Q-ball Imaging Research Articles

High-angular resolution diffusion imaging generation using 3d u-net

PurposeTo investigate the effects on tractography of artificial intelligence-based prediction of motion-probing gradients (MPGs) in diffusion-weighted imaging (DWI).MethodsThe 251 participants in this study were patients with brain tumors or epileptic seizures who underwent MRI to depict tractography. DWI was performed with 64 MPG directions and b = 0 s/mm2 images. The dataset was divided into a training set of 191 (mean age 45.7 [± 19.1] years), a validation set of 30 (mean age 41.6 [± 19.1] years), and a test set of 30 (mean age 49.6 [± 18.3] years) patients. Supervised training of a convolutional neural network was performed using b = 0 images and the first 32 axes of MPG images as the input data and the second 32 axes as the reference data. The trained model was applied to the test data, and tractography was performed using (a) input data only; (b) input plus prediction data; and (c) b = 0 images and the 64 MPG data (as a reference).ResultsIn Q-ball imaging tractography, the average dice similarity coefficient (DSC) of the input plus prediction data was 0.715 (± 0.064), which was significantly higher than that of the input data alone (0.697 [± 0.070]) (p < 0.05). In generalized q-sampling imaging tractography, the average DSC of the input plus prediction data was 0.769 (± 0.091), which was also significantly higher than that of the input data alone (0.738 [± 0.118]) (p < 0.01).ConclusionDiffusion tractography is improved by adding predicted MPG images generated by an artificial intelligence model.

A discrete Funk transform on the Cubed Sphere

Computing accurately Funk transforms from discrete values is crucial in some applications, such as Q-Ball Imaging in medicine. This paper deals with a discrete Funk transform devoted to such a computation. The studied transform is based on a spectral method applied on a least squares fitting, with the special feature that regularization is not performed. We investigate several mathematical and numerical aspects in this context, including stability and pseudoinversion. As a specific instance, we introduce a simple framework based on the equiangular Cubed Sphere to guarantee the stability. Various numerical experiments attest to the accuracy and the convergence of the approach, in particular for synthetic Gaussian signals from Q-Ball Imaging.

Disrupted white matter network of brain structural connectomes in bipolar disorder patients revealed by q-ball imaging

BackgroundStructural and functional brain changes have been found to be associated with altered emotion and cognition in patients with bipolar disorder (BD). Widespread microstructural white matter abnormalities have been observed using traditional structural imaging in BD. q-Ball imaging (QBI) and graph theoretical analysis (GTA) improve the specificity and sensitivity and high accuracy of fiber tracking. We applied QBI and GTA to investigate and compare the structural connectivity alterations and network alterations in patients with and without BD. MethodsSixty-two patients with BD and 62 healthy controls (HCs) completed a MR scan. We evaluated the group differences in generalized fractional anisotropy (GFA) and normalized quantitative anisotropy (NQA) values by voxel-based statistical analysis with QBI. We also evaluated the group differences in topological parameters of GTA and subnetwork interconnections in network-based statistical analysis (NBS). ResultsThe QBI indices in the BD group were significantly lower than those in the HC group in the corpus callosum, cingulate gyrus, and caudate. The GTA indices indicated that the BD group demonstrated less global integration and higher local segregation than the HC group, but they retained small-world properties. NBS evaluation showed that the majority of the more connected subnetworks in BD occurred in thalamo-temporal/parietal connectivity. ConclusionOur findings supported white matter integrity with network alterations in BD.

