PopTract: population-based tractography

Orientation Prior and Consistent Model Selection Increase Sensitivity of Tract-Based Spatial Statistics in Crossing-Fiber Regions

The goal of this paper is to increase the statistical power of crossing-fiber statistics in voxelwise analyses of diffusion-weighted magnetic resonance imaging (DW-MRI) data. In the proposed framework, a fiber orientation atlas and a model complexity atlas were used to fit the ball-and-sticks model to diffusion-weighted images of subjects in a prospective population-based cohort study. Reproducibility and sensitivity of the partial volume fractions in the ball-and-sticks model were analyzed using TBSS (tract-based spatial statistics) and compared to a reference framework. The reproducibility was investigated on two scans of 30 subjects acquired with an interval of approximately three weeks by studying the intraclass correlation coefficient (ICC). The sensitivity to true biological effects was evaluated by studying the regression with age on 500 subjects from 65 to 90 years old. Compared to the reference framework, the ICC improved significantly when using the proposed framework. Higher t-statistics indicated that regression coefficients with age could be determined more precisely with the proposed framework and more voxels correlated significantly with age. The application of a fiber orientation atlas and a model complexity atlas can significantly improve the reproducibility and sensitivity of crossing-fiber statistics in TBSS.

Computational neuroanatomy of baby brains: A review

The first postnatal years are an exceptionally dynamic and critical period of structural, functional and connectivity development of the human brain. The increasing availability of non-invasive infant brain MR images provides unprecedented opportunities for accurate and reliable charting of dynamic early brain developmental trajectories in understanding normative and aberrant growth. However, infant brain MR images typically exhibit reduced tissue contrast (especially around 6 months of age), large within-tissue intensity variations, and regionally-heterogeneous, dynamic changes, in comparison with adult brain MR images. Consequently, the existing computational tools developed typically for adult brains are not suitable for infant brain MR image processing. To address these challenges, many infant-tailored computational methods have been proposed for computational neuroanatomy of infant brains. In this review paper, we provide a comprehensive review of the state-of-the-art computational methods for infant brain MRI processing and analysis, which have advanced our understanding of early postnatal brain development. We also summarize publically available infant-dedicated resources, including MRI datasets, computational tools, grand challenges, and brain atlases. Finally, we discuss the limitations in current research and suggest potential future research directions.

Embarrassingly Parallel Acceleration of Global Tractography via Dynamic Domain Partitioning

Global tractography estimates brain connectivity by organizing signal-generating fiber segments in an optimal configuration that best describes the measured diffusion-weighted data, promising better stability than local greedy methods with respect to imaging noise. However, global tractography is computationally very demanding and requires computation times that are often prohibitive for clinical applications. We present here a reformulation of the global tractography algorithm for fast parallel implementation amendable to acceleration using multi-core CPUs and general-purpose GPUs. Our method is motivated by the key observation that each fiber segment is affected by a limited spatial neighborhood. In other words, a fiber segment is influenced only by the fiber segments that are (or can potentially be) connected to its two ends and also by the diffusion-weighted signal in its proximity. This observation makes it possible to parallelize the Markov chain Monte Carlo (MCMC) algorithm used in the global tractography algorithm so that concurrent updating of independent fiber segments can be carried out. Experiments show that the proposed algorithm can significantly speed up global tractography, while at the same time maintain or even improve tractography performance.

Accelerating Global Tractography Using Parallel Markov Chain Monte Carlo

Global tractography estimates brain connectivity by determining the optimal configuration of signal-generating fiber segments that best describes the measured diffusion-weighted data, promising better stability than local greedy methods with respect to imaging noise. However, global tractography is computationally very demanding and requires computation times that are often prohibitive for clinical applications. We present here a reformulation of the global tractography algorithm for fast parallel implementation amendable to acceleration using multi-core CPUs and general-purpose GPUs. Our method is motivated by the key observation that each fiber segment is affected by a limited spatial neighborhood. That is, a fiber segment is influenced only by the fiber segments that are (or can potentially be) connected to its both ends and also by the diffusion-weighted signal in its proximity. This observation makes it possible to parallelize the Markov chain Monte Carlo (MCMC) algorithm used in the global tractography algorithm so that updating of independent fiber segments can be done concurrently. The experiments show that the proposed algorithm can significantly speed up global tractography, while at the same time maintain or improve tractography performance.

