The analyzed dataset was collected in the course of a series of experiments investigating the role of feedback connections from the posterior middle suprasylvian (pMS) cortex to primary visual areas, in this case area 18 in the cat visual system. To this end, pMS cortex was thermally deactivated using cryoloops (Lomber et al., 1999), while spontaneous or visually evoked activity was recorded in area 18. This procedure is reversible and can therefore be applied numerous times without harming the deactivated brain area. There were four different deactivation conditions: (1) warm, i.e., no deactivation, (2) deactivation of pMS in the ipsilateral hemisphere with respect to the recording, (3) deactivation of pMS in the contralateral hemisphere, and (4) bilateral deactivation of pMS cortex. In the awake behaving animal it has been shown that unilateral deactivation of the pMS cortex results in visual hemineglect (Payne et al., 1996), similar to that described in human patients with a lesion in the parietal cortex (e.g., Rafal, 1994).

Interestingly, and also in accordance to findings in the human, this hemineglect in cats occurs only with unilateral lesions or deactivations of parietal cortex and is reversible once both parietal cortices are deactivated. Thus, this hemineglect phenomenon has to be seen as an attention deficit based on an interhemispheric imbalance rather than a form of blindness.

We applied the analysis methods described below to electrophysiological action potential recordings. For details on the surgical procedures and anesthesia see Galuske et al. (2002). Data were collected in an anesthetized male cat aged 112 years, using an Eckhorn multi-electrode matrix (Thomas Recording, Germany). Sixteen electrodes were placed in area 18 of cat visual cortex, with a distance of 500 μm in the x-y-plane, and individually moveable in the z-direction. Spike signals were recorded with a sampling rate of 22 kHz and band-pass filtered (800–5000 Hz). Multi-unit spike signals were obtained by thresholding. In addition, cooling loops (Lomber et al., 1999) had been placed over pMS cortex in order to induce a reversible deactivation of this region.

The animal was visually stimulated with a black and white high contrast square wave grating. The grating was presented in four different orientations (0°, 45°, 90°, 135°), which moved in either of the two directions perpendicular to the bars of the grating. Hence, eight different stimulus conditions were possible and the order of occurrence of the stimulus conditions was pseudo-randomized. Visual stimulation started with showing a gray screen for 2 s followed by one of the four differently oriented gratings remaining stationary for 2 s before the grating started moving for 4 s. Thus, one trial lasted for 8 s.

One cycle of the experiment consisted in showing 7 repetitions of each of the 8 stimuli in random order. The whole experiment consisted of 3 cycles baseline condition without deactivation, 3 cycles with thermal deactivation, followed by 3 cycles without deactivation after the affected regions of the brain had rewarmed.

All animal experiments were performed in accordance with the guidelines for the use of animals in research of the Society for Neuroscience and the local authorities and overseen by a local veterinarian (license number F122/08, Regierungspräsidium Darmstadt).

Two different metrics were established in order to quantify the degree of synchrony and oscillatory synchrony. Since both phenomena are identified using the correlogram, both metrics are based on the correlogram.

Spike trains were stored as binary vectors with sampling frequency resolution. Ones occurred where a sample value exceeded the chosen threshold and the sample before did not. For the calculation of cross correlations, a binning of 2 ms was introduced.

For the synchrony measure, the cross correlogram λ^raw_xy of the spike trains x and y of two multi-units in the analysis window T was computed:

To correct for rate induced chance coincidences, we normalized the correlograms to the firing rate. To this end, the spikes in the spike trains were convolved with a “jitter kernel” and the resulting cross correlogram was subtracted from the raw correlogram λ^raw_xy. To implement a computationally efficient jitter correction, we rely on convolution with a homogeneous filter with entries TsampleTjitter, with T_sample the time interval between two samples, which corresponds to jittering the spike train randomly within a time interval of T_jitter = 6 ms. The jittered spike train x˜ was thus obtained from spike train x according to x˜:= K * x, where * denotes the convolution. A correlogram was then computed from the two convolved spike trains and subtracted from the original correlogram, to obtain the normalized correlogram λ_xy:= λ^raw_xy − λ^jitter_xy. The convolution approach is equivalent to the random drawing of jitter times from a uniform distribution (following the Wiener-Khinchin theorem, see also Pipa et al., 2008).

