基于神经影像的多尺度动态有向连接理论与算法研究
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摘要
大脑是结构分离却功能整合的平衡体，也是复杂系统中尤为突出的经典实例。人们热衷于利用复杂网络研究人脑这一复杂系统。近年，对复杂脑网络的研究致力于探索其复杂的网络拓扑性质。目前，更多的研究转向于探索复杂脑网络的不同时空尺度的动力学，以及对应的网络结构演化过程。
从解剖和功能水平来理解脑的复杂网络拓扑性质是迄今为止最大的挑战。除利用解剖结构连接（通常指白质纤维束）外，也发展了很多有效的方法来推断大脑连接。其中比较常用的是基于神经活动的同步相关性来推断的功能连接（Functional connectivity，FC），它是指空间远距离神经生理事件间的统计依赖性。另外一类重要的方法是有效连接（Effective connectivity，EC），它试图去揭示脑区间的有向信息传输机制；近年来，已经发展了许多探测有效连接的算法，基于数据驱动的Granger Causality（GC）就是强有效的工具之一。
GC计算的一个主要问题在于如何处理多变量冗余和混淆信息；这个问题是GC应用于神经影像数据集的最大障碍，全文上下都围绕这一主线展开。本论文的工作就是致力于发展、运用和严格的验证GC算法，使其更加坚实有效地应用于神经影像数据集，进而最大限度的获取可靠的有向传输信息。此外，我们也将这些算法应用于认知任务或病患等特定问题的数据上，为理解脑功能及其异常机制提供一个新思路。
本文主要包括三大部分的研究：
第一部分，利用基于典型相关的因果算法重构小尺度动态网络（少量网络节点，100~102级别）。为了探测多变量/群组/模块间的信息交互，从个体到群组水平、多尺度地挖掘网络底层隐涵的丰富信息，本文提出一种典型相关GC算法，它避免了传统的自回归模型估计，消除了瞬时同步交互效应对于因果推断的影响。经过仿真数据的成功测试后，将其用于分析一位癫痫患者发作间期的脑电数据（同步记录的头皮和深部脑电图），分析结果合理地解释了癫痫发作时相关的临床症状（第二章）。
生理信号往往表现出非线性动力学特征，它限制了上述线性典型相关GC算法的功效，在此，本文提出利用核函数技巧（将数据投射到更高维的特征空间），推广了典型相关GC算法，使之适合于估计非线性因果交互作用。同样的，在仿真数据上测试其可行性和有效性后，进一步将其运用到癫痫患者的颅内脑电图数据，重构出了既有线性又有非线性因果交互作用的时空连接网络，为探索癫痫发作时的信息传输路径提供一个新的检测手段（第三章）。
第二部分，关注于处理中尺度网络（大量网络节点，102~103级别）重构时面临的冗余和维数灾难问题。这种网络尺度恰好对应了传统大脑皮层分割的尺度。而大多以功能磁共振成像构造的脑网络是基于分割区域内体素平均的BOLD（blood-oxygenation level-dependent）信号构建起来的；这些信号通常具有样本少、噪声高的特点。用这类信号重构大规模网络，标准的条件GC（conditional GC，CGC）不再适用，本文提出了利用基于携带驱动变量信息的原则来挑选条件变量的技术（即部分条件GC，partially conditioned GC，PCGC）。该方法成功地应用于仿真数据和高密度脑电图。
此外，在BOLD时间序列上推断动态有向交互时，还面临另外一个关键问题：血液动力学（hemodynamic response function，HRF）混淆效应。针对这个问题，本文提出一种新颖的BOLD-fMRI信号盲去卷积技术（第四章），实现了在隐神经水平上推断区域间的因果交互作用。
通过联合这两种方法（盲去卷积和PCGC），可以更加有效地推断静息态下的动态有向信息交互；分析结果显示是否去卷积将对大脑网络的局部拓扑特性产生影响。此外，分析结果还显示条件变量集会服从一个稳健的空间分布（具有模块性特征），且这种分布不受扫描时段（session）和重复时间（repetition time，TR，0.645s，1.4s和2.5s）的影响（第五章），为进一步将PCGC推广到体素水平构建有向网络奠定了基础。
第三部分，大型（海量网络节点，104及以上级别）网络构建，该尺度与fMRI数据中体素的数量级相对应，是典型的海量数据构建复杂大型网络的实例。为此，本文提出一种基于社团划分的PCGC算法，结合去卷积方法，高效地构建出基于体素的隐神经水平有向网络。该算法不仅可以对条件变量降维，还消除了冗余性的影响。通过应用图论方法（如：度、中心性和聚类系数），实现了基于体素水平脑动态网络拓扑特征的刻画（第六章），开启了运用fMRI理解大脑内信息传输的新篇章。
在搭建完不同尺度有向网络构建的理论之后，我们将其应用到利手的静息态功能磁共振成像数据上，探讨利手是如何塑造静息态人脑的。
The last decade has witnessed a continuous rise in studies of complex networks,which have now become an established paradigm to study complex systems, amongwhich the brain, with its balance between anatomical segregation and functionalintegration, is a most prominent example. Although initial efforts focused ondisentangling the intricate topological properties of complex networks, the interest hasnow shifted towards the study of dynamical processes at different temporal and spatialscales and the co-evolution of network structures with those processes.
