299 research outputs found

    Hypothesis Testing For Network Data in Functional Neuroimaging

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    In recent years, it has become common practice in neuroscience to use networks to summarize relational information in a set of measurements, typically assumed to be reflective of either functional or structural relationships between regions of interest in the brain. One of the most basic tasks of interest in the analysis of such data is the testing of hypotheses, in answer to questions such as "Is there a difference between the networks of these two groups of subjects?" In the classical setting, where the unit of interest is a scalar or a vector, such questions are answered through the use of familiar two-sample testing strategies. Networks, however, are not Euclidean objects, and hence classical methods do not directly apply. We address this challenge by drawing on concepts and techniques from geometry, and high-dimensional statistical inference. Our work is based on a precise geometric characterization of the space of graph Laplacian matrices and a nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate our resulting methodologies for testing in the context of networks derived from functional neuroimaging data on human subjects from the 1000 Functional Connectomes Project. In particular, we show that this global test is more statistical powerful, than a mass-univariate approach. In addition, we have also provided a method for visualizing the individual contribution of each edge to the overall test statistic.Comment: 34 pages. 5 figure

    Mapping the primate thalamus: systematic approach to analyze the distribution of subcortical neuromodulatory afferents

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    Neuromodulatory afferents to thalamic nuclei are key for information transmission and thus play critical roles in sensory, motor, and limbic processes. Over the course of the last decades, diverse attempts have been made to map and describe subcortical neuromodulatory afferents to the primate thalamus, including axons using acetylcholine, serotonin, dopamine, noradrenaline, adrenaline, and histamine. Our group has been actively involved in this endeavor. The published descriptions on neuromodulatory afferents to the primate thalamus have been made in different laboratories and are not fully comparable due to methodological divergences (for example, fixation procedures, planes of cutting, techniques used to detect the afferents, different criteria for identification of thalamic nucleiโ€ฆ). Such variation affects the results obtained. Therefore, systematic methodological and analytical approaches are much needed. The present article proposes reproducible methodological and terminological frameworks for primate thalamic mapping. We suggest the use of standard stereotaxic planes to produce and present maps of the primate thalamus, as well as the use of the Anglo-American school terminology (vs. the German school terminology) for identification of thalamic nuclei. Finally, a public repository of the data collected under agreed-on frameworks would be a useful tool for looking up and comparing data on the structure and connections of primate thalamic nuclei. Important and agreed-on efforts are required to create, manage, and fund a unified and homogeneous resource of data on the primate thalamus. Likewise, a firm commitment of the institutions to preserve experimental brain material is much needed because neuroscience work with non-human primates is becoming increasingly rare, making earlier material still more valuableOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. CC and IP-S were the recipients of grants from Chair in Neuroscience UAM-Fundaciรณn Tatiana Pรฉrez de Guzmรกn el Bueno, Spain. MAG-C was the recipient of a Beatriz Galindo senior research position in the School of Medicine, Universidad Autรณnoma de Madrid (BEAGAL18/00098) and of a Grant for I+D Projects to the Beatriz Galindo Program Researchers at Universidad Autรณnoma de Madrid (SI2/PBG/2020โ€“00014) from the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with Universidad Autรณnoma de Madrid in the line of action encouraging young research doctors, in the context of the V PRICIT (Regional Programme of Research and Technological Innovation

    Multiple Shape Registration using Constrained Optimal Control

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    Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) only allow for the study of a single shape. In this paper, we introduce and discuss both a theoretical and practical setting for the simultaneous study of multiple shapes that are either stitched to one another or slide along a submanifold. The method is described within the optimal control formalism, and optimality conditions are given, together with the equations that are needed to implement augmented Lagrangian methods. Experimental results are provided for stitched and sliding surfaces

    3D shape matching and registration : a probabilistic perspective

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    Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

