Capturing the Brain’s Dynamic Responses

Posted by: balthusbemusedbycolor on: April 25, 2009

• In: Science
• Comment!

If you are interested in studying how the human brain processes information in vivo, neuro-electric oscillations provide one of the richest data mines. A key point is that the capacity to characterize cognitive processing in time is more important than localizing it in space and the cost in spatial resolution incurred by electroencephalographic (EEG) methods seems to matter less than the loss in temporal precision incurred by functional neuroimaging methods like the fMRI.

Figure from Yordanova & Kolev (2008)

Neuro-electric phenomena are manifested in three dimensions: Amplitude, Frequency and Time (see figure to the left). Traditional approaches to examining the brain’s event-related dynamics have focused on time-domain representations. The relevant information present in time-domain representations of neuro-electrical signals involves amplitude fluctuations in voltage, as a function of time. This is the approach of classical event-related potentials (ERP) where EEG epochs are repeatedly time-locked to the onset of discrete experimental stimuli. The underlying assumption is that the brain electrophysiology reflects, (1) some baseline level of cerebral electrical activity that is not directly related to processing of the stimulus (“the EEG noise”), plus (2) a bioelectrical signature of stimulus processing (“the evoked response” or the “evoked potential”). A key goal of the experimenter then becomes separating the signal (the electrical pattern associated with the processing of the stimulus) from the noise (the background EEG). By analogy, the evoked response is a small crest that rides on a larger wave of non-event related activity. However, separating the signal from the noise is complicated by the fact that the signal is orders of magnitude smaller than the noise (an ERP of a few micro-volts in comparison to an EEG of approximately 50 microvolts). Accordingly, this approach necessitates a larger number of experimental trials — however, the relation between trial size and signal:noise ratio is not linear. Instead, the signal:noise ratio increases a function of the the square root of the number of trials. To derive the Voltage x Time function (the ERP waveform), the experimenter must average across these repeated trials (see link for an effective explanation). Accordingly, the average ERP waveform represents the averaged electrical activity (on a millisecond scale) that is time-locked to the onset of the event. Averaging leads to a preservation of the time and phase-locked oscillations (evoked responses) while washing out the “EEG noise” which is assumed to have a random phase distribution with regard to event onset. Positive and negative deflections (ERP components) in the resultant Voltage x Time function have specific functional significance, depending also on their latency and scalp topography. For example, the P300 (my favorite) represents a positive voltage deflection occurring approximately 300 milliseconds following the onset of a discrepant stimulus in a repetitive stimulus train (usually elicited using some sort of an experimental oddball paradigm) and the amplitude of this component reflects the allocation of attentional resources (this is very simplified — for one, the P300 is not a monolithic component, and consists of a P3a and P3b “sub-components” that have different functional significance; see the work of John Polich). A basic distinction in the ERP world is between exogenous components that reflect obligatory stimulus processing and late, endogenous components that reflect the cognitive manipulation of stimuli (or anticipation of stimuli, etc.) and more sophisticated computations. Some components (for example, the Mismatch Negativity), however, do not fit neatly into any one category. This approach has been tremendously fruitful. However, one obvious limitation of the approach is that it captures only 2 dimensions of the three dimensional state-space introduced above (Time and Amplitude), with no information concerning the third dimension (Frequency). There is also a more serious concern with this approach in terms of its capacity to capture the brain’s event-related dynamics (to be outlined below).

The ERP waveform can be converted from the time-domain into the frequency-domain using either the Amplitude Frequency Characteristics (AFC) approach or the digital filtering approach. For example, the AFC approach applies a Fast Fourier Transform to extract the frequency characteristics of the event-related waveform and derive an Amplitude x Frequency function. This has informed us, for instance, that the P300 component reflects mostly phase-locked oscillations in the delta (0.5-4 Hz) and theta (4-7 Hz) frequency ranges. A key limitation of the Fourier transform is that the scale at which the frequency content of the signal can be resolved is given by the formula, Frequency Resolution (Hz) = 1/T, where T is the segment length of the signal. Therefore, to achieve a resolution of 1 Hz width requires a signal that is 1 second in duration. This is a considerable problem since most of the brain’s parallel processing occurs at a much finer-time scale and is highly non-stationary. The frequency-approach is therefore only capable of resolving the electrical signal at a coarse temporal scale that makes it of limited value to experimenters interested in examining neurocognitive processing where the most interesting things happen in the first few hundred milliseconds.

Event-Related Brain Oscillations: A New Approach
An additional problem of the traditional way of examining the brain’s event-related responses (time-domain ERP approach) involves the wasteful loss of important information that is embedded in the signal as a result of the signal averaging procedures performed. Normally, the EEG reflects rhythmic electrical activity of thousands of neural generators.

