A software tool to generate simulated white matter structures for the assessment of fibre-tracking algorithms

PhyberSIM: a tool for the generation of ground truth to evaluate brain fiber clustering algorithms

Diffusion Magnetic Resonance Imaging tractography is a non-invasive technique that produces a collection of streamlines representing the main white matter bundle trajectories. Methods, such as fiber clustering algorithms, are important in computational neuroscience and have been the basis of several white matter analysis methods and studies. Nevertheless, these clustering methods face the challenge of the absence of ground truth of white matter fibers, making their evaluation difficult. As an alternative solution, we present an innovative brain fiber bundle simulator that uses spline curves for fiber representation. The methodology uses a tubular model for the bundle simulation based on a bundle centroid and five radii along the bundle. The algorithm was tested by simulating 28 Deep White Matter atlas bundles, leading to low inter-bundle distances and high intersection percentages between the original and simulated bundles. To prove the utility of the simulator, we created three whole-brain datasets containing different numbers of fiber bundles to assess the quality performance of QuickBundles and Fast Fiber Clustering algorithms using five clustering metrics. Our results indicate that QuickBundles tends to split less and Fast Fiber Clustering tends to merge less, which is consistent with their expected behavior. The performance of both algorithms decreases when the number of bundles is increased due to higher bundle crossings. Additionally, the two algorithms exhibit robust behavior with input data permutation. To our knowledge, this is the first whole-brain fiber bundle simulator capable of assessing fiber clustering algorithms with realistic data.

Brain fiber structure estimation based on principal component analysis and RINLM filter

Diffusion magnetic resonance imaging is a technique for non-invasive detection of microstructure in the white matter of the human brain, which is widely used in neuroscience research of the brain. However, diffusion-weighted images(DWI) are sensitive to noise, which affects the subsequent reconstruction of fiber orientation direction, microstructural parameter estimation and fiber tracking. In order to better eliminate the noise in diffusion-weighted images, this study proposes a noise reduction method combining Marchenko-Pastur principal component analysis(MPPCA) and rotation-invariant non-local means filter(RINLM) to further remove residual noise and preserve the image texture detail information. In this study, the algorithm is applied to the fiber structure and the prevailing microstructural models within the human brain voxels based on simulated and real human brain datasets. Experimental comparisons between the proposed method and the state-of-the-art methods are performed in single-fiber, multi-fiber, crossed and curved-fiber regions as well as in different microstructure estimation models. Results demonstrated the superior performance of the proposed method in denoising DWI data, which can reduce the angular error in fiber orientation reconstruction to obtain more valid fiber structure estimation and enable more complete fiber tracking trajectories with higher coverage. Meanwhile, the method reduces the estimation errors of various white matter microstructural parameters and verifies the performance of the method in white matter microstructure estimation.

Tractography passes the test: Results from the diffusion-simulated connectivity (disco) challenge

Estimating structural connectivity from diffusion-weighted magnetic resonance imaging is a challenging task, partly due to the presence of false-positive connections and the misestimation of connection weights. Building on previous efforts, the MICCAI-CDMRI Diffusion-Simulated Connectivity (DiSCo) challenge was carried out to evaluate state-of-the-art connectivity methods using novel large-scale numerical phantoms. The diffusion signal for the phantoms was obtained from Monte Carlo simulations. The results of the challenge suggest that methods selected by the 14 teams participating in the challenge can provide high correlations between estimated and ground-truth connectivity weights, in complex numerical environments. Additionally, the methods used by the participating teams were able to accurately identify the binary connectivity of the numerical dataset. However, specific false positive and false negative connections were consistently estimated across all methods. Although the challenge dataset doesn't capture the complexity of a real brain, it provided unique data with known macrostructure and microstructure ground-truth properties to facilitate the development of connectivity estimation methods.

CACTUS: a computational framework for generating realistic white matter microstructure substrates

Monte-Carlo diffusion simulations are a powerful tool for validating tissue microstructure models by generating synthetic diffusion-weighted magnetic resonance images (DW-MRI) in controlled environments. This is fundamental for understanding the link between micrometre-scale tissue properties and DW-MRI signals measured at the millimetre-scale, optimizing acquisition protocols to target microstructure properties of interest, and exploring the robustness and accuracy of estimation methods. However, accurate simulations require substrates that reflect the main microstructural features of the studied tissue. To address this challenge, we introduce a novel computational workflow, CACTUS (Computational Axonal Configurator for Tailored and Ultradense Substrates), for generating synthetic white matter substrates. Our approach allows constructing substrates with higher packing density than existing methods, up to 95% intra-axonal volume fraction, and larger voxel sizes of up to 500μm3 with rich fibre complexity. CACTUS generates bundles with angular dispersion, bundle crossings, and variations along the fibres of their inner and outer radii and g-ratio. We achieve this by introducing a novel global cost function and a fibre radial growth approach that allows substrates to match predefined targeted characteristics and mirror those reported in histological studies. CACTUS improves the development of complex synthetic substrates, paving the way for future applications in microstructure imaging.

dtiRIM: A generalisable deep learning method for diffusion tensor imaging

Diffusion weighted MRI is an indispensable tool for routine patient screening and diagnostics of pathology. Recently, several deep learning methods have been proposed to quantify diffusion parameters, but poor generalisation to new data prevents broader use of these methods, as they require retraining of the neural network for each new scan protocol. In this work, we present the dtiRIM, a new deep learning method for Diffusion Tensor Imaging (DTI) based on the Recurrent Inference Machines. Thanks to its ability to learn how to solve inverse problems and to use the diffusion tensor model to promote data consistency, the dtiRIM can generalise to variations in the acquisition settings. This enables a single trained network to produce high quality tensor estimates for a variety of cases. We performed extensive validation of our method using simulation and in vivo data, and compared it to the Iterated Weighted Linear Least Squares (IWLLS), the approach of the state-of-the-art MRTrix3 software, and to an implementation of the Maximum Likelihood Estimator (MLE). Our results show that dtiRIM predictions present low dependency on tissue properties, anatomy and scanning parameters, with results comparable to or better than both IWLLS and MLE. Further, we demonstrate that a single dtiRIM model can be used for a diversity of data sets without significant loss in quality, representing, to our knowledge, the first generalisable deep learning based solver for DTI.

