Adaptive independent vector analysis for multi-subject complex-valued fMRI data

Estimation of complete mutual information exploiting nonlinear magnitude-phase dependence: Application to spatial FNC for complex-valued fMRI data

BACKGROUND

Real-valued mutual information (MI) has been used in spatial functional network connectivity (FNC) to measure high-order and nonlinear dependence between spatial maps extracted from magnitude-only functional magnetic resonance imaging (fMRI). However, real-valued MI cannot fully capture the group differences in spatial FNC from complex-valued fMRI data with magnitude and phase dependence.

METHODS

We propose a complete complex-valued MI method according to the chain rule of MI. We fully exploit the dependence among magnitudes and phases of two complex-valued signals using second and fourth-order joint entropies, and propose to use a Gaussian copula transformation with a lower bound property to avoid inaccurate estimation of joint probability density function when computing the joint entropies.

RESULTS

The proposed method achieves more accurate MI estimates than the two histogram-based (normal and symbolic approaches) and kernel density estimation methods for simulated signals, and enhances group differences in spatial functional network connectivity for experimental complex-valued fMRI data.

COMPARISON WITH EXISTING METHODS

Compared with the simplified complex-valued MI and real-valued MI, the proposed method yields higher MI estimation accuracy, leading to 17.4 % and 145.5 % wider MI ranges, and more significant connectivity differences between healthy controls and schizophrenia patients. A unique connection between executive control network (EC) and right frontal parietal areas, and three additional connections mainly related to EC are detected than the simplified complex-valued MI.

CONCLUSIONS

With capability in quantifying MI fully and accurately, the proposed complex-valued MI is promising in providing qualified FNC biomarkers for identifying mental disorders such as schizophrenia.

Dynamic functional network connectivity based on spatial source phase maps of complex-valued fMRI data: Application to schizophrenia

BACKGROUND

Dynamic spatial functional network connectivity (dsFNC) has shown advantages in detecting functional alterations impacted by mental disorders using magnitude-only fMRI data. However, complete fMRI data are complex-valued with unique and useful phase information.

METHODS

We propose dsFNC of spatial source phase (SSP) maps, derived from complex-valued fMRI data (named SSP-dsFNC), to capture the dynamics elicited by the phase. We compute mutual information for connectivity quantification, employ statistical analysis and Markov chains to assess dynamics, ultimately classifying schizophrenia patients (SZs) and healthy controls (HCs) based on connectivity variance and Markov chain state transitions across windows.

RESULTS

SSP-dsFNC yielded greater dynamics and more significant HC-SZ differences, due to the use of complete brain information from complex-valued fMRI data.

COMPARISON WITH EXISTING METHODS

Compared with magnitude-dsFNC, SSP-dsFNC detected additional and meaningful connections across windows (e.g., for right frontal parietal) and achieved 14.6% higher accuracy for classifying HCs and SZs.

CONCLUSIONS

This work provides new evidence about how SSP-dsFNC could be impacted by schizophrenia, and this information could be used to identify potential imaging biomarkers for psychotic diagnosis.

Denoising brain networks using a fixed mathematical phase change in independent component analysis of magnitude-only fMRI data

Brain networks extracted by independent component analysis (ICA) from magnitude-only fMRI data are usually denoised using various amplitude-based thresholds. By contrast, spatial source phase (SSP) or the phase information of ICA brain networks extracted from complex-valued fMRI data, has provided a simple yet effective way to perform the denoising using a fixed phase change. In this work, we extend the approach to magnitude-only fMRI data to avoid testing various amplitude thresholds for denoising magnitude maps extracted by ICA, as most studies do not save the complex-valued data. The main idea is to generate a mathematical SSP map for a magnitude map using a mapping framework, and the mapping framework is built using complex-valued fMRI data with a known SSP map. Here we leverage the fact that the phase map derived from phase fMRI data has similar phase information to the SSP map. After verifying the use of the magnitude data of complex-valued fMRI, this framework is generalized to work with magnitude-only data, allowing use of our approach even without the availability of the corresponding phase fMRI datasets. We test the proposed method using both simulated and experimental fMRI data including complex-valued data from University of New Mexico and magnitude-only data from Human Connectome Project. The results provide evidence that the mathematical SSP denoising with a fixed phase change is effective for denoising spatial maps from magnitude-only fMRI data in terms of retaining more BOLD-related activity and fewer unwanted voxels, compared with amplitude-based thresholding. The proposed method provides a unified and efficient SSP approach to denoise ICA brain networks in fMRI data.

