SCI Publications

The goal of longitudinal shape analysis is to understand how anatomical shape changes over time, in response to biological processes, including growth, aging, or disease. In many imaging studies, it is also critical to understand how these shape changes are affected by other factors, such as sex, disease diagnosis, IQ, etc. Current approaches to longitudinal shape analysis have focused on modeling age-related shape changes, but have not included the ability to handle covariates. In this paper, we present a novel Bayesian mixed-effects shape model that incorporates simultaneous relationships between longitudinal shape data and multiple predictors or covariates to the model. Moreover, we place an Automatic Relevance Determination (ARD) prior on the parameters, that lets us automatically select which covariates are most relevant to the model based on observed data. We evaluate our proposed model and inference procedure on a longitudinal study of Huntington's disease from PREDICT-HD. We first show the utility of the ARD prior for model selection in a univariate modeling of striatal volume, and next we apply the full high-dimensional longitudinal shape model to putamen shapes.

In this paper we present a novel method for analyzing the relationship between functional brain networks and behavioral phenotypes. Drawing from topological data analysis, we first extract topological features using persistent homology from functional brain networks that are derived from correlations in resting-state fMRI. Rather than fixing a discrete network topology by thresholding the connectivity matrix, these topological features capture the network organization across all continuous threshold values. We then propose to use a kernel partial least squares (kPLS) regression to statistically quantify the relationship between these topological features and behavior measures. The kPLS also provides an elegant way to combine multiple image features by using linear combinations of multiple kernels. In our experiments we test the ability of our proposed brain network analysis to predict autism severity from rs-fMRI. We show that combining correlations with topological features gives better prediction of autism severity than using correlations alone.

This paper presents a fast geodesic shooting algorithm for diffeomorphic image registration. We first introduce a novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields. We then show that this space can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registration accuracy. We then leverage the fact that the geodesic evolution equations, as well as the adjoint Jacobi field equations needed for gradient descent methods, can be computed entirely in this finite-dimensional Lie algebra. The result is a geodesic shooting method for large deformation metric mapping (LDDMM) that is dramatically faster and less memory intensive than state-of-the-art methods. We demonstrate the effectiveness of our model to register 3D brain images and compare its registration accuracy, runtime, and memory consumption with leading LDDMM methods. We also show how our algorithm breaks through the prohibitive time and memory requirements of diffeomorphic atlas building.

In this paper, we present a generative Bayesian approach for estimating the low-dimensional latent space of diffeomorphic shape variability in a population of images. We develop a latent variable model for principal geodesic analysis (PGA) that provides a probabilistic framework for factor analysis in the space of diffeomorphisms. A sparsity prior in the model results in automatic selection of the number of relevant dimensions by driving unnecessary principal geodesics to zero. To infer model parameters, including the image atlas, principal geodesic deformations, and the effective dimensionality, we introduce an expectation maximization (EM) algorithm. We evaluate our proposed model on 2D synthetic data and the 3D OASIS brain database of magnetic resonance images, and show that the automatically selected latent dimensions from our model are able to reconstruct unobserved testing images with lower error than both linear principal component analysis (LPCA) in the image space and tangent space principal component analysis (TPCA) in the diffeomorphism space.

Computing image atlases that are representative of a dataset
is an important first step for statistical analysis of images. Most current approaches estimate a single atlas to represent the average of a large population of images, however, a single atlas is not sufficiently expressive to capture distributions of images with multiple modes. In this paper, we present a mixture model for building diffeomorphic multi-atlases that can represent sub-populations without knowing the category of each observed data point. In our probabilistic model, we treat diffeomorphic image transformations as latent variables, and integrate them out using a Monte Carlo Expectation Maximization (MCEM) algorithm via Hamiltonian Monte Carlo (HMC) sampling. A key benefit of our model is that the mixture modeling inference procedure results in an automatic clustering of the dataset. Using 2D synthetic data generated from known parameters, we demonstrate the ability of our model to successfully recover the multi-atlas and automatically cluster the dataset. We also show the effectiveness of the proposed method in a multi-atlas estimation problem for 3D brain images.