Kernel regression estimation of fiber orientation mixtures in diffusion MRI

We present and evaluate a method for kernel regression estimation of fiber orientations and associated volume fractions for diffusion MR tractography and population-based atlas construction in clinical imaging studies of brain white matter. This is a model-based image processing technique in which representative fiber models are estimated from collections of component fiber models in model-valued image data. This extends prior work in nonparametric image processing and multi-compartment processing to provide computational tools for image interpolation, smoothing, and fusion with fiber orientation mixtures. In contrast to related work on multi-compartment processing, this approach is based on directional measures of divergence and includes data-adaptive extensions for model selection and bilateral filtering. This is useful for reconstructing complex anatomical features in clinical datasets analyzed with the ball-and-sticks model, and our framework's data-adaptive extensions are potentially useful for general multi-compartment image processing. We experimentally evaluate our approach with both synthetic data from computational phantoms and in vivo clinical data from human subjects. With synthetic data experiments, we evaluate performance based on errors in fiber orientation, volume fraction, compartment count, and tractography-based connectivity. With in vivo data experiments, we first show improved scan-rescan reproducibility and reliability of quantitative fiber bundle metrics, including mean length, volume, streamline count, and mean volume fraction. We then demonstrate the creation of a multi-fiber tractography atlas from a population of 80 human subjects. In comparison to single tensor atlasing, our multi-fiber atlas shows more complete features of known fiber bundles and includes reconstructions of the lateral projections of the corpus callosum and complex fronto-parietal connections of the superior longitudinal fasciculus I, II, and III.

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.

Anatomy-guided Dense Individualized and Common Connectivity-based Cortical Landmarks (A-DICCCOL)

Establishment of structural and functional correspondences of human brain that can be quantitatively encoded and reproduced across different subjects and populations is one of the key issues in brain mapping. As an attempt to address this challenge, our recently developed Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOL) system reported 358 connectional landmarks, each of which possesses consistent DTI-derived white matter fiber connection pattern that is reproducible in over 240 healthy brains. However, the DICCCOL system can be substantially improved by integrating anatomical and morphological information during landmark initialization and optimization procedures. In this paper, we present a novel anatomy-guided landmark discovery framework that defines and optimizes landmarks via integrating rich anatomical, morphological, and fiber connectional information for landmark initialization, group-wise optimization and prediction, which are formulated and solved as an energy minimization problem. The framework finally determined 555 consistent connectional landmarks. Validation studies demonstrated that the 555 landmarks are reproducible, predictable, and exhibited reasonably accurate anatomical, connectional, and functional correspondences across individuals and populations and thus are named anatomy-guided DICCCOL or A-DICCCOL. This A-DICCCOL system represents common cortical architectures with anatomical, connectional, and functional correspondences across different subjects and would potentially provide opportunities for various applications in brain science.

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S(2). However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S(2). Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions.