    Brain status modeling with non-negative projective dictionary learning

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    Accurate prediction of individualsโ€™ brain age is critical to establish a baseline for normal brain development. This study proposes to model brain development with a novel non-negative projective dictionary learning (NPDL) approach, which learns a discriminative representation of multi-modal neuroimaging data for predicting brain age. Our approach encodes the variability of subjects in different age groups using separate dictionaries, projecting features into a low-dimensional manifold such that information is preserved only for the corresponding age group. The proposed framework improves upon previous discriminative dictionary learning methods by inc

    based on resting state fMRI

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    ํ•™์œ„๋…ผ๋ฌธ(๋ฐ•์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต๋Œ€ํ•™์› : ์œตํ•ฉ๊ณผํ•™๊ธฐ์ˆ ๋Œ€ํ•™์› ๋ถ„์ž์˜ํ•™ ๋ฐ ๋ฐ”์ด์˜ค์ œ์•ฝํ•™๊ณผ, 2021.8. ์œ„์›์„.๋Œ€๋ถ€๋ถ„์˜ ์‹ค์„ธ๊ณ„ ๋„คํŠธ์›Œํฌ์—์„œ ๋„คํŠธ์›Œํฌ์˜ ๊ตฌ์„ฑ์— ์žˆ์–ด์„œ ๊ธฐํ•˜ํ•™์ด ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋ฉฐ, ์ตœ๊ทผ ์—ฐ๊ตฌ์—์„œ ๊ตฌ์กฐ์  ๋‡Œ ๋„คํŠธ์›Œํฌ๋Š” ์Œ๊ณก๊ธฐํ•˜์  ํŠน์„ฑ์„ ๊ฐ€์ง€๊ณ  ์žˆ์Œ์ด ๋ฐํ˜€์กŒ๋‹ค. ๋‡Œ์˜ ๊ตฌ์กฐ์™€ ๊ธฐ๋Šฅ์€ ๋ฐ€์ ‘ํ•œ ์—ฐ๊ด€์„ ์ง€๋‹ˆ๊ณ  ์žˆ์œผ๋ฏ€๋กœ, ๊ธฐ๋Šฅ์  ๋‡Œ ๋„คํŠธ์›Œํฌ ์—ญ์‹œ ์Œ๊ณก๊ธฐํ•˜์  ํŠน์„ฑ์„ ์ง€๋‹ˆ๊ณ  ์žˆ์Œ์„ ์ถ”์ •ํ•  ์ˆ˜ ์žˆ๋‹ค. ์ด๋ฒˆ ์—ฐ๊ตฌ์—์„œ, ์šฐ๋ฆฌ๋Š” ํœด์‹๊ธฐ ๋‡Œ ์ž๊ธฐ๊ณต๋ช…์˜์ƒ(rs-fMRI)์„ ํ†ตํ•ด ์ถ”์ถœํ•œ ๊ธฐ๋Šฅ์  ๋‡Œ ์ปค๋„ฅํ†ฐ(connectome)์„ ๋ถ„์„ํ•˜์—ฌ ์ด ๊ฐ€์„ค์„ ์ฆ๋ช…ํ•˜๊ณ ์ž ํ•˜์˜€์œผ๋ฉฐ, ์ด๋ฅผ ์Œ๊ณก๊ณต๊ฐ„์— ์ž„๋ฒ ๋“œ(embed)ํ•จ์œผ๋กœ์จ ๊ธฐ๋Šฅ์  ๋‡Œ ๋„คํŠธ์›Œํฌ์˜ ํŠน์„ฑ์„ ์ƒˆ๋กœ์ด ์กฐ์‚ฌํ•˜๊ณ ์ž ํ•˜์˜€๋‹ค. ๋„คํŠธ์›Œํฌ์˜ ๊ผญ์ง€์ ์€ 274๊ฐœ์˜ ๋ฏธ๋ฆฌ ์ •์˜๋œ ๊ด€์‹ฌ์˜์—ญ(ROI) ํ˜น์€ 6mm ํฌ๊ธฐ์˜ ๋ณต์…€(voxel)์˜ ๋‘ ๊ฐ€์ง€ ์Šค์ผ€์ผ๋กœ ์ •์˜๋˜์—ˆ์œผ๋ฉฐ, ๊ผญ์ง€์  ์‚ฌ์ด์˜ ์—ฐ๊ฒฐ์„ฑ์€ ์ž๊ธฐ๊ณต๋ช… ์˜์ƒ์—์„œ ๊ฐ ์˜์—ญ์˜ ์‹œ๊ฐ„์— ๋”ฐ๋ฅธ BOLD ์‹ ํ˜ธ์˜ ์ƒ๊ด€๊ด€๊ณ„๋ฅผ ์ธก์ •ํ•˜๊ณ  ์ผ์ • ๋ฌธํ„ฑ๊ฐ’(threshold)์„ ์ ์šฉํ•จ์œผ๋กœ์„œ ๊ฒฐ์ •๋˜์—ˆ๋‹ค. ๋จผ์ € ์Œ๊ณก๊ธฐํ•˜ ๋„คํŠธ์›Œํฌ์˜ ํŠน์ง•์ธ ์Šค์ผ€์ผ-ํ”„๋ฆฌ(scale-free)๋ฅผ ๋งŒ์กฑํ•จ์„ ํ™•์ธํ•˜๊ธฐ ์œ„ํ•ด, ๋„คํŠธ์›Œํฌ์˜ ์ฐจ์ˆ˜(degree) ๋ถ„ํฌ์˜ ๊ธ‰์ˆ˜์„ฑ(power-law)์„ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ์ฐจ์ˆ˜์˜ ํ™•๋ฅ ๋ถ„ํฌ๊ณก์„ ์€ ๋กœ๊ทธ-๋กœ๊ทธ ์Šค์ผ€์ผ์˜ ๊ทธ๋ž˜ํ”„์—์„œ ์šฐํ•˜ํ–ฅํ•˜๋Š” ์ง์„  ๋ชจ์–‘์˜ ๋ถ„ํฌ๋ฅผ ๋ณด์˜€์œผ๋ฉฐ, ์ด๋Š” ์ฆ‰ ์ฐจ์ˆ˜ ๋ถ„ํฌ๊ฐ€ ์ฐจ์ˆ˜์˜ ์Œ์˜ ๊ธ‰์ˆ˜ํ•จ์ˆ˜์— ์˜ํ•ด ๋‚˜ํƒ€๋‚ด์–ด์ง์„ ์˜๋ฏธํ•œ๋‹ค. ์ด์–ด์„œ ๊ธฐ๋Šฅ์  ๋‡Œ ๋„คํŠธ์›Œํฌ์— ๊ฐ€์žฅ ์ ํ•ฉํ•œ ๊ธฐ์ € ๊ธฐํ•˜๋ฅผ ํ™•์ธํ•˜๊ธฐ ์œ„ํ•˜์—ฌ, ๊ทธ๋ž˜ํ”„๋ฅผ ์œ ํด๋ฆฌ๋“œ, ์Œ๊ณก, ๊ตฌ๋ฉด์  ํ‹์„ฑ์„ ๊ฐ€์ง„ ๋‹ค์–‘์ฒด๋“ค์— ์ž„๋ฒ ๋“œํ•˜์—ฌ ์ž„๋ฒ ๋”ฉ์˜ ์ถฉ์‹ค์„ฑ ์ฒ™๋„(fidelity measure)๋“ค์„ ๋น„๊ตํ•˜์˜€๋‹ค. ์ž„๋ฒ ๋“œ ๋Œ€์ƒ์ด ๋œ ์  ๋‹ค์–‘์ฒด๋“ค ์ค‘, 10์ฐจ์› ๋ฐ 2์ฐจ์› ์Œ๊ณก๊ณต๊ฐ„์˜ ํ‰๊ท  ๋’คํ‹€๋ฆผ(distortion)์ด ๋™์ผ ์ฐจ์›์˜ ์œ ํด๋ฆฌ๋“œ ๋‹ค์–‘์ฒด์™€ ๋น„๊ตํ•˜์—ฌ ๋” ๋‚ฎ์•˜๋‹ค. ์ด์–ด, ๋„คํŠธ์›Œํฌ๋ฅผ ๊ตฌ์ฒดํ™” ๋ฐ ์‹œ๊ฐํ™”ํ•˜๊ณ  ๊ทธ ํŠน์ง•์„ ํ™•์ธํ•˜๊ธฐ ์œ„ํ•˜์—ฌ, ๋„คํŠธ์›Œํฌ๋ฅผ ์ด์ฐจ์›์˜ ์Œ๊ณก ์›ํŒ์— 1/โ„2 ๊ธฐํ•˜ํ•™์  ๋ชจ๋ธ์— ๋”ฐ๋ผ ์ž„๋ฒ ๋“œํ•˜์˜€๋‹ค. ์ด ์ด์ฐจ์›์˜ ๊ทน์ขŒํ‘œ ํ˜•ํƒœ์˜ ๋ชจ๋ธ์—์„œ ๋ฐ˜๊ฒฝ ๋ฐ ๊ฐ ์ฐจ์›์˜ ์ขŒํ‘œ๋Š” ๊ฐ๊ฐ ๊ผญ์ง€์ ์˜ ์—ฐ๊ฒฐ ์ธ๊ธฐ๋„ ๋ฐ ์œ ์‚ฌ๋„๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค. ROI ์ˆ˜์ค€์˜ ๋ถ„์„์—์„œ๋Š” ํŠน๋ณ„ํžˆ ๋†’์€ ์ธ๊ธฐ๋„๋ฅผ ๊ฐ–๋Š” ์˜์—ญ์€ ๊ด€์ฐฐ๋˜์ง€ ์•Š์•„ ์ž„๋ฒ ๋“œ๋œ ์›ํŒ์˜ ์ค‘์‹ฌ๋ถ€์— ๋นˆ ๊ณต๊ฐ„์œผ๋กœ ๋‚˜ํƒ€๋‚ฌ๋‹ค. ํ•œํŽธ ๊ฐ™์€ ํ•ด๋ถ€ํ•™์  ์—ฝ(lobe)์— ์†ํ•œ ์˜์—ญ๋“ค์€ ๋น„์Šทํ•œ ๊ฐ๋„ ์˜์—ญ ๋‚ด์— ๋ฐ€์ง‘๋˜์—ˆ์œผ๋ฉฐ, ๋ฐ˜๋Œ€์ธก ๋™์ผ ์—ฝ์— ์†ํ•œ ์˜์—ญ๋“ค ์—ญ์‹œ ๊ทธ ๊ฐ์ขŒํ‘œ์˜ ๋ถ„ํฌ๊ฐ€ ๊ตฌ๋ถ„๋˜์ง€ ์•Š์•˜๋‹ค. ์ด๋Š” ๊ธฐ๋Šฅ์  ๋‡Œ ๋„คํŠธ์›Œํฌ์˜ ํ•ด๋ถ€ํ•™์  ์—ฐ๊ด€์„ฑ๊ณผ ๋ฐ˜๋Œ€์ธก ๋™์ผ ์—ฝ ๊ฐ„์˜ ๊ธฐ๋Šฅ์  ์—ฐ๊ด€์„ฑ์„ ๋‚˜ํƒ€๋‚ด๋Š” ๊ฒƒ์œผ๋กœ ๋ณผ ์ˆ˜ ์žˆ๋‹ค. ๋˜ํ•œ, ๋ณต์…€ ์ˆ˜์ค€์˜ ๋ถ„์„์—์„œ๋Š” ์†Œ๋‡Œ์— ์†ํ•œ ๋ณต์…€๋“ค ์ค‘ ๋‹ค์ˆ˜๊ฐ€ ๋„“์€ ๊ฐ์ขŒํ‘œ ์˜์—ญ์— ํฉ๋ฟŒ๋ ค์ง„ ํ˜„์ƒ์ด ๋‚˜ํƒ€๋‚ฌ์œผ๋ฉฐ, ์ด๋Š” ๊ฐœ๊ฐœ ๋ณต์…€์˜ ๊ธฐ๋Šฅ์  ์ด์งˆ์„ฑ์„ ์‹œ์‚ฌํ•œ๋‹ค. ๋˜ํ•œ, ์ „ ์˜์—ญ์— ๊ฑธ์ณ ๋งค์šฐ ์œ ์‚ฌํ•œ ๊ฐ์ขŒํ‘œ๋ฅผ ๊ฐ€์ง„ ๋ฐฉ์‚ฌํ˜•์˜ ๋ง‰๋Œ€ ๋ชจ์–‘์˜ ์ ์˜ ์ง‘ํ•ฉ์ด ๊ด€์ฐฐ๋˜์—ˆ์œผ๋ฉฐ, ๋†’์€ ๊ธฐ๋Šฅ์  ์œ ์‚ฌ์„ฑ์„ ๊ฐ€์ง„ ๋ณต์…€๋“ค๋กœ ๋ณผ ์ˆ˜ ์žˆ๋‹ค. ๋ณต์…€ ์ˆ˜์ค€์˜ ๋„คํŠธ์›Œํฌ์—์„œ ๋‡Œ์˜ ๋…๋ฆฝ์„ฑ๋ถ„ ๋ถ„์„(ICA) ์˜ ๊ฒฐ๊ณผ๋กœ ๋‚˜์˜จ ์„ฑ๋ถ„ ๋„คํŠธ์›Œํฌ๋“ค์„ ํ”Œ๋กœํŒ…ํ•œ ๊ฒฐ๊ณผ, ๊ฐ ๋„คํŠธ์›Œํฌ ์„ฑ๋ถ„์ด ๋†’์€ ๋ฐ€์ง‘๋„๋ฅผ ๋ณด์—ฌ ๋‘ ๋ฐฉ๋ฒ•๋ก  ๊ฐ„ ๊ฒฐ๊ณผ์˜ ์œ ์‚ฌ์„ฑ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ์žํ์ŠคํŽ™ํŠธ๋Ÿผ์žฅ์• ์˜ ABIDE II ์˜คํ”ˆ ๋ฐ์ดํ„ฐ์…‹์„ ์ด์šฉํ•˜์—ฌ 1/โ„2 ๋ชจ๋ธ์— ๊ทผ๊ฑฐํ•˜์—ฌ, ๋Œ€์กฐ๊ตฐ ํ™˜์ž ๊ทธ๋ฃน๊ณผ ์งˆ๋ณ‘๊ตฐ ํ™˜์ž ๊ฐœ์ธ์˜ ๋„คํŠธ์›Œํฌ๋ฅผ ๋น„๊ตํ•˜๋Š” ๋ถ„์„์„ ์‹œํ–‰ํ•œ ๊ฒฐ๊ณผ, ์งˆ๋ณ‘๊ตฐ์—์„œ ๋‹ค์–‘ํ•œ ํŒจํ„ด์„ ๋ณด์˜€์œผ๋‚˜, ๊ทธ ์ค‘ ์žํ์ฆ ์ง„๋‹จ์„ ๋ฐ›์€ ํ™˜์ž์—์„œ ํ”ผ์งˆ-์„ ์กฐ์ฒด ๊ฒฝ๋กœ์˜ ์ด์ƒ์ด, ์•„์Šคํผ๊ฑฐ์ฆํ›„๊ตฐ ์ง„๋‹จ์„ ๋ฐ›์€ ํ™˜์ž์—์„œ ํ›„์œ„๊ด€์ž๊ณ ๋ž‘ (posterior superior temporal sulcus) ์„ ํฌํ•จํ•˜๋Š” ๊ฒฝ๋กœ์˜ ์ด์ƒ์„ ๋ฐœ๊ฒฌํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋ถ„์„์˜ ์žฌํ˜„์„ฑ์„ ํ™•์ธํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ๊ฐ™์€ ๋„คํŠธ์›Œํฌ๋ฅผ ๋Œ€์ƒ์œผ๋กœ ์ž„๋ฒ ๋”ฉ ๊ณผ์ •์„ ๋ฐ˜๋ณต ์‹œํ–‰ํ•˜์˜€์„ ๋•Œ, ๋„คํŠธ์›Œํฌ ๋ง๋‹จ์˜ ์ผ๋ถ€ ๊ผญ์ง€์ ์„ ์ œ์™ธํ•˜๋ฉด ๋†’์€ ์žฌํ˜„์„ฑ์„ ๋ณด์˜€๋‹ค. ์˜์ƒ์˜ ์‹œ๊ณ„์—ด(time series) ๋‚ด ์ผ๊ด€์„ฑ์„ ํ™•์ธํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ์˜์ƒ์„ ์‹œ๊ฐ„ ๊ตฌ๊ฐ„์— ๋”ฐ๋ผ ๋ถ„๋ฆฌํ•˜์—ฌ ๋ถ„์„ํ•˜์˜€์„ ๋•Œ, 4๊ตฌ๊ฐ„์œผ๋กœ ๋‚˜๋ˆˆ ์‹œ๊ณ„์—ด ์˜์ƒ์—์„œ๋Š” ์œ ์‚ฌํ•œ ๊ฒฐ๊ณผ๋ฅผ ์–ป์—ˆ์œผ๋‚˜ 30์ดˆ ๊ธธ์ด์˜ 30๊ตฌ๊ฐ„์œผ๋กœ ๋‚˜๋‰˜์—ˆ์„ ๋•Œ๋Š” ์ผ๊ด€์ ์ธ ๊ฒฐ๊ณผ๊ฐ€ ๊ด€์ฐฐ๋˜์ง€ ์•Š์•˜๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๋‡Œ ๊ธฐ๋Šฅ์  ๋„คํŠธ์›Œํฌ์— ๋Œ€ํ•œ ๋ถ„์„ ์ค‘ ์ตœ์ดˆ๋กœ ๊ธฐํ•˜ํ•™์  ๊ด€์ ์—์„œ ์ง„ํ–‰๋œ ๊ฒƒ์ด๋ฉฐ, ์ด๋Ÿฌํ•œ ์ƒˆ๋กœ์šด ๊ด€์  ๋ฐ ์งˆ๋ณ‘๊ตฐ ๋Œ€์ƒ์—์„œ ๋‡Œ ๋„คํŠธ์›Œํฌ์˜ ์ด์ƒ์„ ์ฐพ๊ธฐ ์œ„ํ•œ ์ƒˆ๋กœ์šด ๋ฐฉ๋ฒ•๋ก ์„ ์ œ์‹œํ•œ๋‹ค๋Š” ์˜์˜๊ฐ€ ์žˆ๋‹ค.For most of the real-world networks, geometry plays an important role in organizing the network, and recent works have revealed that the geometry in the structural brain network is most likely to be hyperbolic. Therefore, it can be assumed that the geometry of the functional brain network would also be hyperbolic. In this study, we analyzed the functional connectomes from functional magnetic resonance imaging (fMRI) to prove this hypothesis and investigate the characteristics of the network by embedding it into the hyperbolic space, by utilizing human connectome project (HCP) dataset for healthy young adults and Autism Brain Imaging Data Exchange II (ABIDE II) dataset for diseased autism subject and control group. Nodes of the network were defined at two different scales: by 274 predefined ROIs and 6mm-sized voxels. The adjacency between the nodes was determined by computing the correlation of the time-series of the BOLD signal of brain regions and binarized by adopting threshold value. First, we aimed to find out whether the network was scale-free by investigating the degree distribution of the functional brain network. The probability distribution function (PDF) versus degree was plotted as a straight line at a log-log scale graph versus the degree of nodes. This indicates that degree distribution is roughly proportional to a power function of degree, or scale-free. To clarify the most fitting underlying geometry of the network, we then embedded the graph into manifolds of Euclidean, hyperbolic, or spherical spaces and compared the fidelity measures of embeddings. The embedding to the hyperbolic spaces yielded a better fidelity measure compared to