Neuro-evolutionary evidence for a universal fractal primate brain shape

The primate cerebral cortex can take on a bewildering diversity of shapes and sizes within and across species, whilst maintaining archetypal qualities that make it instantly recognisable as a "brain". Here we present a new way of expressing the shape of a cortex explicitly as the hierarchical composition of structures across spatial scales. In computational simulations, as one successively removes sulci and gyri smaller than a specified scale, the cortices of 11 primate species are gradually coarse-grained into less folded brains until lyssencephaly (no folding). We show that this process, in all cases, occurs along a common scale-free morphometric trajectory overlapping with other mammalian species, indicating that these cortices are not only approximately fractal in shape, but also, strikingly, are approximations of the same archetypal fractal shape. These results imply the existence of a single universal gyrification mechanism that operates in a scale-free manner on cortical folds of all sizes, and that there are surprisingly few effective degrees of freedom through which cortical shapes can be selected for by evolution. Finally, we demonstrate that this new understanding can be of practical use: biological processes can now be interrogated in a highly scale-dependent way for increased sensitivity and precision. To our knowledge, this is the most parsimonious universal description of the brain's shape that is at the same time mechanistically insightful, practically useful, and in full agreement with empirical data across species and individuals

Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease-course longitudinal studies

Computational Modeling for Abnormal Brain Tissue Segmentation, Brain Tumor Tracking, and Grading

This dissertation proposes novel texture feature-based computational models for quantitative analysis of abnormal tissues in two neurological disorders: brain tumor and stroke. Brain tumors are the cells with uncontrolled growth in the brain tissues and one of the major causes of death due to cancer. On the other hand, brain strokes occur due to the sudden interruption of the blood supply which damages the normal brain tissues and frequently causes death or persistent disability. Clinical management of these brain tumors and stroke lesions critically depends on robust quantitative analysis using different imaging modalities including Magnetic Resonance (MR) and Digital Pathology (DP) images. Due to uncontrolled growth and infiltration into the surrounding tissues, the tumor regions appear with a significant texture variation in the static MRI volume and also in the longitudinal imaging study. Consequently, this study developed computational models using novel texture features to segment abnormal brain tissues (tumor, and stroke lesions), tracking the change of tumor volume in longitudinal images, and tumor grading in MR images. Manual delineation and analysis of these abnormal tissues in large scale is tedious, error-prone, and often suffers from inter-observer variability. Therefore, efficient computational models for robust segmentation of different abnormal tissues is required to support the diagnosis and analysis processes. In this study, brain tissues are characterized with novel computational modeling of multi-fractal texture features for multi-class brain tumor tissue segmentation (BTS) and extend the method for ischemic stroke lesions in MRI. The robustness of the proposed segmentation methods is evaluated using a huge amount of private and public domain clinical data that offers competitive performance when compared with that of the state-of-the-art methods. Further, I analyze the dynamic texture behavior of tumor volume in longitudinal imaging and develop post-processing frame-work using three-dimensional (3D) texture features. These post-processing methods are shown to reduce the false positives in the BTS results and improve the overall segmentation result in longitudinal imaging. Furthermore, using this improved segmentation results the change of tumor volume has been quantified in three types such as stable, progress, and shrinkage as observed by the volumetric changes of different tumor tissues in longitudinal images. This study also investigates a novel non-invasive glioma grading, for the first time in literature, that uses structural MRI only. Such non-invasive glioma grading may be useful before an invasive biopsy is recommended. This study further developed an automatic glioma grading scheme using the invasive cell nuclei morphology in DP images for cross-validation with the same patients. In summary, the texture-based computational models proposed in this study are expected to facilitate the clinical management of patients with the brain tumors and strokes by automating large scale imaging data analysis, reducing human error, inter-observer variability, and producing repeatable brain tumor quantitation and grading

Quantitative Measurements of Enlarged Perivascular Spaces in the Brain are Associated with Retinal Microvascular Parameters in Older Community-Dwelling Subjects

Background Perivascular Spaces (PVS) become increasingly visible with advancing age on brain MRI, yet their relationship to morphological changes in the underlying microvessels remains poorly understood. Retinal and cerebral microvessels share morphological and physiological properties. We compared computationally-derived PVS morphologies with retinal vessel morphologies in older people. Methods We analysed data from community-dwelling individuals who underwent multimodal brain MRI and retinal fundus camera imaging at mean age 72.55 years (SD=0.71). We assessed centrum semiovale PVS computationally to determine PVS total volume and count, and mean per-subject individual PVS length, width and size. We analysed retinal images using the VAMPIRE software suite, obtaining the Central Retinal Artery and Vein Equivalents (CRVE and CRAE), Arteriole-to-Venule ratio (AVR), and fractal dimension (FD) of both eyes. We investigated associations using general linear models, adjusted for age, gender, and major vascular risk factors. Results In 381 subjects with all measures, increasing total PVS volume and count were associated with decreased CRAE in the left eye (volume β=−0.170, count β=−0.184, p<0.001). No associations of PVS with CRVE were found. The PVS total volume, individual width and size increased with decreasing FD of the arterioles (a) and venules (v) of the left eye (total volume: FDa β=−0.137, FDv β=−0.139, p<0.01; width: FDa β=−0.144, FDv β=−0.158, p<0.01; size: FDa β=−0.157, FDv β=−0.162, p<0.01). Conclusions Increase in PVS number and size visible on MRI reflect arteriolar narrowing and lower retinal arteriole and venule branching complexity, both markers of impaired microvascular health. Computationally-derived PVS metrics may be an early indicator of failing vascular health and should be tested in longitudinal studies.fals

