A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images

Template estimation plays a crucial role in computational anatomy since it provides reference frames for performing statistical analysis of the underlying anatomical population variability. While building models for template estimation, variability in sites and image acquisition protocols need to be accounted for. To account for such variability, we propose a generative template estimation model that makes simultaneous inference of both bias fields in individual images, deformations for image registration, and variance hyperparameters. In contrast, existing maximum a posterori based methods need to rely on either bias-invariant similarity measures or robust image normalization. Results on synthetic and real brain MRI images demonstrate the capability of the model to capture heterogeneity in intensities and provide a reliable template estimation from registration

Sliding at first order: Higher-order momentum distributions for discontinuous image registration

In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a non-differentiable kernel. This allows to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deformation model from the viewpoint of discontinuous systems. To evaluate our approach, we conduct experiments on both artificial images and the publicly available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach in capturing plausible sliding motion

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information.The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of 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 is a forum for the exchange of the theoretical ideas and aims at being 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 first edition of this workshop in 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions

MULTISCALE KERNELS FOR DIFFEOMORPHIC BRAIN IMAGE AND SURFACE MATCHING

Ph.DDOCTOR OF PHILOSOPH

3D-3D Deformable Registration and Deep Learning Segmentation based Neck Diseases Analysis in MRI

Whiplash, cervical dystonia (CD), neck pain and work-related upper limb disorder (WRULD) are the most common diseases in the cervical region. Headaches, stiffness, sensory disturbance to the legs and arms, optical problems, aching in the back and shoulder, and auditory and visual problems are common symptoms seen in patients with these diseases. CD patients may also suffer tormenting spasticity in some neck muscles, with the symptoms possibly being acute and persisting for a long time, sometimes a lifetime. Whiplash-associated disorders (WADs) may occur due to sudden forward and backward movements of the head and neck occurring during a sporting activity or vehicle or domestic accident. These diseases affect private industries, insurance companies and governments, with the socio-economic costs significantly related to work absences, long-term sick leave, early disability and disability support pensions, health care expenses, reduced productivity and insurance claims. Therefore, diagnosing and treating neck-related diseases are important issues in clinical practice. The reason for these afflictions resulting from accident is the impairment of the cervical muscles which undergo atrophy or pseudo-hypertrophy due to fat infiltrating into them. These morphological changes have to be determined by identifying and quantifying their bio-markers before applying any medical intervention. Volumetric studies of neck muscles are reliable indicators of the proper treatments to apply. Radiation therapy, chemotherapy, injection of a toxin or surgery could be possible ways of treating these diseases. However, the dosages required should be precise because the neck region contains some sensitive organs, such as nerves, blood vessels and the trachea and spinal cord. Image registration and deep learning-based segmentation can help to determine appropriate treatments by analyzing the neck muscles. However, this is a challenging task for medical images due to complexities such as many muscles crossing multiple joints and attaching to many bones. Also, their shapes and sizes vary greatly across populations whereas their cross-sectional areas (CSAs) do not change in proportion to the heights and weights of individuals, with their sizes varying more significantly between males and females than ages. Therefore, the neck's anatomical variabilities are much greater than those of other parts of the human body. Some other challenges which make analyzing neck muscles very difficult are their compactness, similar gray-level appearances, intra-muscular fat, sliding due to cardiac and respiratory motions, false boundaries created by intramuscular fat, low resolution and contrast in medical images, noise, inhomogeneity and background clutter with the same composition and intensity. Furthermore, a patient's mode, position and neck movements during the capture of an image create variability. However, very little significant research work has been conducted on analyzing neck muscles. Although previous image registration efforts form a strong basis for many medical applications, none can satisfy the requirements of all of them because of the challenges associated with their implementation and low accuracy which could be due to anatomical complexities and variabilities or the artefacts of imaging devices. In existing methods, multi-resolution- and heuristic-based methods are popular. However, the above issues cause conventional multi-resolution-based registration methods to be trapped in local minima due to their low degrees of freedom in their geometrical transforms. Although heuristic-based methods are good at handling large mismatches, they require pre-segmentation and are computationally expensive. Also, current deformable methods often face statistical instability problems and many local optima when dealing with small mismatches. On the other hand, deep learning-based methods have achieved significant success over the last few years. Although a deeper network can learn more complex features and yields better performances, its depth cannot be increased as this would cause the gradient to vanish during training and result in training difficulties. Recently, researchers have focused on attention mechanisms for deep learning but current attention models face a challenge in the case of an application with compact and similar small multiple classes, large variability, low contrast and noise. The focus of this dissertation is on the design of 3D-3D image registration approaches as well as deep learning-based semantic segmentation methods for analyzing neck muscles. In the first part of this thesis, a novel object-constrained hierarchical registration framework for aligning inter-subject neck muscles is proposed. Firstly, to