Uncertainty estimation in diffusion MRI using the nonlocal bootstrap

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

Large deformation diffeomorphic registration of diffusion-weighted imaging data

Registration plays an important role in group analysis of diffusion-weighted imaging (DWI) data. It can be used to build a reference anatomy for investigating structural variation or tracking changes in white matter. Unlike traditional scalar image registration where spatial alignment is the only focus, registration of DWI data requires both spatial alignment of structures and reorientation of local signal profiles. As such, DWI registration is much more complex and challenging than scalar image registration. Although a variety of algorithms has been proposed to tackle the problem, most of them are restricted by the diffusion model used for registration, making it difficult to fit to the registered data a different model. In this paper we describe a method that allows any diffusion model to be fitted after registration for subsequent multifaceted analysis. This is achieved by directly aligning DWI data using a large deformation diffeomorphic registration framework. Our algorithm seeks the optimal coordinate mapping by simultaneously considering structural alignment, local signal profile reorientation, and deformation regularization. Our algorithm also incorporates a multi-kernel strategy to concurrently register anatomical structures at different scales. We demonstrate the efficacy of our approach using in vivo data and report detailed qualitative and quantitative results in comparison with several different registration strategies.

Group-wise FMRI activation detection on DICCCOL landmarks

Group-wise activation detection in task-based fMRI has been widely used because of its robustness to noises and its capacity to deal with variability of individual brains. However, current group-wise fMRI activation detection methods typically rely on the co-registration of individual brains' fMRI images, which has difficulty in dealing with the remarkable anatomic variation of different brains. As a consequence, the resulted misalignments could significantly degrade the required inter-subject correspondences, thus substantially reducing the sensitivity and specificity of group-wise fMRI activation detection. To deal with these challenges, this paper presents a novel approach to detecting group-wise fMRI activation on our recently developed and validated Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOL). The basic idea here is that the first-level general linear model (GLM) analysis is first performed on the fMRI signal of each corresponding DICCCOL landmark in individual brain's own space, and then the estimated effect sizes of the same landmark from a group of subjects are statistically assessed with the mixed-effect model at the group level. Finally, the consistently activated DICCCOL landmarks are determined and declared in a group-wise fashion in response to external block-based stimuli. Our experimental results have demonstrated that the proposed approach can detect meaningful activations.

Estimating constrained multi-fiber diffusion MR volumes by orientation clustering

Diffusion MRI is a valuable tool for mapping tissue microstructure; however, multi-fiber models present challenges to image analysis operations. In this paper, we present a method for estimating models for such operations by clustering fiber orientations. Our approach is applied to ball-and-stick diffusion models, which include an isotropic tensor and multiple sticks encoding fiber volume and orientation. We consider operations which can be generalized to a weighted combination of fibers and present a method for representing such combinations with a mixture-of-Watsons model, learning its parameters by Expectation Maximization. We evaluate this approach with two experiments. First, we show it is effective for filtering in the presence of synthetic noise. Second, we demonstrate interpolation and averaging by construction of a tractography atlas, showing improved reconstruction of white matter pathways. These experiments indicate that our method is useful in estimating multi-fiber ball-and-stick diffusion volumes resulting from a range of image analysis operations.

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.

Fiber-driven resolution enhancement of diffusion-weighted images

Diffusion-weighted imaging (DWI), while giving rich information about brain circuitry, is often limited by insufficient spatial resolution and low signal-to-noise ratio (SNR). This paper describes an algorithm that will increase the resolution of DW images beyond the scan resolution, allowing for a closer investigation of fiber structures and more accurate assessment of brain connectivity. The algorithm is capable of generating a dense vector-valued field, consisting of diffusion data associated with the full set of diffusion-sensitizing gradients. The fundamental premise is that, to best preserve information, interpolation should always be performed along axonal fibers. To achieve this, at each spatial location, we probe neighboring voxels in various directions to gather diffusion information for data interpolation. Based on the fiber orientation distribution function (ODF), directions that are more likely to be traversed by fibers will be given greater weights during interpolation and vice versa. This ensures that data interpolation is only contributed by diffusion data coming from fibers that are aligned with a specific direction. This approach respects local fiber structures and prevents blurring resulting from averaging of data from significantly misaligned fibers. Evaluations suggest that this algorithm yields results with significantly less blocking artifacts, greater smoothness in anatomical structures, and markedly improved structural visibility.