other manifolds. To get a discrete and visible map and investigate the characteristics of the network, we embedded the network in a two-dimensional hyperbolic disc by the 1/โ„2 model. The radial and angular dimensions in the embedding is interpreted as popularity and similarity dimensions, respectively. The ROI-wise analysis revealed that no nodes with particularly high popularity were found, which was revealed by a vacant area in the center of the disk. Nodes in the same lobe were more likely to be clustered in narrow similarity dimensions, and the nodes from the homotopic lobes were also functionally clustered. The results indicate the anatomic relevance of the functional brain network and the strong functional coherence of the homotopic area of the cerebral cortex. The voxel-wise analysis revealed additional features. A large number of voxels from the cerebellum were scattered in the whole angular position, which might reflect the functional heterogeneity of the cerebellum in the sub-ROI level. Additionally, multiple rod-shaped substructures of radial direction were found, which indicates sets of voxels with functional similarity. When compared with independent component analysis (ICA)-driven results, each large-scale component of the brain acquired by ICA showed a consistent pattern of embedding between the subjects. To find the abnormality of the network in the diseased patient, we utilized the autistic spectrum disorder (ASD) dataset. The two groups of ASD and the control group were found to be comparable in means of the quality of embedding. We calculated the hyperbolic distance between all edges of the network and searched for the alteration of the distance of the individual brain network. Among the variable results among the networks of ASD group subjects, the alteration of the cortico-striatal pathway in an autism patient and posterior superior temporal sulcus (pSTS) in an Aspergerโ€™s syndrome patient were present, respectively. The two different anatomically-scaled layers of the network showed a certain degree of correspondence in terms of degree-degree correlation and spreading pattern of network. But anatomically parcellated ROI did not guarantee the functional similarity between the voxels composing it. Finally, to investigate the reproducibility of the embedding process, we repeatedly performed the embedding process and computed the variance of distance matrices. The result was stable except for end-positioned non-popular