Discussion

103 unperturbed by the artifact removal (Fig. 25A/B, lower panels).

As a second measure of spiking activity, we tested the effect of our method on the entire spiking activity (ESA). The ESA is a continuous signal instead of a point process and is more sensitive and robust in detecting spiking activity since it includes spikes from a larger part of the local population ¹⁸⁷. Furthermore, it does not require setting a threshold, which, on the other hand, makes it more vulnerable for remaining artifact components. The comparison of ESA obtained from data containing an artifact (middle panels) to the very same, original data (upper panels) shows how strongly the artifacts disturbs ESA. In contrast, the comparison of ESA computed from artifact removed data (lower panels, orange traces) to the original ESA (upper panels, red traces) exemplifies the efficiency of artifact removal even for this sensitive measure.

104 For evaluation, we used real neuronal data containing artifacts that strongly disturbed the underlying neuronal signal. In a first step, we analyzed how well the method removed the artifact and restored the neural signal by comparing the signal level shortly before and after stimulation onset. The method described here, effectively reduced the highly significant and substantial effects of stimulation on the signal, such that there was no significant effect detectable anymore. As a second measure, we investigated the efficiency of phase reconstruction within the γ- and β- frequency range, in which stronger phase shifts occur than in lower frequency ranges when artifacts are artificially superimposed. These artifacts were constructed using average artifact shapes originating from actual neuronal data, such that conclusions on the effectiveness of removing these artifacts are expected to apply also to real experimental conditions in which the actual time course of the signal without artifact is unknown. We found that artifacts caused in the γ-frequency range a median absolute phase difference to the original data of 45° shortly after artifact onset. In the β-band, the median absolute difference was still 25°. After removing the artifact, these differences decreased sharply to only 5.6° in the γ-band and 5° in the β-band, corresponding to a reduction of the artifact induced absolute phase deviations by 87.5 % and 78.63 % respectively. Finally, we illustrated that similar to earlier approaches, the restored data enable reliable spike detection and ESA estimation.

Previous methods for removing electrically evoked artifacts have been developed - and are therefore very successful – for accurate spike detection. However, they have several disadvantages if the LFP is the focus of the investigation. A simple method is, for example, to cut out the period contaminated by artifact components and replace it with linear interpolation.

This method has been used successfully by Heffer and Fallon (2008)³⁰⁰ for replacing artifacts lasting on average only 170 µs. On the other hand, the replacement of longer-lasting artifacts like those observed here and by others (e.g., Harding, 1991²⁹⁶; Wagenaar and Potter,2002²⁹⁵) would result in a massive loss of signal components and strongly disturb the time course of the actual signal.

Another approach that is capable of removing such longer-lasting artifacts is the template subtraction. This method needs to average over a large number of stimulation artifacts to obtain a precise estimate of the actual artifact shape. Subsequently, this artifact template is subtracted from each individual stimulation period ^301–303. However, the inspection of our data revealed that individual artifact amplitudes sometimes differed by more than 100 % from the average.

Varying artifact amplitudes have been reported in other studies as well 300,305,306, indicating that this is a common characteristic. Subtraction of a template (or a fit based on the averaged artifact)

105 under these conditions would result in a strongly disturbed signal. It would contain residual artifact components for artifacts larger than the template and mirrored components for those that are smaller. The method presented here is capable of dealing with such substantial differences since it adapts the function to be subtracted to the amplitude of the individual artifact while keeping the characteristic shape for a given recording site constant.

A further approach capable of removing longer-lasting artifacts even when they change in amplitude across trials is based on subtracting an exponential function fitted to each stimulation artifact individually ^296,297. This method is well suited for studies focusing on short events such as spikes and short electrically evoked potentials (EEPs) that ride on a rather slowly decaying artifact. Since spikes and EEPs are defined on a much faster time scale than the slowly decaying part of an artifact, subtraction of a corresponding fit removes the components of the artifact but leaves fast spikes and EEPs unaffected, that do not coincide with the fast transient part of the artifact. In contrast, the LFP contains neural signal components with a time course on the same, rather slow time scale as parts of the artifact. Subtraction of a function fitting the superimposition of both the artifact and these neural signal components might result in dramatic changes of the actual LFP components. Our approach overcomes this problem in two steps.

First, we use the time course of the average artifact for fitting an exponential function. This time course contains almost exclusively the components of the artifact since superimposed neural signal components were averaged out. Therefore the fitted function describes only the shape of the artifact and not components of the neural signal. Second, for the subtraction of this function from the individual artifacts, only the function’s size (amplitude parameter A) and not its shape (determined by all other parameters) is adapted when fitting this function to the individual artifact. These two steps avoid inclusion of neural signal components in the fit, which is subsequently subtracted and thereby avoid distortions of the actual signal. With the same objective, we only use the first, large part of the artifact (here the first two milliseconds) for adapting the fitted function to the individual artifacts amplitudes. Contrary to later parts of the superimposition, the artifact strongly dominates this first period and using it minimizes the impact of neural signal components on the fit, while it is sufficient for fitting its amplitude.

In summary, the here presented method serves well for restoring the comparatively slow signal components as contained in the LFP.

Successful application of the method presented here requires that data and artifact fulfill a few prerequisites. First, equation (1) requires that the decay characteristic of the artifact is exponential. In previously published data ^296,297 but also in our test data-set, an exponential fit explained the decay periods of the artifacts best. However, the method does not depend on a

106 specific function used for fitting and can be adapted easily if another function describes the artifact better. Second, the current method estimates the artifact duration based on the time it takes until the average neuronal signal decays back to pre-stimulation levels. This approach requires that the average of the underlying neuronal activity is flat and shows no systematic modulations (e.g., as a consequence of systematic sensory stimulation) with a fixed temporal relation to the electrical stimulus. If an artifact does not fulfill this requirement, the course of the systematic modulations can be obtained from trials without electrical stimulation and then be subtracted from the average artifact shape before fitting it with equation (1). Third, the method described here handles artifacts with changing sizes across stimulations of the same recording site successfully but requires that they have the same shape (apart from superimposed signal components). While the ability to adapt the size is necessary since we observed substantial changes across successive stimulations, we did not observe changes in the shape (decay characteristics) in our data-set. Well in line, also other studies did not report such changes, which appear unlikely since the decay characteristic of artifacts are considered to be a result of the static filter characteristics of the recording system ²⁹⁶.

To conclude, we have shown that the method for artifact removal and signal reconstruction presented here is a powerful tool for artifact removal and signal reconstruction in data containing large and long-lasting, exponentially decaying electrical artifacts. It restores the actual time course of broadband signals, in particular, the LFP, including its phase and amplitude properties, and is at the same time capable of recovering spiking activity.