handle large-scale local minima, it uses a coarse registration technique which optimizes a new edge position difference (EPD) similarity measure to align large mismatches. Also, a new transformation based on the discrete periodic spline wavelet (DPSW), affine and free-form-deformation (FFD) transformations are exploited. Secondly, to avoid the monotonous nature of using transformations in multiple stages, affine registration technique, which uses a double-pushing system by changing the edges in the EPD and switching the transformation's resolutions, is designed to align small mismatches. The EPD helps in both the coarse and fine techniques to implement object-constrained registration via controlling edges which is not possible using traditional similarity measures. Experiments are performed on clinical 3D magnetic resonance imaging (MRI) scans of the neck, with the results showing that the EPD is more effective than the mutual information (MI) and the sum of squared difference (SSD) measures in terms of the volumetric dice similarity coefficient (DSC). Also, the proposed method is compared with two state-of-the-art approaches with ablation studies of inter-subject deformable registration and achieves better accuracy, robustness and consistency. However, as this method is computationally complex and has a problem handling large-scale anatomical variabilities, another 3D-3D registration framework with two novel contributions is proposed in the second part of this thesis. Firstly, a two-stage heuristic search optimization technique for handling large mismatches,which uses a minimal user hypothesis regarding these mismatches and is computationally fast, is introduced. It brings a moving image hierarchically closer to a fixed one using MI and EPD similarity measures in the coarse and fine stages, respectively, while the images do not require pre-segmentation as is necessary in traditional heuristic optimization-based techniques. Secondly, a region of interest (ROI) EPD-based registration framework for handling small mismatches using salient anatomical information (AI), in which a convex objective function is formed through a unique shape created from the desired objects in the ROI, is proposed. It is compared with two state-of-the-art methods on a neck dataset, with the results showing that it is superior in terms of accuracy and is computationally fast. In the last part of this thesis, an evaluation study of recent U-Net-based convolutional neural networks (CNNs) is performed on a neck dataset. It comprises 6 recent models, the U-Net, U-Net with a conditional random field (CRF-Unet), attention U-Net (A-Unet), nested U-Net or U-Net++, multi-feature pyramid (MFP)-Unet and recurrent residual U-Net (R2Unet) and 4 with more comprehensive modifications, the multi-scale U-Net (MS-Unet), parallel multi-scale U-Net (PMSUnet), recurrent residual attention U-Net (R2A-Unet) and R2A-Unet++ in neck muscles segmentation, with analyses of the numerical results indicating that the R2Unet architecture achieves the best accuracy. Also, two deep learning-based semantic segmentation approaches are proposed. In the first, a new two-stage U-Net++ (TS-UNet++) uses two different types of deep CNNs (DCNNs) rather than one similar to the traditional multi-stage method, with the U-Net++ in the first stage and the U-Net in the second. More convolutional blocks are added after the input and before the output layers of the multi-stage approach to better extract the low- and high-level features. A new concatenation-based fusion structure, which is incorporated in the architecture to allow deep supervision, helps to increase the depth of the network without accelerating the gradient-vanishing problem. Then, more convolutional layers are added after each concatenation of the fusion structure to extract more representative features. The proposed network is compared with the U-Net, U-Net++ and two-stage U-Net (TS-UNet) on the neck dataset, with the results indicating that it outperforms the others. In the second approach, an explicit attention method, in which the attention is performed through a ROI evolved from ground truth via dilation, is proposed. It does not require any additional CNN, as does a cascaded approach, to localize the ROI. Attention in a CNN is sensitive with respect to the area of the ROI. This dilated ROI is more capable of capturing relevant regions and suppressing irrelevant ones than a bounding box and region-level coarse annotation, and is used during training of any CNN. Coarse annotation, which does not require any detailed pixel wise delineation that can be performed by any novice person, is used during testing. This proposed ROI-based attention method, which can handle compact and similar small multiple classes with objects with large variabilities, is compared with the automatic A-Unet and U-Net, and performs best

Editing Fluid Simulations with Jet Particles

Fluid simulation is an important topic in computer graphics in the pursuit of adding realism to films, video games and virtual environments. The results of a fluid simulation are hard to edit in a way that provide a physically plausible solution. Edits need to preserve the incompressibility condition in order to create natural looking water and smoke simulations. In this thesis we present an approach that allows a simple artist-friendly interface for designing and editing complex fluid-like flows that are guaranteed to be incompressible in two and three dimensions. Key to our method is a formulation for the design of flows using jet particles. Jet particles are Lagrangian solutions to a regularised form of Euler’s equations, and their velocity fields are divergence-free which motivates their use in computer graphics. We constrain their dynamics to design divergence-free flows and utilise them effectively in a modern visual effects pipeline. Using just a handful of jet particles we produce visually convincing flows that implicitly satisfy the incompressibility condition. We demonstrate an interactive tool in two dimensions for designing a range of divergence-free deformations. Further we describe methods to couple these flows with existing simulations in order to give the artist creative control beyond the initial outcome. We present examples of local temporal edits to smoke simulations in 2D and 3D. The resulting methods provide promising new ways to design and edit fluid-like deformations and to create general deformations in 3D modelling. We show how to represent existing divergence-free velocity fields using jet particles, and design new vector fields for use in fluid control applications. Finally we provide an efficient implementation for deforming grids, meshes, volumes, level sets, vectors and tensors, given a jet particle flow

