基于静息态脑fMRI数据的时空非线性动力学特性分析
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摘要
作为一种无损伤、不用外源介质和非侵入性的测量技术,核磁共振成像(MRI)为脑功能的研究提供了一种重要的手段。尽管功能核磁共振成像(fMRI)的历史并不长,但是发展却很快,正在逐步成为视觉、语言、工作记忆和其它认知过程脑功能研究的重要工具。
本文首先利用非线性动力学的方法检测静息态人脑fMRI数据的时空非线性特性。采用梯度回波快速成像方法在1.5T的核磁共振成像仪上采集九个健康被试的静息态fMRI数据,并通过相关矩阵的特征值谱分析、关联维数分析和时空Lyapunov指数分析来检测静息态人脑fMRI数据的时空非线性特性。通过模拟、调节AR(1)结构纯噪声数据的特征值谱,并将调节后的特征值谱与fMRI数据的特征值谱比较,获得fMRI数据的本征维数的估计。依据所估计的本征维数,用主成分分析从fMRI数据中抽取若干主成分,这样在保证保留准确的相动力学的基础上,尽可能减轻计算量和降低噪声。然后用时间延迟嵌入的方法对所取得的主成分进行相空间重构,并用Grassberger-Procaccia算法估计多变量序列的关联维数。与此同时,对静息态fMRI数据应用耦合映象格子(CML)方法计算时空Lyapunov指数(STLE)及其嵌入维效应和时间演化。非线性统计显著性检验结果表明,在静息态fMRI数据和相应的surrogate数据之间,关联维数和时空Lyapunov指数存在着明显的差异。而且分数关联维数和正的时空Lyapunov指数刻画了静息态人脑fMRI数据的时空非线性动力学特性。这些结果表明,静息态人脑fMRI数据中存在着非线性结构,因此,结果提示静息态fMRI的波动反映了人脑中内在的基本神经活动模式,不能完全归因于噪声。
另一方面,时空Lyapunov指数的嵌入维效应及其时间演化也表明,静息态人脑fMRI数据中存在确定性的非线性行为以及动力学特性的短暂稳定性。而正的时空Lyapunov指数还表明静息态人脑中存在时空混沌现象,而时空混沌现象提示体素之间的相关性并不是固定不变的,而随着时间变化,这表明静息态人脑中存在动态功能连接和动态脑功能网络。
估计fMRI数据中真实的本征维数(即真实的信号数目)是一个非常重要同时又是非常困难的问题。在本文中,通过构建合适的插值变量,获得了对一阶自回归噪声模型中自回归系数更合理的估计。采用基于一阶自回归噪声模型和三次样条插值相结合的本征维数估计新方法(AR1CSI)、基于一阶自回归噪声模型的本征维数估计方法(AR1)和基于分形的本征维数估计法(FB),分别对仿真数据和静息态fMRI数据进行本征维数估计,结果表明,无论在不同的体素数目、时间长度、信号数目和信噪比还是不同噪声模型的情况下,AR1CSI的本征维数估计方法都比AR1方法及FB方法有更准确的信号数目估计。因此,AR1CSI本征维数估计方法是一种性能更为优异的本征维数估计方法。
传统脑功能激活图的检测方法是基于广义线性模型的,尽管该方法取得了许多重要的结果,由于该方法假定神经刺激和fMRI响应之间呈现线性关系,因而存在着明显的缺陷。当今以聚类分析为代表的数据驱动方法受到了日益广泛的重视。本文将基于数据点消息传递(CPMDP)的聚类分析方法引入fMRI数据的分析。为了提高聚类分析结果的可靠性,提出增加一个附加体素的思想。在fMRI数据分析中,用所有体素时间序列与神经刺激标准响应之间的相关系数来确定附加体素。对混合数据集和听觉刺激fMRI数据进行CPMDP聚类分析,并与k-means聚类分析方法相比,结果表明,CPMDP分析不仅不需要预先规定聚类的类数,而且聚类结果也稳定得多,同时由于增加了附加体素,聚类的可靠性也提高了。因此CPMDP聚类方法是一种性能优秀的fMRI数据分析方法,其性能优于k-means聚类分析方法。
Functional magnetic resonance imaging (fMRI) has emerged as a useful and noninvasive technique for studying the function of the brain. This technique has emerged only in recent years, but it has rapidly developed in to a powerful tool for studying vision, language, working memory, and other cognitive processes.
