Multiscale adaptive smoothing models for the hemodynamic response function in fMRI

In the event-related functional magnetic resonance imaging (fMRI) data analysis, there is an extensive interest in accurately and robustly estimating the hemodynamic response function (HRF) and its associated statistics (e.g., the magnitude and duration of the activation). Most methods to date are developed in the time domain and they have utilized almost exclusively the temporal information of fMRI data without accounting for the spatial information. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) in the frequency domain by integrating the spatial and frequency information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a three-dimensional (3D) volume. We use two sets of simulation studies and a real data set to examine the finite sample performance of MASM in estimating HRFs. Our real and simulated data analyses confirm that MASM outperforms several other state-of-the-art methods, such as the smooth finite impulse response (sFIR) model.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS609 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Extrinsic local regression on manifold-valued data

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach

Extrinsic Local Regression on Manifold-Valued Data

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach

A unified optimization approach for diffusion tensor imaging technique

An optimization approach for diffusion tensor imaging (DTI) technique is proposed, aiming to improve the estimates of tensors, fractional anisotropy (FA), and fiber directions. With the simulated annealing algorithm, the proposed approach simultaneously optimizes imaging parameters (gradient duration/separation, read-out time, and TE), b-values, and diffusion gradient directions either with or without incorporating prior knowledge of tensor fields. In addition, the method through which tensors are estimated, least squares in our study, was also considered in the optimization procedures. Monte-Carlo simulations were performed for three different scenarios of prior fiber distributions including fibers orientated in 1 (CONE1) and 3 (CONE3) cone areas (50 tensors orderly oriented within a diverging angle of 20° in each cone) and a uniform fiber distribution (UNIF). In addition, three imaging acquisition schemes together with different signal-to-noise ratios were tested, including M/N=1/6, 2/12, and 5/30 for each prior fiber distribution where M and N were the number of b=0 and b>0 images, respectively. Our results show that the optimal b-value ranges between 0.7 and 1.0 × 109s/m2 for UNIF. However, the optimal b-value ranges become both higher and wider for CONE1 and CONE3 than that of UNIF. In addition, the biases and standard deviations (SD) of tensors, and SD of FA are substantially reduced and the accuracy of fiber directional estimates is improved using the proposed approach particularly in CONE1 when compared with the conventional approaches. Together, the proposed unified optimization approach may offer a direct and simultaneous means to optimize DTI experiments

STGP: Spatio-temporal Gaussian process models for longitudinal neuroimaging data

Longitudinal neuroimaging data plays an important role in mapping the neural developmental profile of major neuropsychiatric and neurodegenerative disorders and normal brain. The development of such developmental maps is critical for the prevention, diagnosis, and treatment of many brain-related diseases. The aim of this paper is to develop a spatio-temporal Gaussian process (STGP) framework to accurately delineate the developmental trajectories of brain structure and function, while achieving better prediction by explicitly incorporating the spatial and temporal features of longitudinal neuroimaging data. Our STGP integrates a functional principal component model (FPCA) and a partition parametric space-time covariance model to capture the medium-to-large and small-to-medium spatio-temporal dependence structures, respectively. We develop a three-stage efficient estimation procedure as well as a predictive method based on a kriging technique. Two key novelties of STGP are that it can efficiently use a small number of parameters to capture complex non-stationary and non-separable spatio-temporal dependence structures and that it can accurately predict spatio-temporal changes. We illustrate STGP using simulated data sets and two real data analyses including longitudinal positron emission tomography data from the Alzheimers Disease Neuroimaging Initiative (ADNI) and longitudinal lateral ventricle surface data from a longitudinal study of early brain development

Local polynomial regression for symmetric positive definite matrices: Local Polynomial Regression

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

The Bayesian Covariance Lasso

Estimation of sparse covariance matrices and their inverse subject to positive definiteness constraints has drawn a lot of attention in recent years. The abundance of high-dimensional data, where the sample size (n) is less than the dimension (d), requires shrinkage estimation methods since the maximum likelihood estimator is not positive definite in this case. Furthermore, when n is larger than d but not sufficiently larger, shrinkage estimation is more stable than maximum likelihood as it reduces the condition number of the precision matrix. Frequentist methods have utilized penalized likelihood methods, whereas Bayesian approaches rely on matrix decompositions or Wishart priors for shrinkage. In this paper we propose a new method, called the Bayesian Covariance Lasso (BCLASSO), for the shrinkage estimation of a precision (covariance) matrix. We consider a class of priors for the precision matrix that leads to the popular frequentist penalties as special cases, develop a Bayes estimator for the precision matrix, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. The proposed method is permutation invariant and performs shrinkage and estimation simultaneously for non-full rank data. Simulations show that the proposed BCLASSO performs similarly as frequentist methods for non-full rank data

Functional-Mixed Effects Models for Candidate Genetic Mapping in Imaging Genetic Studies

The aim of this paper is to develop a functional mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for effciently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function

Reperfusion Beyond 6 Hours Reduces Infarct Probability in Moderately Ischemic Brain Tissue

We aimed to examine perfusion changes between 3 and 6, and 6 and 24 hours after stroke onset and their impact on tissue outcome