Spatiotemporal nonlinearity in resting-state fMRI of the human brain.

In this work, the spatiotemporal nonlinearity in resting-state fMRI data of the human brain was detected by 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 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, the results suggest that fluctuations presented in resting state may be an inherent model of basal neural activation of human brain, cannot be fully attributed to noise.

Treatment of ill-balanced datasets of fMRI with Modified Fuzzy c-means Method.

In fMRI dataset, the population of actived voxels is always much less than the total population of the voxels, and that produced an ill-balanced dataset. Some methods, such as limiting the analysis to the gray matter voxels where the BOLD signal is expected and removing the voxels that is absolutely non-actived based on statistical criteria, have been used to treat the ill-balanced dataset. In this article, a new method, Modified Fuzzy c-means(MFc), has been proposed to treat the ill-balanced dataset of fMRI. The main difference from other statistical methods is that it is datadriven. iven. The MFc method is used to classify the voxels into two clusters with nearly the same population and all actived voxels are contained in one cluster. Thus we got nearly half voxels to analysis and the ill-balanced dataset can be treated. The efficiency of clustering analysis is also boosted.

Controlling chaos in a chaotic neural network.

The chaotic neural network constructed with chaotic neuron shows the associative memory function, but its memory searching process cannot be stabilized in a stored state because of the chaotic motion of the network. In this paper, a pinning control method focused on the chaotic neural network is proposed. The computer simulation proves that the chaos in the chaotic neural network can be controlled with this method and the states of the network can converge in one of its stored patterns if the control strength and the pinning density are chosen suitable. It is found that in general the threshold of the control strength of a controlled network is smaller at higher pinned density and the chaos of the chaotic neural network can be controlled more easily if the pinning control is added to the variant neurons between the initial pattern and the target pattern.