XNAT housing over a quarter of a million scans. The database provides framework for (1) rapid prototyping, (2) large scale batch processing of images and (3) scalable project management. The system uses the web-based interfaces of XNAT and REDCap to allow for graphical interaction. A python middleware layer, the Distributed Automation for XNAT (DAX) package, distributes computation across the Vanderbilt Advanced Computing Center for Research and Education high performance computing center. All software are made available in open source for use in combining portable batch scripting (PBS) grids and XNAT servers.

Detecting statistically significant differences in quantitative MRI experiments, applied to diffusion tensor imaging

In this work we present a framework for reliably detecting significant differences in quantitative magnetic resonance imaging and evaluate it with diffusion tensor imaging (DTI) experiments. As part of this framework we propose a new spatially regularized maximum likelihood estimator that simultaneously estimates the quantitative parameters and the spatially-smoothly-varying noise level from the acquisitions. The noise level estimation method does not require repeated acquisitions. We show that the amount of regularization in this method can be set a priori to achieve a desired coefficient of variation of the estimated noise level. The noise level estimate allows the construction of a Cramér-Rao-lower-bound based test statistic that reliably assesses the significance of differences between voxels within a scan or across different scans. We show that the regularized noise level estimate improves upon existing methods and results in a substantially increased precision of the uncertainty estimates of the DTI parameters. It enables correct specification of the null distribution of the test statistic and with it the test statistic obtains the highest sensitivity and specificity. The source code of the estimation framework, test statistic and experiment scripts are made available to the community.

Evaluating the accuracy of diffusion MRI models in white matter

Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of commonly used models have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.

PROBABILISTIC FIBER TRACKING USING A MODIFIED LASSO BOOTSTRAP METHOD

Diffusion MRI (dMRI) provides a noninvasive tool for investigating white matter tracts. Probabilistic fiber tracking has been proposed to represent the fiber structures as 3D streamlines while taking the uncertainty introduced by noise into account. In this paper, we propose a probabilistic fiber tracking method based on bootstrapping a multi-tensor model with a fixed tensor basis. The fiber orientation (FO) estimation is formulated as a Lasso problem. Then by resampling the residuals calculated using a modified Lasso estimator to create synthetic diffusion signals, a distribution of FOs is estimated. Probabilistic fiber tracking can then be performed by sampling from the FO distribution. Experiments were performed on a digital crossing phantom and brain dMRI for validation.

Correlation of diffusion tensor tractography and intraoperative macrostimulation during deep brain stimulation for Parkinson disease

Object

The purpose of this study was to investigate whether diffusion tensor imaging (DTI) of the corticospinal tract (CST) is a reliable surrogate for intraoperative macrostimulation through the deep brain stimulation (DBS) leads. The authors hypothesized that the distance on MRI from the DBS lead to the CST as determined by DTI would correlate with intraoperative motor thresholds from macrostimulations through the same DBS lead.

Methods

The authors retrospectively reviewed pre- and postoperative MRI studies and intraoperative macrostimulation recordings in 17 patients with Parkinson disease (PD) treated by DBS stimulation. Preoperative DTI tractography of the CST was coregistered with postoperative MRI studies showing the position of the DBS leads. The shortest distance and the angle from each contact of each DBS lead to the CST was automatically calculated using software-based analysis. The distance measurements calculated for each contact were evaluated with respect to the intraoperative voltage thresholds that elicited a motor response at each contact.

Results

There was a nonsignificant trend for voltage thresholds to increase when the distances between the DBS leads and the CST increased. There was a significant correlation between the angle and the voltage, but the correlation was weak (coefficient of correlation [R] = 0.36).

Conclusions

Caution needs to be exercised when using DTI tractography information to guide DBS lead placement in patients with PD. Further studies are needed to compare DTI tractography measurements with other approaches such as microelectrode recordings and conventional intraoperative MRI–guided placement of DBS leads.