Accurate Preoperative Identification of Motor Speech Area as Termination of Arcuate Fasciculus Depicted by Q-Ball Imaging Tractography

Tractography is one way to predict the distribution of cortical functional domains preoperatively. Diffusion tensor tractography (DTT) is commonly used in clinical practice, but is known to have limitations in delineating crossed fibers, which can be overcome by Q-ball imaging tractography (QBT). We aimed to compare the reliability of these 2 methods based on the spatial correlation between the arcuate fasciculus depicted by tractography and direct cortical stimulation during awake surgery. In this study, 15 patients with glioma underwent awake surgery with direct cortical stimulation. Tractography was depicted in a three-dimensional computer graphic model preoperatively, which was integrated with a photograph of the actual brain cortex using our novel mixed-reality technology. The termination of the arcuate fasciculus depicted by either DTT or QBT and the results of direct cortical stimulation were compared, and sensitivity and specificity were calculated in speech-associated brain gyri: pars triangularis, pars opercularis, ventral precentral gyrus, and middle frontal gyrus. QBT had significantly better sensitivity and lower false-positive rate than DTT in the pars opercularis. The same trend was noted for the other gyri. QBT is more reliable than DTT in identification of the motor speech area and may be clinically useful in brain tumor surgery.

Accuracy and reliability of diffusion imaging models

Diffusion imaging aims to non-invasively characterize the anatomy and integrity of the brain's white matter fibers. We evaluated the accuracy and reliability of commonly used diffusion imaging methods as a function of data quantity and analysis method, using both simulations and highly sampled individual-specific data (927–1442 diffusion weighted images [DWIs] per individual). Diffusion imaging methods that allow for crossing fibers (FSL's BedpostX [BPX], DSI Studio's Constant Solid Angle Q-Ball Imaging [CSA-QBI], MRtrix3’s Constrained Spherical Deconvolution [CSD]) estimated excess fibers when insufficient data were present and/or when the data did not match the model priors. To reduce such overfitting, we developed a novel Bayesian Multi-tensor Model-selection (BaMM) method and applied it to the popular ball-and-stick model used in BedpostX within the FSL software package. BaMM was robust to overfitting and showed high reliability and the relatively best crossing-fiber accuracy with increasing amounts of diffusion data. Thus, sufficient data and an overfitting resistant analysis method enhance precision diffusion imaging. For potential clinical applications of diffusion imaging, such as neurosurgical planning and deep brain stimulation (DBS), the quantities of data required to achieve diffusion imaging reliability are lower than those needed for functional MRI.

A Comparative Study of Diffusion Fiber Reconstruction Models for Pyramidal Tract Branches.

Currently, comparative studies evaluating the quantification accuracy of pyramidal tracts (PT) and PT branches that were tracked based on four mainstream diffusion models are deficient. The present study aims to evaluate four mainstream models using the high-quality Human Connectome Project (HCP) dataset. Diffusion tensor imaging (DTI), diffusion spectral imaging (DSI), generalized Q-space sampling imaging (GQI), and Q-ball imaging (QBI) were used to construct the PT and PT branches in 50 healthy volunteers from the HCP. False and true PT fibers were identified based on anatomic information. One-way repeated measure analysis of variance and post hoc paired-sample t-test were performed to identify the best PT and PT branch quantification model. The number, percentage, and density of true fibers of PT obtained based on GQI and QBI were significantly larger than those based on DTI and DSI (all p < 0.0005, Bonferroni corrected), whereas false fibers yielded the opposite results (all p < 0.0005, Bonferroni corrected). More trunk branches (PTtrunk) were present in the four diffusion models compared with the upper limb (PTUlimb), lower limb (PTLlimb), and cranial (PTcranial) branches. In addition, significantly more true fibers were obtained in PTtrunk, PTUlimb, and PTLlimb based on the GQI and QBI compared with DTI and DSI (all p < 0.0005, Bonferroni corrected). Finally, GQI-based group probabilistic maps showed that the four PT branches exhibited relatively unique spatial distributions. Therefore, the GQI and QBI represent better diffusion models for the PT and PT branches. The group probabilistic maps of PT branches have been shared with the public to facilitate more precise studies on the plasticity of and the damage to the motor pathway.

