Faculty Bibliography

A crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3-D medial model that allows continuous interpolation of the medial manifold and provides a map back and forth between it and the boundary. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system. We use these integrals to optimize correspondence during model construction, reducing variability due to the model parameterization that could potentially mask true shape change effects. Discrimination and hypothesis testing of populations of shapes are expected to benefit, potentially resulting in improved significance of shape differences between populations even with a smaller sample size.

The presence of Rician noise in magnetic resonance imaging (MRI) introduces systematic errors in diffusion tensor imaging (DTI) measurements. This paper evaluates gradient direction schemes and tensor estimation routines to determine how to achieve the maximum accuracy and precision of tensor derived measures for a fixed amount of scan time. We present Monte Carlo simulations that quantify the effect of noise on diffusion measurements and validate these simulation results against appropriate in-vivo images. The predicted values of the systematic and random error caused by imaging noise are essential both for interpreting the results of statistical analysis and for selecting optimal imaging protocols given scan time limitations.

This paper presents a novel and fast probabilistic method for white matter fiber tracking from diffusion weighted MRI (DWI). We formulate fiber tracking on a nonlinear state space model which is able to capture both smoothness regularity of fibers and uncertainties of the local fiber orientations due to noise and partial volume effects. The global tracking model is implemented using particle filtering, which allows us to recursively compute the posterior distribution of the potential fibers. The fiber orientation distribution is theoretically formulated for prolate and oblate tensors separately. Fast and efficient sampling is realised using the von Mises-Fisher distribution on unit spheres. Given a seed point, the method is able to rapidly locate the global optimal fiber and also provide a connectivity map. The proposed method is demonstrated on a brain dataset.

BACKGROUND: The uncinate fasciculus connects limbic structures, such as the hippocampus and amygdala, with frontal regions. This study utilized diffusion tensor imaging to examine the structural integrity of the uncinate fasciculus in late-life depression. METHOD: 18 elderly depressed and 19 elderly nondepressed subjects were matched for age and sex; 8 subjects had mid- to late-onset of depression while 10 subjects had early-onset depression. 3T diffusion tensor imaging-based fiber tract mapping delineated the uncinate fasciculus in each hemisphere, which guided measurement of the fractional anisotropy of the uncinate fasciculus in the temporal stem. After controlling for age and sex, differences between diagnostic groups were assessed. RESULTS: After controlling for age and sex, individuals with early onset depression exhibited lower anisotropy of the left uncinate fasciculus than did mid- and late-onset or nondepressed subjects (F(2,36) = 4.50, p = 0.02). Analyses of the right uncinate fasciculus were not statistically significant. CONCLUSIONS: This provides preliminary evidence that there is a structural connectivity deficit between left frontal and limbic structures in early-onset depression. Further work is needed to determine if this is seen in younger depressed subjects, and if it influences treatment outcomes.

Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a C comprehensive set of tools for the computation of 3D structural statistical shape analysis. It has been applied in several studies on brain morphometry, but can potentially be employed in other 3D shape problems. Its main limitations is the necessity of spherical topology. The input of the proposed shape analysis is a set of binary segmentation of a single brain structure, such as the hippocampus or caudate. These segmentations are converted into a corresponding spherical harmonic description (SPHARM), which is then sampled into a triangulated surfaces (SPHARM-PDM). After alignment, differences between groups of surfaces are computed using the Hotelling T(2) two sample metric. Statistical p-values, both raw and corrected for multiple comparisons, result in significance maps. Additional visualization of the group tests are provided via mean difference magnitude and vector maps, as well as maps of the group covariance information. The correction for multiple comparisons is performed via two separate methods that each have a distinct view of the problem. The first one aims to control the family-wise error rate (FWER) or false-positives via the extrema histogram of non-parametric permutations. The second method controls the false discovery rate and results in a less conservative estimate of the false-negatives. Prior versions of this shape analysis framework have been applied already to clinical studies on hippocampus and lateral ventricle shape in adult schizophrenics. The novelty of this submission is the use of the Hotelling, T2 two-sample group difference metric for the computation of a template free statistical shape analysis. Template free group testing allowed this framework to become independent of any template choice. as well as it improved the sensitivity of our method considerably. In addition to our existing correction methodology for the multiple comparison problem using non-parametric permutation tests, we have extended the testing framework to include False Discovery Rate (FDR). FDR provides a significance correction with higher sensitivity while allowing a expected minimal amount of false-positives compared to our prior testing scheme.

An important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical analysis of sets of interrelated objects. In this paper, we present a framework for discriminant analysis of populations of 3-D multi-object sets. In view of the driving medical applications, a skeletal object parametrization of shape is chosen since it naturally encodes thickening, bending and twisting. In a multi-object setting, we not only consider a joint analysis of sets of shapes but also must take into account differences in pose. Statistics on features of medial descriptions and pose parameters, which include rotational frames and distances, uses a Riemannian symmetric space instead of the standard Euclidean metric. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Joint analysis of 10 subcortical brain structures in a pediatric autism study demonstrates that multi-object analysis of shape results in a better group discrimination than pose, and that the combination of pose and shape performs better than shape alone. Finally, given a discriminating axis of shape and pose, we can visualize the differences between the populations.