Uncertainty estimation in diffusion MRI using the nonlocal bootstrap

In this paper, we propose a new bootstrap scheme, called the nonlocal bootstrap (NLB) for uncertainty estimation. In contrast to the residual bootstrap, which relies on a data model, or the repetition bootstrap, which requires repeated signal measurements, NLB is not restricted by the data structure imposed by a data model and obviates the need for time-consuming multiple acquisitions. NLB hinges on the observation that local imaging information recurs in an image. This self-similarity implies that imaging information coming from spatially distant (nonlocal) regions can be exploited for more effective estimation of statistics of interest. Evaluations using in silico data indicate that NLB produces distribution estimates that are in closer agreement with those generated using Monte Carlo simulations, compared with the conventional residual bootstrap. Evaluations using in vivo data demonstrate that NLB produces results that are in agreement with our knowledge on white matter architecture.

FATCAT: (an efficient) Functional and Tractographic Connectivity Analysis Toolbox

We present a suite of software tools for facilitating the combination of functional magnetic resonance imaging (FMRI) and diffusion-based tractography from a network-focused point of view. The programs have been designed for investigating functionally derived gray matter networks and related structural white matter networks. The software comprises the Functional and Tractographic Connectivity Analysis Toolbox (FATCAT), now freely distributed with AFNI. This toolbox supports common file formats and has been designed to integrate as easily as possible with existing standard FMRI pipelines and diffusion software, such as AFNI, FSL, and TrackVis. The programs are efficient, run by commandline for facilitating group processing, and produce several visualizable outputs. Here, we present the programs and their underlying methods, and we also provide a test example of resting-state FMRI analysis combined with tractography. Tractography results are compared with existing methods, showing significantly reduced runtime and generally similar connectivity, but with important differences such as more circumscribed tract regions and more physiologically identifiable paths produced between several region-of-interest pairs. Currently, FATCAT uses only diffusion tensor-based tractography (one direction per voxel), but higher-order models will soon be included.

Toward objective markers of concussion in sport: a review of white matter and neurometabolic changes in the brain after sports-related concussion

Abstract Sports-related concussion is an issue that has piqued the public's attention of late as concerns surrounding potential long-term sequelae as well as new methods of characterizing the effects of this form of injury continue to develop. For the most part, diagnosis of concussion is based on subjective clinical measures and thus is prone to under-reporting. In the current environment, where conventional imaging modalities, such as computed tomography and magnetic resonance imaging, are unable to elucidate the degree of white matter damage and neurometabolic change, a discussion of two advanced imaging techniques-diffusion tensor imaging (DTI) and magnetic resonance spectroscopy (MRS)-is undertaken with a view to highlighting their potential utility. Our aim is to outline a variety of the approaches to concussion research that have been employed, with special attention given to the clinical considerations and acute complications attributed to concussive injury. DTI and MRS have been at the forefront of research as a result of their noninvasiveness and ease of acquisition, and hence it is thought that the use of these neuroimaging modalities has the potential to aid clinical decision making and management, including guiding return-to-play protocols.

Estimating Uncertainty in White Matter Tractography Using Wild Non-local Bootstrap

Statistics derived from diffusion MRI data, especially those related to tractography, are often highly non-linear and non-Gaussian with unknown complex distributions. In estimating the sampling distributions of these statistics, many existing techniques are limited by their reliance on models that assume normality and that are yet to be verified in complex situations where various noise sources, such as physiologic variation, scanner instability, and imaging noise, might be simultaneously present. In complex conditions as such, a viable solution is the bootstrap, which due to its distribution-independent nature is an appealing tool for the estimation of the variability of almost any statistic, without relying on complicated theoretical calculations, but purely on computer simulation. In this paper, we will examine whether a new bootstrap scheme, called the wild non-local bootstrap (W-NLB), is effective in estimating the uncertainty in tractography data. In contrast to the residual or wild bootstrap, which relies on a predetermined data model, or the repetition bootstrap, which requires repeated signal measurements, W-NLB does not assume a predetermined form of data structure and obviates the need for time-consuming multiple acquisitions. W-NLB hinges on the observation that local imaging information recurs in the image. This self-similarity implies that imaging information coming from spatially distant (non-local) regions can be exploited for more effective estimation of statistics of interest. In silico evaluations indicate that W-NLB produces distribution estimates that are in closer agreement to those generated using Monte Carlo simulations, compared with the conventional residual bootstrap. Evaluations using in vivo data show that W-NLB produces results that are in agreement with our knowledge on the white matter connection architecture.