The degree of synchrony was measured by the largest positive peak in the normalized correlogram within a window of size T_sync = 5 ms around a lag of zero. The synchrony metric κ_sync is thus defined as follows. Let κ=maxl,l∈[−5 ms,5 ms]λxy(l). Then,

In addition to the synchrony measure, we looked at the oscillatory synchrony between the spike trains. The degree of oscillatory synchrony can be determined by considering how much energy is contained in the oscillations of the correlogram in a chosen frequency range. To this end, the correlogram λ_xy was subjected to an N-point Discrete Fourier Transform (DFT) (Oppenheim et al., 1996), in order to extract the frequencies of interest.

The oscillatory synchrony κ_oscsync was then set as the relative power of the signal in a chosen frequency range between f_min and f_max:

The verification of the results obtained with the PARAFAC model of (5) was achieved by carrying out so-called split-half experiments (Harshman and Lundy, 1994). To this end, the set of input data is split into two halves and PARAFAC is carried out for both halves independently. The model is considered to be applicable if the results gained from both halves are similar. In this work, several split-half experiments were carried out, splitting the input data set into odd and even trials.

We use the trilinear PARAFAC model because we assume the data to be (at least) trilinear. To show that a bilinear model, such as principal component analysis (PCA), is not adequate in this context, we also decomposed the correlation matrices using PCA and compared the results. PCA is a widely used technique. An introduction can be found in Jolliffe (2002). In order to make the data array accessible for PCA, it was unfolded into a two-dimensional structure.

The PARAFAC algorithm revealed the influence of electrode pairs and stimuli on the correlations and showed its behavior over time, since the stimulus repetitions were considered in an extra dimension. Figure 2 shows the result of the PARAFAC analysis. The optimal number of factors was chosen as the highest number of factors with no correlated ones and resulted in numbers of 4–6.

The loadings can be interpreted as the strength of influence on the correlation for the respective electrode pair, stimulus condition, and time point: The higher the loading value, the stronger the influence of the respective feature on the correlation.

The correlation values in Figure 2A correspond to repetitions 43–49 in Figures 2B,C. A comparison of these corresponding parts shows that the same effects can be observed in both ways of presentation. This becomes especially clear when the focus is put on the dark blue PARAFAC component in Figures 2B for repetitions 43–49. The component clearly reflects the strong peaks in Figure 2A for the respective stimulus.

Separate analyses were carried out taking into account the distance between the electrodes. For this purpose, the electrodes in a homogenously spaced 4 × 4 grid with grid size d_grid were divided into two sets, the set of neighboring pairs and the set of remote pairs. With (x_i,y_i) the position of electrode i, two electrodes are called neighboring nodes if (5)(x1−x2)2+(y1−y2)2≤2dgrid holds. Any two electrodes fulfilling this constraint are referred to as neighboring pairs, all other electrode pairs are termed remote pairs. In the case of a 4 × 4 grid of electrodes, this results in 42 neighboring pairs and 78 remote pairs.

We found a strong influence of pMS deactivation on the strength of correlations for both ipsi- and bilateral deactivation (see Figure 3). For these conditions, loading values for the deactivation phase were considerably lower than for the warm phases. Also, the variation in the warm phases was higher, indicating a more dynamic correlation pattern. This effect could already be observed in the spontaneous activity before stimulus onset (results not shown).

During contralateral deactivation of pMS (see Figure 3), the effect was much weaker, showing that the activity in area 18 was almost not affected by the deactivation of contralateral pMS.

In order to analyze the measured data with respect to its oscillatory synchrony properties, the oscillatory synchrony measure κ_oscsync was used as input data for the PARAFAC algorithm (Figure 4). For this measure the deactivation effects were most prominent during spontaneous activity. For frequencies between 1 and 10 Hz the deactivation effect could only be observed for bilateral deactivation. Here, it leads to a severe decrease of correlations. The correlations return to initial values in the rewarm phase. For the low gamma frequency range (30–50 Hz), the deactivation effect can also be seen during ipsilateral deactivation of pMS, and it is most pronounced during bilateral deactivation. In both frequency ranges, PARAFAC very soon developed correlated factors. For the oscillatory synchrony, the highest value for the variance explained by the model reached levels of 50% (for the results shown in Figure 4). This value increases when the number of factors F is increased. However, as already mentioned above, the factors become correlated under these conditions.

As a control for the appropriateness of PARAFAC for our data, we performed split-half experiments in which the data set was divided into odd and even trials. Figure 5 shows an example of the results for the data shown in Figure 5. The results show that the method works equally well on both newly created data sets: The loadings are similar and also the variation explained by the model was similar in both cases (71.26 and 70.17%, respectively). Consequently, the PARAFAC model of (5) was considered to be applicable.