nodes. Furthermore, to investigate consistency along time-series of fMRI, we compared network yielded by segments of the time series. The segmented networks showed similar results when divided into four frames, but the result lost consistency when divided into 30 frames of 30 seconds each. This study is the first to investigate the characteristics of the functional brain network on the basis of hyperbolic geometry. We suggest a new method applicable for assessing the network alteration in subjects with a neuropsychiatric disease, and these approaches grant us a new understanding in analyzing the functional brain network with a geometric perspective.1. Introduction 1 1.1. Human brain networks 1 1.1.1. Geometry of human brain networks 2 1.2. Scale-free network 3 1.2.1. Definition of a scale-free network 4 1.3. Embedding of the network in hyperbolic space 5 1.3.1. Hyperbolic spaces and Poincarรฉ disk 5 1.3.2. Geometric model of 1/โ„2 9 1.4. The aim of the present study 10 2. Methods 12 2.1. Subjects and image acquisition 12 2.1.1. Human connectome project (HCP) dataset 12 2.1.2. Autism Brain Imaging Data Exchange II (ABIDE II) dataset 12 2.2. Preprocessing for resting-state fMRI 15 2.3. Resting-state networks and functional connectivity analysis 16 2.3.1. Analyzing degree distribution 18 2.4. Assessing underlying geometry 18 2.4.1. The three component spaces 18 2.4.2. Embedding into spaces 20 2.5. Embedding of the network in the 1/โ„2 model 22 2.6. Comparison with ICA-driven method 23 2.7. Assessing the quality of embedding 23 2.8. Abnormality detection in the diseased subject 24 2.9. Assessing variability of analysis 27 3. Results 29 3.1. Global characteristics of the network 29 3.1.1. The degree distribution 31 3.1.2. Determining the threshold value of network 34 3.2. Graph embedding into spaces 36 3.3. 1/โ„2 model analysis 39 3.4. Quality of the embedding 58 3.5. Alteration of the network in the diseased subject 61 3.6. Variability of results 63 3.6.1. Reproducibility of Mercator 63 3.6.2. Time variance of results 67 4. Discussion 70 4.1. Composition of the network 70 4.2. Scale-freeness of brain network 71 4.3. The underlying geometry of brain network 73 4.4. Hyperbolic plane representation 75 4.4.1. Voxelwise approach 78 4.4.2. Compatibility with ICA 80 4.5. Alteration of the network in ASD subjects 81 4.6. Variability and reproducibility of methods 83 4.7. Further applications 85 5. Conclusion 87 References 89 ๊ตญ๋ฌธ ์ดˆ๋ก 106๋ฐ•