We present a novel geodesic approach to segmentation of white matter tracts from diffusion tensor imaging (DTI). Compared to deterministic and stochastic tractography, geodesic approaches treat the geometry of the brain white matter as a manifold, often using the inverse tensor field as a Riemannian metric. The white matter pathways are then inferred from the resulting geodesics, which have the desirable property that they tend to follow the main eigenvectors of the tensors, yet still have the flexibility to deviate from these directions when it results in lower costs. While this makes such methods more robust to noise, the choice of Riemannian metric in these methods is ad hoc. A serious drawback of current geodesic methods is that geodesics tend to deviate from the major eigenvectors in high-curvature areas in order to achieve the shortest path. In this paper we propose a method for learning an adaptive Riemannian metric from the DTI data, where the resulting geodesics more closely follow the principal eigenvector of the diffusion tensors even in high-curvature regions. We also develop a way to automatically segment the white matter tracts based on the computed geodesics. We show the robustness of our method on simulated data with different noise levels. We also compare our method with tractography methods and geodesic approaches using other Riemannian metrics and demonstrate that the proposed method results in improved geodesics and segmentations using both synthetic and real DTI data.

Keywords: Conformal factor, Diffusion tensor imaging, Front-propagation, Geodesic, Riemannian manifold

We develop a framework for polynomial regression on Riemannian manifolds. Unlike recently developed spline models on Riemannian manifolds, Riemannian polynomials offer the ability to model parametric polynomials of all integer orders, odd and even. An intrinsic adjoint method is employed to compute variations of the matching functional, and polynomial regression is accomplished using a gradient-based optimization scheme. We apply our polynomial regression framework in the context of shape analysis in Kendall shape space as well as in diffeomorphic landmark space. Our algorithm is shown to be particularly convenient in Riemannian manifolds with additional symmetry, such as Lie groups and homogeneous spaces with right or left invariant metrics. As a particularly important example, we also apply polynomial regression to time-series imaging data using a right invariant Sobolev metric on the diffeomorphism group. The results show that Riemannian polynomials provide a practical model for parametric curve regression, while offering increased flexibility over geodesics.

We propose a hierarchical Markov random field model for estimating both group and subject functional networks simultaneously. The model takes into account the within-subject spatial coherence as well as the between-subject consistency of the network label maps. The statistical dependency between group and subject networks acts as a regularization, which helps the network estimation on both layers. We use Gibbs sampling to approximate the posterior density of the network labels and Monte Carlo expectation maximization to estimate the model parameters. We compare our method with two alternative segmentation methods based on K-Means and normalized cuts, using synthetic and real data. The experimental results show that our proposed model is able to identify both group and subject functional networks with higher accuracy on synthetic data, more robustness, and inter-session consistency on the real data.

Keywords: Resting-state functional MRI, Segmentation, Functional connectivity, Hierarchical Markov random field, Bayesian

Longitudinal imaging studies involve tracking changes in individuals by repeated image acquisition over time. The goal of these studies is to quantify biological shape variability within and across individuals, and also to distinguish between normal and disease populations. However, data variability is influenced by outside sources such as image acquisition, image calibration, human expert judgment, and limited robustness of segmentation and registration algorithms. In this paper, we propose a two-stage method for the statistical analysis of longitu- dinal shape. In the first stage, we estimate diffeomorphic shape trajectories for each individual that minimize inconsistencies in segmented shapes across time. This is followed by a longitudinal mixed-effects statistical model in the second stage for testing differences in shape trajectories between groups. We apply our method to a longitudinal database from PREDICT-HD and demonstrate our ap- proach reduces unwanted variability for both shape and derived measures, such as volume. This leads to greater statistical power to distinguish differences in shape trajectory between healthy subjects and subjects with a genetic biomarker for Huntington's disease (HD).

Background: Lateralization of brain structure and function occurs in typical development, and abnormal lateralization is present in various neuropsychiatric disorders. Autism is characterized by a lack of left lateralization in structure and function of regions involved in language, such as Broca and Wernicke areas.
Methods: Using functional connectivity magnetic resonance imaging from a large publicly available sample (n = 964), we tested whether abnormal functional lateralization in autism exists preferentially in language regions or in a more diffuse pattern across networks of lateralized brain regions.
Results: The autism group exhibited significantly reduced left lateralization in a few connections involving language regions and regions from the default mode network, but results were not significant throughout left- and right-lateralized networks. There is a trend that suggests the lack of left lateralization in a connection involving Wernicke area and the posterior cingulate cortex associates with more severe autism.
Conclusions: Abnormal language lateralization in autism may be due to abnormal language development rather than to a deficit in hemispheric specialization of the entire brain.

