FRATS: Functional Regression Analysis of DTI Tract Statistics

The pivotal role of the X-chromosome in the genetic architecture of the human brain

Genes on the X-chromosome are extensively expressed in the human brain. However, little is known for the X-chromosome's impact on the brain anatomy, microstructure, and functional network. We examined 1,045 complex brain imaging traits from 38,529 participants in the UK Biobank. We unveiled potential autosome-X-chromosome interactions, while proposing an atlas outlining dosage compensation (DC) for brain imaging traits. Through extensive association studies, we identified 72 genome-wide significant trait-locus pairs (including 29 new associations) that share genetic architectures with brain-related disorders, notably schizophrenia. Furthermore, we discovered unique sex-specific associations and assessed variations in genetic effects between sexes. Our research offers critical insights into the X-chromosome's role in the human brain, underscoring its contribution to the differences observed in brain structure and functionality between sexes.

Medical decision making for 5D cardiac model: Template matching technique and simulation of the fifth dimension

The purpose of this paper is to develop a 5D cardiac model which is inspired from the 5D model for the lungs. This model depends on five variables: the anatomical structure of the 3D heart, temporal dimension and the function of blood flow as the fifth dimension. To test this hypothesis, we took the same mathematical modeling as a reference for the fifth dimension of pulmonary flow where r→_ρ(t)=r→_v(t)+r_f→(t) wherer→_v(t) is the displacement vectors with approximate magnitudes by linear functions of the tidal volume and r_f→(t) is the blood flow. The scans were acquired for 10 patients,in the 404 series for a total of 18,483 images studied in three cases: healthy patient, case of heart failure and aortic stenosis. Where r→_vand r→_f are the unit vectors along the volume of ejection and the blood flow axes, indicating the direction of motion of the object due to heart volume ejection and blood flow variations, respectively. The quantities of α and β coefficients are determined from real-time patient image data. The alpha and beta coefficients are derived from the following dimension equations[mm / ml] [mm*ms / ml] . Since the cardiac system has two diastolic and systolic phases, we have calculated α₁ and β₁ for telediatolic volume and α₂ and β₂ for telesystolic volume throughout the cardiac cycle as a function of the location of the cuts chosen randomly. Fifth-dimensional experiments are used to track, simulate the behavior of blood flow to detect preliminary indications for the identification of stenosis or valve leakage. The average discrepancy was tabulated as the global fraction of systolic ejection. The results shown in Fig. 3 detect a correspondence between the hunting chamber cut and the flow sequence through the orifice of aorta for this patient with suspicious of having an aortic stenosis disease and an ejection fraction about 71% with a maximum of velocity (Vmax) detected=250 (cm / ms) = 2.5 (m / 10-3 s). In this case this patient has a minor stenosis in the aorta. It should be referred that the normalization of this measures is classified such as : Minor stenosis: area 1.5 cm2, Vmax <3 m / moderate stenosis: area 1.0 - 1.5 cm2, Vmax 3 - 4 m / severe stenosis: area <1.0 cm2, Vmax> 4 m / s. For a patient who has an aortic stenosis the cloud of the points is accumulated comparing to the origin of the axis while the patient with a symptom of insufficiency the points are widened with a remarkable gap in the trajectory. To solve the issue of the bad prediction, the inaccuracy of the clouds points of the model 5D, the lack of the exact measurements to estimate the degree of cardiac insufficiency (leakage or stenosis), a solution of 5D imagery was depicted. Our main contribution is to test the validity of the template-matching algorithm and the fifth dimension simulation to provide more clues to detect the aortic stenosis and cardiac insufficiency in the context of medical decision support.

Parametrization of white matter manifold-like structures using principal surfaces

In this manuscript, we are concerned with data generated from a diffusion tensor imaging (DTI) experiment. The goal is to parameterize manifold-like white matter tracts, such as the corpus callosum, using principal surfaces. The problem is approached by finding a geometrically motivated surface-based representation of the corpus callosum and visualized fractional anisotropy (FA) values projected onto the surface. The method also applies to any other diffusion summary. An algorithm is proposed that 1) constructs the principal surface of a corpus callosum; 2) flattens the surface into a parametric 2D map; 3) projects associated FA values on the map. The algorithm is applied to a longitudinal study containing 466 diffusion tensor images of 176 multiple sclerosis (MS) patients observed at multiple visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 20,000 voxels. Extensive simulation studies demonstrate fast convergence and robust performance of the algorithm under a variety of challenging scenarios.

