Sparse Projections of Medical Images onto Manifolds

Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of-sample extensions are applied by constructing an interpolation function that maps from the input space to the low-dimensional manifold. Commonly used approaches such as the Nyström extension and kernel ridge regression require using all training points. We propose an interpolation function that only depends on a small subset of the input training data. Consequently, in the testing phase each new point only needs to be compared against a small number of input training data in order to project the point onto the low-dimensional space. We interpret our method as an out-of-sample extension that approximates kernel ridge regression. Our method involves solving a simple convex optimization problem and has the attractive property of guaranteeing an upper bound on the approximation error, which is crucial for medical applications. Tuning this error bound controls the sparsity of the resulting interpolation function. We illustrate our method in two clinical applications that require fast mapping of input images onto a low-dimensional space.National Alliance for Medical Image Computing (U.S.) (grant NIH NIBIB NAMIC U54-EB005149)National Institutes of Health (U.S.) (grant NIH NCRR NAC P41-RR13218)National Institutes of Health (U.S.) (grant NIH NIBIB NAC P41-EB-015902

Characterising population variability in brain structure through models of whole-brain structural connectivity

Models of whole-brain connectivity are valuable for understanding neurological function. This thesis seeks to develop an optimal framework for extracting models of whole-brain connectivity from clinically acquired diffusion data. We propose new approaches for studying these models. The aim is to develop techniques which can take models of brain connectivity and use them to identify biomarkers or phenotypes of disease. The models of connectivity are extracted using a standard probabilistic tractography algorithm, modified to assess the structural integrity of tracts, through estimates of white matter anisotropy. Connections are traced between 77 regions of interest, automatically extracted by label propagation from multiple brain atlases followed by classifier fusion. The estimates of tissue integrity for each tract are input as indices in 77x77 ”connectivity” matrices, extracted for large populations of clinical data. These are compared in subsequent studies. To date, most whole-brain connectivity studies have characterised population differences using graph theory techniques. However these can be limited in their ability to pinpoint the locations of differences in the underlying neural anatomy. Therefore, this thesis proposes new techniques. These include a spectral clustering approach for comparing population differences in the clustering properties of weighted brain networks. In addition, machine learning approaches are suggested for the first time. These are particularly advantageous as they allow classification of subjects and extraction of features which best represent the differences between groups. One limitation of the proposed approach is that errors propagate from segmentation and registration steps prior to tractography. This can cumulate in the assignment of false positive connections, where the contribution of these factors may vary across populations, causing the appearance of population differences where there are none. The final contribution of this thesis is therefore to develop a common co-ordinate space approach. This combines probabilistic models of voxel-wise diffusion for each subject into a single probabilistic model of diffusion for the population. This allows tractography to be performed only once, ensuring that there is one model of connectivity. Cross-subject differences can then be identified by mapping individual subjects’ anisotropy data to this model. The approach is used to compare populations separated by age and gender

Machine learning for image-based classification of Alzheimer's disease

Imaging biomarkers for Alzheimer's disease are important for improved diagnosis and monitoring, as well as drug discovery. Automated image-based classification of individual patients could provide valuable support for clinicians. This work investigates machine learning methods aimed at the early identification of Alzheimer's disease, and prediction of progression in mild cognitive impairment. Data are obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Australian Imaging, Biomarker and Lifestyle Flagship Study of Ageing (AIBL). Multi-region analyses of cross-sectional and longitudinal FDG-PET images from ADNI are performed. Information extracted from FDG-PET images acquired at a single timepoint is used to achieve classification results comparable with those obtained using data from research-quality MRI, or cerebrospinal fluid biomarkers. The incorporation of longitudinal information results in improved classification performance. Changes in multiple biomarkers may provide complementary information for the diagnosis and prognosis of Alzheimer's disease. A multi-modality classification framework based on random forest-derived similarities is applied to imaging and biological data from ADNI. Random forests provide consistent similarities for multiple modalities, facilitating the combination of different types of features. Classification based on the combination of MRI volumes, FDG-PET intensities, cerebrospinal fluid biomarkers, and genetics out-performs classification based on any individual modality. Multi-region analysis of MRI acquired at a single timepoint is used to show volumetric differences in cognitively normal individuals differing in amyloid-based risk status for the development of Alzheimer's disease. Reduced volumes in temporo-parietal and orbito-frontal regions in high-risk individuals from both ADNI and AIBL could be indicative of early signs of neurodegeneration. This suggests that volumetric MRI can reveal structural brain changes preceding the onset of clinical symptoms. Taken together, these results suggest that image-based classification can support diagnosis in Alzheimer's disease and preceding stages. Future work may lead to more finely meshed prognostic data that may be useful clinically and for research

Automated Morphometric Characterization of the Cerebral Cortex for the Developing and Ageing Brain

Morphometric characterisation of the cerebral cortex can provide information about patterns of brain development and ageing and may be relevant for diagnosis and estimation of the progression of diseases such as Alzheimer's, Huntington's, and schizophrenia. Therefore, understanding and describing the differences between populations in terms of structural volume, shape and thickness is of critical importance. Methodologically, due to data quality, presence of noise, PV effects, limited resolution and pathological variability, the automated, robust and time-consistent estimation of morphometric features is still an unsolved problem. This thesis focuses on the development of tools for robust cross-sectional and longitudinal morphometric characterisation of the human cerebral cortex. It describes techniques for tissue segmentation, structural and morphometric characterisation, cross-sectional and longitudinally cortical thickness estimation from serial MRI images in both adults and neonates. Two new probabilistic brain tissue segmentation techniques are introduced in order to accurately and robustly segment the brain of elderly and neonatal subjects, even in the presence of marked pathology. Two other algorithms based on the concept of multi-atlas segmentation propagation and fusion are also introduced in order to parcelate the brain into its multiple composing structures with the highest possible segmentation accuracy. Finally, we explore the use of the Khalimsky cubic complex framework for the extraction of topologically correct thickness measurements from probabilistic segmentations without explicit parametrisation of the edge. A longitudinal extension of this method is also proposed. The work presented in this thesis has been extensively validated on elderly and neonatal data from several scanners, sequences and protocols. The proposed algorithms have also been successfully applied to breast and heart MRI, neck and colon CT and also to small animal imaging. All the algorithms presented in this thesis are available as part of the open-source package NiftySeg

On the Manifold Structure of the Space of Brain Images

Abstract. This paper investigates an approach to model the space of brain images through a low-dimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approximation, by a low-dimensional manifold, i.e. a parametrization of the set of images. The approach builds on recent advances in manifold learning that allow to uncover nonlinear trends in data. We combine this manifold learning with distance measures between images that capture shape, in order to learn the underlying structure of a database of brain images. The proposed method is generative. New images can be created from the manifold parametrization and existing images can be projected onto the manifold. By measuring projection distance of a held out set of brain images we evaluate the fit of the proposed manifold model to the data and we can compute statistical properties of the data using this manifold structure. We demonstrate this technology on a database of 436 MR brain images.