Comparison of Diffusion Signal Models for Fiber Tractography in Eloquent Glioma Surgery–Determination of Accuracy Under Awake Craniotomy Conditions

Fiber tractography (FT) has become an important noninvasive tool to ensure maximal safe tumor resection in eloquent glioma surgery. Intraoperatively applied FT is still predominantly based on diffusion tensor imaging (DTI). However, reconstruction schemes of high angular resolution diffusion imaging data for high-resolution FT (HRFT) are gaining increasing attention. The aim of this prospective study was to compare the accuracy of sophisticated HRFT models compared with DTI-FT. Ten patients with eloquent gliomas underwent surgery under awake craniotomy conditions. The localization of acquisition points, representing deteriorations during intraoperative electrostimulation (IOM) and neuropsychological mapping, were documented. The offsets of acquisition points to the respective fiber bundle were calculated. Probabilistic Q-ball imaging (QBI) and constrained spherical deconvolution (CSD)-FT were compared with DTI-FT for the major language-associated fiber bundles (superior longitudinal fasciculus [SLF] II-IV, inferior fronto-occipital fasciculus, and inferior longitudinal fasciculus/medial longitudinal fasciculus). Among 186 offset values, 46% were located closer than 10 mm to the estimated fiber bundle (CSD, 36%; DTI, 40% and QBI, 60%). Moreover, only 10 offsets were further away than 30 mm (5%). Lowest mean minimum offsets (SLF, 7.7 ± 7.9 mm; inferior fronto-occipital fasciculus, 12.7 ± 8.3 mm; inferior longitudinal fasciculus/medial longitudinal fasciculus, 17.7 ± 6.7 mm) were found for QBI, indicating a significant advantage compared with CSD or DTI (P < 0.001), respectively. No significant differences were found between CSD-FT and DTI-FT offsets (P= 0.105), albeit for the compound SLF exclusively (P < 0.001). Comparing HRFT techniques QBI and CSD with DTI, QBI delivered significantly better results with lowest offsets and good correlation to IOM results. Besides, QBI-FT was feasible for neurosurgical preoperative and intraoperative applications. Our findings suggest that a combined approach of QBI-FT and IOM under awake craniotomy is considerable for best preservation of neurological function in the presented setting. Overall, the implementation of selected HRFT models into neuronavigation systems seems to be a promising tool in glioma surgery.

White matter structural connectivity as a biomarker for detecting juvenile myoclonic epilepsy by transferred deep convolutional neural networks with varying transfer rates

Objective. By detecting abnormal white matter changes, diffusion magnetic resonance imaging (MRI) contributes to the detection of juvenile myoclonic epilepsy (JME). In addition, deep learning has greatly improved the detection performance of various brain disorders. However, there is almost no previous study effectively detecting JME by a deep learning approach with diffusion MRI. Approach. In this study, the white matter structural connectivity was generated by tracking the white matter fibers in detail based on Q-ball imaging and neurite orientation dispersion and density imaging. Four advanced deep convolutional neural networks (CNNs) were deployed by using the transfer learning approach, in which the transfer rate searching strategy was proposed to achieve the best detection performance. Main results. Our results showed: (a) Compared to normal control, the white matter’ neurite density of JME was significantly decreased. The most significantly abnormal fiber tracts between the two groups were found to be cortico-cortical connection tracts. (b) The proposed transfer rate searching approach contributed to find each CNN’s best performance, in which the best JME detection accuracy of 92.2% was achieved by using the Inception_resnet_v2 network with a 16% transfer rate. Significance. The results revealed: (a) Through detection of the abnormal white matter changes, the white matter structural connectivity can be used as a useful biomarker for detecting JME, which helps to characterize the pathophysiology of epilepsy. (b) The proposed transfer rate, as a new hyperparameter, promotes the CNNs transfer learning performance in detecting JME.

Going Beyond Diffusion Tensor Imaging Tractography in Eloquent Glioma Surgery–High-Resolution Fiber Tractography: Q-Ball or Constrained Spherical Deconvolution?

