Spatiotemporal Nonlinear Dynamics Analysis Based On FMRI Data Of The Resting-state Human Brain

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...