The Impact of Amplitude and Phase-based MRI Time Series on Functional Connectivity Analysis

Introduction

Over the past decade, functional magnetic resonance imaging (fMRI) has emerged as a non-invasive imaging technique that uses blood oxygen level-dependent (BOLD) contrast to measure brain activity and study brain function (Kwong, 1996). By analyzing the temporal correlation of BOLD time series between spatially distant brain regions, static functional connectivity (FC) can be estimated. Functional connectivity is usually measured by calculating the temporal correlation between time series of different brain regions. Some studies focus on the instantaneous phase (IP) representation of BOLD signals under task conditions (such as finger tapping or visual tasks) for functional connectivity analysis, but the role of instantaneous amplitude (IA) has been less explored.

In this study, we hypothesize that the instantaneous amplitude representation from different brain regions may provide additional information for functional brain networks. To verify this hypothesis, we explore the instantaneous amplitude representation of resting-state BOLD fMRI signals and compare it with the resting-state networks (RSNs) obtained from instantaneous phase representation.

Source of the Paper

This study was authored by Priyanka Mittal (Indian Institute of Technology Mandi, India), Anil K. Sao (Indian Institute of Technology Bhilai, India), and Bharat Biswal (New Jersey Institute of Technology, United States of America), and was published in the journal “Magnetic Resonance Imaging” on April 17, 2023.

Research Methods

Data and Processing

This study used resting-state fMRI data from 100 healthy adults (ages 20-35, 54 females) from the Human Connectome Project (HCP) dataset. Data were acquired using a 3T MRI scanner over four 15-minute runs, with phase encoding directions alternating between left-right and right-left. These four runs were divided into two sessions in which subjects were asked to keep their eyes open and focus on a white cross. Instantaneous amplitude and instantaneous phase representations were extracted from narrow-band filtered BOLD time series using the Hilbert transform, and seed-based methods were used to calculate resting-state networks in the brain.

Experimental Methods

The entire study was divided into three stages:

Stage 1: Signal Preprocessing Preprocessing of fMRI data was performed according to standard HCP procedures, including the removal of various spatial artifacts and head motion effects, alignment of time-series data with structural data, and global intensity normalization.

Stage 2: Signal Transformation and Representation Extraction Narrow-band filtered BOLD signals were converted to complex signals via Hilbert transform to extract instantaneous amplitude (IA), instantaneous phase (IP), and instantaneous frequency (IF) representations.

Stage 3: Functional Connectivity Analysis Using seed-based methods, FC values were calculated between the time series of selected seeds and other brain regions. For the IP representation, the phase-locking value (PLV) was computed between the seed and other voxel IP time series.

Various Representations and Corresponding Experiments

In the experiments, IA, IP, and IF representations were calculated for the frequency range 0.01-0.1 Hz and its sub-bands. For each representation, the spatial consistency of resting-state networks (such as the default mode network, motor network, etc.) was observed under different frequency sub-bands (e.g., 0.01-0.04 Hz, 0.04-0.07 Hz, 0.07-0.1 Hz, etc.).

Data Analysis Methods

Jaccard similarity (JS) was used as a measure of consistency between the two sessions. By spatial comparison of functional connectivity maps between the two sessions, the consistency of each representation method was evaluated across different frequency sub-bands.

Research Results

The experimental results showed that within the frequency range of 0.01-0.1 Hz, resting-state networks based on instantaneous amplitude representation (IA) had the highest similarity to networks based on instantaneous phase representation (IP), especially for motor networks. In higher frequency bands (0.198-0.25 Hz), the consistency of networks represented by IA and IP decreased. By integrating IA and IP representations, the consistency of the default mode network improved by 3-10%, and the consistency of the motor network improved by 15-20% compared to using only IP representation.

Additionally, the use of instantaneous frequency (IF) representation in exploring functional connectivity networks yielded similarities comparable to those obtained using only IP representation. Across all frequency sub-bands, methods based on IA representation showed the highest similarity scores in motor networks, while IP representation performed best in the fronto-parietal network.

Conclusions and Discussions

This study found that methods based on amplitude representation could estimate resting-state networks similar to those derived from instantaneous phase representation, with comparable reproducibility between sessions. The combination of IA and IP representations can improve the results of functional connectivity analysis.

Scientific and Practical Value

The study shows that although most current research focuses on using instantaneous phase representation to estimate functional connectivity, instantaneous amplitude representation also contains useful information. Combining both can significantly enhance the reliability and consistency of resting-state network analysis results. This provides new perspectives for brain functional network research, helping to better interpret brain functional activities in the resting state.

Research Highlights

1. The study innovatively explored the role of instantaneous amplitude representation in functional connectivity analysis, suggesting it as an important complement to instantaneous phase representation.
2. Experimental results indicate that the two representation methods (instantaneous amplitude and instantaneous phase) are complementary and their integration can improve the accuracy of resting-state network analysis results.
3. The study provides a new approach, through frequency sub-band analysis, to enhance the reproducibility of resting-state networks, which is crucial for understanding the impact of different frequency bands on brain functional connectivity.

Research Limitations

Further research is needed to investigate the differences and applicability range of instantaneous amplitude and instantaneous phase representation methods in practical applications. Additionally, the current results are primarily based on resting-state fMRI data; future research should verify the feasibility of these results in other brain activity states (e.g., tasks or natural stimulation).

This study thoroughly explored the role of instantaneous amplitude representation in fMRI time series for resting-state network analysis, revealing its critical importance and providing new directions and methods for future brain functional connectivity research.