Using ICA and realistic BOLD models to obtain joint EEG/fMRI solutions to the problem of source localization
Introduction
Electroencephalogram (EEG) and Functional Magnetic Resonance Imaging (fMRI) are two commonly used modalities for investigating human brain states in cognitive neuroscience experiments. Both are noninvasive, but in other respects they are complimentary. EEG measures voltage changes in electrodes placed on the scalp, whose number ranges commonly from 32 to 256. EEG has millisecond time sensitivity, but spatial information must be inferred through an inversion process, and has at most as many independent spatial measurements as there are electrodes (there may be fewer due to correlations between nearby electrodes) (de Peralta-Menendez and Gonzalez-Andino, 1998, Michel et al., 2004). fMRI measures changes in blood oxygen level (Ogawa et al., 1990, Jens Frahm, 1992) (called the BOLD signal) throughout the brain. It produces a 3D image with a spatial resolution of roughly a few millimeters, but temporal resolution is on the order of a few seconds. Furthermore the BOLD signal is a complicated convolution of brain activity because the blood oxygen level takes several seconds to rise and even longer to fall in response to an impulse of activity. Thus EEG provides an excellent measure of temporal dynamics but a poor measure of spatial locations, and fMRI provides an excellent measure of spatial locations but a poor measure of temporal dynamics.
In this paper we develop two novel methods for source localization using both EEG and fMRI data. By combining the two modalities, the high temporal resolution of EEG can be augmented with the high spatial resolution of fMRI. Existing literature has established the potential gains from combining EEG and Positron Emission Tomography (Heinze et al., 1994), as well as EEG and fMRI (Whittingstall et al., 2007, Gerloff et al., 1996, Dale and Halgren, 2001). However, in past studies the difficulties inherent in combining such dissimilar modalities have led to a reduced scope of the analysis: inclusion of data from only one EEG lead (Calhoun et al., 2006), or avoiding the EEG inverse by using ICA to analyze EEG and fMRI data simultaneously, and thereby obtaining ICA sources that have related EEG and fMRI signals (Moosmann et al., 2008). Other techniques use fMRI to constrain the location of likely sources (Liu et al., 1998, 2006), fitting for the location of dipoles seeded within active fMRI regions (Stancák et al., 2005), or employ an adaptive Wiener filter (Liu and He, 2008) that is updated by EEG and fMRI data.
Here we present two techniques for working with full EEG and fMRI data sets and solving to obtain neural activities throughout the cortex at high spatial and temporal resolution. Our first method uses standard techniques to invert EEG data, but employs fMRI data to constrain the free components of the solution. Throughout this paper, we refer to this technique as our “fMRI regularized inverse”, and we describe it in the fMRI regularized inverse Section. The second method uses model reduction algorithms (Principle Component Analysis, or PCA; and Independent Component Analysis, or ICA) to decrease the size of the inverse problem, and a detailed model of the BOLD signal (discussed in the Model-reduced joint inverse Section) to relate EEG and fMRI data. This enables us to simultaneously fit the EEG and fMRI data. We refer to this method as our “model-reduced joint inverse”, and it is described in the Model-reduced joint inverse Section. The model-reduced joint inverse has the additional advantage of treating the EEG and fMRI data on equal footing, instead of using the fMRI merely as a constraint. In the Testing the algorithms Section, we evaluate and contrast the effectiveness of these techniques on synthetically generated data to demonstrate the potential effectiveness of using this methodology to analyze data recorded from human subjects.