Physical and digital phantoms for validating tractography and assessing artifacts

Fiber tractography is widely used to non-invasively map white-matter bundles in vivo using diffusion-weighted magnetic resonance imaging (dMRI). As it is the case for all scientific methods, proper validation is a key prerequisite for the successful application of fiber tractography, be it in the area of basic neuroscience or in a clinical setting. It is well-known that the indirect estimation of the fiber tracts from the local diffusion signal is highly ambiguous and extremely challenging. Furthermore, the validation of fiber tractography methods is hampered by the lack of a real ground truth, which is caused by the extremely complex brain microstructure that is not directly observable non-invasively and that is the basis of the huge network of long-range fiber connections in the brain that are the actual target of fiber tractography methods. As a substitute for in vivo data with a real ground truth that could be used for validation, a widely and successfully employed approach is the use of synthetic phantoms. In this work, we are providing an overview of the state-of-the-art in the area of physical and digital phantoms, answering the following guiding questions: "What are dMRI phantoms and what are they good for?", "What would the ideal phantom for validation fiber tractography look like?" and "What phantoms, phantom datasets and tools used for their creation are available to the research community?". We will further discuss the limitations and opportunities that come with the use of dMRI phantoms, and what future direction this field of research might take.

The diffusion-simulated connectivity (DiSCo) dataset

The methodological development in the mapping of the brain structural connectome from diffusion-weighted magnetic resonance imaging (DW-MRI) has raised many hopes in the neuroscientific community. Indeed, the knowledge of the connections between different brain regions is fundamental to study brain anatomy and function. The reliability of the structural connectome is therefore of paramount importance. In the search for accuracy, researchers have given particular attention to linking white matter tractography methods – used for estimating the connectome – with information about the microstructure of the nervous tissue. The creation and validation of methods in this context were hampered by a lack of practical numerical phantoms. To achieve this, we created a numerical phantom that mimics complex anatomical fibre pathway trajectories while also accounting for microstructural features such as axonal diameter distribution, myelin presence, and variable packing densities. The substrate has a micrometric resolution and an unprecedented size of 1 cubic millimetre to mimic an image acquisition matrix of 40×40×40 voxels. DW-MRI images were obtained from Monte Carlo simulations of spin dynamics to enable the validation of quantitative tractography. The phantom is composed of 12,196 synthetic tubular fibres with diameters ranging from 1.4 µm to 4.2 µm, interconnecting sixteen regions of interest. The simulated images capture the microscopic properties of the tissue (e.g. fibre diameter, water diffusing within and around fibres, free water compartment), while also having desirable macroscopic properties resembling the anatomy, such as the smoothness of the fibre trajectories. While previous phantoms were used to validate either tractography or microstructure, this phantom can enable a better assessment of the connectome estimation’s reliability on the one side, and its adherence to the actual microstructure of the nervous tissue on the other.

Learning to estimate the fiber orientation distribution function from diffusion-weighted MRI

Estimation of white matter fiber orientation distribution function (fODF) is the essential first step for reliable brain tractography and connectivity analysis. Most of the existing fODF estimation methods rely on sub-optimal physical models of the diffusion signal or mathematical simplifications, which can impact the estimation accuracy. In this paper, we propose a data-driven method that avoids some of these pitfalls. Our proposed method is based on a multilayer perceptron that learns to map the diffusion-weighted measurements, interpolated onto a fixed spherical grid in the q space, to the target fODF. Importantly, we also propose methods for synthesizing reliable simulated training data. We show that the model can be effectively trained with simulated or real training data. Our phantom experiments show that the proposed method results in more accurate fODF estimation and tractography than several competing methods including the multi-tensor model, Bayesian estimation, spherical deconvolution, and two other machine learning techniques. On real data, we compare our method with other techniques in terms of accuracy of estimating the ground-truth fODF. The results show that our method is more accurate than other methods, and that it performs better than the competing methods when applied to under-sampled diffusion measurements. We also compare our method with the Sparse Fascicle Model in terms of expert ratings of the accuracy of reconstruction of several commissural, projection, association, and cerebellar tracts. The results show that the tracts reconstructed with the proposed method are rated significantly higher by three independent experts. Our study demonstrates the potential of data-driven methods for improving the accuracy and robustness of fODF estimation.

Validating pore size estimates in a complex microfiber environment on a human MRI system

PURPOSE

Recent advances in diffusion-weighted MRI provide "restricted diffusion signal fraction" and restricting pore size estimates. Materials based on co-electrospun oriented hollow cylinders have been introduced to provide validation for such methods. This study extends this work, exploring accuracy and repeatability using an extended acquisition on a 300 mT/m gradient human MRI scanner, in substrates closely mimicking tissue, that is, non-circular cross-sections, intra-voxel fiber crossing, intra-voxel distributions of pore-sizes, and smaller pore-sizes overall.

