Comparison of multi-subject ICA methods for analysis of fMRI data

Abstract

Spatial independent component analysis (ICA) applied to functional magnetic resonance imaging (fMRI) data identifies functionally connected networks by estimating spatially independent patterns from their linearly mixed fMRI signals. Several multi-subject ICA approaches estimating subject-specific time courses (TCs) and spatial maps (SMs) have been developed, however, there has not yet been a full comparison of the implications of their use. Here, we provide extensive comparisons of four multi-subject ICA approaches in combination with data reduction methods for simulated and fMRI task data. For multi-subject ICA, the data first undergo reduction at the subject and group levels using principal component analysis (PCA). Comparisons of subject-specific, spatial concatenation, and group data mean subject-level reduction strategies using PCA and probabilistic PCA (PPCA) show that computationally intensive PPCA is equivalent to PCA, and that subject-specific and group data mean subject-level PCA are preferred because of well-estimated TCs and SMs. Second, aggregate independent components are estimated using either noise-free ICA or probabilistic ICA (PICA). Third, subject-specific SMs and TCs are estimated using back-reconstruction. We compare several direct group ICA (GICA) back-reconstruction approaches (GICA1-GICA3) and an indirect back-reconstruction approach, spatio-temporal regression (STR, or dual regression). Results show the earlier group ICA (GICA1) approximates STR, however STR has contradictory assumptions and may show mixed-component artifacts in estimated SMs. Our evidence-based recommendation is to use GICA3, introduced here, with subject-specific PCA and noise-free ICA, providing the most robust and accurate estimated SMs and TCs in addition to offering an intuitive interpretation.

Figure 1

Common steps and choices in a multi‐subject ICA analysis. In this article, we discuss Steps (3)–(8), with attention to (4) subject‐level PCA and (8) back‐reconstruction. The findings in this article recommend using PCA with subject‐specific subject‐level PCA reduction and noise‐free ICA with GICA3 back‐reconstruction. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 2

Simulated data time courses and spatial maps. Among the C = 8 source SMs, one is task‐related (1), two are transiently task‐related (2 and 6), and five are artifact‐related (3, 4, 5, 7, and 8), where five are super‐Gaussian (1, 2, 5, 6, and 8), two are sub‐Gaussian (3 and 7), and one is Gaussian (4).

Figure 3

(a) Mean of values for subject‐level PCA/PPCA reduction for a range of components retained using three methods: subject‐specific (SS), spatial‐concatenation (SC), and group data mean (GM). (b) Mean of values for total PCA reduction for a range of components retained at the subject‐level and group‐level. Smaller RMSE indicates more information retained.

Figure 4

Mean RMSE between estimated and true (a) TC and (b) SM over subjects for the task‐related component (1), RMSE(R̃ _ic,R _ic) and RMSE(S̃ _ic,S _ic), comparing GICA3, GICA1, and STR multi‐subject ICA approaches using subject‐specific (SS), spatial concatenation (SC), and group data mean (GM) subject‐level PCA methods with ICA and PICA. See Table II for more detail. Three cells have been removed because of large values that distorted the scale (TC/SC/ICA/GICA3/15,15; TC/SC/PICA/GICA3/8,8; SM/SS/ICA/GICA1/15,15), other missing values noted with “*” indicate that PICA failed to converge.

Figure 5

For GICA3 with ICA, the task‐related TC is plotted for the 31 subjects with that component present. The five subplots are the true TCs, the TCs estimated using subject‐level PCA subject‐specific, spatial concatenation, and group data mean, and finally the standard deviation of the TCs for each individual for the first four subplots.

Figure 6

Comparison of TC and SM estimation for the simulated data task‐related component (1) for a subject (12) chosen at random, using subject‐specific (SS), spatial concatenation (SC), and group data mean (GM) subject‐level PCA, (b) noise‐free ICA and (c) PICA, and GICA3 and STR. The true TC and SM for the subject is shown in (a). For the TCs and SMs, the left plot is the estimated value and the right plot is the difference with the true TC (SM) which ideally is flat at zero for both the TC and SM.

Figure 7

Estimated TCs, SMs, and differences between them for GICA3 with ICA and STR with ICA and PICA for simulated data for the most (27) and least (26) spatially correlated subjects.

Figure 8

Comparisons of the subject‐specific TC and SM using mean (with NPBS 95% CI) for RMSE(R̃ _ic,R _ic) and RMSE(S̃ _ic,S _ic) for TCs and SMs (notation for GICA3), closer to zero is better. Solid circles are ICA and open circles are PICA, and G3, G1, and SR are GICA3, GICA1, and STR, respectively.

Figure 9

Comparisons of the RMSE between the mean true and mean estimated TC and SM, and (notation for GICA3), closer to zero is better. Solid circles are ICA and open circles are PICA.

Figure 10

Comparison of desired property of the sum of the subject‐specific SMs equaling the ICA aggregate SM, (notation for GICA3), closer to zero is better. Solid circles are ICA and open circles are PICA.

Figure 11

Iterating STR until convergence changes the estimated TCs and SMs from the single‐iterate version. (a) The difference between the initial STR iterate and the resulting TC and SM upon convergence. (b) The difference of the converged TC and SM and the truth, compare to Figure 6b (SS ICA STR).

Figure 12

Iterating STR until convergence differences in RMSE with truth with iteration and with single iteration for TCs and SMs and number of iterations until convergence.

Figure 13

(a) AOD event‐related TC averages for the task‐related component and default mode network for GICA3 and STR. (b) Default mode network group t statistic SM for GICA3 and STR thresholded at uncorrected p‐value = 0.05.

Figure 14

GICA3 and STR estimated z‐scored TCs, SMs, and differences for the most (24) and least (21) spatially correlated subjects between the two methods for AOD fMRI data, DMN component. SMs thresholded at 1.0 and the difference SMs thresholded at 0.5 displayed in nine equally spaced axial slices from 60 mm to −20 mm. Units are in standard deviations.

Figure 15

Unthresholded t statistics for “true” simulated SMs of demographic effects and GICA3 and STR t statistics to compare. More similar to the simulation is better.