As a result of the resolution of intravoxel fiber crossing, high-resolution fiber tractography (HRFT) provides advantages over conventional diffusion tensor imaging (DTI) for fiber tractography (FT). Nevertheless, neurosurgically applied FT is still predominantly based on DTI. Although the application of HRFT is evolving, there is still a lack of data about which method should be preferred. With this prospectively designed study, we present our initial experience comparing an analytical Q-ball imaging (QBI) approach with constrained spherical deconvolution (CSD) and conventional DTI-FT considering a particularly neurosurgical perspective. For 18 patients with eloquent gliomas in the dominant hemisphere, probabilistic FT based on QBI, CSD, and DTI was performed for the major components of the language-associated pathways using a routine diffusion-weighted sequence. Quantitative analysis evaluated tract density, tract volume (TV), tract length (TL), number of fibers, and tract surface (TS) of the fiber object. Both HRFT models showed a significantly larger mean TV, TL, and TS compared with DTI (for QBI vs. DTI: TV (P= 0.0000), TL (P= 0.0048), and TS (P= 0.0129); for CSD vs. DTI: TV (P= 0.0000), TL (P= 0.0008), and TS (P= 0.0010)). However, results of QBI versus CSD did not differ significantly for these variables: TV (P= 0.1415), TL (P= 0.2837), and TS (P= 0.3692). Bland-Altman analysis supports these findings, suggesting systematically higher values for TV, TL, and TS with HRFT but no relevant differences of either QBI or CSD. Neither tumor volume nor peritumoral edema influenced FT results. Our quantitative analysis showed no significant differences regarding TV, TL, and TS for the HRFT methods; however, it suggested advantages over DTI-FT in terms of the display of marginal and terminal fibers. In our recently established setting, QBI-FT shows greater potential for integration into the clinical workflow.

Hybridising cuckoo search algorithm for extracting the ODF maxima in spherical harmonic representation

The diffusion-weighted magnetic resonance imaging (DW-MRI) is a promising method for non-invasive investigation of anatomical connectivity in the human brain. Q-ball imaging (QBI) is a diffusion MRI reconstruction technique which has been proven very successful in resolving multiple intravoxel fibre orientations in MRI (i.e., fibre crossing) based on the standard computation of the orientation distribution function (ODF), which is a 3-dimension spherical function founded to detect the dominant fibre orientations in the underlying volume of a pixel (voxel). However, ODF still has a limitation in determining fibre directions which may be corrupted by neighbour directions. In this paper, we proposed a new method to solve the ODF problem by adapting the hybridisation of the cuckoo search algorithm (i.e., global search) and bat algorithm (i.e., local search), namely, CSBA. The performance of the method is demonstrated by experiments in both synthetic and real data.

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.

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

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. 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. 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. 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.

Post-mortem inference of the human hippocampal connectivity and microstructure using ultra-high field diffusion MRI at 11.7 T

The human hippocampus plays a key role in memory management and is one of the first structures affected by Alzheimer’s disease. Ultra-high magnetic resonance imaging provides access to its inner structure in vivo. However, gradient limitations on clinical systems hinder access to its inner connectivity and microstructure. A major target of this paper is the demonstration of diffusion MRI potential, using ultra-high field (11.7 T) and strong gradients (750 mT/m), to reveal the extra- and intra-hippocampal connectivity in addition to its microstructure. To this purpose, a multiple-shell diffusion-weighted acquisition protocol was developed to reach an ultra-high spatio-angular resolution with a good signal-to-noise ratio. The MRI data set was analyzed using analytical Q-Ball Imaging, Diffusion Tensor Imaging (DTI), and Neurite Orientation Dispersion and Density Imaging models. High Angular Resolution Diffusion Imaging estimates allowed us to obtain an accurate tractography resolving more complex fiber architecture than DTI models, and subsequently provided a map of the cross-regional connectivity. The neurite density was akin to that found in the histological literature, revealing the three hippocampal layers. Moreover, a gradient of connectivity and neurite density was observed between the anterior and the posterior part of the hippocampus. These results demonstrate that ex vivo ultra-high field/ultra-high gradients diffusion-weighted MRI allows the mapping of the inner connectivity of the human hippocampus, its microstructure, and to accurately reconstruct elements of the polysynaptic intra-hippocampal pathway using fiber tractography techniques at very high spatial/angular resolutions.