METHODS

In a single-blind experiment, diffusion-weighted data were collected from a biomimetic phantom on a 3T Connectom system using multiple gradient directions/diffusion times. Repeated scans established short-term and long-term repeatability. The total scan time (54 min) matched similar protocols used in human studies. The number of distinct fiber populations was estimated using spherical deconvolution, and median pore size estimated through the combination of CHARMED and AxCaliber3D framework. Diffusion-based estimates were compared with measurements derived from scanning electron microscopy.

RESULTS

The phantom contained substrates with different orientations, fiber configurations, and pore size distributions. Irrespective of one or two populations within the voxel, the pore-size estimates (~5 μm) and orientation-estimates showed excellent agreement with the median values of pore-size derived from scanning electron microscope and phantom configuration. Measurement repeatability depended on substrate complexity, with lower values seen in samples containing crossing-fibers. Sample-level repeatability was found to be good.

CONCLUSION

While no phantom mimics tissue completely, this study takes a step closer to validating diffusion microstructure measurements for use in vivo by demonstrating the ability to quantify microgeometry in relatively complex configurations.

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

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

ConFiG: Contextual Fibre Growth to generate realistic axonal packing for diffusion MRI simulation

This paper presents Contextual Fibre Growth (ConFiG), an approach to generate white matter numerical phantoms by mimicking natural fibre genesis. ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. Signals simulated from ConFiG phantoms match real diffusion MRI data well, showing that ConFiG phantoms can be used to generate realistic diffusion MRI data. This demonstrates the feasibility of ConFiG to generate realistic synthetic diffusion MRI data for developing and validating microstructure modelling approaches.

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We present ConFiG, a biologically motivated numerical phantom generator for white matter.

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ConFiG produces phantoms with state-of-the-art density and realistic microstructure.

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Diffusion MRI simulations in ConFiG phantoms are comparable to real dMRI signals.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Denoising high angular resolution diffusion imaging data by combining singular value decomposition and non-local means filter

BACKGROUND

High angular resolution diffusion imaging (HARDI) data is typically corrupted with Rician noise. Although larger b-values help to retrieve more accurate angular diffusivity information, they also lead to an increase in noise generation.

NEW METHOD

In order to sufficiently reduce noise in HARDI images and improve the construction of orientation distribution function (ODF) fields, a novel denoising method was developed in this study by combining the singular value decomposition (SVD) and non-local means (NLM) filter. Similar 3D patches were first recruited into a matrix from a search volume. HARDI signals in the matrix were then re-estimated using the SVD low rank approximation, and a NLM filter was employed to filter out any residual noise.

RESULTS

The performance of the proposed method was evaluated against the state-of-the-art denoising methods based on both synthetic and real HARDI datasets. Results demonstrated the superior performance of the developed SVD-NLM method in denoising HARDI data through preserving fine angular structural details and estimating diffusion orientations from improved ODF fields.

CONCLUSION

The proposed SVD-NLM method can improve HARDI quantitative computations, such as MRI brain tissue segmentation and diffusion profile estimation, that rely on the quality of imaging data.

Limits to anatomical accuracy of diffusion tractography using modern approaches

Diffusion MRI fiber tractography is widely used to probe the structural connectivity of the brain, with a range of applications in both clinical and basic neuroscience. Despite widespread use, tractography has well-known pitfalls that limits the anatomical accuracy of this technique. Numerous modern methods have been developed to address these shortcomings through advances in acquisition, modeling, and computation. To test whether these advances improve tractography accuracy, we organized the 3-D Validation of Tractography with Experimental MRI (3D-VoTEM) challenge at the ISBI 2018 conference. We made available three unique independent tractography validation datasets - a physical phantom and two ex vivo brain specimens - resulting in 176 distinct submissions from 9 research groups. By comparing results over a wide range of fiber complexities and algorithmic strategies, this challenge provides a more comprehensive assessment of tractography's inherent limitations than has been reported previously. The central results were consistent across all sub-challenges in that, despite advances in tractography methods, the anatomical accuracy of tractography has not dramatically improved in recent years. Taken together, our results independently confirm findings from decades of tractography validation studies, demonstrate inherent limitations in reconstructing white matter pathways using diffusion MRI data alone, and highlight the need for alternative or combinatorial strategies to accurately map the fiber pathways of the brain.

Mapping connectomes with diffusion MRI: deterministic or probabilistic tractography?

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Optimal Paths for Variants of the 2D and 3D Reeds-Shepp Car with Applications in Image Analysis

We present a PDE-based approach for finding optimal paths for the Reeds-Shepp car. In our model we minimize a (data-driven) functional involving both curvature and length penalization, with several generalizations. Our approach encompasses the two- and three-dimensional variants of this model, state-dependent costs, and moreover, the possibility of removing the reverse gear of the vehicle. We prove both global and local controllability results of the models. Via eikonal equations on the manifoldR d × S d - 1 we compute distance maps w.r.t. highly anisotropic Finsler metrics, which approximate the singular (quasi)-distances underlying the model. This is achieved using a fast-marching (FM) method, building on Mirebeau (Numer Math 126(3):515-557, 2013; SIAM J Numer Anal 52(4):1573-1599, 2014). The FM method is based on specific discretization stencils which are adapted to the preferred directions of the Finsler metric and obey a generalized acuteness property. The shortest paths can be found with a gradient descent method on the distance map, which we formalize in a theorem. We justify the use of our approximating metrics by proving convergence results. Our curve optimization model inR d × S d - 1 with data-driven cost allows to extract complex tubular structures from medical images, e.g., crossings, and incomplete data due to occlusions or low contrast. Our work extends the results of Sanguinetti et al. (Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications LNCS 9423, 2015) on numerical sub-Riemannian eikonal equations and the Reeds-Shepp car to 3D, with comparisons to exact solutions by Duits et al. (J Dyn Control Syst 22(4):771-805, 2016). Numerical experiments show the high potential of our method in two applications: vessel tracking in retinal images for the case d = 2 and brain connectivity measures from diffusion-weighted MRI data for the case d = 3 , extending the work of Bekkers et al. (SIAM J Imaging Sci 8(4):2740-2770, 2015). We demonstrate how the new model without reverse gear better handles bifurcations.

