Characterization of the in vitro propagation of epileptiform electrophysiological activity in organotypic hippocampal slice cultures coupled to 3D microelectrode arrays

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Characterization of the in vitro propagation of epileptiform electrophysiological activity in organotypic hippocampal slice cultures coupled to 3D microelectrode arrays Marzia Pisciottaa , Giovanna Morgavib , Henrik Jahnsena,⁎ a

Division of Neurophysiology, Department of Neuroscience and Pharmacology, University of Copenhagen, Blegdamsvej 3, 2200 Copenhagen N, Denmark b IEIIT-National Research Council, via De Marini 6, 16149 Genoa, Italy

A R T I C LE I N FO

AB S T R A C T

Article history:

Dynamic aspects of the propagation of epileptiform activity have so far received little

Accepted 9 August 2010

attention. With the aim of providing new insights about the spatial features of the

Available online 14 August 2010

propagation of epileptic seizures in the nervous system, we studied in vitro the initiation and propagation of traveling epileptiform waves of electrophysiological activity in the

Keywords:

hippocampus by means of substrate three-dimensional microelectrode arrays (MEAs) for

Hippocampus

extracellular measurements. Pharmacologically disinhibited hippocampal slices

Homosynaptic plasticity

spontaneously generate epileptiform bursts mostly originating in CA3 and propagating to

Epileptiform activity

CA1. Our study specifically addressed the activity-dependent changes of the propagation of

Microelectrode arrays

traveling electrophysiological waves in organotypic hippocampal slices during epileptiform

Propagation velocity

discharge and in particular our question is: what happens to the epileptic signals during

Coherence analysis

their propagation through the slice? Multichannel data analysis enabled us to quantify an activity-dependent increase in the propagation velocity of spontaneous bursts. Moreover, through the evaluation of the coherence of the signals, it was possible to point out that only the lower-frequency components (< 95 Hz) of the electrical activity are completely coherent with respect to the activity originating in the CA3, while components at higher frequencies lose the coherence, possibly suggesting that the cellular mechanism mediating propagation of electrophysiological activity becomes ineffective for those firing rates exceeding an upper bound or that some noise of neuronal origin was added to the signal during propagation. © 2010 Elsevier B.V. All rights reserved.

1.

Introduction

Paroxysmal population discharges and epileptiform activity characterize the in vitro electrophysiological activity of many pharmacologically disinhibited neurobiological systems such as neocortical and hippocampal slices which largely retain the

anatomical and physiological features of the intact in vivo circuitries (Gutnick et al., 1982; Knowles et al., 1987; Menendez de la Prida and Pozo, 2002; Poulsen et al., 2002; Salazar et al., 2003, Miles et al., 1988). Such reduced neurobiological preparations are therefore often used as a simplified experimental model of in vivo neuronal networks synchronization, under

⁎ Corresponding author. Fax: + 45 35 32 76 10. E-mail address: [email protected] (H. Jahnsen). 0006-8993/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.brainres.2010.08.028

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2.

Results

Experiments were carried out on nine organotypic hippocampal slices coupled to the MEAs. During each experiment, epileptic activity was recorded from all the array microelectrodes to spatially monitor the electrophysiological activity across the whole slice. Within a few minutes after the application of picrotoxin 100 μM, spontaneous episodes of

epileptiform activity could be detected extracellularly by the MEA microelectrodes located in CA1–CA3 areas (Fig. 1A), but not in dentate area (data not shown) (Traub et al., 1993). Such electrophysiological bursts could be also elicited by a weak monopolar electrical stimulus, delivered via one microelectrode of the array, located in the CA1–CA3 areas. With the aim of characterizing the propagation velocity of epileptiform activity bursts through the hippocampal tissue,