Keywords: brain lateralization, brain asymmetry, autism, autism spectrum disorder, language, functional magnetic resonance imaging, functional connectivity

The term prediction implies expected outcome in the future, often based on a model and statistical inference. Longitudinal imaging studies offer the possibility to model temporal change trajectories of anatomy across populations of subjects. In the spirit of subject-specific analysis, such normative models can then be used to compare data from new subjects to the norm and to study progression of disease or to predict outcome. This paper follows a statistical inference approach and presents a framework for prediction of future observations based on past measurements and population statistics. We describe prediction in the context of nonlinear mixed effects modeling (NLME) where the full reference population's statistics (estimated fixed effects, variance-covariance of random effects, variance of noise) is used along with the individual's available observations to predict its trajectory. The proposed methodology is generic in regard to application domains. Here, we demonstrate analysis of early infant brain maturation from longitudinal DTI with up to three time points. Growth as observed in DTI-derived scalar invariants is modeled with a parametric function, its parameters being input to NLME population modeling. Trajectories of new subject's data are estimated when using no observation, only the rst or the first two time points. Leave-one-out experiments result in statistics on differences between actual and predicted observations. We also simulate a clinical scenario of prediction on multiple categories, where trajectories predicted from multiple models are classified based on maximum likelihood criteria.

Temporal modeling frameworks often operate on scalar variables by summarizing data at initial stages as statistical summaries of the underlying distributions. For instance, DTI analysis often employs summary statistics, like mean, for regions of interest and properties along fiber tracts for population studies and hypothesis testing. This reduction via discarding of variability information may introduce significant errors which propagate through the procedures. We propose a novel framework which uses distribution-valued variables to retain and utilize the local variability information. Classic linear regression is adapted to employ these variables for model estimation. The increased stability and reliability of our proposed method when compared with regression using single-valued statistical summaries, is demonstrated in a validation experiment with synthetic data. Our driving application is the modeling of age-related changes along DTI white matter tracts. Results are shown for the spatiotemporal population trajectory of genu tract estimated from 45 healthy infants and compared with a Krabbe's patient.

Keywords: linear regression, distribution-valued data, spatiotemporal growth trajectory, DTI, early neurodevelopment

We present a novel algorithm for computing hierarchical geodesic models (HGMs) for diffeomorphic longitudinal shape analysis. The proposed algorithm exploits the inherent parallelism arising out of the independence in the contributions of individual geodesics to the group geodesic. The previous serial implementation severely limits the use of HGMs to very small population sizes due to computation time and massive memory requirements. The conventional method makes it impossible to estimate the parameters of HGMs on large datasets due to limited memory available onboard current GPU computing devices. The proposed parallel algorithm easily scales to solve HGMs on a large collection of 3D images of several individuals. We demonstrate its effectiveness on longitudinal datasets of synthetically generated shapes and 3D magnetic resonance brain images (MRI).

Keywords: LDDMM, HGM, Vector Momentum, Diffeomorphisms, Longitudinal Analysis

4D pathological anatomy modeling is key to understanding complex pathological brain images. It is a challenging problem due to the difficulties in detecting multiple appearing and disappearing lesions across time points and estimating dynamic changes and deformations between them. We propose a novel semi-supervised method, called 4D active cut, for lesion recognition and deformation estimation. Existing interactive segmentation methods passively wait for user to refine the segmentations which is a difficult task in 3D images that change over time. 4D active cut instead actively selects candidate regions for querying the user, and obtains the most informative user feedback. A user simply answers 'yes' or 'no' to a candidate object without having to refine the segmentation slice by slice. Compared to single-object detection of the existing methods, our method also detects multiple lesions with spatial coherence using Markov random fields constraints. Results show improvement on the lesion detection, which subsequently improves deformation estimation.

Keywords: Active learning, graph cuts, longitudinal MRI, Markov Random Fields, semi-supervised learning

This paper proposes a novel method for the analysis of anatomical shapes present in biomedical image data. Motivated by the natural organization of population data into multiple groups, this paper presents a novel hierarchical generative statistical model on shapes. The proposed method represents shapes using pointsets and defines a joint distribution on the population's (i) shape variables and (ii) object-boundary data. The proposed method solves for optimal (i) point locations, (ii) correspondences, and (iii) model-parameter values as a single optimization problem. The optimization uses expectation maximization relying on a novel Markov-chain Monte-Carlo algorithm for sampling in Kendall shape space. Results on clinical brain images demonstrate advantages over the state of the art.