One of the big challenges to date is to understand the non-trivial topologicalorganization of the brain at the structural/anatomical and the functional level. Asidefrom structural connectivity, that typically corresponds to white matter tracts, severalmethods have been employed to infer connectivity in the brain. Functional connectivityis usually inferred on the basis of correlations among neural activity and defined asstatistical dependencies among remote neurophysiological events. Another importantfamily of methods aims to reveal directed information transfer between brain regions(effective connectivity). In recent years, many approaches have been proposed, amongwhich Granger Causality (GC) emerged as a powerful data driven method.
My thesis work has been dedicated to the development, implementation andrigorous validation of approaches to make GC more solid and amenable to be applied toneuroimaging datasets in order to extract from them the maximum amount of reliableinformation on the directed information transfer among the variables. These approacheswere then extensively applied to data with the goal of answering specific questions andof providing a novel insight on brain function and malfunctioning.
One of the main issues with GC is how to deal with the redundant and confoundinginformation arising in multivariate datasets. Addressing this issue was a constantconcern throughout all the project.
In the first part, dynamical networks of moderate size (100~102nodes) werereconstructed by means of a canonical correlation approach to GC. This approach,capable to detect multivariate/groupwise/blockwise information interaction was appliedto simultaneously recorded scalp and depth electroencephalographic (EEG) data fromone epileptic patient during an interictal period (Chapter2).
Then I extended the capability of canonical correlation to include the estimation ofnonlinear causal interaction using the kernel trick, which projects the data into a higherdimensional feature space and provides a convenient way for generalization of the linearcanonical correlation GC. After testing feasibility and effectiveness tested on simulateddata, the approach was applied to intracranial EEG data in epilepsy, resulting in animproved identification of the spatio-temporal causal connectivity network associated tothe disease (Chapter3).
In the second part the issue of redundancy and curse of dimensionality wasaddressed for networks of medium size (102~103nodes). This is the typical size of theparcellation of the brain surface, so the natural target of this phase were datasets whosetime series corresponded to the blood-oxygenation level-dependent (BOLD) recorded infunctional magnetic resonance imaging (fMRI) and averaged across brain regions.These datasets are typically noisy and short. For networks of this size, standardconditional GC (CGC) is no longer effective. I applied a technique that identifies thevariables that share common information with each candidate driver to perform partiallyconditioned GC (PCGC). This approach was tested on simulated data and high densityEEG. Furthermore when evaluating dynamical directed interactions from BOLD timeseries, one is faced to another critical issue, namely the confounding effect ofhemodynamic response function (HRF). I addressed this problem by implementing anovel blind deconvolution technique for BOLD-fMRI signal (Chapter4). This jointapproach (deconvolution and PCGC) proved useful in retrieving dynamical interactionsin resting-state fMRI datasets. The results show that the distributions of conditioningvariable follow a stable spatial pattern, across different session and repetition time (TR,0.645s,1.4s and2.5s)(Chapter5).