Phase Resetting

The phase or the latency of EEG wave trains typically has a random-phase distribution, which can be conceptualized as a random distribution of vectors (clock hands in a visual analogy; see left side of figure) in a radial phase plane (clock face in analogy). The ERP approach leads to an obliteration of those neural processes that are not precisely phase-locked to the onset of experimental stimuli.

However, during event-related brain processing phase-resetting of oscillations is far from complete and there is only partial phase re-setting. Accordingly, the brain’s dynamic responses that are time-locked to the event but phase-variant, will not be reflected in the average ERP. In order to capture those event-related brain dynamics a different approach must be taken — that of event-related brain oscillations (EROs). This new method involves something called EEG time-frequency analysis. This method exploits all 3 dimensions of the hypothetical cube in which neuro-electrical phenomena manifest themselves. Namely, the approach is able to characterize event-related spectral perturbations in the frequency spectrum occurring on a millisecond timescale.

There are various ways of conducting time-frequency analyses of the EEG, but the Morlet wavelet transforms are perhaps the most relevant. The Morlet wavelet is a wavelet with both real and imaginary components. The original (or mother) wavelet begins at the start of the signal, is convolved with the signal yielding a co-efficient value and then progressively slides down the signal’s length (translation), being scaled (dilated and contracted) along the way. The coefficients provide information regarding both magnitude and phase of the signal. The computations required for the analyses are resource expensive, but easily realized within a Matlab computing environment and running EEGLAB or FieldTrip toolboxes. There is an inherent trade-off between frequency and temporal resolution however such that increasing the capacity to characterize the oscillations in time leads to a diminished capacity to resolve the frequency resolution of the signal. This trade-off is an extension of the uncertainty principle, where it is impossible to have precise information regarding a signal in both time and frequency domains (i.e., the product of time and frequency variance is constant, such that decreasing one variance leads to an increase in the other).

An informative way of illustrating event-related brain dynamics is to use Time x Frequency plots, where frequency is represented on the y-axis, time (in milliseconds) on the x-axis and amplitude/magnitude is plotted as a color-coded signal. I’ve performed a wavelet analysis on the data below, which is drawn from an EEGLAB sample dense-array EEG data set. The experiment examined visual spatial attention and the signal has here been time-locked to the onset of a discrete stimulus (a green square) that participants were instructed to anticipate.

Convolution With a 3 Cycle Morlet Wavelet

The top figure represents Event-Related Power or the Event-Related Spectral Perturbation, expressed in dB units. This represents the change in the frequency content of the signal, relative to a -500 millisecond pre-event baseline. The bottom figure represents the Inter-Trial Coherence or Phase Locking Factor. This represents the degree of phase-locking of the signal, across repeated trials, and is expressed on a scale from 0 (no phase locking) to 1 (perfect phase locking). [Not to be confused with traditional EEG coherence, which usually measures the correlation of spatially separate electrical signals, in a narrow-band frequency range. Disturbances in gamma-band phase-locking have been reported in psychiatric conditions, such as schizophrenia]. Changing the number of cycles in the original Morlet wavelet offers a different Time x Frequency snapshot of the signal. This is demonstrated in the next figure, where I used a wavelet with 9 cycles (rather than 3) to convolve the same time-locked signal.

Convolution With a 9 Cycle Morlet Wavelet

Future Questions
I find this approach particularly exciting, because it promises to offer more sensitivity into my questions of interest — namely, how the affective salience of signals affect attention dynamics and the role of individual differences in this particular process (to put it simply, think of attention as an amplifier, with variable settings that are influenced by the evaluative/motivational relevance of the signals, as well as learning mechanisms and inherited variation in specific brain circuits — incidentally, the amplifier analogy may be more than a simple metaphor as attested to by the literature on single cell recordings in monkeys in selective visual attention experiments). Brain oscillations have been proposed as potentially more powerful endophenotype markers (markers that are more proximate to genomic mechanisms than complex phenotypic expressions). The genetics of brain oscillations is becoming an exciting area of study. Here is some further reading for those interested:

Basar, E., Schurmann, M., Demiralp, T., Basar-Eroglu, C., & Ademoglu, A. (2001). Event-related oscillations are ‘real brain responses’ – wavelet analysis and new strategies. International Journal of Psychophysiology, 39, 91-127.

Makeing, S., Debener, S., Onton, J., & Delorme, A. (2004). Mining event-related brain dynamics. Trends in Cognitive Sciences, 9, 204-210.

Van Quyen, M.L., & Bragin, A. (2007). Analysis of dynamic brain oscillations: methodological advances. Trends in Neurosciences, 30, 365-373.