    Automated Extraction of Biomarkers for Alzheimer's Disease from Brain Magnetic Resonance Images

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    In this work, different techniques for the automated extraction of biomarkers for Alzheimer's disease (AD) from brain magnetic resonance imaging (MRI) are proposed. The described work forms part of PredictAD (www.predictad.eu), a joined European research project aiming at the identification of a unified biomarker for AD combining different clinical and imaging measurements. Two different approaches are followed in this thesis towards the extraction of MRI-based biomarkers: (I) the extraction of traditional morphological biomarkers based on neuronatomical structures and (II) the extraction of data-driven biomarkers applying machine-learning techniques. A novel method for a unified and automated estimation of structural volumes and volume changes is proposed. Furthermore, a new technique that allows the low-dimensional representation of a high-dimensional image population for data analysis and visualization is described. All presented methods are evaluated on images from the Alzheimer's Disease Neuroimaging Initiative (ADNI), providing a large and diverse clinical database. A rigorous evaluation of the power of all identified biomarkers to discriminate between clinical subject groups is presented. In addition, the agreement of automatically derived volumes with reference labels as well as the power of the proposed method to measure changes in a subject's atrophy rate are assessed. The proposed methods compare favorably to state-of-the art techniques in neuroimaging in terms of accuracy, robustness and run-time