In the last part I addressed the reconstruction of large networks (from104nodesonwards). This is the typical number of voxels in a fMRI dataset. I developed anadditional strategy to reduce the number of conditioning variables in a faster and moreefficient way. With this approach it was possible to uncover the architecture of directednetworks at the voxel level and investigate its degree, betweenness and clusteringcoefficient hubs (Chapter6).
从解剖和功能水平来理解脑的复杂网络拓扑性质是迄今为止最大的挑战。除利用解剖结构连接（通常指白质纤维束）外，也发展了很多有效的方法来推断大脑连接。其中比较常用的是基于神经活动的同步相关性来推断的功能连接（Functional connectivity，FC），它是指空间远距离神经生理事件间的统计依赖性。另外一类重要的方法是有效连接（Effective connectivity，EC），它试图去揭示脑区间的有向信息传输机制；近年来，已经发展了许多探测有效连接的算法，基于数据驱动的Granger Causality（GC）就是强有效的工具之一。
GC计算的一个主要问题在于如何处理多变量冗余和混淆信息；这个问题是GC应用于神经影像数据集的最大障碍，全文上下都围绕这一主线展开。本论文的工作就是致力于发展、运用和严格的验证GC算法，使其更加坚实有效地应用于神经影像数据集，进而最大限度的获取可靠的有向传输信息。此外，我们也将这些算法应用于认知任务或病患等特定问题的数据上，为理解脑功能及其异常机制提供一个新思路。
本文主要包括三大部分的研究：
第一部分，利用基于典型相关的因果算法重构小尺度动态网络（少量网络节点，100~102级别）。为了探测多变量/群组/模块间的信息交互，从个体到群组水平、多尺度地挖掘网络底层隐涵的丰富信息，本文提出一种典型相关GC算法，它避免了传统的自回归模型估计，消除了瞬时同步交互效应对于因果推断的影响。经过仿真数据的成功测试后，将其用于分析一位癫痫患者发作间期的脑电数据（同步记录的头皮和深部脑电图），分析结果合理地解释了癫痫发作时相关的临床症状（第二章）。
生理信号往往表现出非线性动力学特征，它限制了上述线性典型相关GC算法的功效，在此，本文提出利用核函数技巧（将数据投射到更高维的特征空间），推广了典型相关GC算法，使之适合于估计非线性因果交互作用。同样的，在仿真数据上测试其可行性和有效性后，进一步将其运用到癫痫患者的颅内脑电图数据，重构出了既有线性又有非线性因果交互作用的时空连接网络，为探索癫痫发作时的信息传输路径提供一个新的检测手段（第三章）。
第二部分，关注于处理中尺度网络（大量网络节点，102~103级别）重构时面临的冗余和维数灾难问题。这种网络尺度恰好对应了传统大脑皮层分割的尺度。而大多以功能磁共振成像构造的脑网络是基于分割区域内体素平均的BOLD（blood-oxygenation level-dependent）信号构建起来的；这些信号通常具有样本少、噪声高的特点。用这类信号重构大规模网络，标准的条件GC（conditional GC，CGC）不再适用，本文提出了利用基于携带驱动变量信息的原则来挑选条件变量的技术（即部分条件GC，partially conditioned GC，PCGC）。该方法成功地应用于仿真数据和高密度脑电图。
此外，在BOLD时间序列上推断动态有向交互时，还面临另外一个关键问题：血液动力学（hemodynamic response function，HRF）混淆效应。针对这个问题，本文提出一种新颖的BOLD-fMRI信号盲去卷积技术（第四章），实现了在隐神经水平上推断区域间的因果交互作用。
通过联合这两种方法（盲去卷积和PCGC），可以更加有效地推断静息态下的动态有向信息交互；分析结果显示是否去卷积将对大脑网络的局部拓扑特性产生影响。此外，分析结果还显示条件变量集会服从一个稳健的空间分布（具有模块性特征），且这种分布不受扫描时段（session）和重复时间（repetition time，TR，0.645s，1.4s和2.5s）的影响（第五章），为进一步将PCGC推广到体素水平构建有向网络奠定了基础。
第三部分，大型（海量网络节点，104及以上级别）网络构建，该尺度与fMRI数据中体素的数量级相对应，是典型的海量数据构建复杂大型网络的实例。为此，本文提出一种基于社团划分的PCGC算法，结合去卷积方法，高效地构建出基于体素的隐神经水平有向网络。该算法不仅可以对条件变量降维，还消除了冗余性的影响。通过应用图论方法（如：度、中心性和聚类系数），实现了基于体素水平脑动态网络拓扑特征的刻画（第六章），开启了运用fMRI理解大脑内信息传输的新篇章。
在搭建完不同尺度有向网络构建的理论之后，我们将其应用到利手的静息态功能磁共振成像数据上，探讨利手是如何塑造静息态人脑的。
The last decade has witnessed a continuous rise in studies of complex networks,which have now become an established paradigm to study complex systems, amongwhich the brain, with its balance between anatomical segregation and functionalintegration, is a most prominent example. Although initial efforts focused ondisentangling the intricate topological properties of complex networks, the interest hasnow shifted towards the study of dynamical processes at different temporal and spatialscales and the co-evolution of network structures with those processes.