A

A B C D E F G

1 mV

H 20 s

B

A B C D E F

0 .5 m V

physiological as well as pathological conditions. In particular, hippocampal slices received great attention in the last two decades, and they have been extensively studied because the in vivo pathological increase in the synchronization of epileptiform activity through the hippocampus is thought to contribute to temporal lobe epilepsy, in which reverberating activity between entorhinal cortex and hippocampus is a central event (Pare et al., 1992). Actually, it is widely accepted that hippocampal networks can be rapidly recruited due to the large positive feedback provided by recurrent axon collaterals, and they are believed to play a crucial role as an in vivo generator of epileptic activity, or even as an amplifier of epileptic activity (Lothman et al., 1991; Pallud et al., 2008). The study of the propagation of electrical synchronous activity in such neuronal networks is of a paramount importance for the understanding of the cellular basis of some form of central nervous system pathologies. In addition, the propagation of synchronous discharges in many different neurobiological system may be used as a probe for the investigation of the network circuitry and synaptic physiology (Gutnick and Wadman, 1986; Traub et al., 1993, Hu et al., 2005; Orman et al., 2008) and it might provide important information at the network level. In the last few years, substrate arrays of microelectrodes have proved to constitute an excellent tool for the investigation of the spatiotemporal evolution of in vitro electrophysiological activity, as they can be effectively employed to simultaneously record and stimulate the collective activity of networks of dissociated neurons in culture (Chiappalone et al., 2006; Vajda et al., 2008; Berdondini et al., 2009) as well as of brain tissue slices (Köhling et al., 2005; Heuschkel et al., 2003; Thiébaud et al., 1999), emphasizing the electrophysiological dynamics at the network level. In the case of the propagation of travelling waves of excitation through a brain slice, these arrays are useful tools for the assessment of the spreading direction and velocity of the population spikes (PSs). In this work, we demonstrate what happens to the epileptic signal during propagation through the hippocampal slice. More precisely, we have studied the problem through the use of spectral coherence analysis that provides complementary information to the classical analysis of temporal signals. We measured the propagation of epileptiform bursts of activity in a standard experimental model of in vitro epilepsy by means of 3D substrate microelectrode arrays, supporting experimental data with nonconventional signal processing tools. From the physiological point of view, many different biophysical mechanisms are known to determine and dynamically modulate the properties of the propagation of travelling pulses of excitation through an in vitro brain tissue slice (Holsheimer and Lopes da Silva, 1989).

G H 5 ms

C E G

F C D B A H

Fig. 1 – Epileptic activity induced by 100 μM picrotoxin in an organotypic brain slice. A) Burst activity recorded by means of eight different electrodes of the array. B) Population spikes (PS) that constitute the bursts in A. The time delay was calculated between the time corresponding to the minimum value of the PS recorded by H electrode and all the other time values recorded by the different electrodes. C) Sketch of the actual alignment of an organotypic hippocampal slice coupled to the microelectrode array, during a typical experiment. Letters indicate the location of 8 active array microelectrodes, selected out of the 28 available. Light gray-coloured areas identify the granule cell body layer of the dentate gyrus (DG) and the pyramidal cell body layer of the cornu ammonis (CA).

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the time delays (Fig. 1B) for each spike composing a burst were measured with respect to corresponding leading population spike occurring in the region where the epileptiform waves originated (i.e., always located in the CA3 area—see Fig. 1C, electrode H), representing the latency of the travelling pulses in different places of the slice anatomy and inversely proportional to the spreading velocity. Average measured propagation velocities were within the range reported by previous investigators (Orman et al., 2008; Knowles et al., 1987; Holsheimer and Lopes da Silva, 1989). However, whenever the latencies with respect to the population spike detected by the CA3 microelectrode were plotted vs. burst duration, delays smoothly decreased until a steady-state value was reached, indicating an activity-dependent increase in the propagation velocity (see Fig. 2). The temporal evolution of the latencies, during the total duration of each burst, was qualitatively spatially homogeneous and it was well fitted by a single exponential decay (i.e. τ ranges between 14 s—C electrode and 35 s—A electrode, see Fig. 2). Such a phenomenon was observed at each spontaneous activity burst and it was qualitatively consistent in four other slices, suggesting a general activity-dependent increase in the propagation velocity within individual bursts, characterized by similar kinetics in different regions along the direction of propagation in the same slice. Latencies slowly recovered back to higher values during long periods of inactivity. We have not yet characterized and analysed this phenomenon, but Poolos et al. (1987) have previously described both increase and decrease in conduction velocity in the hippocampus during repetitive stimulation.

2.1. Coherence analysis and upper bound for frequency content of propagating signals First we calculated the power spectral density of baseline and epileptiform activity. The difference between the spectra showed that the bursting activity had a frequency content between a few and 250 Hz (Fig. 3A).

