Schematic of the probabilistic ICA model ().

Estimation of largely overlapping signals in the presence of noise: two source signals with spatial correlation of ρ∼0.5 were introduced into Gaussian noise (σ=3) to form an artificial dataset of size 250×10 000 (a). In the presence of noise, the spatial correlation of least-square estimates is significantly reduced (b). Estimating principal components from the data results in a poor representation in the temporal and spatial domain (c). ICA estimates from the same data (d) show much improved detection power and represent the spatial maps and time-courses well. Thresholded maps (e) are again highly correlated at ρ∼0.47. Note that spatial ICA maps, like PCA maps, are constrained to be orthogonal. This restriction itself, therefore, does not necessarily imply poor spatial representation of signals, even in cases where ‘true’ spatial maps are highly correlated.

Comparison of seed-voxel-based correlation analysis and PICA: for seed-voxel based analysis, an activation dataset is first analysed to identify the location of most significant response to external stimulation (a). The time-course of the coinciding voxel in the resting data is used as a reference time-course for a correlation analysis of all other time-courses acquired under rest. The resulting correlation map (b) shows significant resting correlation in similar motor areas as the activation map, but also identifies part of the ipsi-lateral motor cortex. In addition, other regions outside of these motor areas were also found, including medial and lateral posterior parietal areas and prefrontal regions. In a PICA decomposition of the resting data (c), similar cortical regions are identified by two (out of 40) separate spatial maps. The multiple regression framework implicit in a PICA decomposition separates resting correlations in motor areas (left) from other cortical areas. This separation is induced by the fact that the associated time-courses are significantly different: the associated normalized power spectra show different peak frequencies. All spatial maps were thresholded using mixture modelling (at p>0.5) and are shown in radiological convention.

Investigating the relationship between physiological noise and low-frequency fluctuations in the spatial and temporal domain. The different components estimated from the low-TR data (left) show a clear separation of physiological artefacts induced by the cardiac cycle (a) and the respiratory cycle (b) from low-frequency fluctuations (c) both in the spatial maps and the corresponding power spectra. At higher TR, the temporal signature of the cardiac and respiratory cycles become aliased and no longer identifiable in the frequency domain. The spatial maps (d,e), however, show a high degree of correspondence with maps (a) and (b) (spatial correlation of 0.64 and 0.42, respectively), suggesting that the PICA approach is able to separate relatively uninteresting physiological noise from other effects such as resting-state maps, even in cases where the physiological noise fluctuations become aliased in the temporal domain.

Investigating the spatial structure of resting-state fluctuation. PICA analysis of EPI data acquired at 2×2 mm resolution in the x–y plane suggests that the resting-state fluctuations are well localized in grey matter (a). Furthermore, they appear to be spatially different from BVNs, which mainly show larger blood vessels and surrounding tissue (b).

Different PICA-estimated resting patterns: saggital, coronal and axial views of different spatial maps associated with low-frequency resting patterns estimated from a group of 10 subjects. All images have been coregistered into the space of the MNI template. The coordinates refer to mm distances from the anterior commissure and images are shown in radiological convention.