Cook's Distance Measures for Varying Coefficient Models with Functional Responses

The aim of this paper is to develop Cook's distance measures for assessing the influence of both atypical curves and observations under varying coefficient model for functional responses. Our Cook's distance measures include Cook's distances for deleting multiple curves and for deleting multiple grid points, and their scaled Cook's distances. We systematically investigate some theoretical properties of these diagnostic measures. Simulation studies are conducted to evaluate the finite sample properties of these Cook's distances under different scenarios. A real diffusion tensor tract data set is analyzed to illustrate the use of our diagnostic measures.

Quantitative Analysis of Myelin and Axonal Remodeling in the Uninjured Motor Network After Stroke

Contralesional brain connectivity plasticity was previously reported after stroke. This study aims at disentangling the biological mechanisms underlying connectivity plasticity in the uninjured motor network after an ischemic lesion. In particular, we measured generalized fractional anisotropy (GFA) and magnetization transfer ratio (MTR) to assess whether poststroke connectivity remodeling depends on axonal and/or myelin changes. Diffusion-spectrum imaging and magnetization transfer MRI at 3T were performed in 10 patients in acute phase, at 1 and 6 months after stroke, which was affecting motor cortical and/or subcortical areas. Ten age- and gender-matched healthy volunteers were scanned 1 month apart for longitudinal comparison. Clinical assessment was also performed in patients prior to magnetic resonance imaging (MRI). In the contralesional hemisphere, average measures and tract-based quantitative analysis of GFA and MTR were performed to assess axonal integrity and myelination along motor connections as well as their variations in time. Mean and tract-based measures of MTR and GFA showed significant changes in a number of contralesional motor connections, confirming both axonal and myelin plasticity in our cohort of patients. Moreover, density-derived features (peak height, standard deviation, and skewness) of GFA and MTR along the tracts showed additional correlation with clinical scores than mean values. These findings reveal the interplay between contralateral myelin and axonal remodeling after stroke.

A longitudinal functional analysis framework for analysis of white matter tract statistics

Many longitudinal imaging studies have been/are being widely conducted to use diffusion tensor imaging (DTI) to better understand white matter maturation in normal controls and diseased subjects. There is an urgent demand for the development of statistical methods for analyzing diffusion properties along major fiber tracts obtained from longitudinal DTI studies. Jointly analyzing fiber-tract diffusion properties and covariates from longitudinal studies raises several major challenges including (i) infinite-dimensional functional response data, (ii) complex spatial-temporal correlation structure, and (iii) complex spatial smoothness. To address these challenges, this article is to develop a longitudinal functional analysis framework (LFAF) to delineate the dynamic changes of diffusion properties along major fiber tracts and their association with a set of covariates of interest (e.g., age and group status) and the structure of the variability of these white matter tract properties in various longitudinal studies. Our LFAF consists of a functional mixed effects model for addressing all three challenges, an efficient method for spatially smoothing varying coefficient functions, an estimation method for estimating the spatial-temporal correlation structure, a test procedure with a global test statistic for testing hypotheses of interest associated with functional response, and a simultaneous confidence band for quantifying the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of LFAF and to demonstrate that LFAF significantly outperforms a voxel-wise mixed model method. We apply LFAF to study the spatial-temporal dynamics of white-matter fiber tracts in a clinical study of neurodevelopment.

