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Edited by: Shangbin Chen, Huazhong University of Science and Technology, China

Reviewed by: Tim David, University of Canterbury, New Zealand; Yicheng Xie, Zhejiang University, China

This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology

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Cortical spreading depolarisation (CSD) is a transient disruption of ion balance that propagates along the cortex. It has been identified as an important factor in the progression of cerebral damage associated with stroke or traumatic brain injury. We analysed local field potential signals during CSD in old and young rats to look for age-related differences. We compared CSDs elicited under physiological conditions (baseline), during ischaemia and during reperfusion. We applied short-time Fourier transform and a windowed implementation of multifractal detrended fluctuation analysis to follow the electrophysiological signature of CSD. Both in the time-dependent spectral profiles and in the multifractal spectrum width, CSDs appeared as transient dips, which we described on the basis of their duration, depression and recovery slope and degree of drop and rise. The most significant age-related difference we found was in the depression slope, which was significantly more negative in the beta band and less negative in the delta band of old animals. In several parameters, we observed an attenuation-regeneration pattern in reaction to ischaemia and reperfusion, which was absent in the old age group. The age-related deviation from the pattern took two forms: the rise parameter did not show any attenuation in ischaemic conditions for old animals, whilst the depression slope in most frequency bands remained attenuated during reperfusion and did not regenerate in this age group. Though the multifractal spectrum width proved to be a reliable indicator of events like CSDs or ischaemia onset, we failed to find any case where it would add extra detail to the information provided by the Fourier description.

Cortical spreading depolarisation or depression (CSD) is a self-propagating wave of depolarisation along the cortex (Leão,

A decisive factor that is under extensive study is aging. Age brings multiple changes to the biochemistry and cellular make-up of the cortex, and, in accordance with this, several age-related differences in CSD dynamics have come to light: for example, the speed of propagation is slower (Guedes et al.,

One of the most direct and spectacular electrophysiological indicators of the onset of CSDs is the direct current (DC) potential, which is essentially the component of the local field potential (LFP) that remains after low-pass filtering. Most studies use the transient deflection in the DC potential as the electrophysiological signature of CSD and use its morphological parameters to characterise CSD evolution. Yet CSDs also cause the full-band LFP amplitude to drop, reflecting a period of highly attenuated function and a loss of excitability in the neural tissue, and making the full-band LFP as feasible a target in offline investigations as the DC potential.

Exploring the spectral fine structure of cortical electrophysiological signals in the established frequency bands (delta to gamma) may also contribute to our understanding of CSD dynamics. The alpha-to-delta ratio (ADR), for example, has proved to be a predictor of worse recovery from ischaemia in humans (Claassen et al.,

An emergent tool in the study of complex system dynamics is multifractal analysis. Heralded as a promising method to disentangle multi-scale interactions and phase transitions in complex systems, it has recently gained ground in several areas of biomedical research and psychology from the segmentation of medical images (Lopes and Betrouni,

In this paper, we set out to explore how aging impacts the evolution of the spectral power of LFP during CSDs in distinct frequency bands (delta, theta, alpha and beta). Furthermore, we seek to incorporate multifractal analysis into the investigation of CSD dynamics to see if it reveals anything beyond the insights provided by the Fourier technique.

The data we analyse in this paper originate from an earlier study reported, and all surgical and experimental procedures are, therefore, identical to those previously published (Menyhárt et al.,

The animals were anaesthetised with isoflurane. After a baseline period lasting 50 min, we induced global forebrain ischaemia with the bilateral occlusion of the common carotid arteries (two-vessel occlusion, 2VO). An hour later, we released the carotid arteries to allow the reperfusion of the forebrain. Reperfusion also lasted for an hour. In all experimental stages (i.e., baseline, ischaemia, and reperfusion), we elicited three CSDs with the topical application of 1 M KCl at even intervals of 15 min (see Figure

The experimental protocol. 2VO indicates two-vessel occlusion.

In the rat, the bilateral occlusion of the common carotid arteries is a widely accepted procedure to induce incomplete global forebrain ischaemia (Farkas et al.,

We monitored the local field potential (LFP) in the cortex with a glass capillary electrode through a cranial window, relative to an Ag/AgCl reference electrode implanted under the skin of the neck of the animal. The LFP signal was amplified, filtered, conditioned and finally digitised at a sampling frequency of 1 kHz by a setup identical to that described in Hertelendy et al. (

We carried out all signal analysis tasks (spectral and multifractal) in a self-developed .NET environment written in C#. Fast Fourier transforms were calculated using a .NET wrapper around FFTW (

