Group statistics of DTI fiber bundles using spatial functions of tensor measures

Multivariate Analyses Applied to Healthy Neurodevelopment in Fetal, Neonatal, and Pediatric MRI

Multivariate analysis (MVA) is a class of statistical and pattern recognition techniques that involve the processing of data that contains multiple measurements per sample. MVA can be used to address a wide variety of neurological medical imaging related challenges including the evaluation of healthy brain development, the automated analysis of brain tissues and structures through image segmentation, evaluating the effects of genetic and environmental factors on brain development, evaluating sensory stimulation's relationship with functional brain activity and much more. Compared to adult imaging, pediatric, neonatal and fetal imaging have attracted less attention from MVA researchers, however, recent years have seen remarkable MVA research growth in pre-adult populations. This paper presents the results of a systematic review of the literature focusing on MVA applied to healthy subjects in fetal, neonatal and pediatric magnetic resonance imaging (MRI) of the brain. While the results of this review demonstrate considerable interest from the scientific community in applications of MVA technologies in brain MRI, the field is still young and significant research growth will continue into the future.

A diffusion tensor MRI atlas of the postmortem rhesus macaque brain

The rhesus macaque (Macaca mulatta) is the most widely used nonhuman primate for modeling the structure and function of the brain. Brain atlases, and particularly those based on magnetic resonance imaging (MRI), have become important tools for understanding normal brain structure, and for identifying structural abnormalities resulting from disease states, exposures, and/or aging. Diffusion tensor imaging (DTI)-based MRI brain atlases are widely used in both human and macaque brain imaging studies because of the unique contrasts, quantitative diffusion metrics, and diffusion tractography that they can provide. Previous MRI and DTI atlases of the rhesus brain have been limited by low contrast and/or low spatial resolution imaging. Here we present a microscopic resolution MRI/DTI atlas of the rhesus brain based on 10 postmortem brain specimens. The atlas includes both structural MRI and DTI image data, a detailed three-dimensional segmentation of 241 anatomic structures, diffusion tractography, cortical thickness estimates, and maps of anatomic variability among atlas specimens. This atlas incorporates many useful features from previous work, including anatomic label nomenclature and ontology, data orientation, and stereotaxic reference frame, and further extends prior analyses with the inclusion of high-resolution multi-contrast image data.

Applications of functional data analysis: A systematic review

BACKGROUND

Functional data analysis (FDA) is increasingly being used to better analyze, model and predict time series data. Key aspects of FDA include the choice of smoothing technique, data reduction, adjustment for clustering, functional linear modeling and forecasting methods.

METHODS

A systematic review using 11 electronic databases was conducted to identify FDA application studies published in the peer-review literature during 1995-2010. Papers reporting methodological considerations only were excluded, as were non-English articles.

RESULTS

In total, 84 FDA application articles were identified; 75.0% of the reviewed articles have been published since 2005. Application of FDA has appeared in a large number of publications across various fields of sciences; the majority is related to biomedicine applications (21.4%). Overall, 72 studies (85.7%) provided information about the type of smoothing techniques used, with B-spline smoothing (29.8%) being the most popular. Functional principal component analysis (FPCA) for extracting information from functional data was reported in 51 (60.7%) studies. One-quarter (25.0%) of the published studies used functional linear models to describe relationships between explanatory and outcome variables and only 8.3% used FDA for forecasting time series data.

CONCLUSIONS

Despite its clear benefits for analyzing time series data, full appreciation of the key features and value of FDA have been limited to date, though the applications show its relevance to many public health and biomedical problems. Wider application of FDA to all studies involving correlated measurements should allow better modeling of, and predictions from, such data in the future especially as FDA makes no a priori age and time effects assumptions.

Along-tract statistics allow for enhanced tractography analysis

Diffusion imaging tractography is a valuable tool for neuroscience researchers because it allows the generation of individualized virtual dissections of major white matter tracts in the human brain. It facilitates between-subject statistical analyses tailored to the specific anatomy of each participant. There is prominent variation in diffusion imaging metrics (e.g., fractional anisotropy, FA) within tracts, but most tractography studies use a "tract-averaged" approach to analysis by averaging the scalar values from the many streamline vertices in a tract dissection into a single point-spread estimate for each tract. Here we describe a complete workflow needed to conduct an along-tract analysis of white matter streamline tract groups. This consists of 1) A flexible MATLAB toolkit for generating along-tract data based on B-spline resampling and compilation of scalar data at different collections of vertices along the curving tract spines, and 2) Statistical analysis and rich data visualization by leveraging tools available through the R platform for statistical computing. We demonstrate the effectiveness of such an along-tract approach over the tract-averaged approach in an example analysis of 10 major white matter tracts in a single subject. We also show that these techniques easily extend to between-group analyses typically used in neuroscience applications, by conducting an along-tract analysis of differences in FA between 9 individuals with fetal alcohol spectrum disorders (FASDs) and 11 typically-developing controls. This analysis reveals localized differences between FASD and control groups that were not apparent using a tract-averaged method. Finally, to validate our approach and highlight the strength of this extensible software framework, we implement 2 other methods from the literature and leverage the existing workflow tools to conduct a comparison study.

