Variability in single trials

Cortical activity evoked by repeated identical sensory stimulation is extremely variable. The source of this variability is often assigned to "random ongoing background activity" which is considered to be irrelevant to the processing of the stimuli and can therefore be eliminated by ensemble averaging. Although averaging leads to well-defined and largely reproducible responses, it eliminates the relevant activity which is not precisely time-locked to the stimulus. If we are to understand brain function, we cannot ignore this variability and need to be able to analyze it in a quantitative way. To achieve this goal we have developed new ways of looking at variability and found that the model (signal plus noise) that is the foundation of the averaging process is not valid: variability of mass electrical activity is not simply an epiphenomenon; it reflects local and global function-related brain dynamics. 

The evidence from diverse experiments within different sensory systems (visual, auditory and somatosensory) shows that what we see in the average signal is a mixture of histories, where responses from different sets of single trials corresponding to different neural networks are merged.

Visual system

Flickering circular checkerboard patterns were presented to subjects in three experimental runs each consisting of 240 trials (for the description of the experiment see Moradi et al., 2003). In this example we analyzed the variability of M70 response component reflected in the MEG sensors over the occipital and parietal areas. First, a single time course was synthesized from the multichannel MEG data, in a way that amplified the contribution from the complex of generators, being responsible for the dominant M70 response. The extracted time courses from different single trials were then handled using Pattern Analysis principles. A Vector Quantization (VQ) scheme partitioned the single trials into groups, which were used to characterize and represent the response variability in an organized way. After grouping the single trials, the prototypes of regional evoked activity were computed via within-group averaging, and then compared with the averaged response. 

Single trial variability of M70

Single trial variability of M70 response. Top row: A 2D representation of the employed codebook is given, based on the minimal spanning tree (MST) graph of the reference vectors. Each node corresponds to one reference vector and nearby nodes correspond to similar reference vectors. The index attached to each node has resulted from the graph-theoretic ordering of the reference vectors. This ordering enables the handling of the codebook in the form of an ordered list of reference vectors. The depicted ranks of the reference vectors also define the ranking of the corresponding Voronoi regions. Bottom row: The ordered list of the prototypical M70 responses. The MST-based ordering of the reference vectors (top row) defined the rank of each of the groups that the single trial signals formed after the application of the VQ procedure. The display of the computed within-group averages has been organized according to the ranking of the corresponding groups. To emphasize the highly variable nature of the M70 response, all subaverages have been plotted using a common amplitude scale and are accompanied by the ensemble average (black thin trace).

For two subjects (S1 and S2), top panel shows the cartography of  the codebook vectors, which were used in the VQ procedure. This graph has been used to order the formed groups. Bottom panel includes the within-group averages together with the ensemble average  (thin, black trace). The figure demonstrates several distinct classes of single trials (ordered from 1 to 10) and is clear that these distinct response dynamics are fused into a single time course by ensemble averaging. Furthermore, the ongoing rhythmic activity before the stimulus onset is functionally coupled with the response. This suggests a "state-dependent stimulus-evoked response." 

N. A. Laskaris et al., Neuroimage 20, 765-783 (2003). PDF >>


Auditory system

Three subjects listened to auditory stimuli (1 kHz tones with 200 ms duration, 10 ms rise/decay time at 45 dB) in a MEG experiment. Exploratory data analysis of single trial MEG data was carried out as described above and here. Single trials were partitioned into groups and ranked. The prototypes of regional evoked activity were also computed by within-group averaging. 


Single trial variability of auditory responses

Single trial variability of early auditory response. Top row: A 2D representation of the employed codebook is given, based on the minimal spanning tree (MST) graph of the reference vectors. Each node corresponds to one reference vector and nearby nodes correspond to similar reference vectors. The index attached to each node has resulted from the graph-theoretic ordering of the reference vectors. This ordering enables the handling of the codebook in the form of an ordered list of reference vectors. The depicted ranks of the reference vectors also define the ranking of the corresponding Voronoi regions. Bottom row: The ordered list of the prototypical M70 responses. The MST-based ordering of the reference vectors (top row) defined the rank of each of the groups that the single trial signals formed after the application of the VQ procedure. The display of the computed within-group averages has been organized according to the ranking of the corresponding groups. To emphasize the highly variable nature of the M70 response, all subaverages have been plotted using a common amplitude scale and are accompanied by the ensemble average (black thin trace).

The left panel of the figure shows the activation time course of auditory cortex after ensemble averaging (all trials, black trace), and averaging of the ten lowest (blue trace) and highest (red trace) ranked single trials. The difference between the distinct single trial groups and the ensemble average are apparent. The right panel shows the localization of the early auditory cortex activity based on the averaged MEG signals of the ten lowest-rank single trials (left column) and the ensemble average (right column).

N. A. Laskaris, A. A. Ioannides, Clin.Neurophysiol. 112, 689-712 (2001). PDF >>


Somatosensory system

Subjects hand (median nerve) was electrically simulated at two levels: weak (above sensory threshold, well below movement threshold) and strong (above movement threshold, but below pain threshold). We will use animations derived from the analysis of the MEG data obtained from this experiment to demonstrate why more attention should be given to variability in single trials. The animations display the activity in just one single axial slice through the primary somatosensory area, which is the first cortical area excited by the stimulus. Green outlines indicate the central sulcus. 

Brain activity estimated from averaged data

This animation shows the estimated brain activity obtained from averaged MEG data for weak (top row) and strong (bottom row) stimulation of the left (left column) and right (right column) median nerve.

As you see only just a blip is seen for strong right arm stimulation at about 20 ms. Much of the literature on the subject describes how this unitary event, and a few other such isolated peaks in the average change under different manipulations. It is as if the brain is inactive except for that momentary activation.

Brain activity from averaged data together with single trials

This animation shows the average (the top left figurine) and individual single trials (the first 8) for the strong stimulation of the right median nerve (displayed in sequence in the next 8 figurines). To emphasize the dynamic behaviour of the system we use separate normalization for each time point and image.

In single trials the activity evoked by the stimulus is not all that different from the activity at other time points before or well after the onset of the stimulus. What these results imply is that the activation evoked by the stimulus is not very different than the background activation going on all the time. What seems to be happening soon after the hand is stimulated is an increased stability in the response around the primary somatosensory cortex which however is varying in its detail from trial to trial. What survives into the average is this increased stability.