Spatial transformation of DWI data using non-negative sparse representation

This paper presents an algorithm to transform and reconstruct diffusion-weighted imaging (DWI) data for alignment of micro-structures in association with spatial transformations. The key idea is to decompose the diffusion signal profile, a function defined on a unit sphere, into a series of weighted diffusion basis functions (DBFs), reorient these weighted DBFs independently based on the local affine transformation, and then recompose the reoriented weighted DBFs to obtain the final transformed diffusion signal profile. The decomposition is performed in a sparse representation framework in recognition of the fact that each diffusion signal profile is often resulting from a small number of fiber populations. A non-negative constraint is further imposed so that noise-induced negative lobes in the profile can be avoided. The proposed framework also explicitly models the isotropic component of the diffusion signals to avoid undesirable artifacts during transformation. In contrast to existing methods, the current algorithm allows the transformation to be executed directly in the signal space, thus allowing any diffusion models to be fitted to the data after transformation.

DICCCOL: dense individualized and common connectivity-based cortical landmarks

Is there a common structural and functional cortical architecture that can be quantitatively encoded and precisely reproduced across individuals and populations? This question is still largely unanswered due to the vast complexity, variability, and nonlinearity of the cerebral cortex. Here, we hypothesize that the common cortical architecture can be effectively represented by group-wise consistent structural fiber connections and take a novel data-driven approach to explore the cortical architecture. We report a dense and consistent map of 358 cortical landmarks, named Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOLs). Each DICCCOL is defined by group-wise consistent white-matter fiber connection patterns derived from diffusion tensor imaging (DTI) data. Our results have shown that these 358 landmarks are remarkably reproducible over more than one hundred human brains and possess accurate intrinsically established structural and functional cross-subject correspondences validated by large-scale functional magnetic resonance imaging data. In particular, these 358 cortical landmarks can be accurately and efficiently predicted in a new single brain with DTI data. Thus, this set of 358 DICCCOL landmarks comprehensively encodes the common structural and functional cortical architectures, providing opportunities for many applications in brain science including mapping human brain connectomes, as demonstrated in this work.

DICCCOL: dense individualized and common connectivity-based cortical landmarks

Is there a common structural and functional cortical architecture that can be quantitatively encoded and precisely reproduced across individuals and populations? This question is still largely unanswered due to the vast complexity, variability, and nonlinearity of the cerebral cortex. Here, we hypothesize that the common cortical architecture can be effectively represented by group-wise consistent structural fiber connections and take a novel data-driven approach to explore the cortical architecture. We report a dense and consistent map of 358 cortical landmarks, named Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOLs). Each DICCCOL is defined by group-wise consistent white-matter fiber connection patterns derived from diffusion tensor imaging (DTI) data. Our results have shown that these 358 landmarks are remarkably reproducible over more than one hundred human brains and possess accurate intrinsically established structural and functional cross-subject correspondences validated by large-scale functional magnetic resonance imaging data. In particular, these 358 cortical landmarks can be accurately and efficiently predicted in a new single brain with DTI data. Thus, this set of 358 DICCCOL landmarks comprehensively encodes the common structural and functional cortical architectures, providing opportunities for many applications in brain science including mapping human brain connectomes, as demonstrated in this work.

Tractography: where do we go from here?

Diffusion tractography offers enormous potential for the study of human brain anatomy. However, as a method to study brain connectivity, tractography suffers from limitations, as it is indirect, inaccurate, and difficult to quantify. Despite these limitations, appropriate use of tractography can be a powerful means to address certain questions. In addition, while some of tractography's limitations are fundamental, others could be alleviated by methodological and technological advances. This article provides an overview of diffusion magnetic resonance tractography methods with a focus on how future advances might address challenges in measuring brain connectivity. Parts of this review are somewhat provocative, in the hope that they may trigger discussions possibly lacking in a field where the apparent simplicity of the methods (compared to their functional magnetic resonance imaging counterparts) can hide some fundamental issues that ultimately hinder the interpretation of findings, and cast doubt as to what tractography can really teach us about human brain anatomy.