7

D A F C B

time delay (ms)

6 5 4 3 2 1 0

250

300

350

400

450

500

550

600

time (s) Fig. 2 – Time delay vs. burst duration calculated between the electrode H and the electrodes A, B, D, C, and F (see the sketch in Fig. 1C). The curves were fitted by an exponential function (see text) giving the following values of the τ parameter: 35±13 s A; 16± 3 s B; 16±3 s D; 14± 2 s ,C and 23±4 s F.

Then we used the cumulant density function (Halliday and Rosenberg, 1999, see also Discussion 4.3 and 4.4) to test if there was a significant amount of “cross-talk” between the electrodes of the array, i.e. if electrodes pick up only local electrophysiological activity or if they also sample from distant sites close to other electrodes of the array. We used 20-s epochs of raw data. The results for electrodes F and H of Fig. 1 are seen in Fig. 3B. One curve (red, 95% confidence interval: ± 7.3 × 10−5, shown as horizontal lines) is the cumulant density function during epileptiform activity. The other curve (blue, 95% confidence interval: ± 4.3× 10−5, not shown) is the cumulant density function during baseline activity. Note that there is a significant contribution from 50 Hz hum (lag = 20, 40, 60 etc.) in both situations. During epileptiform activity there is also a significant contribution at time lag≈ −6 ms (arrow) corresponding to the conduction time between electrodes F and H (see Fig. 1B). The difference between the blue and red curves is shown as a black trace. The fact that the most pronounced difference in cumulant density is seen at a non-zero time-lag, supports the assumption that our electrodes only pick up N1 noise and locally generated biological activity and not any distal biological activity. Finally, the coherence function was calculated between signals detected at different (active) electrodes to estimate how much power of a signal recorded in a place was direct effect of the one recorded at the site where epileptic discharge originated (see also par. 4.4 of Experimental procedures). We analyzed five experiments in which spontaneous bursting activity occurred. The microelectrode whose activity first originated and spread to the others was always located in the CA3 region, and it was used as the reference waveform for the coherence analysis. The numerical estimation of the coherence involved 10-s time windows, and care was devoted to check that coherence resulted independent from the positioning of the analysis time window with respect to the bursts. For each couple of channels, we calculated the coherence γ21, also during the absence of any visible electrophysiological signals on both channels (i.e., noisy signals' baseline) to estimate the impact of the intrinsic “noise” N1 on the electrophysiological recorded responses, decorrelating them. In such a case, it is helpful to regard Eq. (4) as a signal model for the estimation of γ2. During each experiment, seven pairs of histograms (see Fig. 3) were obtained, representing the coherence measure as a function of the frequency, estimated over 10 s of baseline traces and 10 s of epileptiform activity. The value 0.8 was set as a threshold to precisely state whether the two waveforms were coherent or not, for a particular range of frequencies. Fig. 4A shows the coherence as a function of frequency, estimated by processing the baseline traces as a function of the geometrical distance between the reference microelectrode in CA3 and all others, located in CA1 zone. Coherence appeared site-independent and was near 1 at all frequencies. This implies that for the frequency range 0–335 Hz, the power carried by the signal detected by individual microelectrodes originates from a common source which is most likely external noise. Results were different from those obtained during the baseline activity when the coherence was estimated over 10 s of an epileptiform burst. We assumed this signal was a superposition of the electrophysiological signal (x2), the baseline signal (x1), under nonbiological electrical noise N1 overlapping another

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A

B

3.0e-4

0.003

2.0e-4

Cumulant density

Power density

2.5e-4

0.004

1.5e-4 1.0e-4

0.002

0.001

0.000

5.0e-5

-0.001

0.0 0

100

200

300

400

500

600

-80

Frequency (Hz)

D

1

-40

-20

0

20

40

60

80

Lag between electrode H and F (ms)

1

Burst

Baseline

Coherence

Coherence

C

-60

0.5

0

0.5

0 0

400

800

0

Frequency (Hz)

400

800

Frequency (Hz)

