Numerical modeling in electro- and magnetoencephalography

This Thesis concerns the application of two numerical methods, Boundary Element Method (BEM) and Finite Element Method (FEM) to forward problem solution of bioelectromagnetic source localization in the brain. The aim is to improve the accuracy of the forward problem solution in estimating the electrical activity of the human brain from electric and magnetic field measurements outside the head. Electro- and magnetoencephalography (EEG, MEG) are the most important tools enabling us to gather knowledge about the human brain non-invasively. This task is alternatively named brain mapping. An important step in brain mapping is determining from where the brain signals originate. Using appropriate mathematical models, a localization of the sources of measured signals can be performed. A general motivation of this work was the fact that source localization accuracy can be improved by solving the forward problem with higher accuracy. In BEM studies, accurate representation of model geometry using higher order elements improves the solution of the forward problem. In FEM, complex conductivity information can be incorporated into numerical model. Using Whitney-type finite elements instead of using singular sources such as point dipoles, primary and volume currents are represented as continuous sources. With comparison to analytical solutions available in simple geometries such as sphere, the studied numerical methods show improvements in the forward problem solution of bioelectromagnetic source imaging.reviewe

Cot-side imaging of functional connectivity in the developing brain during sleep using wearable high-density diffuse optical tomography

Studies of cortical function in newborn infants in clinical settings are extremely challenging to undertake with traditional neuroimaging approaches. Partly in response to this challenge, functional near-infrared spectroscopy (fNIRS) has become an increasingly common clinical research tool but has significant limitations including a low spatial resolution and poor depth specificity. Moreover, the bulky optical fibres required in traditional fNIRS approaches present significant mechanical challenges, particularly for the study of vulnerable newborn infants. A new generation of wearable, modular, high-density diffuse optical tomography (HD-DOT) technologies has recently emerged that overcomes many of the limitations of traditional, fibre-based and low-density fNIRS measurements. Driven by the development of this new technology, we have undertaken the first cot-side study of newborn infants using wearable HD-DOT in a clinical setting. We use this technology to study functional brain connectivity (FC) in newborn infants during sleep and assess the effect of neonatal sleep states, active sleep (AS) and quiet sleep (QS), on resting state FC. Our results demonstrate that it is now possible to obtain high-quality functional images of the neonatal brain in the clinical setting with few constraints. Our results also suggest that sleep states differentially affect FC in the neonatal brain, consistent with prior reports