LONGITUDINAL GROWTH MODELING OF DISCRETE-TIME FUNCTIONS WITH APPLICATION TO DTI TRACT EVOLUTION IN EARLY NEURODEVELOPMENT

We present a new framework for spatiotemporal analysis of parameterized functions attributed by properties of 4D longitudinal image data. Our driving application is the measurement of temporal change in white matter diffusivity of fiber tracts. A smooth temporal modeling of change from a discrete-time set of functions is obtained with an extension of the logistic growth model to time-dependent spline functions, capturing growth with only a few descriptive parameters. An unbiased template baseline function is also jointly estimated. Solution is demonstrated via energy minimization with an extension to simultaneous modeling of trajectories for multiple subjects. The new framework is validated with synthetic data and applied to longitudinal DTI from 15 infants. Interpretation of estimated model growth parameters is facilitated by visualization in the original coordinate space of fiber tracts.

FMEM: functional mixed effects modeling for the analysis of longitudinal white matter Tract data

Many longitudinal imaging studies have collected repeated diffusion tensor magnetic resonance imaging data to understand white matter maturation and structural connectivity pattern in normal controls and diseased subjects. There is an urgent demand for the development of statistical methods for the analysis of diffusion properties along fiber tracts and clinical data obtained from longitudinal studies. Jointly analyzing repeated fiber-tract diffusion properties and covariates (e.g., age or gender) raises several major challenges including (i) infinite-dimensional functional response data, (ii) complex spatial-temporal correlation structure, and (iii) complex spatial smoothness. To address these challenges, this article is to develop a functional mixed effects modeling (FMEM) framework to delineate the dynamic changes of diffusion properties along major fiber tracts and their association with a set of covariates of interest and the structure of the variability of these white matter tract properties in various longitudinal studies. Our FMEM consists of a functional mixed effects model for addressing all three challenges, an efficient method for spatially smoothing varying coefficient functions, an estimation method for estimating the spatial-temporal correlation structure, a test procedure with local and global test statistics for testing hypotheses of interest associated with functional response, and a simultaneous confidence band for quantifying the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FMEM and to demonstrate that FMEM significantly outperforms the standard pointwise mixed effects modeling approach. We apply FMEM to study the spatial-temporal dynamics of white-matter fiber tracts in a clinical study of neurodevelopment.

Bayesian scalar-on-image regression with application to association between intracranial DTI and cognitive outcomes

Diffusion tensor imaging (DTI) measures water diffusion within white matter, allowing for in vivo quantification of brain pathways. These pathways often subserve specific functions, and impairment of those functions is often associated with imaging abnormalities. As a method for predicting clinical disability from DTI images, we propose a hierarchical Bayesian "scalar-on-image" regression procedure. Our procedure introduces a latent binary map that estimates the locations of predictive voxels and penalizes the magnitude of effect sizes in these voxels, thereby resolving the ill-posed nature of the problem. By inducing a spatial prior structure, the procedure yields a sparse association map that also maintains spatial continuity of predictive regions. The method is demonstrated on a simulation study and on a study of association between fractional anisotropy and cognitive disability in a cross-sectional sample of 135 multiple sclerosis patients.

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.

VARYING COEFFICIENT MODEL FOR MODELING DIFFUSION TENSORS ALONG WHITE MATTER TRACTS

Diffusion tensor imaging provides important information on tissue structure and orientation of fiber tracts in brain white matter in vivo. It results in diffusion tensors, which are 3×3 symmetric positive definite (SPD) matrices, along fiber bundles. This paper develops a functional data analysis framework to model diffusion tensors along fiber tracts as functional data in a Riemannian manifold with a set of covariates of interest, such as age and gender. We propose a statistical model with varying coefficient functions to characterize the dynamic association between functional SPD matrix-valued responses and covariates. We calculate weighted least squares estimators of the varying coefficient functions for the Log-Euclidean metric in the space of SPD matrices. We also develop a global test statistic to test specific hypotheses about these coefficient functions and construct their simultaneous confidence bands. Simulated data are further used to examine the finite sample performance of the estimated varying co-efficient functions. We apply our model to study potential gender differences and find a statistically significant aspect of the development of diffusion tensors along the right internal capsule tract in a clinical study of neurodevelopment.