Validation of diffusion MRI estimates of compartment size and volume fraction in a biomimetic brain phantom using a human MRI scanner with 300 mT/m maximum gradient strength

Diffusion microstructural imaging techniques have attracted great interest in the last decade due to their ability to quantify axon diameter and volume fraction in healthy and diseased human white matter. The estimates of compartment size and volume fraction continue to be debated, in part due to the lack of a gold standard for validation and quality control. In this work, we validate diffusion MRI estimates of compartment size and volume fraction using a novel textile axon ("taxon") phantom constructed from hollow polypropylene yarns with distinct intra- and extra-taxonal compartments to mimic white matter in the brain. We acquired a comprehensive set of diffusion MRI measurements in the phantom using multiple gradient directions, diffusion times and gradient strengths on a human MRI scanner equipped with maximum gradient strength (G_max) of 300 mT/m. We obtained estimates of compartment size and restricted volume fraction through a straightforward extension of the AxCaliber/ActiveAx frameworks that enables estimation of mean compartment size in fiber bundles of arbitrary orientation. The voxel-wise taxon diameter estimates of 12.2 ± 0.9 μm were close to the manufactured inner diameter of 11.8 ± 1.2 μm with G_max = 300 mT/m. The estimated restricted volume fraction demonstrated an expected decrease along the length of the fiber bundles in accordance with the known construction of the phantom. When G_max was restricted to 80 mT/m, the taxon diameter was overestimated, and the estimates for taxon diameter and packing density showed greater uncertainty compared to data with G_max = 300 mT/m. In conclusion, the compartment size and volume fraction estimates resulting from diffusion measurements on a human scanner were validated against ground truth in a phantom mimicking human white matter, providing confidence that this method can yield accurate estimates of parameters in simplified but realistic microstructural environments. Our work also demonstrates the importance of a biologically analogous phantom that can be applied to validate a variety of diffusion microstructural imaging methods in human scanners and be used for standardization of diffusion MRI protocols for neuroimaging research.

The challenge of mapping the human connectome based on diffusion tractography

Tractography based on non-invasive diffusion imaging is central to the study of human brain connectivity. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain data set with ground truth tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. Here, we report the encouraging finding that most state-of-the-art algorithms produce tractograms containing 90% of the ground truth bundles (to at least some extent). However, the same tractograms contain many more invalid than valid bundles, and half of these invalid bundles occur systematically across research groups. Taken together, our results demonstrate and confirm fundamental ambiguities inherent in tract reconstruction based on orientation information alone, which need to be considered when interpreting tractography and connectivity results. Our approach provides a novel framework for estimating reliability of tractography and encourages innovation to address its current limitations.

Though tractography is widely used, it has not been systematically validated. Here, authors report results from 20 groups showing that many tractography algorithms produce both valid and invalid bundles.

3D-SSF: A bio-inspired approach for dynamic multi-subject clustering of white matter tracts

There is growing interest in the study of white matter (WM) variation across subjects, and in particular the analysis of specific WM bundles, to better understand brain development and aging, as well as to improve early detection of some diseases. Several WM multi-subject clustering methods have been proposed to study WM bundles. These methods aim to overcome the complexity of the problem, which includes the huge size of the WM tractography datasets generated from multiple subjects, the existence of various streamlines with different positions, lengths and geometric forms, as well as the presence of outliers. However, the current methods are not sufficiently flexible to address all of these constraints. Here we introduce a novel dynamic multi-subject clustering framework based on a distributed multiagent implementation of the Multiple Species Flocking model, that we name 3D-Streamlines Stream Flocking (3D-SSF). Specifically, we consider streamlines from different subjects as data streams, and each streamline is assigned to a mobile agent. Agents work together following flocking rules in order to form a flock. Thanks to a similarity function, the agents that are associated with similar streamlines form a flock, whereas the agents that are associated with dissimilar streamlines are considered outliers. We use various experiments performed on noisy synthetic and real human brain data to validate 3D-SSF and demonstrate that it is more efficient and robust to outliers compared to other classical approaches. 3D-SSF is able to extract WM bundles at a population level, while considering WM variation across subjects and eliminating outlier streamlines.

Hollow Polypropylene Yarns as a Biomimetic Brain Phantom for the Validation of High-Definition Fiber Tractography Imaging

Current brain imaging methods largely fail to provide detailed information about the location and severity of axonal injuries and do not anticipate recovery of the patients with traumatic brain injury. High-definition fiber tractography appears as a novel imaging modality based on water motion in the brain that allows for direct visualization and quantification of the degree of axons damage, thus predicting the functional deficits due to traumatic axonal injury and loss of cortical projections. This neuroimaging modality still faces major challenges because it lacks a "gold standard" for the technique validation and respective quality control. The present work aims to study the potential of hollow polypropylene yarns to mimic human white matter axons and construct a brain phantom for the calibration and validation of brain diffusion techniques based on magnetic resonance imaging, including high-definition fiber tractography imaging. Hollow multifilament polypropylene yarns were produced by melt-spinning process and characterized in terms of their physicochemical properties. Scanning electronic microscopy images of the filaments cross section has shown an inner diameter of approximately 12 μm, confirming their appropriateness to mimic the brain axons. The chemical purity of polypropylene yarns as well as the interaction between the water and the filament surface, important properties for predicting water behavior and diffusion inside the yarns, were also evaluated. Restricted and hindered water diffusion was confirmed by fluorescence microscopy. Finally, the yarns were magnetic resonance imaging scanned and analyzed using high-definition fiber tractography, revealing an excellent choice of these hollow polypropylene structures for simulation of the white matter brain axons and their suitability for constructing an accurate brain phantom.