In this paper, the spatiotemporal nonlinearity in resting-state fMRI datasets of human brain was detected by use of the nonlinear dynamics methods. Nine human subjects during resting state were imaged using single-shot gradient echo planar imaging on a 1.5T scanner. Eigenvalue spectra for the covariance matrix, correlation dimensions and Spatiotemporal Lyapunov Exponents were calculated to detect the spatiotemporal nonlinearity in resting-state fMRI data. By simulating, adjusting, and comparing the eigenvalue spectra of pure correlated noise with the corresponding real fMRI data, the intrinsic dimensionality was estimated. The intrinsic dimensionality was used to extract the first few principal components from the real fMRI data using Principal Component Analysis, which will preserve the correct phase dynamics, while reducing both computational load and noise level of the data. Then the phase-space was reconstructed using the time-delay embedding method for their principal components and the correlation dimension was estimated by the Grassberger-Procaccia algorithm of multiple variable series. The Spatiotemporal Lyapunov Exponents, as well as their effects of embedding dimension and temporal evolutions, were calculated by using the method based on coupled map lattices. Through nonlinearity testing, there are significant differences of correlation dimensions and Spatiotemporal Lyapunov Exponents between fMRI data and their surrogate data. The fractal dimension and the positive Spatiotemporal Lyapunov Exponents characterize the spatiotemporal nonlinear dynamics property of resting-state fMRI data. Therefore, there is nonlinear structure in the fMRI data of the resting state human brain and it suggests that fluctuations presented in resting state may be an inherent model of basal neural activation of human brain, cannot be fully attributed to noise.
On the other hand, the effect of embedding dimension and the temporal evolution of the Spatiotemporal Lyapunov Exponents also show that there is nonlinearity and determinism in resting-state human brain, as well as brief dynamics stability. Furthermore, the results demonstrate that there is a spatiotemporal chaos phenomenon in resting-state brain. At the same time, the spatiotemporal chaos phenomenon suggests that the correlation between voxels varies with time and there is a dynamic functional connection or network in resting-state human brain.
Estimating the true dimensionality of the data to determine what is essential in the data is an important but a difficult problem in fMRI dataset. By constructing proper interpolation variable, more reasonable estimation of the coefficient of an autoregressive noise model of order 1 can be made. Simulation data and real fMRI dataset of resting-state in human brains are used to compare the performance of the new method incorporating an autoregressive noise model of order 1 with cubic spline interpolation (AR1CSI) with that of the method based only on an autoregressive noise model of order 1 (AR1) and a fractal-based intrinsic dimension estimating method (FB). As illustrated in simulated datasets and real fMRI datasets of resting-state human brain, the AR1CSI method leads to more accurate estimate of the model order at many circumstances, no matter what the voxel number, the temporal size of the data, the signal number and the SNR are. Comparing with AR1 and FB method, the performance for estimating the model order in fMRI dataset can be improved by AR1CSI method.