Reconstruction of white matter tracts via repeated deterministic streamline tracking--initial experience

Diffusion Tensor Imaging (DTI) and fiber tractography are established methods to reconstruct major white matter tracts in the human brain in-vivo. Particularly in the context of neurosurgical procedures, reliable information about the course of fiber bundles is important to minimize postoperative deficits while maximizing the tumor resection volume. Since routinely used deterministic streamline tractography approaches often underestimate the spatial extent of white matter tracts, a novel approach to improve fiber segmentation is presented here, considering clinical time constraints. Therefore, fiber tracking visualization is enhanced with statistical information from multiple tracking applications to determine uncertainty in reconstruction based on clinical DTI data. After initial deterministic fiber tracking and centerline calculation, new seed regions are generated along the result’s midline. Tracking is applied to all new seed regions afterwards, varying in number and applied offset. The number of fibers passing each voxel is computed to model different levels of fiber bundle membership. Experimental results using an artificial data set of an anatomical software phantom are presented, using the Dice Similarity Coefficient (DSC) as a measure of segmentation quality. Different parameter combinations were classified to be superior to others providing significantly improved results with DSCs of 81.02%±4.12%, 81.32%±4.22% and 80.99%±3.81% for different levels of added noise in comparison to the deterministic fiber tracking procedure using the two-ROI approach with average DSCs of 65.08%±5.31%, 64.73%±6.02% and 65.91%±6.42%. Whole brain tractography based on the seed volume generated by the calculated seeds delivers average DSCs of 67.12%±0.86%, 75.10%±0.28% and 72.91%±0.15%, original whole brain tractography delivers DSCs of 67.16%, 75.03% and 75.54%, using initial ROIs as combined include regions, which is clearly improved by the repeated fiber tractography method.

Simultaneous analysis and quality assurance for diffusion tensor imaging

Diffusion tensor imaging (DTI) enables non-invasive, cyto-architectural mapping of in vivo tissue microarchitecture through voxel-wise mathematical modeling of multiple magnetic resonance imaging (MRI) acquisitions, each differently sensitized to water diffusion. DTI computations are fundamentally estimation processes and are sensitive to noise and artifacts. Despite widespread adoption in the neuroimaging community, maintaining consistent DTI data quality remains challenging given the propensity for patient motion, artifacts associated with fast imaging techniques, and the possibility of hardware changes/failures. Furthermore, the quantity of data acquired per voxel, the non-linear estimation process, and numerous potential use cases complicate traditional visual data inspection approaches. Currently, quality inspection of DTI data has relied on visual inspection and individual processing in DTI analysis software programs (e.g. DTIPrep, DTI-studio). However, recent advances in applied statistical methods have yielded several different metrics to assess noise level, artifact propensity, quality of tensor fit, variance of estimated measures, and bias in estimated measures. To date, these metrics have been largely studied in isolation. Herein, we select complementary metrics for integration into an automatic DTI analysis and quality assurance pipeline. The pipeline completes in 24 hours, stores statistical outputs, and produces a graphical summary quality analysis (QA) report. We assess the utility of this streamlined approach for empirical quality assessment on 608 DTI datasets from pediatric neuroimaging studies. The efficiency and accuracy of quality analysis using the proposed pipeline is compared with quality analysis based on visual inspection. The unified pipeline is found to save a statistically significant amount of time (over 70%) while improving the consistency of QA between a DTI expert and a pool of research associates. Projection of QA metrics to a low dimensional manifold reveal qualitative, but clear, QA-study associations and suggest that automated outlier/anomaly detection would be feasible.