Fiber tracking: A qualitative and quantitative comparison between four different software tools on the reconstruction of major white matter tracts

PURPOSE

Diffusion tensor imaging (DTI) enables in vivo reconstruction of white matter (WM) pathways. Considering the emergence of numerous models and fiber tracking techniques, we herein aimed to compare, both quantitatively and qualitatively, the fiber tracking results of four DTI software (Brainance, Philips FiberTrak, DSI Studio, NordicICE) on the reconstruction of representative WM tracts.

MATERIALS AND METHODS

Ten healthy participants underwent 30-directional diffusion tensor imaging on a 3T-Philips Achieva TX MR-scanner. All data were analyzed by two independent sites of experienced raters with the aforementioned software and the following WM tracts were reconstructed: corticospinal tract (CST); forceps major (Fmajor); forceps minor (Fminor); cingulum bundle (CB); superior longitudinal fasciculus (SLF); inferior fronto-occipital fasciculus (IFOF). Visual inspection of the resulted tracts and statistical analysis (inter-rater and betweensoftware agreement; paired t-test) on fractional anisotropy (FA), axial and radial diffusivity (Daxial, Dradial) were applied for qualitative and quantitative evaluation of DTI software results.

RESULTS

Qualitative evaluation of the extracted tracts confirmed anatomical landmarks at least for the core part of each tract, even though differences in the number of fibers extracted and the whole tract were evident, especially for the CST, Fmajor, Fminor and SLF. Descriptive values did not deviate from the expected range of values for healthy adult population. Substantial inter-rater agreement (intraclass correlation coefficient [ICC], Bland-Altman analysis) was found for all tracts (ICC; FA: 0.839-0.989, Daxial: 0.704-0.991, Dradial: 0.972-0.993). Low agreement for FA, Daxial and Dradial (ICC; Bland-Altman analysis) and significant paired t-test differences (p < 0.05) were detected regarding between-software agreement.

CONCLUSIONS

Qualitative comparison of four different DTI software in addition to substantial inter-rater but poor between-software agreement highlight the differences on existing fiber tracking methodologies and several particularities of each WM tract, further supporting the need for further study in both clinical and research settings.

D-BRAIN: Anatomically Accurate Simulated Diffusion MRI Brain Data

Diffusion Weighted (DW) MRI allows for the non-invasive study of water diffusion inside living tissues. As such, it is useful for the investigation of human brain white matter (WM) connectivity in vivo through fiber tractography (FT) algorithms. Many DW-MRI tailored restoration techniques and FT algorithms have been developed. However, it is not clear how accurately these methods reproduce the WM bundle characteristics in real-world conditions, such as in the presence of noise, partial volume effect, and a limited spatial and angular resolution. The difficulty lies in the lack of a realistic brain phantom on the one hand, and a sufficiently accurate way of modeling the acquisition-related degradation on the other. This paper proposes a software phantom that approximates a human brain to a high degree of realism and that can incorporate complex brain-like structural features. We refer to it as a Diffusion BRAIN (D-BRAIN) phantom. Also, we propose an accurate model of a (DW) MRI acquisition protocol to allow for validation of methods in realistic conditions with data imperfections. The phantom model simulates anatomical and diffusion properties for multiple brain tissue components, and can serve as a ground-truth to evaluate FT algorithms, among others. The simulation of the acquisition process allows one to include noise, partial volume effects, and limited spatial and angular resolution in the images. In this way, the effect of image artifacts on, for instance, fiber tractography can be investigated with great detail. The proposed framework enables reliable and quantitative evaluation of DW-MR image processing and FT algorithms at the level of large-scale WM structures. The effect of noise levels and other data characteristics on cortico-cortical connectivity and tractography-based grey matter parcellation can be investigated as well.

Ensemble Tractography

Tractography uses diffusion MRI to estimate the trajectory and cortical projection zones of white matter fascicles in the living human brain. There are many different tractography algorithms and each requires the user to set several parameters, such as curvature threshold. Choosing a single algorithm with specific parameters poses two challenges. First, different algorithms and parameter values produce different results. Second, the optimal choice of algorithm and parameter value may differ between different white matter regions or different fascicles, subjects, and acquisition parameters. We propose using ensemble methods to reduce algorithm and parameter dependencies. To do so we separate the processes of fascicle generation and evaluation. Specifically, we analyze the value of creating optimized connectomes by systematically combining candidate streamlines from an ensemble of algorithms (deterministic and probabilistic) and systematically varying parameters (curvature and stopping criterion). The ensemble approach leads to optimized connectomes that provide better cross-validated prediction error of the diffusion MRI data than optimized connectomes generated using a single-algorithm or parameter set. Furthermore, the ensemble approach produces connectomes that contain both short- and long-range fascicles, whereas single-parameter connectomes are biased towards one or the other. In summary, a systematic ensemble tractography approach can produce connectomes that are superior to standard single parameter estimates both for predicting the diffusion measurements and estimating white matter fascicles.