The results of the PCA showed two distinct features: (1) The phases of pMS deactivation are not very prominent (see Figure 6) A high number of principal components is needed until a reasonable proportion of the total variance is explained. We showed that, for our example data set, with four and six PARAFAC components, the model is able to explain 70.07%, respectively 76.26% of the variance in the data. In comparison, 17 PCA components were needed to reach 70% of cumulated variance.

Even though this is a very methodological contribution we would like to illustrate how far this unique combination of different methodological approaches may help to reveal the neuronal basis of brain states. It should be emphasized that we only analyzed a randomly selected set of data from these experiments in order to examine to what extent the application of PARAFAC could help to better describe brain states and their transition. Unilateral deactivation of pMS cortex is linked to the neurological syndrome of visual neglect, an attentional deficit with impairment in motion, spatial, and attentional processing in one half of the visual field (Lomber, 2001). Bilateral pMS deactivation, by contrast, leads to a remarkable restitution of behavior (Lomber and Payne, 1996). Our PARAFAC analysis is able to reveal distinct effects of the deactivation of the pMS cortex on correlated activity in area 18 (see Figure 3, left and right columns, middle parts of bottom panels): during ipsi-, and even more during bilateral pMS deactivation, the strength of correlated activity in area 18 decreases. This is in accordance with our expectations, as unilateral deactivation of the pMS cortex eliminates the strong feedback input from pMS to the ipsilateral area 18 (Symonds and Rosenquist, 1984). However, while the feedback input from the ipsilateral pMS is missing, the affected primary visual area still gets feedforward input from LGN and also lateral input from its non-affected contralateral homotopic area and the contralateral pMS (Segraves and Innocenti, 1985).

When the middle panels of Figures 2B,C are examined, the analysis seems to allocate the factors in such a way that each factor depicts the situation for one distinct stimulus condition. For each of the stimuli, a certain pattern of correlated electrode pairs emerges, i.e., a different network is observed. In Figure 2C, with the 6th factor (shown in magenta), another set of correlated electrode pairs that is present when a diagonally left/downwards moving stimulus is presented, becomes visible. The same electrode pairs are also correlated for the stimulus moving in the opposite direction, and a slight anticorrelation can be observed for the perpendicular stimulus. The bottom panels show the time course of effects, indicating a larger trial-to-trial variability during the warm phases as compared to the ipsi- and bilateral cooling sequences and similar variability for the warm condition and contralateral cooling (see Figure 3). Hence, each stimulus produces a distinct network activity, but all of those networks become less variable during the ipsi- and bilateral deactivation phases.

The neuronal correlate of visual neglect has been proposed to be based on an imbalance of activity between hemispheres, which, presumably among other effects, leads to a disinhibition of areas in the non-affected hemisphere, which in turn leads to further inhibition of the already attenuated area (Payne and Rushmore, 2004). This is in accordance with the low level of correlated activity in ipsilateral area 18 (relative to the deactivation) and the observed correlation level in the contralateral area 18, which resembles the warm condition. When both pMS cortices are deactivated, as in the bilateral deactivation condition, the input from the contralateral areas is also reduced. Hence, the degree of correlated activity in area 18 is further lowered. In addition to the strength of correlation, the trial-to-trial variability is also diminished (see Figure 3, right column). This could indicate a less dynamic neuronal network, operating on a lower activity level, which is less able to adapt to and process new stimulus inputs than the normally functioning visual network. However, the lower but balanced correlation level seems to enable at least some functions that are impaired by unilateral deactivation: Behavioral studies indicate that during bilateral deactivation of pMS cortex, the animal is still able to complete simple orienting tasks, while it encounters problems with more abstract tasks, such as the so-called landmark-discrimination task, in which the cat is asked to choose between two wells, one of which contains food, the correct side of the well-being cued by one of six equally spaced landmarks, three left and three right of the midline (Lomber and Payne, 2000). Thus, although the animal is able to successfully complete some tasks, which may be owed to the restored equilibrium of activity levels in both hemispheres, there is an impairment of cognitive functions. Figure 4 shows that a strong decrease in the variation of correlated activity is even present in the spontaneous activity before stimulus onset, indicating a different processing mode of the respective neuronal network (see bottom panel, deactivation phase). As these are only speculations based on a very preliminary analysis of only a part of the dataset, these findings and conclusions have to be validated on the full database from these experiments. Also, further analyses should be conducted to examine the detected effects in greater detail. Nevertheless, PARAFAC proved to be a highly sensitive and helpful tool to identify relevant changes in neuronal processing modes on a multi-dimensional scale which open the window for a more targeted analysis of brain states linked to perceptual (and other) performance.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.