Computing a concise representation of the anatomical variability found in large sets of images is an important rst step in many statistical shape analyses. In this paper, we present a generative Bayesian approach for automatic dimensionality reduction of shape variability represented through diffeomorphic mappings. To achieve this, we develop a latent variable model for principal geodesic analysis (PGA) that provides a probabilistic framework for factor analysis on diffeomorphisms. Our key contribution is a Bayesian inference procedure for model parameter estimation and simultaneous detection of the effective dimensionality of the latent space. We evaluate our proposed model for atlas and principal geodesic estimation on the OASIS brain database of magnetic resonance images. We show that the automatically selected latent dimensions from our model are able to reconstruct unseen brain images with lower error than equivalent linear principal components analysis (LPCA) models in the image space, and it also outperforms tangent space PCA (TPCA) models in the diffeomorphism setting.

The natural history of brain growth in autism spectrum disorders remains unclear. Cross-sectional studies have identified regional abnormalities in brain volume and cortical thickness in autism, although substantial discrepancies have been reported. Preliminary longitudinal studies using two time points and small samples have identified specific regional differences in cortical thickness in the disorder. To clarify age-related trajectories of cortical development, we examined longitudinal changes in cortical thickness within a large mixed cross-sectional and longitudinal sample of autistic subjects and age- and gender-matched typically developing controls. Three hundred and forty-five magnetic resonance imaging scans were examined from 97 males with autism (mean age = 16.8 years; range 3-36 years) and 60 males with typical development (mean age = 18 years; range 4-39 years), with an average interscan interval of 2.6 years. FreeSurfer image analysis software was used to parcellate the cortex into 34 regions of interest per hemisphere and to calculate mean cortical thickness for each region. Longitudinal linear mixed effects models were used to further characterize these findings and identify regions with between-group differences in longitudinal age-related trajectories. Using mean age at time of first scan as a reference (15 years), differences were observed in bilateral inferior frontal gyrus, pars opercularis and pars triangularis, right caudal middle frontal and left rostral middle frontal regions, and left frontal pole. However, group differences in cortical thickness varied by developmental stage, and were influenced by IQ. Differences in age-related trajectories emerged in bilateral parietal and occipital regions (postcentral gyrus, cuneus, lingual gyrus, pericalcarine cortex), left frontal regions (pars opercularis, rostral middle frontal and frontal pole), left supramarginal gyrus, and right transverse temporal gyrus, superior parietal lobule, and paracentral, lateral orbitofrontal, and lateral occipital regions. We suggest that abnormal cortical development in autism spectrum disorders undergoes three distinct phases: accelerated expansion in early childhood, accelerated thinning in later childhood and adolescence, and decelerated thinning in early adulthood. Moreover, cortical thickness abnormalities in autism spectrum disorders are region-specific, vary with age, and may remain dynamic well into adulthood.

In this paper we present a novel Bayesian approach for fractional segmentation of white matter tracts and simultaneous estimation of a multi-tensor diffusion model. Our model consists of several white matter tracts, each with a corresponding weight and tensor compartment in each voxel. By incorporating a prior that assumes the tensor fields inside each tract are spatially correlated, we are able to reliably estimate multiple tensor compartments in fiber crossing regions, even with low angular diffusion-weighted imaging (DWI). Our model distinguishes the diffusion compartment associated with each tract, which reduces the effects of partial voluming and achieves more reliable statistics of diffusion measurements.We test our method on synthetic data with known ground truth and show that we can recover the correct volume fractions and tensor compartments. We also demonstrate that the proposed method results in improved segmentation and diffusion measurement statistics on real data in the presence of crossing tracts and partial voluming.

The human brain undergoes rapid organization and structuring early in life. Longitudinal imaging enables the study of these changes over a developmental period within individuals through estimation of population growth trajectory and its variability. In this paper, we focus on maturation of white and gray matter as is depicted in structural and diffusion MRI of healthy subjects with repeated scans. We provide a framework for joint analysis of both structural MRI and DTI (Diffusion Tensor Imaging) using multivariate nonlinear mixed effect modeling of temporal changes. Our framework constructs normative growth models for all the modalities that take into account the correlation among the modalities and individuals, along with estimation of the variability of the population trends. We apply our method to study early brain development, and to our knowledge this is the first multimodel longitudinal modeling of diffusion and signal intensity changes for this growth stage. Results show the potential of our framework to study growth trajectories, as well as neurodevelopmental disorders through comparison against the constructed normative models of multimodal 4D MRI.