Histological validation of diffusion MRI fiber orientation distributions and dispersion

Diffusion magnetic resonance imaging (dMRI) is widely used to probe tissue microstructure, and is currently the only non-invasive way to measure the brain's fiber architecture. While a large number of approaches to recover the intra-voxel fiber structure have been utilized in the scientific community, a direct, 3D, quantitative validation of these methods against relevant histological fiber geometries is lacking. In this study, we investigate how well different high angular resolution diffusion imaging (HARDI) models and reconstruction methods predict the ground-truth histologically defined fiber orientation distribution (FOD), as well as investigate their behavior over a range of physical and experimental conditions. The dMRI methods tested include constrained spherical deconvolution (CSD), Q-ball imaging (QBI), diffusion orientation transform (DOT), persistent angular structure (PAS), and neurite orientation dispersion and density imaging (NODDI) methods. Evaluation criteria focus on overall agreement in FOD shape, correct assessment of the number of fiber populations, and angular accuracy in orientation. In addition, we make comparisons of the histological orientation dispersion with the fiber spread determined from the dMRI methods. As a general result, no HARDI method outperformed others in all quality criteria, with many showing tradeoffs in reconstruction accuracy. All reconstruction techniques describe the overall continuous angular structure of the histological FOD quite well, with good to moderate correlation (median angular correlation coefficient > 0.70) in both single- and multiple-fiber voxels. However, no method is consistently successful at extracting discrete measures of the number and orientations of FOD peaks. The major inaccuracies of all techniques tend to be in extracting local maxima of the FOD, resulting in either false positive or false negative peaks. Median angular errors are ∼10° for the primary fiber direction and ∼20° for the secondary fiber, if present. For most methods, these results did not vary strongly over a wide range of acquisition parameters (number of diffusion weighting directions and b value). Regardless of acquisition parameters, all methods show improved successes at resolving multiple fiber compartments in a voxel when fiber populations cross at near-orthogonal angles, with no method adequately capturing low to moderate angle (<60°) crossing fibers. Finally, most methods are limited in their ability to capture orientation dispersion, resulting in low to moderate, yet statistically significant, correlation with histologically-derived dispersion with both HARDI and NODDI methodologies. Together, these results provide quantitative measures of the reliability and limitations of dMRI reconstruction methods and can be used to identify relative advantages of competing approaches as well as potential strategies for improving accuracy.

High angular resolution diffusion imaging abnormalities in the early stages of amyotrophic lateral sclerosis

ObjectiveUsing magnetic resonance (MR) high angular resolution diffusion imaging (HARDI), we aimed at revealing possible microstructural alterations in the early stage of amyotrophic lateral sclerosis (ALS), still not completely elucidated. MethodsWe studied 22 patients with ALS, in stages 1 or 2 according to the King's staging system, compared to 18 healthy controls (HCs). Statistical mapping of HARDI-derived parameters and tractography measures were performed using the Q-ball imaging diffusion data model. ResultsWhen compared to HCs, the ALS group showed a highly significant decrease of generalized fractional anisotropy (GFA) and fiber length and density in the corticospinal tracts (CSTs) and in the corpus callosum (CC) (p<0.05, corrected level of significance). Moreover, stratifying the ALS population considering the disease phenotype, larger areas of decreased GFA were found in patients with bulbar phenotype compared to those with classic phenotype in several bilateral associative fiber tracts, such as superior and inferior longitudinal, inferior fronto-occipital and uncinate fasciculi. ConclusionsOur whole-brain HARDI results provided preliminary evidence of an early pattern of microstructural degeneration in ALS, mainly involving the CSTs and the CC, although divergent patterns of microstructural abnormalites could be related to different disease phenotypes.