Diffusion MRI and tractography opened a new avenue for studying white matter fascicles and their tissue properties in the living human brain. There are many different tractography methods, and each requires the user to set several parameters. A limitation of tractography is that the results depend on the selection of algorithms and parameters. Here, we analyze an ensemble method, Ensemble Tractography (ET), that reduces the effect of algorithm and parameter selection. ET creates a large set of candidate streamlines using an ensemble of algorithms and parameter values and then selects the streamlines with strong support from the data using a global fascicle evaluation method. Compared to single parameter connectomes, ET connectomes predict diffusion MRI signals better and cover a wider range of white matter volume. Importantly, ET connectomes include both short- and long-association fascicles, which are not typically found together in single-parameter connectomes.

Strengths and weaknesses of state of the art fiber tractography pipelines--A comprehensive in-vivo and phantom evaluation study using Tractometer

Many different tractography approaches and corresponding isolated evaluation attempts have been presented over the last years, but a comparative and quantitative evaluation of tractography algorithms still remains a challenge, particularly in-vivo. The recently presented evaluation framework Tractometer is the first attempt to approach this challenge in a quantitative, comparative, persistent and open-access way. Tractometer is currently based on the evaluation of several global connectivity and tract-overlap metrics on hardware phantom data. The work presented in this paper focuses on extending Tractometer with a metric that enables the assessment of the local consistency of tractograms with the underlying image data that is not only applicable to phantom dataset but allows the quantitative and purely data-driven evaluation of in-vivo tractography. We furthermore present an extensive reference-based evaluation study of 25,000 tractograms obtained on phantom and in-vivo datasets using the presented local metric as well as all the methods already established in Tractometer. The experiments showed that the presented local metric successfully reflects the behavior of in-vivo tractography under different conditions and that it is consistent with the results of previous studies. Additionally our experiments enabled a multitude of conclusions with implications for fiber tractography in general, including recommendations regarding optimal choice of a local modeling technique, tractography algorithm, and parameterization, confirming and complementing the results of earlier studies.

Realistic simulation of artefacts in diffusion MRI for validating post-processing correction techniques

In this paper we demonstrate a simulation framework that enables the direct and quantitative comparison of post-processing methods for diffusion weighted magnetic resonance (DW-MR) images. DW-MR datasets are employed in a range of techniques that enable estimates of local microstructure and global connectivity in the brain. These techniques require full alignment of images across the dataset, but this is rarely the case. Artefacts such as eddy-current (EC) distortion and motion lead to misalignment between images, which compromise the quality of the microstructural measures obtained from them. Numerous methods and software packages exist to correct these artefacts, some of which have become de-facto standards, but none have been subject to rigorous validation. In the literature, improved alignment is assessed using either qualitative visual measures or quantitative surrogate metrics. Here we introduce a simulation framework that allows for the direct, quantitative assessment of techniques, enabling objective comparisons of existing and future methods. DW-MR datasets are generated using a process that is based on the physics of MRI acquisition, which allows for the salient features of the images and their artefacts to be reproduced. We apply this framework in three ways. Firstly we assess the most commonly used method for artefact correction, FSL's eddy_correct, and compare it to a recently proposed alternative, eddy. We demonstrate quantitatively that using eddy_correct leads to significant errors in the corrected data, whilst eddy is able to provide much improved correction. Secondly we investigate the datasets required to achieve good correction with eddy, by looking at the minimum number of directions required and comparing the recommended full-sphere acquisitions to equivalent half-sphere protocols. Finally, we investigate the impact of correction quality by examining the fits from microstructure models to real and simulated data.

Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. In the first method we use the enhancement PDE for contextual regularization of a fiber orientation distribution (FOD) that is obtained on individual voxels from high angular resolution diffusion imaging (HARDI) data via constrained spherical deconvolution (CSD). Thereby we improve the FOD as input for subsequent tractography. Secondly, we introduce the fiber to bundle coherence (FBC), a measure for quantification of fiber alignment. The FBC is computed from a tractography result using the same PDE framework and provides a criterion for removing the spurious fibers. We validate the proposed combination of CSD and enhancement on phantom data and on human data, acquired with different scanning protocols. On the phantom data we find that PDE enhancements improve both local metrics and global metrics of tractography results, compared to CSD without enhancements. On the human data we show that the enhancements allow for a better reconstruction of crossing fiber bundles and they reduce the variability of the tractography output with respect to the acquisition parameters. Finally, we show that both the enhancement of the FODs and the use of the FBC measure on the tractography improve the stability with respect to different stochastic realizations of probabilistic tractography. This is shown in a clinical application: the reconstruction of the optic radiation for epilepsy surgery planning.

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.

Automated multi-subject fiber clustering of mouse brain using dominant sets

Mapping of structural and functional connectivity may provide deeper understanding of brain function and disfunction. Diffusion Magnetic Resonance Imaging (DMRI) is a powerful technique to non-invasively delineate white matter (WM) tracts and to obtain a three-dimensional description of the structural architecture of the brain. However, DMRI tractography methods produce highly multi-dimensional datasets whose interpretation requires advanced analytical tools. Indeed, manual identification of specific neuroanatomical tracts based on prior anatomical knowledge is time-consuming and prone to operator-induced bias. Here we propose an automatic multi-subject fiber clustering method that enables retrieval of group-wise WM fiber bundles. In order to account for variance across subjects, we developed a multi-subject approach based on a method known as Dominant Sets algorithm, via an intra- and cross-subject clustering. The intra-subject step allows us to reduce the complexity of the raw tractography data, thus obtaining homogeneous neuroanatomically-plausible bundles in each diffusion space. The cross-subject step, characterized by a proper space-invariant metric in the original diffusion space, enables the identification of the same WM bundles across multiple subjects without any prior neuroanatomical knowledge. Quantitative analysis was conducted comparing our algorithm with spectral clustering and affinity propagation methods on synthetic dataset. We also performed qualitative analysis on mouse brain tractography retrieving significant WM structures. The approach serves the final goal of detecting WM bundles at a population level, thus paving the way to the study of the WM organization across groups.