Fig. 3 – A) Power density of 20 s of baseline (blue) and 20 s of epileptiform (red) activity. The difference is plotted in black. Note that the significant contribution from hum (50 Hz and harmonics) and that the epileptiform activity contributes in the range from a few Hz to about 250 Hz. B) Cumulant density functions for baseline (blue) and epileptiform activity (red) for signals recorded by electrodes F and H in Fig. 1. The difference is shown in black. The 95% confidence interval for the red trace is also shown as two horizontal lines. Note that there is a significant contribution in cumulant density at time lag −6 ms (arrow). See text for further explanation. C) and D) Examples of histograms showing the coherence value vs. frequency calculated on 10 s of a baseline signal (C)) and of epileptiform activity (D)) recorded from an electrode situated in CA1 region and the reference electrode situated in CA3 region of the slice. The horizontal thick line represents the threshold assigned to identify the range of frequency for which the signals are either coherent or noncoherent.

signal N2 of a different nature. Actually, under such a simplified interpretative framework, the coherence function represented by Eq. (4) can now be described by the following equation: 2 + x2 Þðx1 + x2 Þd jHj P2 2 Sðx1 + x2 Þðx1 + x2 Þd jHj + jN1 + N2 j

P

γ22 ð f Þ =

Sðx1

P

ð1Þ

Fig. 4B shows the coherence γ2 for the same range of frequencies, calculated on the same electrodes as in A but during seizure-like activity: for frequencies ranging between 95 and 335 Hz the signals lost their coherence in a mild sitedependent way, while for low frequencies, the signals remain almost completely coherent. Each point represents the

average ± SEM over 5–3 recordings at the same distance. For frequencies above 335 Hz, the coherence was low and similar to that of the baseline traces. This is not surprising since these frequencies do not contain any contribution from the epileptiform activity.

3.

Discussion

The main results of our work are that properties of picrotoxininduced seizure-like activity in organotypic slice cultures can be investigated by coupling the cultures to silicon-based

50

A

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1,0

coherence

0,8 0-47Hz

0,6

48-95Hz 96-143Hz

0,4

144-191Hz 192-239Hz 240-287Hz

0,2

288-335Hz

0,0 0

400

800

1200

1600

distance µm

B 1,0

coherence

0,8 0,6 0,4 0,2 0,0 0

400

800

1200

1600

distance µm Fig. 4 – The coherence values in the range 0–335 Hz are plotted vs. geometrical distance among the electrodes calculated from the origin of the epileptic discharge (reference electrode). A) The baseline signals recorded in different positions of CA1 are coherent with the baseline recorded in CA3 zone for this range of frequencies (γ1 coherence ≥0.8). B) The seizure-like activity propagates through the slice maintaining the coherence (γ2 coherence≥0.8) only for low-frequency components (<95 Hz). The higher frequency (95–335 Hz) components lose their coherence.

electrode arrays. We found that the epileptiform activity propagates in the tissue with an increasing speed, that it has a frequency content between a few Hz and 250 Hz and that coherence between signals from different electrodes is lost at high frequencies. Our picrotoxin-induced activity in vitro differs from in vivo seizure activity in frequency content. We do not see the fast ripples reported in vivo (see for instance, the review by Engel et al., 2009). Therefore, our picrotoxin model is not suitable for investigating the fast components of seizures, but our preparation could easily be used in combination with other seizure-inducing procedures as for instance increasing the extracellular potassium concentration. The loss of coherence for high frequency means that noise (N2) of particular frequencies contributed to modify the difference in phase between the signals over time. The nature of this noise can be only neuronal, because all the other contributes to the noise, due for example to the high electric impedance of the electrode, were included in N1. It is not strange that the coherence