Statistical shape analysis for bio-structures : local shape modelling, techniques and applications

A Statistical Shape Model (SSM) is a statistical representation of a shape obtained from data to study variation in shapes. Work on shape modelling is constrained by many unsolved problems, for instance, difficulties in modelling local versus global variation. SSM have been successfully applied in medical image applications such as the analysis of brain anatomy. Since brain structure is so complex and varies across subjects, methods to identify morphological variability can be useful for diagnosis and treatment. The main objective of this research is to generate and develop a statistical shape model to analyse local variation in shapes. Within this particular context, this work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point Distribution Model and uses a combination of other well known techniques: Fractal analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space representation for the problem of contour localisation. Similarly, Diffusion Maps are employed as a spectral shape clustering tool to identify sets of local partitions useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis method based on the Gaussian and Laplacian pyramids is explained and used to compare the featured Local Shape Model. Experimental results on a number of real contours such as animal, leaf and brain white matter outlines have been shown to demonstrate the effectiveness of the proposed model. These results show that local shape models are efficient in modelling the statistical variation of shape of biological structures. Particularly, the development of this model provides an approach to the analysis of brain images and brain morphometrics. Likewise, the model can be adapted to the problem of content based image retrieval, where global and local shape similarity needs to be measured

Doctor of Philosophy

dissertationNeurodegenerative diseases are an increasing health care problem in the United States. Quantitative neuroimaging provides a noninvasive method to illuminate individual variations in brain structure to better understand and diagnose these disorders. The overall objective of this research is to develop novel clinical tools that summarize and quantify changes in brain shape to not only help better understand age-appropriate changes but also, in the future, to dissociate structural changes associated with aging from those caused by dementing neurodegenerative disorders. Because the tools we will develop can be applied for individual assessment, achieving our goals could have a significant clinical impact. An accurate, practical objective summary measure of the brain pathology would augment current subjective visual interpretation of structural magnetic resonance images. Fractal dimension is a novel approach to image analysis that provides a quantitative measure of shape complexity describing the multiscale folding of the human cerebral cortex. Cerebral cortical folding reflects the complex underlying architectural features that evolve during brain development and degeneration including neuronal density, synaptic proliferation and loss, and gliosis. Building upon existing technology, we have developed innovative tools to compute global and local (voxel-wise and regional) cerebral cortical fractal dimensions and voxel-wise cortico-fractal surfaces from high-contrast MR images. Our previous research has shown that fractal dimension correlates with cognitive function and changes during the course of normal aging. We will now apply unbiased diffeomorphic atlasing methodology to dramatically improve the alignment of complex cortical surfaces. Our novel methods will create more accurate, detailed geometrically averaged images to take into account the intragroup differences and make statistical inferences about spatiotemporal changes in shape of the cerebral cortex across the adult human lifespan

Medical Image Segmentation Using Multifractal Analysis

Image segmentation plays a key role in image analysis processes. The operations performed on a segmented image tend to affect it differently than if they were performed on the original image; therefore, segmenting an image can show radically different results from the original image and successfully doing so can yield features and other important information about the image. Proper image analysis is of high importance to the medical community as accurately classifying different conditions and diseases can be facilitated with excellent patient imaging. Multifractal analysis can be leveraged for performing texture classification and image segmentation. In this paper, we propose fusion-based algorithms utilizing multifractal analysis for medical image segmentation. We use two specific multifractal masks: square and quincunx. Our techniques show new insights by using methods such as histogram decomposition in conjunction with new techniques, such as fusion. By fusing different slope images, we can extract more features thus making our proposed algorithms more robust and accurate than traditional multifractal analysis techniques. These methods are further capable of reliably segmenting medical images by implementing multifractal analysis techniques in coordination with methods such as gaussian blurring and morphological operations. The resulting image can then be easily analyzed by medical professionals for diagnosing medical conditions. The outcomes show that the proposed algorithms extract dominant features that are more encompassing and powerful than classical techniques

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Employing Symmetry Features for Automatic Misalignment Correction in Neuroimages

A novel method to automatically compute the symmetry plane and to correct the 3D orientation of neuro-images is presented. In acquisition of neuroimaging scans, the lack of perfect alignment of a patient's head makes it challenging to evaluate brain images. By deploying a shape-based criterion, the symmetry plane is defined as a plane that best matches external surface points on one side of the head, with their counterparts on the other side. In our method, the head volume is represented as a re-parameterized surface point cloud, where each location is parameterized by its elevation (latitude), azimuth (longitude), and radius. The search for the best matching surfaces is implemented in a multi-resolution paradigm, and the computation time is significantly decreased. The algorithm was quantitatively evaluated using in both simulated data and in real T1, T2, Flair magnetic resonance patient images. This algorithm is found to be fast (< 10s per MR volume), robust and accurate (< .6 degree of Mean Angular Error), invariant to the acquisition noise, slice thickness, bias field, and pathological asymmetries