Robust Inter-Modality Multi-Atlas Segmentation for PACS-based DTI Quality Control

Anatomical contexts (spatial labels) are critical for interpretation of medical imaging content. Numerous approaches have been devised for segmentation, query, and retrieval within the Picture Archive and Communication System (PACS) framework. To date, application-based methods for anatomical localization and tissue classification have yielded the most successful results, but these approaches typically rely upon the availability of standardized imaging sequences. With the ever expanding scope of PACS archives - including multiple imaging modalities, multiple image types within a modality, and multi-site efforts, it is becoming increasingly burdensome to devise a specific method for each data type. To address the challenge of generalizing segmentations from one modality to another, we consider multi-atlas segmentation to transfer label information from labeled T1-weighted MRI data to unlabeled B₀ data collected in a diffusion tensor imaging (DTI) experiment. The label transfer approach is fully automated and enables a generalizable cross-modality segmentation method. Herein, we propose a multi-tier multi-atlas segmentation framework for the segmentation of previously unlabeled imaging modalities (e.g., B₀ images for DTI analysis). We show that this approach can be used to construct informed structure-wise noise estimates for fractional anisotropy (FA) measurements of DTI. Although this label transfer methodology is demonstrated in the context of quality control of DTI images, the proposed framework is applicable to any application where the segmentation of unlabeled modalities is limited due to the current collection of available atlases.

Longitudinal change detection: inference on the diffusion tensor along white matter pathways

Diffusion weighted magnetic resonance imaging (DW-MRI) makes it possible to probe brain connections in vivo. This paper presents a change detection framework that relies on white matter pathways with application to neuromyelitis optica (NMO). The objective is to detect local or global fiber diffusion property modifications between two longitudinal DW-MRI acquisitions of a patient. To this end, we develop two frameworks based on statistical tests on tensor eigenvalues to detect local or global changes along the white matter pathways: a pointwise test that compares tensor populations extracted in bundles cross sections and a fiberwise test that compares paired tensors along all the fiber bundles. Experiments on both synthetic and real data highlight the benefit of considering fiber based statistical tests compared to standard voxelwise strategies.

Parametric representation of multiple white matter fascicles from cube and sphere diffusion MRI

The characterization of the complex diffusion signal arising from the brain remains an open problem. Many representations focus on characterizing the global shape of the diffusion profile at each voxel and are limited to the assessment of connectivity. In contrast, Multiple Fascicle Models (MFM) seek to represent the contribution from each white matter fascicle and may be useful in the investigation of both white matter connectivity and diffusion properties of each individual fascicle. However, the most appropriate representation of multiple fascicles remains unclear. In particular, a multiple tensor representation of multiple fascicles has frequently been reported to be numerically challenging and unstable. We provide here the first analytical demonstration that when using a diffusion MRI acquisition with only one non-zero b-value, such as in conventional single-shell HARDI acquisition, a co-linearity in model parameters makes the precise model estimation impossible. Motivated by this theoretical result, we propose the novel CUSP (CUbe and SPhere) optimal acquisition scheme to achieve multiple non-zero b-values. It combines the gradients of a single-shell HARDI with gradients in its enclosing cube, in which varying b-values can be acquired by modulation of the gradient strength, without modifying the minimum echo time. Compared to a multi-shell HARDI acquisition, our scheme has significantly increased signal-to-noise ratio. We propose a novel estimation algorithm that enables efficient, robust and accurate estimation of the parameters of a multi-tensor model. In conjunction with a CUSP acquisition, it enables full estimation of the multi-tensor model. We present an evaluation of CUSP-MFM on both synthetic phantoms and invivo data. We report qualitative and quantitative experimental evaluations which demonstrate the ability of CUSP-MFM to characterize multiple fascicles from short duration acquisitions. CUSP-MFM enables rapid and effective investigation of multiple white matter fascicles, in both normal development and in disease and injury, in research and clinical practice.