    Mapping Topographic Structure in White Matter Pathways with Level Set Trees

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    Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output

    Statistical Computing on Non-Linear Spaces for Computational Anatomy

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    International audienceComputational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings

    Molecular estimation of neurodegeneration pseudotime in older brains.

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    The temporal molecular changes that lead to disease onset and progression in Alzheimer\u27s disease (AD) are still unknown. Here we develop a temporal model for these unobserved molecular changes with a manifold learning method applied to RNA-Seq data collected from human postmortem brain samples collected within the ROS/MAP and Mayo Clinic RNA-Seq studies. We define an ordering across samples based on their similarity in gene expression and use this ordering to estimate the molecular disease stage-or disease pseudotime-for each sample. Disease pseudotime is strongly concordant with the burden of tau (Braak score, Pโ€‰=โ€‰1.0 ร— 10-5), Aฮฒ (CERAD score, P = 1.8 ร— 10-5), and cognitive diagnosis (P = 3.5 ร— 10-7) of late-onset (LO) AD. Early stage disease pseudotime samples are enriched for controls and show changes in basic cellular functions. Late stage disease pseudotime samples are enriched for late stage AD cases and show changes in neuroinflammation and amyloid pathologic processes. We also identify a set of late stage pseudotime samples that are controls and show changes in genes enriched for protein trafficking, splicing, regulation of apoptosis, and prevention of amyloid cleavage pathways. In summary, we present a method for ordering patients along a trajectory of LOAD disease progression from brain transcriptomic data
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