Before all further analysis, we filtered the local field potential (LFP), removing excessive spikes that had likely resulted from measurement artefacts, in order to prevent them from contaminating the spectrum. To avoid subjectivity in deciding what constitutes an artefact, we calculated the Bollinger bands (moving average ± moving standard deviation) in a window of 10,000 points, and marked segments where the magnitude of the signal exceeded a threshold of the local mean plus 4.2 times the local standard deviation as potential artefacts. We reviewed each automatic detection and only considered a segment as artefact if its slope was uncharacteristically steep. We removed confirmed artefacts and replaced them with a slope-corrected copy of the preceding interval of equal length. We applied cubic spline interpolation in a 5-point radius of the junctions between the original signal and the correction to ensure that the signal stays smooth. We found no more than 10 artefacts on average per CSD event, which altogether lasted <1 s, about 0.1–0.15% of the duration of a CSD event. The process is illustrated in Figure

The basis of the spectral investigations is the short-time Fourier transform (STFT) of the relevant LFP sequence _{k} of width _{m} =

From the STFT, a time-dependent power spectral density _{m}, _{n}) can be calculated as follows:

The integrated spectral power _{m}) = _{m} of a given frequency range between _{min} = _{min}Δ_{max} = _{max}Δ

The four frequency ranges of brain electrical activity defined in Table

The frequency ranges used in the analysis.

Alpha | 8 | 13 |

Beta | 13 | 30 |

Delta | 1 | 3 |

Theta | 3 | 8 |

In addition to the Fourier spectrum, we also applied multifractal detrended fluctuation analysis (MFDFA) to our LFP sequences. We followed the procedure laid out in Kantelhardt et al. (

wherein 〈_{s} segments altogether, where _{ν}, after which we calculated the local variance as

in the forward direction (0 ≤ ν < _{s}), and as

in the reverse direction (_{s} ≤ ν < 2_{s}), where _{ν} is the local trend for the νth segment, obtained using

The fractal properties of our time series

and the singularity dimension as

What we called the multifractal spectrum was the

In a similar way to STFT, we applied a windowed implementation of MFDFA: we calculated the multifractal properties in a 60-s window, then advanced the window by a step of 1 s and repeated the process, obtaining time-dependent functions comparable to the spectral powers discussed above.

In our investigations, the segment size varied from 16 to 512 as powers of 2. The maximum segment size was constrained by the requirement of scale invariance discussed in Ihlen (

Cortical spreading depolarisation events appeared as periods of transient drop in all spectral powers and in the multifractal spectrum width. To quantify the properties of these intervals, we searched for the best 4th-order polynomial fit for the depression in the signal. The initial candidates for the beginning and the end of such depression intervals we selected manually, but then an automatic algorithm could override these if it found a better fit with an endpoint within 10 s of the initial estimate. Polynomials which showed non-monotonicity in the neighbourhood of the endpoints were rejected. We designated five characteristic points to describe depression profiles (see Figure

Baseline point, whose

Depression point, which is simply the minimum of the polynomial in the depression profile;

Mid-depression point, where the polynomial takes on a value equal to the arithmetic mean of the baseline value and the depression value;

Recovery point, whose

Mid-recovery point, where the polynomial assumes a value equal to the arithmetic mean of the depression value and the recovery value.

We standardised each depression profile by subtracting the mean and dividing by the standard deviation, where the mean and the standard deviation were calculated for a signal segment that lasted from the end of the previous CSD to the beginning of the next. We evaluated the following quantifiers for a standardised depression profile (see Figure

Depression duration—the time that passes from mid-depression to mid-recovery;

Depression slope—the derivative of the polynomial fit at the mid-depression point (divided by the standard deviation as discussed above);

Drop—the difference between the standardised baseline value and the standardised depression value;

Recovery slope—the derivative of the polynomial fit at the mid-recovery point (divided by the standard deviation as discussed above); and

Rise—the difference between the standardised recovery value and the standardised depression value.

We used R for all our statistical calculations. Except where otherwise noted, we divided our data into six subgroups according to age (young or old) and experimental stage (baseline, ischaemia, and reperfusion). We did not include the first CSD in the baseline group as it represents a markedly different physiological state to all subsequent CSDs, even those in the baseline group. In each experimental group, we applied a Grubbs test to decide whether extreme values are outliers. Proven outliers were removed. Then we used two-way ANOVA with age and experimental stage as factors, followed by Tukey's honest significant differences (HSD) as a

Changes in the physiological state of the specimens were reflected unambiguously in the spectral power in all bands and also in multifractal spectrum width. CSDs and ischaemia induction (2VO) caused both spectral powers and multifractal spectrum width to drop (see Figure

Signs of a CSD and of ischaemia induction (2VO) in the alpha power

Ischaemia lengthened the LFP depression in all frequency bands (see Figure

Duration of depression in different frequency bands for all experimental stages. Significance levels are given as ^{#}^{##}^{$}^{$$}

Though the duration of depression was clearly shorter in old animals throughout all experimental stages (most visibly in the baseline stage), this categorisation did not show any statistically significant difference according to age. To reveal potential aging effects, we run another two-way ANOVA restricted to the baseline stage, this time with age and frequency band as its factors (see Figure