of the baseline is near 1: the electrodes are similar and near each other, therefore they record, in practice, the same external electric noise. Moreover, the Johnson noise contribution is negligible with respect to the external noise. Since recordings have been done with tissue coupled to the array, impedance could change among different electrodes, thus giving different cut in frequencies of recorded noise. As a result, the coherence function should drop near zero since N1 (noise in this case produced by different filtering) in (4) is significantly different from zero. Our experimental results show that from 0 to 335 Hz, the above problem does not exist. Thus, we conclude that our system is a good one to check if something different happens when the electrophysiological activity rises above baseline. The computation of the coherence function over the signals when seizure-like activity was recorded has demonstrated that N1 is negligible for frequencies ranging between 0 and 335 Hz. The power spectral analysis applied on epileptiform activity has demonstrated that the electrophysiological frequencies range between few Hz and 250 Hz (Fig. 3A). The frequency content higher than 96 Hz belongs to population spike signals recorded by the array; in fact we found that in our experiments their frequency range is always between 80 and 220 Hz. Lower frequencies characterize the burst activity, fluctuating between 2 and 12 Hz. The noise N2 does not modify the frequency content of the epileptic bursts during their propagation through the path CA3–CA1 of the slice. It is not present at the beginning of the propagation (reference electrode), but it is revealed only by the second electrode used for the coherence calculation. It could be due to several biological mechanisms: activation of intrinsic electroresponsive membrane properties of neurons near the second electrode or the turning on of local or afferent synaptic pathways which are able to interfere with the direct way of the epileptic propagation and return a variable phase difference for the frequency that constitutes the single population spike. If fact, it could be due to any additional electrophysiological activity near the second recording electrode. In other words, the population spikes that cross the slice from the origin of the seizure-like activity are not correlated with those recorded by an electrode situated at a certain distance from the reference, the coherence between incoming and outgoing is lost. The loss of coherence is because N2, the neuronal noise, covers the original signal for frequencies higher than 95 Hz. Highly synchronized discharges of neuronal subpopulations in the in vitro hippocampal networks during epileptiform activity alter the threshold for synaptic long-term plasticity induced by external stimulation (Lopantsev et al., 2009; Abegg et al., 2004; Bains et al., 1999). The main consequence of this is that the probability of future synchronous network activation increases. Activity-dependent synaptic transmission might contribute to regulate the propagation of further high-frequency synchronous network activity in the hippocampus under normal physiological conditions, reducing the probability of correlated electrophysiological activity that might result in a pathological positive feedback. Presynaptic factors controlling glutamate release at excitatory synapses between CA3 and CA1 neurons could be sufficient to constrain the velocity of propagation of travelling pulses from CA3 to CA1, in a similar way they regulate the probability and duration of synchronous discharges (Jones et

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al., 2007; Staley et al., 1998), but the increase in conduction velocity which was seen during epileptiform activity is most likely due to factors affecting excitability of axons, i.e. accumulation of potassium ions extracellularly producing depolarization and thus an increase in excitability or to changes in extracellular volume (shrinkage) due to water movement into the extracellular space. This might increase the current density extracellularly during the propagation of actions potentials and thus increase conduction velocity. More complex mechanisms, such as those responsible for the increase in the rate of discharge (i.e., the “wind-up” phenomena observed in the spinal cord), seem not to be involved in the hippocampal physiology. Plasticity of glutamate-mediated synaptic transmission might constitute an appropriate “braking” mechanism at the network level to dampen pathological activity providing a compensatory mechanism that can be activated and progressively “repair” the system instability, but it needs to be investigated further. By designing new experimental protocols focused on the dynamics of propagation of synchronized population activity in hippocampal slices as well as in other brain preparations, we expect to get additional useful hints on the corresponding cellular and subcellular bases and to increase our understanding of the mechanisms contributing to the propagation of in vivo epileptic activity. There is, as always, when in vitro preparations are used, a need for confirmation of the results in the intact brain. However, at present, we have no reason to believe that the results presented here do not apply in the epileptic brain.

4.

Experimental procedures

4.1.

Slice cultures and pharmacology

Organotypic slice cultures of neonatal (5–6 days old) Wistar rat hippocampi were prepared as described in Jahnsen et al. (1999) and selected for recording after 1–3 weeks in culture (i.e., membrane insert method). Before starting each experiment, brain tissue slices were transferred into an interface recording chamber, aligned over the MEA, and incubated for about 30 minutes. The slice was continuously perfused, but never submerged, at the rate of 2 ml/min with artificial cerebrospinal fluid (ACSF), heated in a constant temperature bath at 32 °C and balanced with 95% O2/5% CO2, resulting in a pH of 7.35–7.40. ACSF was composed (in mM) of: NaCl 134.3, KCl 5.4, NaH2PO4 0.3, KH2PO4 0.4, NaHCO3 18, CaCl2 3.3, MgSO4 0.4, MgCl2 2, glucose 5.6 (see Jahnsen et al., 1999). In few cases, with the aim of characterizing the nature of the extracellularly recorded signals as population spikes, the pharmacological block of the spiking initiation mechanisms was reversibly obtained by adding tetrodotoxin (TTX) at a concentration of 1 μM, blocking any evoked or spontaneous detectable activity. The induction of spontaneous seizure-like activity was obtained by adding picrotoxin (PTX) at the concentration of 100 μM, to block the ionotropic type A GABA γ-aminobutyric acid) receptors, known to mediate fast inhibitory synaptic transmission in the hippocampus (Knowles et al., 1987).