Local Polynomial Regression for Symmetric Positive Definite Matrices

Local polynomial regression has received extensive attention for the nonparametric estimation of regression functions when both the response and the covariate are in Euclidean space. However, little has been done when the response is in a Riemannian manifold. We develop an intrinsic local polynomial regression estimate for the analysis of symmetric positive definite (SPD) matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space. The primary motivation and application of the proposed methodology is in computer vision and medical imaging. We examine two commonly used metrics, including the trace metric and the Log-Euclidean metric on the space of SPD matrices. For each metric, we develop a cross-validation bandwidth selection method, derive the asymptotic bias, variance, and normality of the intrinsic local constant and local linear estimators, and compare their asymptotic mean square errors. Simulation studies are further used to compare the estimators under the two metrics and to examine their finite sample performance. We use our method to detect diagnostic differences between diffusion tensors along fiber tracts in a study of human immunodeficiency virus.

Semiparametric Bayesian local functional models for diffusion tensor tract statistics

We propose a semiparametric Bayesian local functional model (BFM) for the analysis of multiple diffusion properties (e.g., fractional anisotropy) along white matter fiber bundles with a set of covariates of interest, such as age and gender. BFM accounts for heterogeneity in the shape of the fiber bundle diffusion properties among subjects, while allowing the impact of the covariates to vary across subjects. A nonparametric Bayesian LPP2 prior facilitates global and local borrowings of information among subjects, while an infinite factor model flexibly represents low-dimensional structure. Local hypothesis testing and credible bands are developed to identify fiber segments, along which multiple diffusion properties are significantly associated with covariates of interest, while controlling for multiple comparisons. Moreover, BFM naturally group subjects into more homogeneous clusters. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of BFM. We apply BFM to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment in new born infants.

Diffusion tensor imaging-based characterization of brain neurodevelopment in primates

Primate neuroimaging provides a critical opportunity for understanding neurodevelopment. Yet the lack of a normative description has limited the direct comparison with changes in humans. This paper presents for the first time a cross-sectional diffusion tensor imaging (DTI) study characterizing primate brain neurodevelopment between 1 and 6 years of age on 25 healthy undisturbed rhesus monkeys (14 male, 11 female). A comprehensive analysis including region-of-interest, voxel-wise, and fiber tract-based approach demonstrated significant changes of DTI properties over time. Changes in fractional anisotropy (FA), mean diffusivity, axial diffusivity (AD), and radial diffusivity (RD) exhibited a heterogeneous pattern across different regions as well as along fiber tracts. Most of these patterns are similar to those from human studies yet a few followed unique patterns. Overall, we observed substantial increase in FA and AD and a decrease in RD for white matter (WM) along with similar yet smaller changes in gray matter (GM). We further observed an overall posterior-to-anterior trend in DTI property changes over time and strong correlations between WM and GM development. These DTI trends provide crucial insights into underlying age-related biological maturation, including myelination, axonal density changes, fiber tract reorganization, and synaptic pruning processes.

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.

Penalized functional regression analysis of white-matter tract profiles in multiple sclerosis

Diffusion tensor imaging (DTI) enables noninvasive parcellation of cerebral white matter into its component fiber bundles or tracts. These tracts often subserve specific functions, and damage to the tracts can therefore result in characteristic forms of disability. Attempts to quantify the extent of tract-specific damage have been limited in part by substantial spatial variation of imaging properties from one end of a tract to the other, variation that can be compounded by the effects of disease. Here, we develop a "penalized functional regression" procedure to analyze spatially normalized tract profiles, which powerfully characterize such spatial variation. The central idea is to identify and emphasize portions of a tract that are more relevant to a clinical outcome score, such as case status or degree of disability. The procedure also yields a "tract abnormality score" for each tract and MRI index studied. Importantly, the weighting function used in this procedure is constrained to be smooth, and the statistical associations are estimated using generalized linear models. We test the method on data from a cross-sectional MRI and functional study of 115 multiple-sclerosis cases and 42 healthy volunteers, considering a range of quantitative MRI indices, white-matter tracts, and clinical outcome scores, and using training and testing sets to validate the results. We show that attention to spatial variation yields up to 15% (mean across all tracts and MRI indices: 6.4%) improvement in the ability to discriminate multiple sclerosis cases from healthy volunteers. Our results confirm that comprehensive analysis of white-matter tract-specific imaging data improves with knowledge and characterization of the normal spatial variation.

