109 research outputs found

    Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

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    We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

    Multi-Scale Information, Network, Causality, and Dynamics: Mathematical Computation and Bayesian Inference to Cognitive Neuroscience and Aging

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    The human brain is estimated to contain 100 billion or so neurons and 10 thousand times as many connections. Neurons never function in isolation: each of them is connected to 10, 000 others and they interact extensively every millisecond. Brain cells are organized into neural circuits often in a dynamic way, processing specific types of information and providing th

    Dynamic brain networks explored by structure-revealing methods

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    The human brain is a complex system able to continuously adapt. How and where brain activity is modulated by behavior can be studied with functional magnetic resonance imaging (fMRI), a non-invasive neuroimaging technique with excellent spatial resolution and whole-brain coverage. FMRI scans of healthy adults completing a variety of behavioral tasks have greatly contributed to our understanding of the functional role of individual brain regions. However, by statistically analyzing each region independently, these studies ignore that brain regions act in concert rather than in unison. Thus, many studies since have instead examined how brain regions interact. Surprisingly, structured interactions between distinct brain regions not only occur during behavioral tasks but also while a subject rests quietly in the MRI scanner. Multiple groups of regions interact very strongly with each other and not only do these groups bear a striking resemblance to the sets of regions co-activated in tasks, but many of these interactions are also progressively disrupted in neurological diseases. This suggests that spontaneous fluctuations in activity can provide novel insights into fundamental organizing principles of the human brain in health and disease. Many techniques to date have segregated regions into spatially distinct networks, which ignores that any brain region can take part in multiple networks across time. A more natural view is to estimate dynamic brain networks that allow flexible functional interactions (or connectivity) over time. The estimation and analysis of such dynamic functional interactions is the subject of this dissertation. We take the perspective that dynamic brain networks evolve in a low-dimensional space and can be described by a small number of characteristic spatiotemporal patterns. Our proposed approaches are based on well-established statistical methods, such as principal component analysis (PCA), sparse matrix decompositions, temporal clustering, as well as a multiscale analysis by novel graph wavelet designs. We adapt and extend these methods to the analysis of dynamic brain networks. We show that PCA and its higher-order equivalent can identify co-varying functional interactions, which reveal disturbed dynamic properties in multiple sclerosis and which are related to the timing of stimuli for task studies, respectively. Further we show that sparse matrix decompositions provide a valid alternative approach to PCA and improve interpretability of the identified patterns. Finally, assuming an even simpler low-dimensional space and the exclusive temporal expression of individual patterns, we show that specific transient interactions of the medial prefrontal cortex are disturbed in aging and relate to impaired memory

    A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem

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    The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique

    Functional Brain Imaging by EEG: A Window to the Human Mind

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    Brain activity reconstruction from non-stationary M/EEG data using spatiotemporal constraints

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    Magneto/Electroencephalography (M/EEG)-based neuroimaging is a widely used noninvasive technique for functional analysis of neuronal activity. One of the most prominent advantages of using M/EEG measures is the very low implementation cost and its height temporal resolution. However, the number of locations measuring magnetic/electrical is relatively small (a couple of hundreds at best) while the discretized brain activity generators (sources) are several thousand. This fact corresponds an ill-posed mathematical problem commonly known as the M/EEG inverse problem. To solve such problems, additional information must be apriori assumed to obtain a unique and optimal solution. In the present work, a methodology to improve the accuracy and interpretability of the inverse problem solution is proposed, using physiologically motivated assumptions. Firstly, a method constraining the solution to a sparse representation in the space-time domain is introduce given a set of methodologies to syntonize the present parameters. Secondly, we propose a new source connectivity approach explicitly including spatiotemporal information of the neural activity extracted from M/EEG recordings. The proposed methods are compared with the state-of-art techniques in a simulated environment, and afterward, are validated using real-world data. In general, the contributed approaches are efficient and competitive compared to state-of-art brain mapping methodsResumen : El mapeo cerebral basado en señales de magneto/electroencefalografía (M/EEG), es una técnica muy usada para el análisis de la actividad neuronal en forma no invasiva. Una de las ventajas que provee la utilización de señales M/EEG es su bajo costo de implementación además de su sobresaliente resolución temporal. Sin embargo el número de posiciones magnéticas/eléctricas medidas son extremadamente bajas comparadas con la cantidad de puntos discretizados dentro del cerebro sobre los cuales se debe realizar la estimación de la actividad. Esto conlleva a un problema mal condicionado comúnmente conocido como el problema inverso de M/EEG. Para resolver este tipo de problemas, información apriori debe ser supuesta para así obtener una solución única y óptima. En el presente trabajo investigativo, se propone una metodología para mejorar la exactitud e interpretación a la solución del problema inverso teniendo en cuenta el contexto fisiológico del problema. En primer lugar se propone un algoritmo en el cual se representa la actividad cerebral a través de un conjunto de funciones espacio-temporales dando metodologías para sintonizar los parámetros presentes. En segundo lugar, proponemos un nuevo enfoque mediante conectividad en fuentes que explícitamente incluye información espacial y temporal de la actividad neuronal extraída del M/EEG. Los métodos propuestos son comparados con métodos del estado del arte usando señales simuladas, y finalmente son validados usando datos reales de M/EEG. En general, los métodos propuestos son eficientes y competitivos en comparación a los métodos de referenciaMaestrí

    Closed-loop approaches for innovative neuroprostheses

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    The goal of this thesis is to study new ways to interact with the nervous system in case of damage or pathology. In particular, I focused my effort towards the development of innovative, closed-loop stimulation protocols in various scenarios: in vitro, ex vivo, in vivo

    Bayesian Modeling and Estimation Techniques for the Analysis of Neuroimaging Data

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    Brain function is hallmarked by its adaptivity and robustness, arising from underlying neural activity that admits well-structured representations in the temporal, spatial, or spectral domains. While neuroimaging techniques such as Electroencephalography (EEG) and magnetoencephalography (MEG) can record rapid neural dynamics at high temporal resolutions, they face several signal processing challenges that hinder their full utilization in capturing these characteristics of neural activity. The objective of this dissertation is to devise statistical modeling and estimation methodologies that account for the dynamic and structured representations of neural activity and to demonstrate their utility in application to experimentally-recorded data. The first part of this dissertation concerns spectral analysis of neural data. In order to capture the non-stationarities involved in neural oscillations, we integrate multitaper spectral analysis and state-space modeling in a Bayesian estimation setting. We also present a multitaper spectral analysis method tailored for spike trains that captures the non-linearities involved in neuronal spiking. We apply our proposed algorithms to both EEG and spike recordings, which reveal significant gains in spectral resolution and noise reduction. In the second part, we investigate cortical encoding of speech as manifested in MEG responses. These responses are often modeled via a linear filter, referred to as the temporal response function (TRF). While the TRFs estimated from the sensor-level MEG data have been widely studied, their cortical origins are not fully understood. We define the new notion of Neuro-Current Response Functions (NCRFs) for simultaneously determining the TRFs and their cortical distribution. We develop an efficient algorithm for NCRF estimation and apply it to MEG data, which provides new insights into the cortical dynamics underlying speech processing. Finally, in the third part, we consider the inference of Granger causal (GC) influences in high-dimensional time series models with sparse coupling. We consider a canonical sparse bivariate autoregressive model and define a new statistic for inferring GC influences, which we refer to as the LASSO-based Granger Causal (LGC) statistic. We establish non-asymptotic guarantees for robust identification of GC influences via the LGC statistic. Applications to simulated and real data demonstrate the utility of the LGC statistic in robust GC identification
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