The most popular analysis of fMRI data involves fitting a general linear model (GLM). GLM is based on the suggestion that the temporal hemodynamic response possesses linear characteristics and that the response is independent of prior responses. Through this analysis approach has produced a wealth of important findings, they have several limitations. As an important data-driven, exploratory analysis tool, clustering methods have generated a great deal of interest. In this paper, clustering by passing messages between data points (CPMDP) is introduced into the analysis of fMRI data. In order to increase the reliability of analysis, an additive voxel as an exemplar is introduced, and the correlation coefficients between the ideal responses of stimulation and voxel series of fMRI data are used to generate the additive voxel. The analysis results of hybrid datasets and fMRI dataset with auditory stimulation prove that, compared with k-means clustering method, CPMDP need not to define the number of clusters in advance and can result in stable results. Furthermore, due to add an additive voxel as an exemplar, the reliability of analysis is also improved. For fMRI data analysis, CPMDP is also an excellent method
本文首先利用非线性动力学的方法检测静息态人脑fMRI数据的时空非线性特性。采用梯度回波快速成像方法在1.5T的核磁共振成像仪上采集九个健康被试的静息态fMRI数据,并通过相关矩阵的特征值谱分析、关联维数分析和时空Lyapunov指数分析来检测静息态人脑fMRI数据的时空非线性特性。通过模拟、调节AR(1)结构纯噪声数据的特征值谱,并将调节后的特征值谱与fMRI数据的特征值谱比较,获得fMRI数据的本征维数的估计。依据所估计的本征维数,用主成分分析从fMRI数据中抽取若干主成分,这样在保证保留准确的相动力学的基础上,尽可能减轻计算量和降低噪声。然后用时间延迟嵌入的方法对所取得的主成分进行相空间重构,并用Grassberger-Procaccia算法估计多变量序列的关联维数。与此同时,对静息态fMRI数据应用耦合映象格子(CML)方法计算时空Lyapunov指数(STLE)及其嵌入维效应和时间演化。非线性统计显著性检验结果表明,在静息态fMRI数据和相应的surrogate数据之间,关联维数和时空Lyapunov指数存在着明显的差异。而且分数关联维数和正的时空Lyapunov指数刻画了静息态人脑fMRI数据的时空非线性动力学特性。这些结果表明,静息态人脑fMRI数据中存在着非线性结构,因此,结果提示静息态fMRI的波动反映了人脑中内在的基本神经活动模式,不能完全归因于噪声。
另一方面,时空Lyapunov指数的嵌入维效应及其时间演化也表明,静息态人脑fMRI数据中存在确定性的非线性行为以及动力学特性的短暂稳定性。而正的时空Lyapunov指数还表明静息态人脑中存在时空混沌现象,而时空混沌现象提示体素之间的相关性并不是固定不变的,而随着时间变化,这表明静息态人脑中存在动态功能连接和动态脑功能网络。
估计fMRI数据中真实的本征维数(即真实的信号数目)是一个非常重要同时又是非常困难的问题。在本文中,通过构建合适的插值变量,获得了对一阶自回归噪声模型中自回归系数更合理的估计。采用基于一阶自回归噪声模型和三次样条插值相结合的本征维数估计新方法(AR1CSI)、基于一阶自回归噪声模型的本征维数估计方法(AR1)和基于分形的本征维数估计法(FB),分别对仿真数据和静息态fMRI数据进行本征维数估计,结果表明,无论在不同的体素数目、时间长度、信号数目和信噪比还是不同噪声模型的情况下,AR1CSI的本征维数估计方法都比AR1方法及FB方法有更准确的信号数目估计。因此,AR1CSI本征维数估计方法是一种性能更为优异的本征维数估计方法。
传统脑功能激活图的检测方法是基于广义线性模型的,尽管该方法取得了许多重要的结果,由于该方法假定神经刺激和fMRI响应之间呈现线性关系,因而存在着明显的缺陷。当今以聚类分析为代表的数据驱动方法受到了日益广泛的重视。本文将基于数据点消息传递(CPMDP)的聚类分析方法引入fMRI数据的分析。为了提高聚类分析结果的可靠性,提出增加一个附加体素的思想。在fMRI数据分析中,用所有体素时间序列与神经刺激标准响应之间的相关系数来确定附加体素。对混合数据集和听觉刺激fMRI数据进行CPMDP聚类分析,并与k-means聚类分析方法相比,结果表明,CPMDP分析不仅不需要预先规定聚类的类数,而且聚类结果也稳定得多,同时由于增加了附加体素,聚类的可靠性也提高了。因此CPMDP聚类方法是一种性能优秀的fMRI数据分析方法,其性能优于k-means聚类分析方法。
Functional magnetic resonance imaging (fMRI) has emerged as a useful and noninvasive technique for studying the function of the brain. This technique has emerged only in recent years, but it has rapidly developed in to a powerful tool for studying vision, language, working memory, and other cognitive processes.
