Physics of Brain Folding

The human brain is characterized by its folded structure, being the most folded brain among all primates. The process by which these folds emerge, called gyrogenesis, is still not fully understood. The brain is divided into an outer region, called gray matter, which grows at a faster rate than the inner region, called white matter. It is hypothesized that this imbalance in growth -- and the mechanical stress thereby generated -- drives gyrogenesis, which is the focus of this thesis. Finite element simulations are performed where the brain is modeled as a non-linear elastic and growth is introduced via a multiplicative decomposition. A small section of the brain, represented by a rectangular slab, is analyzed. This slab is divided into a thin hard upper layer mimicking the gray matter, and a soft substrate, mimicking the white matter. The top layer is then grown tangentially, while the underlying substrate does not grow. JuFold, the software developed to perform these simulations, is introduced, and its design is explained. An overview of its capabilities, and examples of simulation possibilities are shown. Additionally, one patent-leading application of JuFold in the realm of material science showcases its flexibility. Simulations are first performed by minimizing the elastic energy, corresponding to the slow growth regime. Systems with homogeneous cortices are studied, where growth initially compresses, and then buckles the cortical region, which generates wavy patterns with wavelength proportional to cortical thickness. After buckling, the sulcal regions (i.e. the valleys of the system) are thinner than the gyral regions (i.e. the hills). Introducing thickness inhomogeneities along the cortex lead to new and localized configurations, which are strongly dependent not only on the thickness of the region, but also on its gradient. Furthermore, cortical landmarks appear sequentially, consistent with the hierarchical folding observed during gestation. A linear stability theory is developed based on thin plate theory and is compared with homogeneous and inhomogeneous systems. Next, we turn to more physically stringent dynamic simulations. For slow growth rate and time-constant thickness, the results obtained through energy minimization are recovered, justifying previous literature. For faster growth, an overshoot of the wavenumber and a broad wavenumber spectrum are observed immediately after buckling. After a relaxation period, where the average wavenumber decreases and the wavenumber spectrum narrows, it is observed that the system stabilizes into a finite spectrum, whose average wavelength is smaller than that expected from energy minimization arguments. Cortical inhomogeneities are further explored in this new regime. Systems with inhomogeneous cortical thickness are revisited, with effects similar to the homogeneous cortex (i.e., results are consistent between the slow growth and the quasistatic regimes, and overshoot is observed in the fast growth regimes). Systems with inhomogeneous cortical growth are simulated, with this new type of inhomogeneity inducing fissuration and localized folding. The interplay between these two inhomogeneities is studied, and their interaction is shown to be nonlinear, with each inhomogeneity type inhibiting the folding effects of the other. That is, the folding profile of each individual region emerges as a result of the local inhomogeneity, and the system does not display an intermediate behavior. Finally, these results are compared with an extended linear stability theory. Taken together, our simulations and analytical theory expose new phenomena predicted by an incremented buckling hypothesis for folding and show a series of new avenues which could give rise to the important cortical features in the mammalian brain, especially those related to higher-order folding

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

Cortical Surface Registration and Shape Analysis

A population analysis of human cortical morphometry is critical for insights into brain development or degeneration. Such an analysis allows for investigating sulcal and gyral folding patterns. In general, such a population analysis requires both a well-established cortical correspondence and a well-defined quantification of the cortical morphometry. The highly folded and convoluted structures render a reliable and consistent population analysis challenging. Three key challenges have been identified for such an analysis: 1) consistent sulcal landmark extraction from the cortical surface to guide better cortical correspondence, 2) a correspondence establishment for a reliable and stable population analysis, and 3) quantification of the cortical folding in a more reliable and biologically meaningful fashion. The main focus of this dissertation is to develop a fully automatic pipeline that supports a population analysis of local cortical folding changes. My proposed pipeline consists of three novel components I developed to overcome the challenges in the population analysis: 1) automatic sulcal curve extraction for stable/reliable anatomical landmark selection, 2) group-wise registration for establishing cortical shape correspondence across a population with no template selection bias, and 3) quantification of local cortical folding using a novel cortical-shape-adaptive kernel. To evaluate my methodological contributions, I applied all of them in an application to early postnatal brain development. I studied the human cortical morphological development using the proposed quantification of local cortical folding from neonate age to 1 year and 2 years of age, with quantitative developmental assessments. This study revealed a novel pattern of associations between the cortical gyrification and cognitive development.Doctor of Philosoph

The Human Connectome Project's neuroimaging approach

Noninvasive human neuroimaging has yielded many discoveries about the brain. Numerous methodological advances have also occurred, though inertia has slowed their adoption. This paper presents an integrated approach to data acquisition, analysis and sharing that builds upon recent advances, particularly from the Human Connectome Project (HCP). The 'HCP-style' paradigm has seven core tenets: (i) collect multimodal imaging data from many subjects; (ii) acquire data at high spatial and temporal resolution; (iii) preprocess data to minimize distortions, blurring and temporal artifacts; (iv) represent data using the natural geometry of cortical and subcortical structures; (v) accurately align corresponding brain areas across subjects and studies; (vi) analyze data using neurobiologically accurate brain parcellations; and (vii) share published data via user-friendly databases. We illustrate the HCP-style paradigm using existing HCP data sets and provide guidance for future research. Widespread adoption of this paradigm should accelerate progress in understanding the brain in health and disease

Development of High Angular Resolution Diffusion Imaging Analysis Paradigms for the Investigation of Neuropathology

Diffusion weighted magnetic resonance imaging (DW-MRI), provides unique insight into the microstructure of neural white matter tissue, allowing researchers to more fully investigate white matter disorders. The abundance of clinical research projects incorporating DW-MRI into their acquisition protocols speaks to the value this information lends to the study of neurological disease. However, the most widespread DW-MRI technique, diffusion tensor imaging (DTI), possesses serious limitations which restrict its utility in regions of complex white matter. Fueled by advances in DW-MRI acquisition protocols and technologies, a group of exciting new DW-MRI models, developed to address these concerns, are now becoming available to clinical researchers. The emergence of these new imaging techniques, categorized as high angular resolution diffusion imaging (HARDI), has generated the need for sophisticated computational neuroanatomic techniques able to account for the high dimensionality and structure of HARDI data. The goal of this thesis is the development of such techniques utilizing prominent HARDI data models. Specifically, methodologies for spatial normalization, population atlas building and structural connectivity have been developed and validated. These methods form the core of a comprehensive analysis paradigm allowing the investigation of local white matter microarcitecture, as well as, systemic properties of neuronal connectivity. The application of this framework to the study of schizophrenia and the autism spectrum disorders demonstrate its sensitivity sublte differences in white matter organization, as well as, its applicability to large population DW-MRI studies