Proceedings of the Second International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'08) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceThe goal of computational anatomy is to analyze and to statistically model the anatomy of organs in different subjects. Computational anatomic methods are generally based on the extraction of anatomical features or manifolds which are then statistically analyzed, often through a non-linear registration. There are nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behavior of intra-subject deformations. However, it is more difficult to relate the anatomies of different subjects. In the absence of any justified physical model, diffeomorphisms provide a general mathematical framework that enforce topological consistency. Working with such infinite dimensional space raises some deep computational and mathematical problems, in particular for doing statistics. Likewise, modeling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed (e.g. smooth left-invariant metrics, focus on well-behaved subspaces of diffeomorphisms, modeling surfaces using courants, etc.) The goal of the Mathematical Foundations of Computational Anatomy (MFCA) workshop is to foster the interactions between the mathematical community around shapes and the MICCAI community around computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop aims at being a forum for the exchange of the theoretical ideas and a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the very successful first edition of this workshop in 2006 (see http://www.inria.fr/sophia/asclepios/events/MFCA06/), the second edition was held in New-York on September 6, in conjunction with MICCAI 2008. Contributions were solicited in Riemannian and group theoretical methods, Geometric measurements of the anatomy, Advanced statistics on deformations and shapes, Metrics for computational anatomy, Statistics of surfaces. 34 submissions were received, among which 9 were accepted to MICCAI and had to be withdrawn from the workshop. Each of the remaining 25 paper was reviewed by three members of the program committee. To guaranty a high level program, 16 papers only were selected

Normative spatiotemporal fetal brain maturation with satisfactory development at 2 years

Maturation of the human fetal brain should follow precisely scheduled structural growth and folding of the cerebral cortex for optimal postnatal function1 . We present a normative digital atlas of fetal brain maturation based on a prospective international cohort of healthy pregnant women2 , selected using World Health Organization recommendations for growth standards3 . Their fetuses were accurately dated in the first trimester, with satisfactory growth and neurodevelopment from early pregnancy to 2 years of age4,5 . The atlas was produced using 1,059 optimal quality, three dimensional ultrasound brain volumes from 899 of the fetuses and an automated analysis pipeline6–8 . The atlas corresponds structurally to published magnetic resonance images9 , but with finer anatomical details in deep grey matter. The between study site variability represented less than 8.0% of the total variance of all brain measures, supporting pooling data from the eight study sites to produce patterns of normative maturation. We have thereby generated an average representation of each cerebral hemisphere between 14 and 31 weeks’ gestation with quantification of intracranial volume variability and growth patterns. Emergent asymmetries were detectable from as early as 14 weeks, with peak asymmetries in regions associated with language development and functional lateralization between 20 and 26 weeks’ gestation. These patterns were validated in 1,487 three-dimensional brain volumes from 1,295 different fetuses in the same cohort. We provide a unique spatiotemporal benchmark of fetal brain maturation from a large cohort with normative postnatal growth and neurodevelopment

Morphogenetic Principles of Brain Organisation in Health and Disease

Non-invasive neuroimaging methods, such as MRI, provide a window into the structure of the mammalian brain. However, despite the ubiquity of these methods, the biological interpretation of the information obtained using these tools remains elusive. In order to accurately link this macroscale data to microscale measurements, it is critical that the construct validity is high. This thesis provides novel analyses, pipelines and methods to: i) generate and validate maps of brain organisation obtained via MRI, and ii) demonstrate the utility of these methods in capturing elements of cognition and psychopathology. First, in Chapter 1, I review some of the neuroscientific context for the new methods presented, from cytoarchitecture to gene expression to connectomes. Chapters 2-4 introduce a new method, “Morphometric Similarity Mapping”, which captures the brain organisation of an individual by mapping the relationships of multiple features of the cerebral cortex. Chapter 2 focuses on the development of the analysis pipeline and the graph theoretical features of the resulting morphometric similarity networks (MSNs), with an emphasis on reproducibility. Chapter 3 highlights the generalisability of MSNs to the macaque monkey, linking MSNs to ex vivo tract tracing experiments and presenting new tools for processing non-human imaging data; as well as evidence that MSN topography is organised by cytoarchitectonic features. Chapter 4 is focused on determining the transcriptomic correlates of MSNs using publicly available gene expression maps, and on applying MSNs to examine the relationship between brain organisation and intelligence. Chapter 5 is dedicated to rigorous evaluation of the applicability of MSNs to measure specific disease-relevant phenotypes in 8 rare genetic disorder cohorts. This includes the validation of novel methods for utilising data from both single-cell sequencing technologies and differential gene expression experiments (in multiple tissue types) in analysing neuroimaging and bulk transcriptomic brain maps. Chapter 6 provides a brief summary and presents some ongoing and future projects expanding on this original work. It also importantly discusses a general framework of comparing brain maps, including MSNs and gene expression, as well as other canonical maps of brain structure and function. Altogether, this thesis presents and evaluates novel methods and applications for integrating multimodal neuroimaging data with genetic data derived from multiple tissue types and through various acquisition strategies. It also includes tools for performing these analyses in non-human primates, and pipelines for statistically comparing brain maps. These results not only provide insight into the manifestation of brain-related changes due to various components of human variation, but also provides a framework for evaluating this variation at multiple biological scales purely from non-invasive neuroimaging data