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

Improving automatic rigging for 3D humanoid characters

In the field of computer animation the process of creating an animated character is usually a long and tedious task. An animation character is usually efined by a 3D mesh (a set of triangles in the space) that gives its external appearance or shape to the character. It also used to have an inner structure, the skeleton. When a skeleton is associated to a character mesh, this association is called skeleton binding, and a skeleton bound to a character mesh is an animation rig. Rigging from scratch a character can be a very boring process. The definition and creation of a centered skeleton together with the ’painting’, by an artist,of the influence parameters between the skeleton and the mesh (the skinning) s the most demanding part to achieve an acceptable behavior for a character. This rigging process can be simplified and accelerated using an automatic rigging method. Automatic rigging methods consist in taking as input a 3D mesh, generate a skeleton based in the shape of the original model, bound the input mesh to the generated skeleton, and finally to compute a set of parameters based in a chosen skinning method. The main objective of this thesis is to generate a method for rigging a 3D arbitrary model with minimum user interaction. This can be useful to people without experience in the animation field or to experienced people to accelerate the rigging process from days to hours or minutes depending the needed quality. Having in mind this situation we have designed our method as a set of tools that can be applied to general input models defined by an artist. The contributions made in the development of this thesis can be summarized as: • Generation of an animation Rig: Having an arbitrary closed mesh we have implemented a thinning method to create first an unrefined geometry skeleton that captures the topology and pose of the input character. Using this geometric skeleton as starting point we use a refining method that creates an adjusted logic skeleton based in a template, or may be defined by the user, that is compatible with the current animation formats. The output logic skeleton is specific for each character, and it is bounded to the input mesh to create an animation rig. • Skinning: Having defined an animation rig for an arbitrary mesh we have developed an improved skinning method; this method is based on the Linear Blend Skinning(LBS) algorithm. Our contributions in the skinning field can be sub-divided in: – We propose a segmentation method that works as the core element in a weight assigning algorithm and a skinning lgorithm, we also have developed an automatic algorithm to compute the skin weights of the LBS Skinning of a rigged polygonal mesh. – Our proposed skinning algorithm uses as base the features of the LBS Skinning. The main purpose of the developed algorithm is to solve the well-known ”candy wrap” artifact; that produces a substantial loss of volume when a link of an animation skeleton is rotated over its own axis. We have compared our results with the most important methods in the skinning field, such as Dual Quaternion Skinning (DQS) and LBS, achieving a better performance over DQS and an improvement in quality over LBS. • Animation tools: We have developed a set of Autodesk Maya commands that works together as rig tool, using our previous proposed methods. • Animation loader: Moreover, an animation loader tool has been implemented, that allows the user to load animations from a skeleton with different structure to a rigged 3D model. The contributions previously described has been published in 3 research papers, the first two were presented in international congresses and the third one was acepted for its publication in an JCR indexed journal.En el campo de la animación por computadora el proceso de crear un personaje de animación es comúnmente una tarea larga y tediosa. Un personaje de animación está definido usualmente por una malla tridimensional (un conjunto de triángulos en el espacio) que le dan su apariencia externa y forma al personaje. Es igualmente común que este tenga una estructura interna, un esqueleto de animación. Cuando un esqueleto esta asociado con una malla tridimensional, a esta asociación se le llama ligado de esqueleto, y un esqueleto ligado a la mallade un personaje es conocido en inglés como "animation rig" (el conjunto de elementos necesarios, que unidos sirven para animar un personaje). Hacer el rigging desde cero de un personaje puede ser un proceso muy tedioso. La definición y creación de un esqueleto centrado en la malla junto con el "pintado" por medio de un artista de los parámetros de influencia entre el esqueleto y la malla 3D (lo que se conoce como skinning) es la parte mas demandante para alcanzar un compartimiento aceptable al deformase (moverse) la malla de un personaje. Los métodos de rigging automáticos consisten en tomar una malla tridimensional como elemento de entrada, generar un esqueleto basado en la forma del modelo original, ligar la malla de entrada al esqueleto generado y finamente calcular el conjunto de parámetros utilizados por el método de skinning elegido. El principal objetivo de esta tesis es el generar un método de rigging para un modelo tridimensional arbitrario con una interacción mínima del usuario. Este método puede ser útil para gente con poca experiencia en el campo de la animación, o para gente experimentada que quiera acelerar el proceso de rigging de días a horas o inclusive minutos, dependiendo de la calidad requerida. Teniendo en mente esta situación, hemos diseñado nuestro método como un conjunto de herramientas las cuales pueden ser aplicadas a modelos de entrada generados por cualquier artista. Las contribuciones hechas en el desarrollo de esta tesis pueden resumirse a: -Generación de un rig de animación: Teniendo una malla cerrada cualquiera, hemos implementado un método para crear primero un esqueleto geométrico sin refinar, el cual capture la pose y la topología del personaje usado como elemento de entrada. Tomando este esqueleto geométrico como punto de partida usamos un método de refinado que crea un "esqueleto lógico" adaptado a la forma del geométrico basándonos en una plantilla definida por el usuario o previamente definida, que sea compatible con los formatos actuales de animación. El esqueleto lógico generado será especifico para cada personaje, y esta ligado a la malla de entrada para así crear un rig de animación. - Skinning: Teniendo definido un rig de animación para una malla de entrada arbitraria, hemos desarrollado un método mejorado de skinning, este método sera basado en el algoritmo "Linear Blending Skinnig" (algoritmo de skinning por combinación lineal, LBS por sus siglas en inglés). Nuestras contribuciones en el campo del skinnig son: - Proponemos un nuevo método de segmentación de mallas que sea la parte medular para algoritmos de asignación automática de pesos y de skinning, también hemos desarrollado un algoritmo automático que calcule los pesos utilizados por el algoritmo LBS para una malla poligonal que tenga un rig de animación. - Nuestro algoritmo de skinning propuesto usará como base las características del algoritmo LBS. El principal propósito del algoritmo desarrollado es el solucionar el defecto conocido como "envoltura de caramelo" (candy wrapper artifact), que produce una substancial perdida de volumen al rotar una de las articulaciones del esqueleto de animación sobre su propio eje. Nuestros resultados son comparados con los métodos mas importantes en el campo del skinning tal como Cuaterniones Duales (Dual Quaternions Skinning, DQS) y LBS, alcanzando un mejor desempeño que DQS y una mejora importante sobre LBSPostprint (published version

\u3ci\u3eH\u3c/i\u3e\u3csup\u3e1\u3c/sup\u3e-conforming Finite Elements on Nonstandard Meshes