One of the big challenges to date is to understand the non-trivial topologicalorganization of the brain at the structural/anatomical and the functional level. Asidefrom structural connectivity, that typically corresponds to white matter tracts, severalmethods have been employed to infer connectivity in the brain. Functional connectivityis usually inferred on the basis of correlations among neural activity and defined asstatistical dependencies among remote neurophysiological events. Another importantfamily of methods aims to reveal directed information transfer between brain regions(effective connectivity). In recent years, many approaches have been proposed, amongwhich Granger Causality (GC) emerged as a powerful data driven method.
My thesis work has been dedicated to the development, implementation andrigorous validation of approaches to make GC more solid and amenable to be applied toneuroimaging datasets in order to extract from them the maximum amount of reliableinformation on the directed information transfer among the variables. These approacheswere then extensively applied to data with the goal of answering specific questions andof providing a novel insight on brain function and malfunctioning.
One of the main issues with GC is how to deal with the redundant and confoundinginformation arising in multivariate datasets. Addressing this issue was a constantconcern throughout all the project.
In the first part, dynamical networks of moderate size (100~102nodes) werereconstructed by means of a canonical correlation approach to GC. This approach,capable to detect multivariate/groupwise/blockwise information interaction was appliedto simultaneously recorded scalp and depth electroencephalographic (EEG) data fromone epileptic patient during an interictal period (Chapter2).
Then I extended the capability of canonical correlation to include the estimation ofnonlinear causal interaction using the kernel trick, which projects the data into a higherdimensional feature space and provides a convenient way for generalization of the linearcanonical correlation GC. After testing feasibility and effectiveness tested on simulateddata, the approach was applied to intracranial EEG data in epilepsy, resulting in animproved identification of the spatio-temporal causal connectivity network associated tothe disease (Chapter3).
In the second part the issue of redundancy and curse of dimensionality wasaddressed for networks of medium size (102~103nodes). This is the typical size of theparcellation of the brain surface, so the natural target of this phase were datasets whosetime series corresponded to the blood-oxygenation level-dependent (BOLD) recorded infunctional magnetic resonance imaging (fMRI) and averaged across brain regions.These datasets are typically noisy and short. For networks of this size, standardconditional GC (CGC) is no longer effective. I applied a technique that identifies thevariables that share common information with each candidate driver to perform partiallyconditioned GC (PCGC). This approach was tested on simulated data and high densityEEG. Furthermore when evaluating dynamical directed interactions from BOLD timeseries, one is faced to another critical issue, namely the confounding effect ofhemodynamic response function (HRF). I addressed this problem by implementing anovel blind deconvolution technique for BOLD-fMRI signal (Chapter4). This jointapproach (deconvolution and PCGC) proved useful in retrieving dynamical interactionsin resting-state fMRI datasets. The results show that the distributions of conditioningvariable follow a stable spatial pattern, across different session and repetition time (TR,0.645s,1.4s and2.5s)(Chapter5).
In the last part I addressed the reconstruction of large networks (from104nodesonwards). This is the typical number of voxels in a fMRI dataset. I developed anadditional strategy to reduce the number of conditioning variables in a faster and moreefficient way. With this approach it was possible to uncover the architecture of directednetworks at the voxel level and investigate its degree, betweenness and clusteringcoefficient hubs (Chapter6).
引文
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