Doctor of Philosophy in Computing

dissertationStatistical shape analysis has emerged as an important tool for the quantitative analysis of anatomy in many medical imaging applications. The correspondence based approach to evaluate shape variability is a popular method, based on comparing configurations of carefully placed landmarks on each shape. In recent years, methods for automatic placement of landmarks have enhanced the ability of this approach to capture statistical properties of shape populations. However, biomedical shapes continue to present considerable difficulties in automatic correspondence optimization due to inherent geometric complexity and the need to correlate shape change with underlying biological parameters. This dissertation addresses these technical difficulties and presents improved shape correspondence models. In particular, this dissertation builds on the particle-based modeling (PBM) framework described by Joshua Cates' 2010 Ph.D. dissertation. In the PBM framework, correspondences are modeled as a set of dynamic points or a particle system, positioned automatically on shape surfaces by optimizing entropy contained in the model, with the idea of balancing model simplicity against accuracy of the particle system representation of shapes. This dissertation is a collection of four papers that extend the PBM framework to include shape regression and longitudinal analysis and also adds new methods to improve modeling of complex shapes. It also includes a summary of two applications from the field of orthopaedics. Technical details of the PBM framework are provided in Chapter 2, after which the first topic related to the study of shape change over time is addressed (Chapters 3 and 4). In analyses of normative growth or disease progression, shape regression models allow characterization of the underlying biological process while also facilitating comparison of a sample against a normative model. The first paper introduces a shape regression model into the PBM framework to characterize shape variability due to an underlying biological parameter. It further confirms the statistical significance of this relationship via systematic permutation testing. Simple regression models are, however, not sufficient to leverage information provided by longitudinal studies. Longitudinal studies collect data at multiple time points for each participant and have the potential to provide a rich picture of the anatomical changes occurring during development, disease progression, or recovery. The second paper presents a linear-mixed-effects (LME) shape model in order to fully leverage the high-dimensional, complex features provided by longitudinal data. The parameters of the LME shape model are estimated in a hierarchical manner within the PBM framework. The topic of geometric complexity present in certain biological shapes is addressed next (Chapters 5 and 6). Certain biological shapes are inherently complex and highly variable, inhibiting correspondence based methods from producing a faithful representation of the average shape. In the PBM framework, use of Euclidean distances leads to incorrect particle system interactions while a position-only representation leads to incorrect correspondences around sharp features across shapes. The third paper extends the PBM framework to use efficiently computed geodesic distances and also adds an entropy term based on the surface normal. The fourth paper further replaces the position-only representation with a more robust distance-from-landmark feature in the PBM framework to obtain isometry invariant correspondences. Finally, the above methods are applied to two applications from the field of orthopaedics. The first application uses correspondences across an ensemble of human femurs to characterize morphological shape differences due to femoroacetabular impingement. The second application involves an investigation of the short bone phenotype apparent in mouse models of multiple osteochondromas. Metaphyseal volume deviations are correlated with deviations in length to quantify the effect of cancer toward the apparent shortening of long bones (femur, tibia-fibula) in mouse models

Bayesian generative learning of brain and spinal cord templates from neuroimaging datasets

In the field of neuroimaging, Bayesian modelling techniques have been largely adopted and recognised as powerful tools for the purpose of extracting quantitative anatomical and functional information from medical scans. Nevertheless the potential of Bayesian inference has not yet been fully exploited, as many available tools rely on point estimation techniques, such as maximum likelihood estimation, rather than on full Bayesian inference. The aim of this thesis is to explore the value of approximate learning schemes, for instance variational Bayes, to perform inference from brain and spinal cord MRI data. The applications that will be explored in this work mainly concern image segmentation and atlas construction, with a particular emphasis on the problem of shape and intensity prior learning, from large training data sets of structural MR scans. The resulting computational tools are intended to enable integrated brain and spinal cord morphometric analyses, as opposed to the approach that is most commonly adopted in neuroimaging, which consists in optimising separate tools for brain and spine morphometrics