SSPNet: An interpretable 3D-CNN for classification of schizophrenia using phase maps of resting-state complex-valued fMRI data

Convolutional neural networks (CNNs) have shown promising results in classifying individuals with mental disorders such as schizophrenia using resting-state fMRI data. However, complex-valued fMRI data is rarely used since additional phase data introduces high-level noise though it is potentially useful information for the context of classification. As such, we propose to use spatial source phase (SSP) maps derived from complex-valued fMRI data as the CNN input. The SSP maps are not only less noisy, but also more sensitive to spatial activation changes caused by mental disorders than magnitude maps. We build a 3D-CNN framework with two convolutional layers (named SSPNet) to fully explore the 3D structure and voxel-level relationships from the SSP maps. Two interpretability modules, consisting of saliency map generation and gradient-weighted class activation mapping (Grad-CAM), are incorporated into the well-trained SSPNet to provide additional information helpful for understanding the output. Experimental results from classifying schizophrenia patients (SZs) and healthy controls (HCs) show that the proposed SSPNet significantly improved accuracy and AUC compared to CNN using magnitude maps extracted from either magnitude-only (by 23.4 and 23.6% for DMN) or complex-valued fMRI data (by 10.6 and 5.8% for DMN). SSPNet captured more prominent HC-SZ differences in saliency maps, and Grad-CAM localized all contributing brain regions with opposite strengths for HCs and SZs within SSP maps. These results indicate the potential of SSPNet as a sensitive tool that may be useful for the development of brain-based biomarkers of mental disorders.

Sparse representation of complex-valued fMRI data based on spatiotemporal concatenation of real and imaginary parts

BACKGROUND

Spatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data.

NEW METHODS

We propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise.

RESULTS

The K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method.

COMPARISON WITH EXISTING METHODS

Compared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps.

CONCLUSIONS

The proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.

Characteristics and variability of functional brain networks

Functional brain networks were constructed from functional magnetic resonance imaging (fMRI) data originating from 96 healthy adults. These networks possessed a total of 360 nodes, derived from the latest multi-modal brain parcellation method. A novel group network (overlay network) analysis model is proposed to study common attributes as well as differences found in the human brain by analysis of the functional brain network. Currently, the mean network is generally used to represent the group network. But mean networks have a modularity problem making them distinct from real networks. The overlay network is constructed by calculating the connections between the whole brain network regions, and then filtering the connections by limiting the threshold value. We find that the overlay network is closer to the real network condition of the group in terms of network characteristics related to modularity. Multiple network features are applied to investigate the discrepancies between the new group network and the mean network. Individual divergences between brain regions of everyone are also explored. Results show that the brain network of different people has a high consistency in the global measures, while there exist great differences for local measures in brain regions. Some brain regions show variability over other brain regions on most measures. In addition, we explored the impact of different thresholds on the overlay network and find that different thresholds have a greater impact on the clustering coefficient, maximized modularity, strength, and global efficiency.

Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data With a Phase Sparsity Constraint

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed l₀ norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

The multidimensional brain

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers that, taking into account the big data outburst and novel available computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones. In this review, I show how further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions. I then describe how to extract hidden multidimensional information from real or artificial neurodata series, and make clear how our mind dilutes, rather than concentrates as currently believed, inputs coming from the environment. Finally, I argue that the principle "the higher the dimension, the greater the information" may explain the occurrence of mental activities and elucidate the mechanisms of human diseases associated with dimensionality reduction.