4.2.

51

Microelectrode arrays

Biocompatible custom microelectrode arrays (MEAs) consisted of 28 silicon nitride passivated three-dimensional Pt-tip microelectrodes embedded on a perforate silicon substrate (i.e., porosity 35%) (Thiébaud et al., 1999; Jahnsen et al., 1999). Electrodes were 47 μm high of which only the top 15 μm is the exposed Pt-tips, having a curvature of 0.5 μm. The layout of the array microelectrodes was spatially uniform and appropriate for the coupling to acute as well as organotypic slice cultures (see Fig. 1). Individual microelectrodes (i.e., the recording/stimulation sites) were uniformly spaced 300 μm from each other and covered an overall area of approximately 1.2 mm2. The three-dimensional microelectrodes, characterizing the custom MEAs employed in the present research, allow a better signal-to-noise ratio by improving the electrical coupling with the inner neuronal layers of thick slices of brain tissue. This reduces the attenuation of the detected signals, as previously investigated (Heuschkel et al., 2002; Bove et al., 1996) provided that microelectrodes can penetrate the tissue slice thus skipping the outer cell layers, mainly composed by unhealthy/dead neurons that were traumatized after tissue explant and slicing.

4.3.

Electrophysiology and signal processing

In the present research, MEAs were reliably used to extracellularly record spontaneous and evoked electrophysiological activity of organotypic hippocampal brain slices. Slices were placed on the microarray so that each Pt-tip microelectrode was coupled with a different anatomical tissue region. Simultaneous conventional extracellular recordings by means of field potential glass micropipettes 1–10 MΩ, filled with 0.3 M NaCl solution and placed in the CA1 cell bodies layer, were routinely performed as a control and sometimes intracellular recordings were also obtained with sharp electrodes filled with 0.5 M K-acetate. The evoked electrophysiological responses recorded in CA1 after delivering electrical shocks in the CA3 region, were employed as a gauge of the brain tissue viability. One of the Pt-tip microelectrodes, among those located in the CA3 region, was selected for monopolar electrical stimulation delivered through biphasic voltage steps at 3–7.5 V, each 200 μs long. Recorded signals were processed with an 8-channel low-noise custom amplifier, sampled at 6 kHz, stored on a personal computer by using Spike2 acquisition software (CED, England) and offline analyzed by using the software Spike2, Origin (version 6.0, Microcal Software Inc.) and C-code custom analysis routines. Cumulant density was calculated using a script for MatLab published by David Halliday on www.neurospec.org (2010).

4.4.

Estimation of time delays and coherence data analysis

During each experiment, electrophysiological signals were continuously monitored across the whole MEA, and delays were offline estimated as the time intervals between the peaks of the corresponding population spikes (PSs), detected at different (active) microelectrodes. Traditional cross-correlation estimation was not considered as it would have averaged out any time-dependent change in the distribution of the

52

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delays, given the nonstationary features of the phenomena we were interested in addressing. Beyond traditional analysis, raw multichannel electrophysiological recordings were Fast-Fourier transformed and analysed by means of the “coherence measure” (Marple, 1987). By definition, the coherence of two waveforms is a quantitative index characterising their similarity in the frequency domain. As a consequence, the coherence is a function of the frequency and it ranges from 0 (i.e., totally noncoherent waveforms) to 1. In particular, two signals x(t) and y(t) are fully coherent at a given frequency when their phase shift at that frequency is constant in any time subinterval within an observation time window, and the amplitudes of the components at that frequency have a constant ratio. Therefore the coherence between two signals x(t) and y(t) can be calculated through the numerical estimation of the cross spectral density (i.e., Sxy(f)), and normalised by the power spectral density of both waveforms (i.e. Sxx(f), Syy(f) – see Papoulis, 1991) as indicated below:

γ2 ð f Þ =

P

P

P

P

Syx ð f Þd Sxy ð f Þ Sxx ð f Þd Syy ð f Þ

;