Uncertainty estimations for quantitative in vivo MRI T1 mapping

Mapping the longitudinal relaxation time (T(1)) of brain tissue is of great interest for both clinical research and MRI sequence development. For an unambiguous interpretation of in vivo variations in T(1) images, it is important to understand the degree of variability that is associated with the quantitative T(1) parameter. This paper presents a general framework for estimating the uncertainty in quantitative T(1) mapping by combining a slice-shifted multi-slice inversion recovery EPI technique with the statistical wild-bootstrap approach. Both simulations and experimental analyses were performed to validate this novel approach and to evaluate the estimated T(1) uncertainty in several brain regions across four healthy volunteers. By estimating the T(1) uncertainty, it is shown that the variation in T(1) within anatomic regions for similar tissue types is larger than the uncertainty in the measurement. This indicates that heterogeneity of the inspected tissue and/or partial volume effects can be the main determinants for the observed variability in the estimated T(1) values. The proposed approach to estimate T(1) and its uncertainty without the need for repeated measurements may also prove to be useful for calculating effect sizes that are deemed significant when comparing group differences.

Two-tensor model-based bootstrapping on classified tensor morphologies: estimation of uncertainty in fiber orientation and probabilistic tractography

In this manuscript, fast and clinically feasible model-based bootstrapping algorithms using a geometrically constrained two-tensor diffusion model are employed for estimating uncertainty in fiber orientation. A Monte-Carlo-based tensor morphology voxel classification algorithm is initially applied using single-tensor bootstrap samples before the use of a two-tensor model-based bootstrapping algorithm. Classification of tensor morphologies allows the tensor morphology to be considered when selecting the most appropriate bootstrap procedure. A constrained two-tensor model approach can greatly reduce data acquisition and computational times for whole bootstrap data volume generation compared to other multifiber model techniques, facilitating widespread clinical use. For comparison, we propose a new repetition-bootstrap algorithm based on classified voxels and the constrained two-tensor model. Tractography with these bootstrapping algorithms is also developed to estimate the connection probabilities between brain regions, especially regions with complex fiber configurations. Experimental results on synthetic data, a hardware phantom and human brain data demonstrate the superior performance of our algorithms compared to conventional approaches.

White matter integrity, fiber count, and other fallacies: the do's and don'ts of diffusion MRI

Diffusion-weighted MRI (DW-MRI) has been increasingly used in imaging neuroscience over the last decade. An early form of this technique, diffusion tensor imaging (DTI) was rapidly implemented by major MRI scanner companies as a scanner selling point. Due to the ease of use of such implementations, and the plausibility of some of their results, DTI was leapt on by imaging neuroscientists who saw it as a powerful and unique new tool for exploring the structural connectivity of human brain. However, DTI is a rather approximate technique, and its results have frequently been given implausible interpretations that have escaped proper critique and have appeared misleadingly in journals of high reputation. In order to encourage the use of improved DW-MRI methods, which have a better chance of characterizing the actual fiber structure of white matter, and to warn against the misuse and misinterpretation of DTI, we review the physics of DW-MRI, indicate currently preferred methodology, and explain the limits of interpretation of its results. We conclude with a list of 'Do's and Don'ts' which define good practice in this expanding area of imaging neuroscience.

Comparing model-based and model-free analysis methods for QUASAR arterial spin labeling perfusion quantification

Amongst the various implementations of arterial spin labeling MRI methods for quantifying cerebral perfusion, the QUASAR method is unique. By using a combination of labeling with and without flow suppression gradients, the QUASAR method offers the separation of macrovascular and tissue signals. This permits local arterial input functions to be defined and "model-free" analysis, using numerical deconvolution, to be used. However, it remains unclear whether arterial spin labeling data are best treated using model-free or model-based analysis. This work provides a critical comparison of these two approaches for QUASAR arterial spin labeling in the healthy brain. An existing two-component (arterial and tissue) model was extended to the mixed flow suppression scheme of QUASAR to provide an optimal model-based analysis. The model-based analysis was extended to incorporate dispersion of the labeled bolus, generally regarded as the major source of discrepancy between the two analysis approaches. Model-free and model-based analyses were compared for perfusion quantification including absolute measurements, uncertainty estimation, and spatial variation in cerebral blood flow estimates. Major sources of discrepancies between model-free and model-based analysis were attributed to the effects of dispersion and the degree to which the two methods can separate macrovascular and tissue signal.