Statistical analysis of fiber bundles using multi-tensor tractography: application to first-episode schizophrenia

This work proposes a new method to detect abnormalities in fiber bundles of first-episode (FE) schizophrenia patients. Existing methods have either examined a particular region of interest or used voxel-based morphometry or used tracts generated using the single tensor model for locating statistically different fiber bundles. Further, a two-sample t test, which assumes a Gaussian distribution for each population, is the most widely used statistical hypothesis testing algorithm. In this study, we use the unscented Kalman filter based two-tensor tractography algorithm for tracing neural fiber bundles of the brain that connect 105 different cortical and subcortical regions. Next, fiber bundles with significant connectivity across the entire population were determined. Several diffusion measures derived from the two-tensor model were computed and used as features in the subsequent analysis. For each fiber bundle, an affine-invariant descriptor was computed, thus obviating the need for precise registration of patients to an atlas. A kernel-based statistical hypothesis testing algorithm, which makes no assumption regarding the distribution of the underlying population, was then used to determine the abnormal diffusion properties of all fiber bundles for 20 FE patients and 20 age-matched healthy controls. Of the 1254 fiber bundles with significant connectivity, 740 fiber bundles were found to be significantly different in at least one diffusion measure after correcting for multiple comparisons. Thus, the changes affecting first-episode patients seem to be global in nature (spread throughout the brain).

Tract-based probability densities of diffusivity measures in DT-MRI

We evaluate probability density functions of diffusivity measures in DTI fiber tracts as biomarkers. For this, we estimate univariate and bivariate densities, such as joint probability densities of the tract arc length and FA, MD, RD, and AD, in the transcallosal fibers in the brain. We demonstrate the utility of estimated densities in hypothesis testing of differences between a group of patients with VCI and a control group. We also use the estimated densities in classifying individual subjects in these two groups. Results show that these estimates and derived quantities, such as entropy, can detect group differences with high statistical power as well as help obtain low classification errors.

A statistical model of white matter fiber bundles based on currents

The purpose of this paper is to measure the variability of a population of white matter fiber bundles without imposing unrealistic geometrical priors. In this respect, modeling fiber bundles as currents seems particularly relevant, as it gives a metric between bundles which relies neither on point nor on fiber correspondences and which is robust to fiber interruption. First, this metric is included in a diffeomorphic registration scheme which consistently aligns sets of fiber bundles. In particular, we show that aligning directly fiber bundles may solve the aperture problem which appears when fiber mappings are constrained by tensors only. Second, the measure of variability of a population of fiber bundles is based on a statistical model which considers every bundle as a random diffeomorphic deformation of a common template plus a random non-diffeomorphic perturbation. Thus, the variability is decomposed into a geometrical part and a "texture" part. Our results on real data show that both parts may contain interesting anatomical features.

Group analysis of DTI fiber tract statistics with application to neurodevelopment

Diffusion tensor imaging (DTI) provides a unique source of information about the underlying tissue structure of brain white matter in vivo including both the geometry of major fiber bundles as well as quantitative information about tissue properties represented by derived tensor measures. This paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images. Unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images. The diffeomorphic transformations between each subject and the atlas provide spatial normalization for the comparison of tract statistics. Diffusion properties, such as fractional anisotropy (FA) and tensor norm, along fiber tracts are modeled as multivariate functions of arc length. Hypothesis testing is performed non-parametrically using permutation testing based on the Hotelling T(2) statistic. The linear discriminant embedded in the T(2) metric provides an intuitive, localized interpretation of detected differences. The proposed methodology was tested on two clinical studies of neurodevelopment. In a study of 1 and 2 year old subjects, a significant increase in FA and a correlated decrease in Frobenius norm was found in several tracts. Significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly (MVM) demonstrating the potential of this method for clinical studies.

The geometric median on Riemannian manifolds with application to robust atlas estimation

One of the primary goals of computational anatomy is the statistical analysis of anatomical variability in large populations of images. The study of anatomical shape is inherently related to the construction of transformations of the underlying coordinate space, which map one anatomy to another. It is now well established that representing the geometry of shapes or images in Euclidian spaces undermines our ability to represent natural variability in populations. In our previous work we have extended classical statistical analysis techniques, such as averaging, principal components analysis, and regression, to Riemannian manifolds, which are more appropriate representations for describing anatomical variability. In this paper we extend the notion of robust estimation, a well established and powerful tool in traditional statistical analysis of Euclidian data, to manifold-valued representations of anatomical variability. In particular, we extend the geometric median, a classic robust estimator of centrality for data in Euclidean spaces. We formulate the geometric median of data on a Riemannian manifold as the minimizer of the sum of geodesic distances to the data points. We prove existence and uniqueness of the geometric median on manifolds with non-positive sectional curvature and give sufficient conditions for uniqueness on positively curved manifolds. Generalizing the Weiszfeld procedure for finding the geometric median of Euclidean data, we present an algorithm for computing the geometric median on an arbitrary manifold. We show that this algorithm converges to the unique solution when it exists. In this paper we exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images. Using this approach, we also present a robust brain atlas estimation technique based on the geometric median in the space of deformable images.