ICA if fMRI based on a convolutive mixture model

Modeling & Analysis Abstract The fMRI signal has many sources: Stimulus induced activation, other brain activations, confounds including several physiological signal components, the most prominent being the cardiac pulsation at about 1 Hz, and breathing induced motion (0.2-1 Hz). Most fMRI data sets are acquired at sampling frequencies 0.2-0.5 Hz, hence the heart and breathing signals are aliased and not represented faithfully.

Whether the heart signal is aliased or not, the fMRI signal is of a complicated spatio-temporal nature and is consequently approached by many different signal processing strategies. Global linear dependencies can be probed by independent component analysis (ICA) based on higher order statistics or spatio-temporal properties.

With ICA we separate the different sources of the fMRI signal. ICA can be performed assuming either spatial or temporal independency. A major challenge with previous independent component analyses is the convolutive nature of the mixing process in fMRI. In temporal ICA we assume that the measured fMRI response is an instantaneous, spatially varying, mixture of independent time functions.

However, the convolutive structure of the hemodynamic response implies that the fMRI response at a given time is the weighted sum of previous activation in the same location for say 10 secs or more. Similarly, the spatial structure of the hemodynamic response implies that neighboring regions activity “spill over” and give rise to a spatially convolutive mixing relevant for spatial ICA.

Convolutive ICA has many computational problems and no standard solution is available. In this study a new predictive estimation method is used for finding the mixing coefficients and the source signals of a convolutive mixture and it is applied in temporal mode. The mixing is represented by “mixture coefficient images” quantifying the local response to a given source at a certain time lag.

This is the first communication to address this important issue in the context of fMRI ICA. Data: A single slice holding 128x128 pixels and passing through primary visual cortex was acquired with a time interval between successive scans of TR=0.333 msec. This sampling frequency is high enough to allow faithful representation of the heart signal.

Visual stimulation in the form of a flashing annular checkerboard pattern was interleaved with periods of fixation. A run consisting of 30 scans of fixation, 31 scans of stimulation, and 60 scans of post-stimulus fixation was repeated 10 times (data acquired by Dr. Egill Rostrup, Hvidovre Hospital, DK).

Results We apply a model with time lags 0-39*TR (=13sec), requiring 40 mixing coefficient images. In the figure we show the 40 images for the temporal component most related to the stimulus reference function. The lower mid part of the images shows the visual areas that are (anti)correlated in (blue)red superimposed on the grand average fMRI image.

The red colored regions show increased activation when stimulation sets in. The temporal structure of the response images (left to right, starting with zero lag in the upper left corner) shows the characteristic quick response build up, followed by a negative undershoot which is visible towards the end of the image sequence.