ð2Þ

where the average is performed over data blocks of nonoverlapping time intervals. For each frequency, γ2(f) is maximal if a constant phase between x(t) and y(t) exists, provided that the ratio between the amplitudes of the two signals is constant in the frequency domain. We envisage an interesting application of the coherence measure for the processing of multichannel electrophysiological data, as it can be considered a measure of causality between two correlated waveforms: if γ2(f) = 1, all the power content in one signal is due to that of the other one (i.e., indicating a full and complete correlation between x(t) and y(t) and thus the absence of any uncorrelated noise component); on the other hand, γ2(f) = 0 would imply that no feature characterising one signal is linked to those found in the other one. The coherence function indicates how much of the response energy is correlated to the stimulus energy. If there is another signal present in the response, either from excessive noise or from another signal, the quality of the network response measurement is poor. The coherence function can be used to identify both excessive noise and causality, that is, identify which of the multiple signal sources are contributing to the response signal. A 0 for a given frequency line indicates no correlation between the response and the stimulus signal. A 1 for a given frequency line indicates that the response energy is 100% due to the stimulus signal; in other words, there is no interference at that frequency. If we just assume that x(t) represents the electrophysiological activity of a neuronal population detected by an individual microelectrode array, propagating through the excitable tissue and later detected by a far microelectrode as a signal y(t), on a first approximation we might decompose y(t) into two terms: the first due to x(t) (i.e., the propagating signal) attenuated and delayed by some “effective transfer function” h(t), and the second, an intrinsic local electrophysiological activity n(t), unrelated to x(t) (i.e. the noise component). By largely

simplifying the complex nonlinear dynamics of a propagating electrophysiological signal, we might describe y(t) in the frequency domain as follows: Yðf Þ = Xðf ÞHðf Þ + Nðf Þ;

ð3Þ

where X(f), H(f), and N(f) are the Fourier transforms of x(t), h(t), and n(t), respectively. In the context of such a “toy-example”, the coherence analysis basically constitutes a measure of how much energy in y(t) is directly related to x(t), for each frequency. Actually, as reported by Eq. (4),  2

γ ðfÞ =

P

Sxxd H

2

P

Sxxd jHj2 P P P P 2 = P 2 Sxxd jHj2 + jNj2 Sxx Sxxd jHj + jNj

ð4Þ

the coherence is always less than 1, being maximal when there is no “noise” component. To estimate if the electrodes of the array picked up electrophysiological signals by long distance field effect we calculated the cumulant density function. It is a statistical parameter providing a measure of the linear dependence between two signals and is calculated as the inverse Fourier transform of the cross spectrum of the signals. For a description of the function and its use in time series data, see Halliday and Rosenberg (1999).

Acknowledgments The work was supported by the Universities of Copenhagen and Genova, by the National Research Council of Italy – targeted project “Biotechnology”, and by the European Commission (contract BIO4-97-2307). The authors are grateful to Dr. M. Koudelka-Hep of the Institute of Microtechnology, University of Neuchâtel, for kindly providing the threedimensional MEAs and to Mark Schram Christensen and Tue Hvass Petersen, Department of Exercise and Sport Sciences, University of Copenhagen for suggesting and helping with the cumulant density plots.

REFERENCES

Abegg, M.H., Savic, N., Ehrengruber, M.U., McKinney, R.A., Gähwiler, B.H., 2004. Epileptiform activity in rat hippocampus strengthens excitatory synapses. J. Physiol. 15 (554), 439–448. Bains, J.S., Longacher, J.M., Staley, K.J., 1999. Reciprocal interactions between CA3 network activity and strength of recurrent collateral synapses. Nat. Neurosci. 2, 720–726. Berdondini, L., Massobrio, P., Chiappalone, M., Tedesco, M., Imfeld, K., Maccione, A., Gandolfo, M., Koudelka-Hep, M., Martinoia, S., 2009. Extracellular recordings from locally dense microelectrode arrays coupled to dissociated cortical cultures. J. Neurosci. Methods 177 (2), 386–396. Bove, M., Grattarola, M., Martinoia, S., 1996. Coupling of network neurones to substrate planar microtransducers—a review. Neurobiology 20, 251–264. Chiappalone, M., Bove, M., Vato, A., Tedesco, M., Martinoia, S., 2006. Dissociated cortical networks show spontaneously

