Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning

This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.

Phase Ambiguity Correction and Visualization Techniques for Complex-Valued ICA of Group fMRI Data

Analysis of functional magnetic resonance imaging (fMRI) data in its native, complex form has been shown to increase the sensitivity both for data-driven techniques, such as independent component analysis (ICA), and for model-driven techniques. The promise of an increase in sensitivity and specificity in clinical studies, provides a powerful motivation for utilizing both the phase and magnitude data; however, the unknown and noisy nature of the phase poses a challenge. In addition, many complex-valued analysis algorithms, such as ICA, suffer from an inherent phase ambiguity, which introduces additional difficulty for group analysis. We present solutions for these issues, which have been among the main reasons phase information has been traditionally discarded, and show their effectiveness when used as part of a complex-valued group ICA algorithm application. The methods we present thus allow the development of new fully complex data-driven and semi-blind methods to process, analyze, and visualize fMRI data.We first introduce a phase ambiguity correction scheme that can be either applied subsequent to ICA of fMRI data or can be incorporated into the ICA algorithm in the form of prior information to eliminate the need for further processing for phase correction. We also present a Mahalanobis distance-based thresholding method, which incorporates both magnitude and phase information into a single threshold, that can be used to increase the sensitivity in the identification of voxels of interest. This method shows particular promise for identifying voxels with significant susceptibility changes but that are located in low magnitude (i.e. activation) areas. We demonstrate the performance gain of the introduced methods on actual fMRI data.

Order Selection of the Linear Mixing Model for Complex-valued FMRI Data

Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, which motivates the use of complex-valued data analysis methods. Due to the high dimension and high noise level of fMRI data, order selection and dimension reduction are important procedures for multivariate analysis methods such as independent component analysis (ICA). In this work, we develop a complex-valued order selection method to estimate the dimension of signal subspace using information-theoretic criteria. To correct the effect of sample dependence to information-theoretic criteria, we develop a general entropy rate measure for complex Gaussian random process to calibrate the independent and identically distributed (i.i.d.) sampling scheme in the complex domain. We show the effectiveness of the approach for order selection on both simulated and actual fMRI data. A comparison between the results of order selection and ICA on real-valued and complex-valued fMRI data demonstrates that a fully complex analysis extracts more information about brain activation.