We present a finite element method for linear elliptic partial differential equations on bounded planar domains that are meshed with cells that are permitted to be curvilinear and multiply connected. We employ Poisson spaces, as used in virtual element methods, consisting of globally continuous functions that locally satisfy a Poisson problem with polynomial data. This dissertation presents four peer-reviewed articles concerning both the theory and computation of using such spaces in the context of finite elements. In the first paper, we propose a Dirichlet-to-Neumann map for harmonic functions by way of computing the trace of a harmonic conjugate by numerically solving a second-kind integral equation; with the trace of a given harmonic function and its conjugate, we may obtain interior values and derivatives (such as the gradient). In the second paper, we establish some properties of a local Poisson space (i.e. when restricted to a single mesh cell), including its dimension, and provide a construction of a basis of this space. An interpolation operator for this space is introduced, and bounds on the interpolation error are proved and verified computationally in the lowest order case. In the third paper, we demonstrate that computations with higher-order spaces are computationally feasible by showing that both the H1 semi-inner product and the L2 inner product can be computed in the local Poisson space using only path integrals over boundary of the mesh cell, without need for any volumetric quadrature. Reducing the L2 inner product to a boundary integral involves determining an anti-Laplacian of a harmonic function, i.e. a biharmonic function whose Laplacian is given; we provide a construction of the trace and normal derivative of such a function. In the fourth paper, we show that the H1 semi-inner product and L2 inner product can be likewise computed on mesh cells that are punctured , i.e. multiply connected. The primary difficulty arises due to the fact that a given harmonic function is not guaranteed to have a harmonic conjugate, but can be corrected for by introducing logarithmic singularities centered at chosen points in the holes. In addition to these four papers, we also provide a brief update on ongoing extensions of this work, including a full implementation of the finite element method and application to computing terms that arise in problems with advection terms and generalized diffusion operators

Study of the Term Neonatal Brain Injury with combined Diffuse Optical Tomography and Electroencephalography

This thesis describes the application of combined diffuse optical tomography (DOT) and electroencephalography (EEG) in the investigation of neonatal term brain injury. With hypoxic ischaemic encephalopathy (HIE) and perinatal stroke being the most frequent contributors to brain injury in the term neonatal population, the first part of the thesis focuses on the description and ongoing requirement for their further investigation. In continuation to that, the characteristics and unique properties of both DOT and EEG are described and explored. The combination of these two modalities was utilised in elucidating the relationship between neuronal activity and cerebral haemodynamics both in physiological processes as well as in disease, by the infant’s cot side. This work differs to previous studies using near-infrared technologies and EEG, as a denser whole head array was used, offering the potential of 3-dimensional image reconstruction of the cortical haemodynamic events in relation to electro-cortical activity. These methods were applied in the study of critically ill infants presenting with seizures in the first few days of life. The relevant results are presented in three separate chapters of the thesis. Distinct neurophysiological phenomena such as seizures and burst suppression were detected and studied in association to underlying HIE. On the grounds of a pre-existing pilot study of our research group, distinct prolonged de-oxygenated cortical areas were identified following electrical seizure activity. Further exploration of infants with seizures provided limited supporting evidence. The investigation of burst suppression in HIE led to the first ever identification of repeated, waveform, cortical haemodynamic events in response to bursts of electrical activity with some spatial correlation to regions of brain injury. Further analysis of the low frequencies within the diffuse optical signal in cases of perinatal stroke, showed a consistent interhemispheric difference between the healthy and stroke-affected brain regions. The limitations, prospects and conclusions are presented in the final chapter. The use of simultaneous DOT and EEG offers a unique neuro-monitoring and neuro-investigating tool in the neonatal intensive care environment, which is safe, portable, and cost-effective, Ongoing research is required for the exploration and development of the methodology and its potential diagnostic properties

Efficient computation of discrete Voronoi diagram and homotopy-preserving simplified medial axis of a 3d polyhedron

The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the Blum medial axis, a well known skeletal representation. Voronoi diagrams and medial axes have been shown useful for many 3D computations and operations, including proximity queries, motion planning, mesh generation, finite element analysis, and shape analysis. However, their application to complex 3D polyhedral and deformable models has been limited. This is due to the difficulty of computing exact Voronoi diagrams in an efficient and reliable manner. In this dissertation, we bridge this gap by presenting efficient algorithms to compute discrete Voronoi diagrams and simplified medial axes of 3D polyhedral models with geometric and topological guarantees. We apply these algorithms to complex 3D models and use them to perform interactive proximity queries, motion planning and skeletal computations. We present three new results. First, we describe an algorithm to compute 3D distance fields of geometric models by using a linear factorization of Euclidean distance vectors. This formulation maps directly to the linearly interpolating graphics rasterization hardware and enables us to compute distance fields of complex 3D models at interactive rates. We also use clamping and culling algorithms based on properties of Voronoi diagrams to accelerate this computation. We introduce surface distance maps, which are a compact distance vector field representation based on a mesh parameterization of triangulated two-manifolds, and use them to perform proximity computations. Our second main result is an adaptive sampling algorithm to compute an approximate Voronoi diagram that is homotopy equivalent to the exact Voronoi diagram and preserves topological features. We use this algorithm to compute a homotopy-preserving simplified medial axis of complex 3D models. Our third result is a unified approach to perform different proximity queries among multiple deformable models using second order discrete Voronoi diagrams. We introduce a new query called N-body distance query and show that different proximity queries, including collision detection, separation distance and penetration depth can be performed based on Nbody distance query. We compute the second order discrete Voronoi diagram using graphics hardware and use distance bounds to overcome the sampling errors and perform conservative computations. We have applied these queries to various deformable simulations and observed up to an order of magnitude improvement over prior algorithms