P. Thomas Fletcher

Deformable M-Reps for 3D Medical Image Segmentation

M-reps (formerly called DSLs) are a multiscale medial means for modeling and rendering 3D solid geometry. They are particularly well suited to model anatomic objects and in particular to capture prior geometric information effectively in deformable models segmentation approaches. The representation is based on figural models, which define objects at coarse scale by a hierarchy of figures—each figure generally a slab representing a solid region and its boundary simultaneously. This paper focuses on the use of single figure models to segment objects of relatively simple structure.A single figure is a sheet of medial atoms, which is interpolated from the model formed by a net, i.e., a mesh or chain, of medial atoms (hence the name m-reps), each atom modeling a solid region via not only a position and a width but also a local figural frame giving figural directions and an object angle between opposing, corresponding positions on the boundary implied by the m-rep. The special capability of an m-rep is to provide spatial and orientational correspondence between an object in two different states of deformation. This ability is central to effective measurement of both geometric typicality and geometry to image match, the two terms of the objective function optimized in segmentation by deformable models. The other ability of m-reps central to effective segmentation is their ability to support segmentation at multiple levels of scale, with successively finer precision. Objects modeled by single figures are segmented first by a similarity transform augmented by object elongation, then by adjustment of each medial atom, and finally by displacing a dense sampling of the m-rep implied boundary. While these models and approaches also exist in 2D, we focus on 3D objects.The segmentation of the kidney from CT and the hippocampus from MRI serve as the major examples in this paper. The accuracy of segmentation as compared to manual, slice-by-slice segmentation is reported.

Functional connectivity magnetic resonance imaging classification of autism

Group differences in resting state functional magnetic resonance imaging connectivity between individuals with autism and typically developing controls have been widely replicated for a small number of discrete brain regions, yet the whole-brain distribution of connectivity abnormalities in autism is not well characterized. It is also unclear whether functional connectivity is sufficiently robust to be used as a diagnostic or prognostic metric in individual patients with autism. We obtained pairwise functional connectivity measurements from a lattice of 7266 regions of interest covering the entire grey matter (26.4 million connections) in a well-characterized set of 40 male adolescents and young adults with autism and 40 age-, sex- and IQ-matched typically developing subjects. A single resting state blood oxygen level-dependent scan of 8 min was used for the classification in each subject. A leave-one-out classifier successfully distinguished autism from control subjects with 83% sensitivity and 75% specificity for a total accuracy of 79% (P = 1.1 × 10(-7)). In subjects <20 years of age, the classifier performed at 89% accuracy (P = 5.4 × 10(-7)). In a replication dataset consisting of 21 individuals from six families with both affected and unaffected siblings, the classifier performed at 71% accuracy (91% accuracy for subjects <20 years of age). Classification scores in subjects with autism were significantly correlated with the Social Responsiveness Scale (P = 0.05), verbal IQ (P = 0.02) and the Autism Diagnostic Observation Schedule-Generics combined social and communication subscores (P = 0.05). An analysis of informative connections demonstrated that region of interest pairs with strongest correlation values were most abnormal in autism. Negatively correlated region of interest pairs showed higher correlation in autism (less anticorrelation), possibly representing weaker inhibitory connections, particularly for long connections (Euclidean distance >10 cm). Brain regions showing greatest differences included regions of the default mode network, superior parietal lobule, fusiform gyrus and anterior insula. Overall, classification accuracy was better for younger subjects, with differences between autism and control subjects diminishing after 19 years of age. Classification scores of unaffected siblings of individuals with autism were more similar to those of the control subjects than to those of the subjects with autism. These findings indicate feasibility of a functional connectivity magnetic resonance imaging diagnostic assay for autism.

Riemannian geometry for the statistical analysis of diffusion tensor data

The tensors produced by diffusion tensor magnetic resonance imaging (DT-MRI) represent the covariance in a Brownian motion model of water diffusion. Under this physical interpretation, diffusion tensors are required to be symmetric, positive-definite. However, current approaches to statistical analysis of diffusion tensor data, which treat the tensors as linear entities, do not take this positive-definite constraint into account. This difficulty is due to the fact that the space of diffusion tensors does not form a vector space. In this paper we show that the space of diffusion tensors is a type of curved manifold known as a Riemannian symmetric space. We then develop methods for producing statistics, namely averages and modes of variation, in this space. We show that these statistics preserve natural geometric properties of the tensors, including the constraint that their eigenvalues be positive. The symmetric space formulation also leads to a natural definition for interpolation of diffusion tensors and a new measure of anisotropy. We expect that these methods will be useful in the registration of diffusion tensor images, the production of statistical atlases from diffusion tensor data, and the quantification of the anatomical variability caused by disease. The framework presented in this paper should also be useful in other applications where symmetric, positive-definite tensors arise, such as mechanics and computer vision.

Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors

Diffusion tensor magnetic resonance imaging (DT-MRI) is emerging as an important tool in medical image analysis of the brain. However, relatively little work has been done on producing statistics of diffusion tensors. A main difficulty is that the space of diffusion tensors, i.e., the space of symmetric, positive-definite matrices, does not form a vector space. Therefore, standard linear statistical techniques do not apply. We show that the space of diffusion tensors is a type of curved manifold known as a Riemannian symmetric space. We then develop methods for producing statistics, namely averages and modes of variation, in this space. In our previous work we introduced principal geodesic analysis, a generalization of principal component analysis, to compute the modes of variation of data in Lie groups. In this work we expand the method of principal geodesic analysis to symmetric spaces and apply it to the computation of the variability of diffusion tensor data. We expect that these methods will be useful in the registration of diffusion tensor images, the production of statistical atlases from diffusion tensor data, and the quantification of the anatomical variability caused by disease.

Microstructural connectivity of the arcuate fasciculus in adolescents with high-functioning autism.

The arcuate fasciculus is a white matter fiber bundle of great importance in language. In this study, diffusion tensor imaging (DTI) was used to infer white matter integrity in the arcuate fasciculi of a group of subjects with high-functioning autism and a control group matched for age, handedness, IQ, and head size. The arcuate fasciculus for each subject was automatically extracted from the imaging data using a new volumetric DTI segmentation algorithm. The results showed a significant increase in mean diffusivity (MD) in the autism group, due mostly to an increase in the radial diffusivity (RD). A test of the lateralization of DTI measurements showed that both MD and fractional anisotropy (FA) were less lateralized in the autism group. These results suggest that white matter microstructure in the arcuate fasciculus is affected in autism and that the language specialization apparent in the left arcuate of healthy subjects is not as evident in autism, which may be related to poorer language functioning.

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.

Fiber tract-oriented statistics for quantitative diffusion tensor MRI analysis

Diffusion tensor imaging (DTI) has become the major modality to study properties of white matter and the geometry of fiber tracts of the human brain. Clinical studies mostly focus on regional statistics of fractional anisotropy (FA) and mean diffusivity (MD) derived from tensors. Existing analysis techniques do not sufficiently take into account that the measurements are tensors, and thus require proper interpolation and statistics based on tensors, and that regions of interest are fiber tracts with complex spatial geometry. We propose a new framework for quantitative tract-oriented DTI analysis that includes tensor interpolation and averaging, using nonlinear Riemannian symmetric space. As a result, tracts of interest are represented by the geometry of the medial spine attributed with tensor statistics calculated within cross-sections. Examples from a clinical neuroimaging study of the early developing brain illustrate the potential of this new method to assess white matter fiber maturation and integrity.

Rician noise removal in diffusion tensor MRI

Rician noise introduces a bias into MRI measurements that can have a significant impact on the shapes and orientations of tensors in diffusion tensor magnetic resonance images. This is less of a problem in structural MRI, because this bias is signal dependent and it does not seriously impair tissue identification or clinical diagnoses. However, diffusion imaging is used extensively for quantitative evaluations, and the tensors used in those evaluations are biased in ways that depend on orientation and signal levels. This paper presents a strategy for filtering diffusion tensor magnetic resonance images that addresses these issues. The method is a maximum a posteriori estimation technique that operates directly on the diffusion weighted images and accounts for the biases introduced by Rician noise. We account for Rician noise through a data likelihood term that is combined with a spatial smoothing prior. The method compares favorably with several other approaches from the literature, including methods that filter diffusion weighted imagery and those that operate directly on the diffusion tensors.

Longitudinal changes in cortical thickness in autism and typical development.

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.

Atypical Diffusion Tensor Hemispheric Asymmetry in Autism

Background: Biological measurements that distinguish individuals with autism from typically developing individuals and those with other developmental and neuropsychiatric disorders must demonstrate very high performance to have clinical value as potential imaging biomarkers. We hypothesized that further study of white matter microstructure (WMM) in the superior temporal gyrus (STG) and temporal stem (TS), two brain regions in the temporal lobe containing circuitry central to language, emotion, and social cognition, would identify a useful combination of classification features and further understand autism neuropathology. Methods: WMM measurements from the STG and TS were examined from 30 high‐functioning males satisfying full criteria for idiopathic autism aged 7–28 years and 30 matched controls and a replication sample of 12 males with idiopathic autism and 7 matched controls who participated in a previous case–control diffusion tensor imaging (DTI) study. Language functioning, adaptive functioning, and psychotropic medication usage were also examined. Results: In the STG, we find reversed hemispheric asymmetry of two separable measures of directional diffusion coherence, tensor skewness, and fractional anisotropy. In autism, tensor skewness is greater on the right and fractional anisotropy is decreased on the left. We also find increased diffusion parallel to white matter fibers bilaterally. In the right not left TS, we find increased omnidirectional, parallel, and perpendicular diffusion. These six multivariate measurements possess very high ability to discriminate individuals with autism from individuals without autism with 94% sensitivity, 90% specificity, and 92% accuracy in our original and replication samples. We also report a near‐significant association between the classifier and a quantitative trait index of autism and significant correlations between two classifier components and measures of language, IQ, and adaptive functioning in autism.