In this paper, the spatiotemporal nonlinearity in resting-state fMRI datasets of human brain was detected by use of the nonlinear dynamics methods. Nine human subjects during resting state were imaged using single-shot gradient echo planar imaging on a 1.5T scanner. Eigenvalue spectra for the covariance matrix, correlation dimensions and Spatiotemporal Lyapunov Exponents were calculated to detect the spatiotemporal nonlinearity in resting-state fMRI data. By simulating, adjusting, and comparing the eigenvalue spectra of pure correlated noise with the corresponding real fMRI data, the intrinsic dimensionality was estimated. The intrinsic dimensionality was used to extract the first few principal components from the real fMRI data using Principal Component Analysis, which will preserve the correct phase dynamics, while reducing both computational load and noise level of the data. Then the phase-space was reconstructed using the time-delay embedding method for their principal components and the correlation dimension was estimated by the Grassberger-Procaccia algorithm of multiple variable series. The Spatiotemporal Lyapunov Exponents, as well as their effects of embedding dimension and temporal evolutions, were calculated by using the method based on coupled map lattices. Through nonlinearity testing, there are significant differences of correlation dimensions and Spatiotemporal Lyapunov Exponents between fMRI data and their surrogate data. The fractal dimension and the positive Spatiotemporal Lyapunov Exponents characterize the spatiotemporal nonlinear dynamics property of resting-state fMRI data. Therefore, there is nonlinear structure in the fMRI data of the resting state human brain and it suggests that fluctuations presented in resting state may be an inherent model of basal neural activation of human brain, cannot be fully attributed to noise.
On the other hand, the effect of embedding dimension and the temporal evolution of the Spatiotemporal Lyapunov Exponents also show that there is nonlinearity and determinism in resting-state human brain, as well as brief dynamics stability. Furthermore, the results demonstrate that there is a spatiotemporal chaos phenomenon in resting-state brain. At the same time, the spatiotemporal chaos phenomenon suggests that the correlation between voxels varies with time and there is a dynamic functional connection or network in resting-state human brain.
Estimating the true dimensionality of the data to determine what is essential in the data is an important but a difficult problem in fMRI dataset. By constructing proper interpolation variable, more reasonable estimation of the coefficient of an autoregressive noise model of order 1 can be made. Simulation data and real fMRI dataset of resting-state in human brains are used to compare the performance of the new method incorporating an autoregressive noise model of order 1 with cubic spline interpolation (AR1CSI) with that of the method based only on an autoregressive noise model of order 1 (AR1) and a fractal-based intrinsic dimension estimating method (FB). As illustrated in simulated datasets and real fMRI datasets of resting-state human brain, the AR1CSI method leads to more accurate estimate of the model order at many circumstances, no matter what the voxel number, the temporal size of the data, the signal number and the SNR are. Comparing with AR1 and FB method, the performance for estimating the model order in fMRI dataset can be improved by AR1CSI method.
The most popular analysis of fMRI data involves fitting a general linear model (GLM). GLM is based on the suggestion that the temporal hemodynamic response possesses linear characteristics and that the response is independent of prior responses. Through this analysis approach has produced a wealth of important findings, they have several limitations. As an important data-driven, exploratory analysis tool, clustering methods have generated a great deal of interest. In this paper, clustering by passing messages between data points (CPMDP) is introduced into the analysis of fMRI data. In order to increase the reliability of analysis, an additive voxel as an exemplar is introduced, and the correlation coefficients between the ideal responses of stimulation and voxel series of fMRI data are used to generate the additive voxel. The analysis results of hybrid datasets and fMRI dataset with auditory stimulation prove that, compared with k-means clustering method, CPMDP need not to define the number of clusters in advance and can result in stable results. Furthermore, due to add an additive voxel as an exemplar, the reliability of analysis is also improved. For fMRI data analysis, CPMDP is also an excellent method
引文
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