Double-wavelet transform for multi-subject resting state functional magnetic resonance imaging data

Abstract

Conventional regions of interest (ROIs)-level resting state fMRI (functional magnetic resonance imaging) response analyses do not rigorously model the underlying spatial correlation within each ROI. This can result in misleading inference. Moreover, they tend to estimate the temporal covariance matrix with the assumption of stationary time series, which may not always be valid. To overcome these limitations, we propose a double-wavelet approach that simplifies temporal and spatial covariance structure because wavelet coefficients are approximately uncorrelated under mild regularity conditions. This property allows us to analyze much larger dimensions of spatial and temporal resting-state fMRI data with reasonable computational burden. Another advantage of our double-wavelet approach is that it does not require the stationarity assumption. Simulation studies show that our method reduced false positive and false negative rates by properly taking into account spatial and temporal correlations in data. We also demonstrate advantages of our method by using resting-state fMRI data to study the difference in resting-state functional connectivity between healthy subjects and patients with major depressive disorder.

Keywords: double-wavelet transform; functional magnetic resonance imaging; multi-subject; resting state; spatio-temporal model.

FIGURE 1

Coefficient structures using the double-wavelet transform. (a) an example using the Reverse Biorthogonal 3.1 wavelet as spatial wavelet and the Haar wavelet as a temporal wavelet on a simulated 3-D ROI data (2-D in spatial domain and 1-D in temporal domain). (b) S_LL, S_LH, S_HL and S_HH represent the wavelet coefficients from the 2-D wavelet transform on the spatial data in low-low (horizontal-vertical) frequency band (LL), low-high(horizontal-vertical) frequency band (LH), high-low (horizontal-vertical) frequency band (HL), and high-high (horizontal-vertical) frequency band (HH) respectively; T_L and T_H represent the wavelet coefficients from the 1-D wavelet transform on the temporal data in low and high frequency band respectively.

FIGURE 2

MSE, Bias² and Variance for the AVG-FC, DW, DW-L1-Low and DW-L2-Low approaches based on a single subject analysis when the underlying true correlation between two ROIs varies from 0 to 1 for stationary time series. Each row corresponds to each spatial correlation type.

FIGURE 3

MSE, Bias² and Variance for the AVG-FC, DW, DW-L1-Low and DW-L2-Low approaches based on a single subject analysis when the underlying true correlation between two ROIs varies from 0 to 1 for non-stationary time series. Each row corresponds to each spatial correlation type.

FIGURE 4

MSE for the DW and AVG-FC approaches based on single subject analysis among five ROIs. The x-axis is the underlying correlation for different pairs, for example, “1–0.6” means the first pair with true correlation 0.6.

FIGURE 5

Rejection rates for the DW and AVG-FC approaches based on multiple subject analysis between two ROIs, with respect to sample size.