Biomimetic phantom for the validation of diffusion magnetic resonance imaging

PURPOSE

A range of advanced diffusion MRI (dMRI) techniques are currently in development which characterize the orientation of white matter fibers using diffusion tensor imaging (DTI). There is a need for a physical phantom with microstructural features of the brain's white matter to help validate these methods.

METHODS

Hollow, co-electrospun, aligned fibers with a tuneable size distribution have been produced in bulk and with an MR visible solvent infused into the pores. The morphology and size of the phantoms was assessed using scanning electron microscopy (SEM) and compared with DTI results obtained on both a clinical and preclinical scanner.

RESULTS

By varying inner diameter of the phantom fibers (from SEM: 9.5 μm, 11.9 μm, 13.4 μm) the radial diffusivity and fractional anisotropy, calculated from DTI, vary between 0.38 ± 0.05 × 10(3) and 0.61 ± 0.06 × 10(3) cm s(-1) and between 0.45 ± 0.05 and 0.33 ± 0.04, respectively.

CONCLUSION

We envisage that these materials will be used for the validation of novel and established methods within the field of diffusion MRI, as well as for routine quality assurance purposes and for establishing scanner performance in multicenter trials.

Evaluation and statistical inference for human connectomes

Diffusion-weighted imaging coupled with tractography is the only method for in vivo mapping of human white-matter fascicles. Tractography takes diffusion measurements as input and produces a large collection of white-matter fascicles as output; the connectome. We introduce a method to evaluate the evidence supporting connectomes. Linear Fascicle Evaluation (LiFE) takes any connectome as input and predicts diffusion measurements as output, using the difference between the measured and predicted diffusion signals to measure prediction error. Finally, we introduce two metrics that use the prediction error to evaluate the evidence supporting properties of the connectome. One metric compares the mean prediction error between alternative hypotheses, and the second metric compares full distributions of prediction error. We use these metrics to (1) compare tractography algorithms, and (2) test hypotheses about tracts and connections.

A flocking based method for brain tractography

We propose a new method to estimate axonal fiber pathways from Multiple Intra-Voxel Diffusion Orientations. Our method uses the multiple local orientation information for leading stochastic walks of particles. These stochastic particles are modeled with mass and thus they are subject to gravitational and inertial forces. As result, we obtain smooth, filtered and compact trajectory bundles. This gravitational interaction can be seen as a flocking behavior among particles that promotes better and robust axon fiber estimations because they use collective information to move. However, the stochastic walks may generate paths with low support (outliers), generally associated to incorrect brain connections. In order to eliminate the outlier pathways, we propose a filtering procedure based on principal component analysis and spectral clustering. The performance of the proposal is evaluated on Multiple Intra-Voxel Diffusion Orientations from two realistic numeric diffusion phantoms and a physical diffusion phantom. Additionally, we qualitatively demonstrate the performance on in vivo human brain data.

Diffusion tensor MRI phantom exhibits anomalous diffusion

This paper reports diffusion weighted MRI measurements of cyclohexane in a novel diffusion tensor MRI phantom composed of hollow coaxial electrospun fibers (average diameter 10.2 μm). Recent studies of the phantom demonstrated its potential as a calibration standard at low b values (less than 1000 s/mm<;sup>2<;/sup>) for mean diffusivity and fractional anisotropy. In this paper, we extend the characterization of cyclohexane diffusion in this heterogeneous, anisotropic material to high b values (up to 5000 s/mm<;sup>2<;/sup>), where the apparent diffusive motion of the cyclohexane exhibits anomalous behavior (i.e., the molecular mean squared displacement increases with time raised to the fractional power 2α/β). Diffusion tensor MRI was performed at 9.4 T using an Agilent imaging scanner and the data fit to a fractional order Mittag-Leffler (generalized exponential) decay model. Diffusion along the fibers was found to be Gaussian (2α/β=l), while diffusion across the fibers was sub-diffusive (2α/β<;l). Fiber tract reconstruction of the data was consistent with scanning electron micrograph images of the material. These studies suggest that this phantom material may be used to calibrate MR systems in both the normal (Gaussian) and anomalous diffusion regimes.

Fiberfox: facilitating the creation of realistic white matter software phantoms

PURPOSE

Phantom-based validation of diffusion-weighted image processing techniques is an important key to innovation in the field and is widely used. Openly available and user friendly tools for the flexible generation of tailor-made datasets for the specific tasks at hand can greatly facilitate the work of researchers around the world.

METHODS

We present an open-source framework, Fiberfox, that enables (1) the intuitive definition of arbitrary artificial white matter fiber tracts, (2) signal generation from those fibers by means of the most recent multi-compartment modeling techniques, and (3) simulation of the actual MR acquisition that allows for the introduction of realistic MRI-related effects into the final image.

RESULTS

We show that real acquisitions can be closely approximated by simulating the acquisition of the well-known FiberCup phantom. We further demonstrate the advantages of our framework by evaluating the effects of imaging artifacts and acquisition settings on the outcome of 12 tractography algorithms.

CONCLUSION

Our findings suggest that experiments on a realistic software phantom might change the conclusions drawn from earlier hardware phantom experiments. Fiberfox may find application in validating and further developing methods such as tractography, super-resolution, diffusion modeling or artifact correction.