Multi-atlas segmentation using clustering, local non-linear manifold embeddings and target-specific templates

Multi-atlas segmentation (MAS) has become an established technique for the automated delineation of anatomical structures. The often manually annotated labels from each of multiple pre-segmented images (atlases) are typically transferred to a target through the spatial mapping of corresponding structures of interest. The mapping can be estimated by pairwise registration between each atlas and the target or by creating an intermediate population template for spatial normalisation of atlases and targets. The former is done at runtime which is computationally expensive but provides high accuracy. In the latter approach the template can be constructed from the atlases offline requiring only one registration to the target at runtime. Although this is computationally more efficient, the composition of deformation fields can lead to decreased accuracy. Our goal was to develop a MAS method which was both efficient and accurate. In our approach we create a target-specific template (TST) which has a high similarity to the target and serves as intermediate step to increase registration accuracy. The TST is constructed from the atlas images that are most similar to the target. These images are determined in low-dimensional manifold spaces on the basis of deformation fields in local regions of interest. We also introduce a clustering approach to divide atlas labels into meaningful sub-regions of interest and increase local specificity for TST construction and label fusion. Our approach was tested on a variety of MR brain datasets and applied to an in-house dataset. We achieve state-of-the-art accuracy while being computationally much more efficient than competing methods. This efficiency opens the door to the use of larger sets of atlases which could lead to further improvement in segmentation accuracy

Normative spatiotemporal fetal brain maturation with satisfactory development at 2 years.

Maturation of the human fetal brain should follow precisely scheduled structural growth and folding of the cerebral cortex for optimal postnatal function1. We present a normative digital atlas of fetal brain maturation based on a prospective international cohort of healthy pregnant women2, selected using World Health Organization recommendations for growth standards3. Their fetuses were accurately dated in the first trimester, with satisfactory growth and neurodevelopment from early pregnancy to 2 years of age4,5. The atlas was produced using 1,059 optimal quality, three-dimensional ultrasound brain volumes from 899 of the fetuses and an automated analysis pipeline6-8. The atlas corresponds structurally to published magnetic resonance images9, but with finer anatomical details in deep grey matter. The between-study site variability represented less than 8.0% of the total variance of all brain measures, supporting pooling data from the eight study sites to produce patterns of normative maturation. We have thereby generated an average representation of each cerebral hemisphere between 14 and 31 weeks' gestation with quantification of intracranial volume variability and growth patterns. Emergent asymmetries were detectable from as early as 14 weeks, with peak asymmetries in regions associated with language development and functional lateralization between 20 and 26 weeks' gestation. These patterns were validated in 1,487 three-dimensional brain volumes from 1,295 different fetuses in the same cohort. We provide a unique spatiotemporal benchmark of fetal brain maturation from a large cohort with normative postnatal growth and neurodevelopment

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

Multi-atlas segmentation using clustering, local non-linear manifold embeddings and target-specific templates

Multi-atlas segmentation (MAS) has become an established technique for the automated delineation of anatomical structures. The often manually annotated labels from each of multiple pre-segmented images (atlases) are typically transferred to a target through the spatial mapping of corresponding structures of interest. The mapping can be estimated by pairwise registration between each atlas and the target or by creating an intermediate population template for spatial normalisation of atlases and targets. The former is done at runtime which is computationally expensive but provides high accuracy. In the latter approach the template can be constructed from the atlases offline requiring only one registration to the target at runtime. Although this is computationally more efficient, the composition of deformation fields can lead to decreased accuracy. Our goal was to develop a MAS method which was both efficient and accurate. In our approach we create a target-specific template (TST) which has a high similarity to the target and serves as intermediate step to increase registration accuracy. The TST is constructed from the atlas images that are most similar to the target. These images are determined in low-dimensional manifold spaces on the basis of deformation fields in local regions of interest. We also introduce a clustering approach to divide atlas labels into meaningful sub-regions of interest and increase local specificity for TST construction and label fusion. Our approach was tested on a variety of MR brain datasets and applied to an in-house dataset. We achieve state-of-the-art accuracy while being computationally much more efficient than competing methods. This efficiency opens the door to the use of larger sets of atlases which could lead to further improvement in segmentation accuracy