Spatial source phase: A new feature for identifying spatial differences based on complex-valued resting-state 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.

Identification of Methamphetamine Abstainers by Resting-State Functional Magnetic Resonance Imaging

Methamphetamine (MA) can cause brain structural and functional impairment, but there are few studies on whether this difference will sustain on MA abstainers. The purpose of this study is to investigate the correlation of brain networks in MA abstainers. In this study, 47 people detoxified for at least 14 months and 44 normal people took a resting-state functional magnetic resonance imaging (RS-fMRI) scan. A dynamic (i.e., time-varying) functional connectivity (FC) is obtained by applying sliding windows in the time courses on the independent components (ICs). The windowed correlation data for each IC were then clustered by k-means. The number of subjects in each cluster was used as a new feature for individual identification. The results show that the classifier achieved satisfactory performance (82.3% accuracy, 77.7% specificity, and 85.7% sensitivity). We find that there are significant differences in the brain networks of MA abstainers and normal people in the time domain, but the spatial differences are not obvious. Most of the altered functional connections (time-varying) are identified to be located at dorsal default mode network. These results have shown that changes in the correlation of the time domain may play an important role in identifying MA abstainers. Therefore, our findings provide valuable insights in the identification of MA and elucidate the pathological mechanism of MA from a resting-state functional integration point of view.

Modularity-Guided Functional Brain Network Analysis for Early-Stage Dementia Identification

Function brain network (FBN) analysis has shown great potential in identifying brain diseases, such as Alzheimer's disease (AD) and its prodromal stage, namely mild cognitive impairment (MCI). It is essential to identify discriminative and interpretable features from function brain networks, so as to improve classification performance and help us understand the pathological mechanism of AD-related brain disorders. Previous studies usually extract node statistics or edge weights from FBNs to represent each subject. However, these methods generally ignore the topological structure (such as modularity) of FBNs. To address this issue, we propose a modular-LASSO feature selection (MLFS) framework that can explicitly model the modularity information to identify discriminative and interpretable features from FBNs for automated AD/MCI classification. Specifically, the proposed MLFS method first searches the modular structure of FBNs through a signed spectral clustering algorithm, and then selects discriminative features via a modularity-induced group LASSO method, followed by a support vector machine (SVM) for classification. To evaluate the effectiveness of the proposed method, extensive experiments are performed on 563 resting-state functional MRI scans from the public ADNI database to identify subjects with AD/MCI from normal controls and predict the future progress of MCI subjects. Experimental results demonstrate that our method is superior to previous methods in both tasks of AD/MCI identification and MCI conversion prediction, and also helps discover discriminative brain regions and functional connectivities associated with AD.

Phase fMRI defines brain resting-state functional hubs within central and posterior regions

From a brain functional connectivity (FC) matrix, we can identify the hub nodes by a new method of eigencentrality mapping, which not only counts for one node's centrality but also all other nodes' centrality values through correlation connections in an eigenvector of the FC matrix. For the resting-state functional MRI (fMRI) data (complex-valued EPI images in nature), both magnitude and phase images are useful for brain FC analysis. We herein report on brain functional hubness analysis by constructing the FC matrix from phase fMRI data and identifying the hub nodes by eigencentrality mapping. In our study, we collected a cohort of 160 complex-valued fMRI dataset (consisting of magnitude and phase in pairs), and performed independent component analysis (ICA), FC matrix calculation (in size of 50 × 50) and FC matrix eigen decomposition; thereby obtained the 50-node eigencentrality values in the eigenvector associated with the largest eigenvalue. We also compared the hub structures inferred from FC matrices under different thresholding. Alternatively, we obtained the geometric hubs among p value the 50 nodes involved in the FC matrix through the use of harmonic centrality metric. Our results showed that phase fMRI data analysis defines the resting-state brain functional hubs primarily in the central region (subcortex) and the posterior region (parieto-occipital lobes and cerebella). The brain central hubness was supported by the geometric central hubness, which, however, is distinct from the magnitude-inferred hubness in brain superior region (frontal and parietal lobes). Our findings pose a new understanding of (or a debate over) brain functional connectivity architecture.

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.

Adjunct ketamine treatment of depression in treatment-resistant schizophrenia patients is unsatisfactory in pilot and secondary follow-up studies

OBJECTIVE

To investigate the effects of adjunct ketamine treatment on chronic treatment-resistant schizophrenia patients with treatment-resistant depressive symptoms (CTRS-TRD patients), including alterations in brain function.

METHODS

Intravenous ketamine (0.5 mg/kg body weight) was administered to CTRS-TRD patients over a 1-hr period on days 1, 4, 7, 10, 13, 16, 19, 22, and 25 of our initial pilot study. This treatment method was subsequently repeated 58 days after the start of the pilot study for a secondary follow-up study. Calgary Depression Scale for Schizophrenia (CDSS), Positive and Negative Syndrome Scale (PANSS), and regional homogeneity (ReHo) results were used to assess treatment effects and alterations in brain function throughout the entire duration of our studies.

RESULTS

Between day 7 and day 14 of the first treatment, CDSS scores were reduced by 63.8% and PANSS scores were reduced by 30.04%. In addition, ReHo values increased in the frontal, temporal, and parietal lobes. However, by day 21, depressive symptoms relapsed. During the second treatment period, CDSS and PANSS scores exhibited no significant differences compared to baseline between day 58 and day 86. On day 65, ReHo values were higher in the temporal, frontal, and parietal lobes. However, on day 79, the increase in ReHo values completely disappeared.

CONCLUSIONS

Depressive symptoms in CTRS-TRD patients were alleviated with adjunct ketamine treatment for only 1 week during the first treatment period. Moreover, after 1 month, the antidepressant effects of ketamine on CTRS-TRD patients completely disappeared. Correspondingly, ReHo alterations induced by ketamine in the CTRS-TRD patients were not maintained for more than 3 weeks. These pilot findings indicate that adjunct ketamine treatment is not satisfactory for CTRS-TRD patients.

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.

Spatial source phase: A new feature for identifying spatial differences based on complex-valued resting-state fMRI data

Spatial source phase, the phase information of spatial maps extracted from functional magnetic resonance imaging (fMRI) data by data-driven methods such as independent component analysis (ICA), has rarely been studied. While the observed phase has been shown to convey unique brain information, the role of spatial source phase in representing the intrinsic activity of the brain is yet not clear. This study explores the spatial source phase for identifying spatial differences between patients with schizophrenia (SZs) and healthy controls (HCs) using complex-valued resting-state fMRI data from 82 individuals. ICA is first applied to preprocess fMRI data, and post-ICA phase de-ambiguity and denoising are then performed. The ability of spatial source phase to characterize spatial differences is examined by the homogeneity of variance test (voxel-wise F-test) with false discovery rate correction. Resampling techniques are performed to ensure that the observations are significant and reliable. We focus on two components of interest widely used in analyzing SZs, including the default mode network (DMN) and auditory cortex. Results show that the spatial source phase exhibits more significant variance changes and higher sensitivity to the spatial differences between SZs and HCs in the anterior areas of DMN and the left auditory cortex, compared to the magnitude of spatial activations. Our findings show that the spatial source phase can potentially serve as a new brain imaging biomarker and provide a novel perspective on differences in SZs compared to HCs, consistent with but extending previous work showing increased variability in patient data.