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

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

Diffusion weighted image denoising using overcomplete local PCA

Diffusion Weighted Images (DWI) normally shows a low Signal to Noise Ratio (SNR) due to the presence of noise from the measurement process that complicates and biases the estimation of quantitative diffusion parameters. In this paper, a new denoising methodology is proposed that takes into consideration the multicomponent nature of multi-directional DWI datasets such as those employed in diffusion imaging. This new filter reduces random noise in multicomponent DWI by locally shrinking less significant Principal Components using an overcomplete approach. The proposed method is compared with state-of-the-art methods using synthetic and real clinical MR images, showing improved performance in terms of denoising quality and estimation of diffusion parameters.

Characterization of cerebral white matter properties using quantitative magnetic resonance imaging stains

The image contrast in magnetic resonance imaging (MRI) is highly sensitive to several mechanisms that are modulated by the properties of the tissue environment. The degree and type of contrast weighting may be viewed as image filters that accentuate specific tissue properties. Maps of quantitative measures of these mechanisms, akin to microstructural/environmental-specific tissue stains, may be generated to characterize the MRI and physiological properties of biological tissues. In this article, three quantitative MRI (qMRI) methods for characterizing white matter (WM) microstructural properties are reviewed. All of these measures measure complementary aspects of how water interacts with the tissue environment. Diffusion MRI, including diffusion tensor imaging, characterizes the diffusion of water in the tissues and is sensitive to the microstructural density, spacing, and orientational organization of tissue membranes, including myelin. Magnetization transfer imaging characterizes the amount and degree of magnetization exchange between free water and macromolecules like proteins found in the myelin bilayers. Relaxometry measures the MRI relaxation constants T1 and T2, which in WM have a component associated with the water trapped in the myelin bilayers. The conduction of signals between distant brain regions occurs primarily through myelinated WM tracts; thus, these methods are potential indicators of pathology and structural connectivity in the brain. This article provides an overview of the qMRI stain mechanisms, acquisition and analysis strategies, and applications for these qMRI stains.

NEURONAL WHITE MATTER PARCELLATION USING SPATIALLY COHERENT NORMALIZED CUTS

This work presents an automated method for partitioning neuronal white matter (WM) into regions of interest with uniform WM architecture. These regions can then be used to replace atlas-derived regions for any subsequent statistical analysis. The fiber orientation distribution function is used as a model of WM architecture resulting in a voxel similarity function sensitive to both fiber orientations and configurations. The method utilizes the normalized cuts algorithm to partition WM voxels based on this similarity function along with a connected component labeling algorithm to ensure spatial compactness. We illustrate the algorithms ability to discern regions based on both orientation and complexity through its application to a simulated fiber crossing and an in-vivo dataset.

Modeling diffusion-weighted MRI as a spatially variant gaussian mixture: application to image denoising

PURPOSE

This work describes a spatially variant mixture model constrained by a Markov random field to model high angular resolution diffusion imaging (HARDI) data. Mixture models suit HARDI well because the attenuation by diffusion is inherently a mixture. The goal is to create a general model that can be used in different applications. This study focuses on image denoising and segmentation (primarily the former).

METHODS

HARDI signal attenuation data are used to train a Gaussian mixture model in which the mean vectors and covariance matrices are assumed to be independent of spatial locations, whereas the mixture weights are allowed to vary at different lattice positions. Spatial smoothness of the data is ensured by imposing a Markov random field prior on the mixture weights. The model is trained in an unsupervised fashion using the expectation maximization algorithm. The number of mixture components is determined using the minimum message length criterion from information theory. Once the model has been trained, it can be fitted to a noisy diffusion MRI volume by maximizing the posterior probability of the underlying noiseless data in a Bayesian framework, recovering a denoised version of the image. Moreover, the fitted probability maps of the mixture components can be used as features for posterior image segmentation.

RESULTS

The model-based denoising algorithm proposed here was compared on real data with three other approaches that are commonly used in the literature: Gaussian filtering, anisotropic diffusion, and Rician-adapted nonlocal means. The comparison shows that, at low signal-to-noise ratio, when these methods falter, our algorithm considerably outperforms them. When tractography is performed on the model-fitted data rather than on the noisy measurements, the quality of the output improves substantially. Finally, ventricle and caudate nucleus segmentation experiments also show the potential usefulness of the mixture probability maps for classification tasks.

CONCLUSIONS

The presented spatially variant mixture model for diffusion MRI provides excellent denoising results at low signal-to-noise ratios. This makes it possible to restore data acquired with a fast (i.e., noisy) pulse sequence to acceptable noise levels. This is the case in diffusion MRI, where a large number of diffusion-weighted volumes have to be acquired under clinical time constraints.

Novel spherical phantoms for Q-ball imaging under in vivo conditions

For the validation of complex diffusion imaging techniques like q-ball imaging that aim to resolve multiple fiber directions, appropriate phantoms are highly desirable. However, previous q-ball imaging phantoms had diffusion anisotropies well below those of in vivo white matter. In this work, fiber phantoms of well-defined geometry are presented. The fibers are wound on a spherical spindle yielding high packing densities and consequently high diffusion anisotropies (fractional anisotropy 0.93 ± 0.02 at b = 500 s/mm(2)). Phantoms with 90° and 45° crossing angle were constructed both with two crossing types. In the "stacked" crossing, two fiber strings were wound consecutively to simulate two touching fibers, in the "interleaved" crossing, fibers were wound alternately. The stacked crossing allows the alteration of partial volumes, whereas the interleaved crossing provides constant partial volumes, allowing e.g. the easy alteration of the SNR by varying the slice thickness. Exemplary q-ball imaging validation measurements using different b-values and slice thicknesses are presented.