Of all the parameters we investigated, the slope of depression showed the effects of aging the most clearly (see Figure ^{−1} for ^{−1} for ^{−1} for ^{−1} for ^{−1} for ^{−1} for ^{−1} for ^{−1} for

Depression slope in the different frequency bands of LFP power. Significance levels are given as ^{*}^{**}^{#}^{##}^{$}^{$$}

The drop in the spectral power did not show any significant difference between experimental groups. When we focused on the frequency bands in the baseline stage, however, we could discern some frequency dependence (see Figure ^{−5}). In the multifractal spectrum width, one could observe a smaller drop during ischaemia than in the baseline state, which was significant for young animals (1.67 ± 0.07 for

Drop during baseline CSDs in the different frequency bands of the LFP power. Significance levels were obtained using two-way ANOVA with age and frequency band as factors, with Tukey's HSD as a ^{@@} ^{&&} ^{++}

^{#}

The recovery slope followed the same attenuation-regeneration pattern as the depression slope in young animals, though this effect proved significant only in the theta (0.019 ± 0.004s^{−1} for ^{−1} for ^{−1} for ^{−1} for

Recovery slope the different frequency bands of the LFP power. Significance levels were obtained using three-way ANOVA with age, experimental stage and frequency band as factors, with Tukey's HSD as a ^{##}^{$}^{$$}^{@}^{@@}^{&&}

A similar attenuation-regeneration dynamics also seemed to manifest itself in the rise after the CSD-induced transient depression for young animals (e.g., in the alpha band: 1.93 ± 0.22 for

Rise in the different frequency bands of the LFP power. Significance levels are given as ^{*}^{$}

Intraoperative electrocorticogram (ECoG) monitoring is an invasive approach to aid tumour resection or surgery for the alleviation of epilepsy (Yang et al.,

Though age-associated changes have been revealed in the spectral composition of ECoG in rats–whilst aging causes high-frequency power to decrease, it also enhances delta power (Bagetta et al.,

What we have found extends on the power spectrum-related conclusions in our earlier report (Hertelendy et al.,

The most significant difference we found between young and old animals appeared in the depression slope of spectral powers after the onset of CSD. Under physiological conditions, CSD-induced decline in the beta power was much steeper in the old age group, whilst during reperfusion, the rate at which delta power decreased in reaction to CSDs was less in absolute value in old animals. The latter might be in accord with earlier findings where less negative or even positive delta slope (termed aDCI, acute delta change index) predicted worse outcomes in ischaemic stroke patients (Finnigan et al.,

Several parameters investigated here followed a pattern where values decreased during ischaemia as compared to baseline then were restored during reperfusion. This behaviour was most consistent in the recovery slope. These data are consistent with the profound differences in the pattern of CSDs that occur in the intact and ischaemic cerebral cortex. As such, CSD as indicated by the negative deflection of the DC potential lasts significantly longer under ischaemia as compared with the intact condition (Menyhárt et al.,

Most age-related effects we found represented a deviation from this pattern. The attenuation of the depression slope of beta and delta spectral powers proved permanent in old animals and was not followed by regeneration. Another type of age-related deviation could be observed in the rise after CSD-induced depressions in the spectral powers: here the attenuation step was absent from the spectrum of old animals and the rise values remained about the same throughout all experimental stages. Finally, we noted an isolated departure from attenuation-regeneration dynamics in the recovery slope of the alpha power of old animals, where again no attenuation occurred during ischaemia.

One argument for the application of fractal analysis instead of or in addition to traditional linear investigation methods such as Fourier transform is the perceived inability of the latter to quantify the scale-dependent properties of complex biological systems that stem from the interplay of many levels of substructure (Chakraborty et al.,

In addition to the monofractal studies above, several multifractal analyses have targeted the brain. The multifractal spectrum width calculated for the EEG database of epilepsy patients has been shown to be less in ictal periods than in interictal ones (Zhang et al.,

To our knowledge, this paper is the first to extend earlier monofractal studies (do Nascimento et al.,

One goal of ours was to find out whether multifractal analysis yields any additional information on the dynamics of the local field potential during CSDs as compared to the Fourier spectrum. The MFDFA parameter we chose to follow in this study, the multifractal spectrum width, has failed to reveal anything more than our STFT-based profiles–in fact, it has proved largely insensitive to age or experimental stage. The only exception to this was the drop in the profile as a reaction to CSD, which, in young animals, was significantly less during ischaemia than the baseline, but it did not fit into any discernible pattern.

PM: analysis and interpretation of data, drafting the article; ÁM: substantial contributions to conception and design, acquisition of data; FB: revising the manuscript critically for important intellectual content; EF: substantial contributions to conception and design, analysis and interpretation of data, drafting the article, and revising it critically for important intellectual content.

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.

PM thanks Szabina Tudja for ideas and thoughtful discussions.

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