Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

A dynamical model reveals gene co-localizations in nucleus

Co-localization of networks of genes in the nucleus is thought to play an important role in determining gene expression patterns. Based upon experimental data, we built a dynamical model to test whether pure diffusion could account for the observed co-localization of genes within a defined subnuclear region. A simple standard Brownian motion model in two and three dimensions shows that preferential co-localization is possible for co-regulated genes without any direct interaction, and suggests the occurrence may be due to a limitation in the number of available transcription factors. Experimental data of chromatin movements demonstrates that fractional rather than standard Brownian motion is more appropriate to model gene mobilizations, and we tested our dynamical model against recent static experimental data, using a sub-diffusion process by which the genes tend to colocalize more easily. Moreover, in order to compare our model with recently obtained experimental data, we studied the association level between genes and factors, and presented data supporting the validation of this dynamic model. As further applications of our model, we applied it to test against more biological observations. We found that increasing transcription factor number, rather than factory number and nucleus size, might be the reason for decreasing gene co-localization. In the scenario of frequency-or amplitude-modulation of transcription factors, our model predicted that frequency-modulation may increase the co-localization between its targeted genes

3D shape matching and registration : a probabilistic perspective

Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201

Multimodal image analysis of the human brain

Gedurende de laatste decennia heeft de snelle ontwikkeling van multi-modale en niet-invasieve hersenbeeldvorming technologieën een revolutie teweeg gebracht in de mogelijkheid om de structuur en functionaliteit van de hersens te bestuderen. Er is grote vooruitgang geboekt in het beoordelen van hersenschade door gebruik te maken van Magnetic Reconance Imaging (MRI), terwijl Elektroencefalografie (EEG) beschouwd wordt als de gouden standaard voor diagnose van neurologische afwijkingen. In deze thesis focussen we op de ontwikkeling van nieuwe technieken voor multi-modale beeldanalyse van het menselijke brein, waaronder MRI segmentatie en EEG bronlokalisatie. Hierdoor voegen we theorie en praktijk samen waarbij we focussen op twee medische applicaties: (1) automatische 3D MRI segmentatie van de volwassen hersens en (2) multi-modale EEG-MRI data analyse van de hersens van een pasgeborene met perinatale hersenschade. We besteden veel aandacht aan de verbetering en ontwikkeling van nieuwe methoden voor accurate en ruisrobuuste beeldsegmentatie, dewelke daarna succesvol gebruikt worden voor de segmentatie van hersens in MRI van zowel volwassen als pasgeborenen. Daarenboven ontwikkelden we een geïntegreerd multi-modaal methode voor de EEG bronlokalisatie in de hersenen van een pasgeborene. Deze lokalisatie wordt gebruikt voor de vergelijkende studie tussen een EEG aanval bij pasgeborenen en acute perinatale hersenletsels zichtbaar in MRI

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and Uncertainty

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced datasets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image analysis. The present thesis introduces a new concept for the estimation and propagation of uncertainty involved in image analysis operators and new segmentation algorithms that are suitable for terabyte-scale analyses of 3D+t microscopy images.Comment: 218 pages, 58 figures, PhD thesis, Department of Mechanical Engineering, Karlsruhe Institute of Technology, published online with KITopen (License: CC BY-SA 3.0, http://dx.doi.org/10.5445/IR/1000057821

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and Uncertainty

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced data sets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image analysis. The present work introduces a new concept for the estimation and propagation of uncertainty involved in image analysis operators and new segmentation algorithms that are suitable for terabyte-scale analyses of 3D+t microscopy images