Examining the development of brain structure in utero with fetal MRI, acquired as part of the Developing Human Connectome Project

The human brain is an incredibly complex organ, and the study of it traverses many scales across space and time. The development of the brain is a protracted process that begins embryonically but continues into adulthood. Although neural circuits have the capacity to adapt and are modulated throughout life, the major structural foundations are laid in utero during the fetal period, through a series of rapid but precisely timed, dynamic processes. These include neuronal proliferation, migration, differentiation, axonal pathfinding, and myelination, to name a few. The fetal origins of disease hypothesis proposed that a variety of non-communicable diseases emerging in childhood and adulthood could be traced back to a series of risk factors effecting neurodevelopment in utero (Barker 1995). Since this publication, many studies have shown that the structural scaffolding of the brain is vulnerable to external environmental influences and the perinatal developmental window is a crucial determinant of neurological health later in life. However, there remain many fundamental gaps in our understanding of it. The study of human brain development is riddled with biophysical, ethical, and technical challenges. The Developing Human Connectome Project (dHCP) was designed to tackle these specific challenges and produce high quality open-access perinatal MRI data, to enable researchers to investigate normal and abnormal neurodevelopment (Edwards et al., 2022). This thesis will focus on investigating the diffusion-weighted and anatomical (T2) imaging data acquired in the fetal period, between the second to third trimester (22 – 37 gestational weeks). The limitations of fetal MR data are ill-defined due to a lack of literature and therefore this thesis aims to explore the data through a series of critical and strategic analysis approaches that are mindful of the biophysical challenges associated with fetal imaging. A variety of analysis approaches are optimised to quantify structural brain development in utero, exploring avenues to relate the changes in MR signal to possible neurobiological correlates. In doing so, the work in this thesis aims to improve mechanistic understanding about how the human brain develops in utero, providing the clinical and medical imaging community with a normative reference point. To this aim, this thesis investigates fetal neurodevelopment with advanced in utero MRI methods, with a particular emphasis on diffusion MRI. Initially, the first chapter outlines a descriptive, average trajectory of diffusion metrics in different white matter fiber bundles across the second to third trimester. This work identified unique polynomial trajectories in diffusion metrics that characterise white matter development (Wilson et al., 2021). Guided by previous literature on the sensitivity of DWI to cellular processes, I formulated a hypothesis about the biophysical correlates of diffusion signal components that might underpin this trend in transitioning microstructure. This hypothesis accounted for the high sensitivity of the diffusion signal to a multitude of simultaneously occurring processes, such as the dissipating radial glial scaffold, commencement of pre-myelination and arborization of dendritic trees. In the next chapter, the methods were adapted to address this hypothesis by introducing another dimension, and charting changes in diffusion properties along developing fiber pathways. With this approach it was possible to identify compartment-specific microstructural maturation, refining the spatial and temporal specificity (Wilson et al., 2023). The results reveal that the dynamic fluctuations in the components of the diffusion signal correlate with observations from previous histological work. Overall, this work allowed me to consolidate my interpretation of the changing diffusion signal from the first chapter. It also serves to improve understanding about how diffusion signal properties are affected by processes in transient compartments of the fetal brain. The third chapter of this thesis addresses the hypothesis that cortical gyrification is influenced by both underlying fiber connectivity and cytoarchitecture. Using the same fetal imaging dataset, I analyse the tissue microstructural change underlying the formation of cortical folds. I investigate correlations between macrostructural surface features (curvature, sulcal depth) and tissue microstructural measures (diffusion tensor metrics, and multi-shell multi-tissue decomposition) in the subplate and cortical plate across gestational age, exploring this relationship both at the population level and within subjects. This study provides empirical evidence to support the hypotheses that microstructural properties in the subplate and cortical plate are altered with the development of sulci. The final chapter explores the data without anatomical priors, using a data-driven method to extract components that represent coordinated structural maturation. This analysis aims to examine if brain regions with coherent patterns of growth over the fetal period converge on neonatal functional networks. I extract spatially independent features from the anatomical imaging data and quantify the spatial overlap with pre-defined neonatal resting state networks. I hypothesised that coherent spatial patterns of anatomical development over the fetal period would map onto the functional networks observed in the neonatal period. Overall, this thesis provides new insight about the developmental contrast over the second to third trimester of human development, and the biophysical correlates affecting T2 and diffusion MR signal. The results highlight the utility of fetal MRI to research critical mechanisms of structural brain maturation in utero, including white matter development and cortical gyrification, bridging scales from neurobiological processes to whole brain macrostructure. their gendered constructions relating to women