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.

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.

Mumford–Shah and Potts Regularization for Manifold-Valued Data

Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are computationally challenging even for scalar data. For manifold-valued data, the problem becomes even more involved since typical features of vector spaces are not available. In this paper, we propose algorithms for Mumford-Shah and for Potts regularization of manifold-valued signals and images. For the univariate problems, we derive solvers based on dynamic programming combined with (convex) optimization techniques for manifold-valued data. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging), we show that our algorithms compute global minimizers for any starting point. For the multivariate Mumford-Shah and Potts problems (for image regularization) we propose a splitting into suitable subproblems which we can solve exactly using the techniques developed for the corresponding univariate problems. Our method does not require any a priori restrictions on the edge set and we do not have to discretize the data space. We apply our method to diffusion tensor imaging (DTI) as well as Q-ball imaging. Using the DTI model, we obtain a segmentation of the corpus callosum.

Multi-Shell Hybrid Diffusion Imaging (HYDI) at 7 Tesla in TgF344-AD Transgenic Alzheimer Rats.

Diffusion weighted imaging (DWI) is widely used to study microstructural characteristics of the brain. Diffusion tensor imaging (DTI) and high-angular resolution imaging (HARDI) are frequently used in radiology and neuroscience research but can be limited in describing the signal behavior in composite nerve fiber structures. Here, we developed and assessed the benefit of a comprehensive diffusion encoding scheme, known as hybrid diffusion imaging (HYDI), composed of 300 DWI volumes acquired at 7-Tesla with diffusion weightings at b = 1000, 3000, 4000, 8000 and 12000 s/mm2 and applied it in transgenic Alzheimer rats (line TgF344-AD) that model the full clinico-pathological spectrum of the human disease. We studied and visualized the effects of the multiple concentric “shells” when computing three distinct anisotropy maps–fractional anisotropy (FA), generalized fractional anisotropy (GFA) and normalized quantitative anisotropy (NQA). We tested the added value of the multi-shell q-space sampling scheme, when reconstructing neural pathways using mathematical frameworks from DTI and q-ball imaging (QBI). We show a range of properties of HYDI, including lower apparent anisotropy when using high b-value shells in DTI-based reconstructions, and increases in apparent anisotropy in QBI-based reconstructions. Regardless of the reconstruction scheme, HYDI improves FA-, GFA- and NQA-aided tractography. HYDI may be valuable in human connectome projects and clinical research, as well as magnetic resonance research in experimental animals.

Fiber ball imaging

By modeling axons as thin cylinders, it is shown that the inverse Funk transform of the diffusion MRI (dMRI) signal intensity obtained on a spherical shell in q-space gives an estimate for a fiber orientation density function (fODF), where the accuracy improves with increasing b-value provided the signal-to-noise ratio is sufficient. The method is similar to q-ball imaging, except that the Funk transform of q-ball imaging is replaced by its inverse. We call this new approach fiber ball imaging. The fiber ball method is demonstrated for healthy human brain, and fODF estimates are compared to diffusion orientation distribution function (dODF) approximations obtained with q-ball imaging. The fODFs are seen to have sharper features than the dODFs, reflecting an enhancement of the higher degree angular frequencies. The inverse Funk transform of the dMRI signal intensity data provides a simple and direct method of estimating a fODF. In addition, fiber ball imaging leads to an estimate for the ratio of the fraction of MRI visible water confined to the intra-axonal space divided by the square root of the intra-axonal diffusivity. This technique may be useful for white matter fiber tractography, as well as other types of microstructural modeling of brain tissue.