Quantification of cortical folding using MR image data

The cerebral cortex is a thin layer of tissue lining the brain where neural circuits perform important high level functions including sensory perception, motor control and language processing. In the third trimester the fetal cortex folds rapidly from a smooth sheet into a highly convoluted arrangement of gyri and sulci. Premature birth is a high risk factor for poor neurodevelopmental outcome and has been associated with abnormal cortical development, however the nature of the disruption to developmental processes is not fully understood. Recent developments in magnetic resonance imaging have allowed the acquisition of high quality brain images of preterms and also fetuses in-utero. The aim of this thesis is to develop techniques which quantify folding from these images in order to better understand cortical development in these two populations. A framework is presented that quantifies global and regional folding using curvature-based measures. This methodology was applied to fetuses over a wide gestational age range (21.7 to 38.9 weeks) for a large number of subjects (N = 80) extending our understanding of how the cortex folds through this critical developmental period. The changing relationship between the folding measures and gestational age was modelled with a Gompertz function which allowed an accurate prediction of physiological age. A spectral-based method is outlined for constructing a spatio-temporal surface atlas (a sequence of mean cortical surface meshes for weekly intervals). A key advantage of this method is the ability to do group-wise atlasing without bias to the anatomy of an initial reference subject. Mean surface templates were constructed for both fetuses and preterms allowing a preliminary comparison of mean cortical shape over the postmenstrual age range 28-36 weeks. Displacement patterns were revealed which intensified with increasing prematurity, however more work is needed to evaluate the reliability of these findings.Open Acces

CaTCHing the functional and structural properties of chromosome folding

Proper development requires that genes are expressed at the right time, in the right tissue, and at the right transcriptional level. In metazoans, this involves long-range cis-regulatory elements such as enhancers, which can be located up to hundreds of kilobases away from their target promoters. How enhancers find their target genes and avoid aberrant interactions with non-target genes is currently under intense investigations. The predominant model for enhancer function involves its direct physical looping between the enhancer and target promoter. The three-dimensional organization of chromatin, which accommodates promoter- enhancer interactions, therefore might play an important role in the specificity of these interactions. In the last decade, the development of a class of techniques called chromosome conformation capture (3C) and its derivatives have revolutionized the field of chromatin folding. In particular, the genome-wide version of 3C, Hi-C, revealed that mammalian chromosomes possess a rich hierarchy of folding layers, from multi-megabase compartments corresponding to mutually exclusive associations of active and inactive chromatin to topologically associating domains (TADs), which reflect regions with preferential internal interactions. Although the mechanisms that give rise to this hierarchy are still poorly understood, there is increasing evidence to suggest that TADs represent fundamental functional units for establishing the correct pattern of enhancer-promoter interactions. This is thought to occur through two complementary mechanisms: on the one hand, TADs are thought to increase the chances that regulatory elements meet each other by confining them within the same domain; on the other hand, by segregation of physical interactions across the boundary to avoid unwanted events to occur frequently. It is however unclear whether the properties that have been attributed to TADs are specific to TADs, or rather common features among the whole hierarchy. To address this question, I have implemented an algorithm named Caller of Topological Chromosomal Hierarchies (CaTCH). CaTCH is able to detect nested hierarchies of domains, allowing a comprehensive analysis of structural and functional properties across the folding hierarchy. By applying CaTCH to published Hi-C data in mouse embryonic stem cells (ESCs) and neural progenitor cells (NPCs), I showed that TADs emerge as a functionally privileged scale. In particular, TADs appear to be the scale where accumulation of CTCF at domain boundaries and transcriptional co-regulation during differentiation is maximal. Moreover, TADs appear to be the folding scale where the partitioning of interactions within transcriptionally active domains (and notably between active enhancers and promoters) is optimized. 3C-based methods have enabled fundamental discoveries such as the existence of TADs and CTCF-mediated chromatin loops. 3C methods detect chromatin interactions as ligation products after crosslinking the DNA. Crosslinking and ligation have been often criticized as potential sources of experimental biases, raising the question of whether TADs and CTCF- mediated chromatin loops actually exist in living cells. To address this, in collaboration with Josef Redolfi, we developed a new method termed ‘DamC’ which combines DNA methylation with physical modeling to detect chromosomal interactions in living cells, at the molecular scale, without relying on crosslinking and ligation. By applying DamC to mouse ESCs, we provide the first in vivo and crosslinking- and ligation-free validation of chromosomal structures detected by 3C-methods, namely TADs and CTCF-mediated chromatin loops. DamC, together with 3C-based methods, thus have shown that mammalian chromosomes possess a rich hierarchy of folding layers. An important challenge in the field is to understand the mechanisms that drive the establishment these folding layers. In this sense, polymer physics represent a powerful tool to gain mechanistic insights into the hierarchical folding of mammalian chromosomes. In polymer models, the scaling of contact probability, i.e. the contact probability as a function of genomic distance, has been often used to benchmark polymer simulations and test alternative models. However, the scaling of contact probability is only one of the many properties that characterize polymer models raising the question of whether it would be enough to discriminate alternative polymer models. To address this, I have built finite-size heteropolymer models characterized by random interactions. I showed that finite-size effects, together with the heterogeneity of the interactions, are sufficient to reproduce the observed range of scaling of contact probability. This suggests that one should be careful in discriminating polymer models of chromatin folding based solely on the scaling. In conclusion, my findings have contributed to achieve a better understanding of chromatin folding, which is essential to really understand how enhancers act on promoters. The comprehensive analyses using CaTCH have provided conceptually new insights into how the architectural functionality of TADs may be established. My work on heteropolymer models has highlighted the fact that one should be careful in using solely scaling to discriminate physical models for chromatin folding. Finally, the ability to detect TADs and chromatin loops using DamC represents a fundamental result since it provides the first orthogonal in vivo validation of chromosomal structures that had essentially relied on a single technology