Extracting information from functional connectivity maps via function-on-scalar regression

Functional connectivity of an individual human brain is often studied by acquiring a resting state functional magnetic resonance imaging scan, and mapping the correlation of each voxel's BOLD time series with that of a seed region. As large collections of such maps become available, including multisite data sets, there is an increasing need for ways to distill the information in these maps in a readily visualized form. Here we propose a two-step analytic strategy. First, we construct connectivity-distance profiles, which summarize the connectivity of each voxel in the brain as a function of distance from the seed, a functional relationship that has attracted much recent interest. Next, these profile functions are regressed on predictors of interest, whether categorical (e.g., acquisition site or diagnostic group) or continuous (e.g., age). This procedure can provide insight into the roles of multiple sources of variation, and detect large-scale patterns not easily available from conventional analyses. We illustrate the proposed methods with a resting state data set pooled across four imaging sites.

FADTTS: functional analysis of diffusion tensor tract statistics

The aim of this paper is to present a functional analysis of a diffusion tensor tract statistics (FADTTS) pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest, such as age, diagnostic status and gender, and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies. The FADTTS integrates five statistical tools: (i) a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates, (ii) a weighted least squares estimation of the varying coefficient functions, (iii) a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties, (iv) a global test statistic to test hypotheses of interest, and (v) a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions. Simulated data are used to evaluate the finite sample performance of FADTTS. We apply FADTTS to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. FADTTS can be used to facilitate the understanding of normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles. The advantages of FADTTS compared with the other existing approaches are that they are capable of modeling the structured inter-subject variability, testing the joint effects, and constructing their simultaneous confidence bands. However, FADTTS is not crucial for estimation and reduces to the functional analysis method for the single measure.

Longitudinal functional principal component analysis

We introduce models for the analysis of functional data observed at multiple time points. The dynamic behavior of functional data is decomposed into a time-dependent population average, baseline (or static) subject-specific variability, longitudinal (or dynamic) subject-specific variability, subject-visit-specific variability and measurement error. The model can be viewed as the functional analog of the classical longitudinal mixed effects model where random effects are replaced by random processes. Methods have wide applicability and are computationally feasible for moderate and large data sets. Computational feasibility is assured by using principal component bases for the functional processes. The methodology is motivated by and applied to a diffusion tensor imaging (DTI) study designed to analyze differences and changes in brain connectivity in healthy volunteers and multiple sclerosis (MS) patients. An R implementation is provided.87.

Multivariate varying coefficient models for DTI tract statistics

Diffusion tensor imaging (DTI) is important for characterizing the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. There has been extensive interest in the analysis of diffusion properties measured along fiber tracts as a function of age, diagnostic status, and gender, while controlling for other clinical variables. However, the existing methods have several limitations including the independent analysis of diffusion properties, a lack of method for accounting for multiple covariates, and a lack of formal statistical inference, such as estimation theory and hypothesis testing. This paper presents a statistical framework, called VCMTS, to specifically address these limitations. The VCMTS framework consists of four integrated components: a varying coefficient model for characterizing the association between fiber bundle diffusion properties and a set of covariates, the local polynomial kernel method for estimating smoothed multiple diffusion properties along individual fiber bundles, global and local test statistics for testing hypotheses of interest along fiber tracts, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of four diffusion properties along the splenium and genu of the corpus callosum tract in a study of neurodevelopment in healthy rhesus monkeys. Significant time effects on the four diffusion properties were found.

Generalized semiparametrically structured ordinal models

Semiparametrically structured models are defined as a class of models for which the predictors may contain parametric parts, additive parts of covariates with an unspecified functional form, and interactions which are described as varying coefficients. In the case of an ordinal response the complexity of the predictor is determined by different sorts of effects. Global effects and category-specific effects are distinguished; the latter allow the effect to vary across response categories. A general framework is developed in which global as well as category-specific effects may have unspecified functional form. The framework extends various existing methods of modeling ordinal responses. The Wilkinson-Rogers notation is extended to incorporate smooth model parts and varying coefficient terms, the latter being important for the smooth specification of category-specific effects.