Section snippets
EEG source localization
We begin with a brief, general description of EEG source localization (Michel et al., 2004). This background provides the starting point for our first method of combining EEG and fMRI (fMRI regularized inverse Section) which begins with EEG, but makes use of the fact that the basic problem of EEG source localization is underconstrained. When EEG is considered alone, different methods employ different techniques for regularization —selecting a particular solution out of an infinite family of
fMRI regularized inverse
One way to improve upon regularization schemes is to use an independent source of data (in our case, fMRI) to choose between the infinitely many solutions allowed by the EEG data. Our regularization strategy is to start with a minimum norm inverse of EEG data, and then alter it in ways that improve agreement with fMRI data, without altering the quality of the fit to EEG data. We accomplish this by adding vectors in the null space of the lead field matrix (Ahlfors and Simpson, 2004). We still
Model-reduced joint inverse
To better incorporate fMRI data into source localization, we next incorporate a model that provides detail beyond merely noting that the BOLD signal is proportional to neural activity. As mentioned previously, the BOLD signal response is delayed (by roughly 4 s for a brief impulse of neural activity). Our fMRI regularized inverse takes advantage of the correlation between BOLD signal and neural activity, but using the correlation alone is not ideal because the BOLD signal does not simply mirror
Testing the algorithms
We tested each source localization technique by generating a data set with known activity patterns and then comparing the actual activities to the solutions produced by the inversion technique. Inversion of multiple sources was a critical test, as many existing EEG inversion techniques (such as those based on ad hoc regularization schemes) have particular difficulty with multiple sources. We tested the techniques against sources that were distributed over moderate-sized regions of the brain
Conclusions
The fMRI regularized inverse solution provides results that are only a slight improvement over a simple minimum norm solution. Any regularized solution involves selection of a single point near or within the (very large) null space of the lead field matrix. The main advantage of our fMRI regularized inverse is that it arrives at a unique solution in a data-driven manner, and therefore represents an improvement largely in conceptual framework rather than solution quality. We suspect that any
Acknowledgments
This work was supported by the David and Lucile Packard Foundation, NSF grant number DMR-0606092, and the Institute for Collaborative Biotechnologies through grants DAAD19-03-D-0004 and W911NF-07-1-0072.
References (38)
- et al.
Geometrical interpretation of fmri-guided meg/eeg inverse estimates
NeuroImage
(2004) - et al.
Dynamics of blood flow and oxygenation changes during brain activation: the balloon model
Magn. Reson. Med.
(1998) - et al.
Neuronal chronometry of target detection: Fusion of hemodynamic and event-related potential data
NeuroImage
(2006) - et al.
Improved localization of cortical activity by combining eeg and meg with mri cortical surface reconstruction
J. Cogn. Neurosci.
(1993) - et al.
Spatiotemporal mapping of brain activity by integration of multiple imaging modalities
Curr. Opin. Neurobiol.
(2001) - et al.
A critical analysis of linear inverse solutions to the neuroelectromagnetic inverse problem
IEEE Trans. Biomed. Eng.
(1998) - et al.
Discussing the capabilities of laplacian minimization
Brain Topogr.
(2000) - et al.
Comparison of algorithms for the localization of focal sources: Evaluation with simulated data and analysis of experimental data
Int. J. Bioelectromagn.
(2002) - et al.
Imaging the electrical activity of the brain: Electra
Hum. Brain Mapp.
(2000) - et al.
Rapidly recomputable eeg forward models for realistic head shapes
Phys. Med. Biol.
(2001)
Multiple sparse priors for the m/eeg inverse problem
NeuroImage
Coregistration of eeg and fmri in a simple motor task
Hum. Brain Mapp.
Electrical neuroimaging based on biophysical constraints
NeuroImage
What does fmri tell us about neuronal activity?
Nat. Rev. Neurosci.
Spikes versus bold: what does neuroimaging tell us about neuronal activity?
Nat. Neurosci.
Combined spatial and temporal imaging of brain activity during visual selective attention in humans
Nature
Interpreting magnetic fields of the brain: minimum norm estimates
Med. Biol. Eng. Comput.
Survey on independent component analysis
Neural Comput. Surv.
Dynamic mr imaging of human brain oxygenation during rest and photic stimulation
J. Magn. Reson. Imaging
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