Visual Exploration And Information Analytics Of High-Dimensional Medical Images

Data visualization has transformed how we analyze increasingly large and complex data sets. Advanced visual tools logically represent data in a way that communicates the most important information inherent within it and culminate the analysis with an insightful conclusion. Automated analysis disciplines - such as data mining, machine learning, and statistics - have traditionally been the most dominant fields for data analysis. It has been complemented with a near-ubiquitous adoption of specialized hardware and software environments that handle the storage, retrieval, and pre- and postprocessing of digital data. The addition of interactive visualization tools allows an active human participant in the model creation process. The advantage is a data-driven approach where the constraints and assumptions of the model can be explored and chosen based on human insight and confirmed on demand by the analytic system. This translates to a better understanding of data and a more effective knowledge discovery. This trend has become very popular across various domains, not limited to machine learning, simulation, computer vision, genetics, stock market, data mining, and geography. In this dissertation, we highlight the role of visualization within the context of medical image analysis in the field of neuroimaging. The analysis of brain images has uncovered amazing traits about its underlying dynamics. Multiple image modalities capture qualitatively different internal brain mechanisms and abstract it within the information space of that modality. Computational studies based on these modalities help correlate the high-level brain function measurements with abnormal human behavior. These functional maps are easily projected in the physical space through accurate 3-D brain reconstructions and visualized in excellent detail from different anatomical vantage points. Statistical models built for comparative analysis across subject groups test for significant variance within the features and localize abnormal behaviors contextualizing the high-level brain activity. Currently, the task of identifying the features is based on empirical evidence, and preparing data for testing is time-consuming. Correlations among features are usually ignored due to lack of insight. With a multitude of features available and with new emerging modalities appearing, the process of identifying the salient features and their interdependencies becomes more difficult to perceive. This limits the analysis only to certain discernible features, thus limiting human judgments regarding the most important process that governs the symptom and hinders prediction. These shortcomings can be addressed using an analytical system that leverages data-driven techniques for guiding the user toward discovering relevant hypotheses. The research contributions within this dissertation encompass multidisciplinary fields of study not limited to geometry processing, computer vision, and 3-D visualization. However, the principal achievement of this research is the design and development of an interactive system for multimodality integration of medical images. The research proceeds in various stages, which are important to reach the desired goal. The different stages are briefly described as follows: First, we develop a rigorous geometry computation framework for brain surface matching. The brain is a highly convoluted structure of closed topology. Surface parameterization explicitly captures the non-Euclidean geometry of the cortical surface and helps derive a more accurate registration of brain surfaces. We describe a technique based on conformal parameterization that creates a bijective mapping to the canonical domain, where surface operations can be performed with improved efficiency and feasibility. Subdividing the brain into a finite set of anatomical elements provides the structural basis for a categorical division of anatomical view points and a spatial context for statistical analysis. We present statistically significant results of our analysis into functional and morphological features for a variety of brain disorders. Second, we design and develop an intelligent and interactive system for visual analysis of brain disorders by utilizing the complete feature space across all modalities. Each subdivided anatomical unit is specialized by a vector of features that overlap within that element. The analytical framework provides the necessary interactivity for exploration of salient features and discovering relevant hypotheses. It provides visualization tools for confirming model results and an easy-to-use interface for manipulating parameters for feature selection and filtering. It provides coordinated display views for visualizing multiple features across multiple subject groups, visual representations for highlighting interdependencies and correlations between features, and an efficient data-management solution for maintaining provenance and issuing formal data queries to the back end