BR A IN RE S E A RCH 1 3 58 ( 20 1 0 ) 4 6 –5 3

correlated activity patterns during in vitro development. Brain Res. 1093 (1), 41–53. Engel, J., Bragin, A., Staba, R., Mody, I., 2009. High frequency oscillations: what is normal and what is not. Epilepsia 50 (4), 598–604. Gutnick, M.J., Connors, B.W., Prince, D.A., 1982. Mechanisms of neocortical epileptogenesis in vitro. J. Neurophysiol. 48 (6), 1321–1335. Gutnick, M.J., Wadman, W.J., 1986. Intrinsic neuronal connectivity in neocortical brain slices as revealed by non-uniform propagation of paroxysmal discharges. Soc Neurosci Abstr. 16, 349. Halliday, D.M., Rosenberg, J.R., 1999. Time and frequency analysis of spike train and time series data. In: Windhorst, Uwe, Johansson, Håkan (Eds.), Modern techniques in neuroscience research. Springer Verlag, pp. 503–543. Heuschkel, M.O., Fejtl, M., Raggenbass, M., Bertrand, D., Renaud, P., 2002. A three-dimensional multi-electrode array for multi-site stimulation and recording in acute brain slices. J. Neurosci. Methods 114 (2), 135–148. Holsheimer, J., Lopes da Silva, F.H., 1989. Propagation velocity of epileptiform activity in the hippocampus. Exp. Brain Res. 77, 69–78. Hu, B., Karnup, S., Zhou, L., Stelzer, A., 2005. Reversal of hippocampal LTP by spontaneous seizure-like activity: role of group I mGluR and cell depolarization. J. Neurophysiol. 93 (1), 316–336. Jahnsen, H., Kristensen, B.W., Thiébaud, P., Noraberg, J., Jakobsen, B., Bove, M., Martinoia, S., Koudelka-Hep, M., Grattarola, M., Zimmer, J., 1999. Coupling of organotypic brain slice cultures to silicon-based array of electrodes. J. Neurosci. Methods 18, 160–172. Jones, J., Stubblefield, E.A., Benke, T.A., Staley, K.J., 2007. Desynchronization of glutamate release prolongs synchronous CA3 network activity. J. Neurophysiol. 97 (5), 3812–3818. Knowles, W.D., Traub, R.D., Strowbridge, B.W., 1987. The initiation and spread of epileptiform bursts in the in vitro hippocampal slice. Neuroscience 21 (2), 441–455. Köhling, R., Melani, R., Koch, U., Speckmann, E.J., Koudelka-Hep, M., Thiébaud, P., Balestrino, M., 2005. Detection of electrophysiological indicators of neurotoxicity in human and rat brain slices by a three-dimensional microelectrode array. Altern. Lab. Anim. 33 (6), 579–589. Lopantsev, V., Both, M., Draguhn, A., 2009. Rapid plasticity at inhibitory and excitatory synapses in the hippocampus induced by ictal epileptiform discharges. Eur. J. Neurosci. 29 (6), 1153–1164. Lothman, E.W., Bertram, E.H., Stringer, J.L., 1991. Functional anatomy of hippocampal seizures. Prog. Neurobiol. 37 (1), 1–82.

53

Marple, S.L., 1987. Digital spectral analysis with application: from Prentice Hall PTR. Simon & Schuster Company Englewood Cliffs, New Jersey. 07632. Menendez de la Prida, L., Pozo, M.A., 2002. Excitatory and inhibitory control of epileptiform discharges in combined hippocampal/entorhinal cortical slices. Brain Res. 940, 27–35. Miles, R., Traub, R.D., Wong, R.K., 1988. Spread of synchronous firing in longitudinal slices from the CA3 region of the hippocampus. J. Neurophysiol. 60 (4), 1481–1496. Orman, R., Von Gizycki, H., Lytton, W.W., Stewart, M., 2008. Local axon collaterals of area CA1 support spread of epileptiform discharges within CA1, but propagation is unidirectional. Hippocampus 18 (10), 1021–1033. Pallud, J., Devaux, B., Depaulis, A., 2008. Changes in spontaneous epileptic activity after selective intrahippocampal transection in a model of chronic mesial temporal lobe epilepsy Neurochirurgie 54 (3), 135–140. Papoulis, A., 1991. Probability, Random Variables and Stochastic Processes. McGraw-Hill Higher Education. Pare, D., DeCurtis, M., Llinas, R., 1992. Role of the hippocampal-entorhinal loop in temporal lobe epilepsy: extra- and intracellular study in the isolated guinea pig brain in vitro. J. Neurosci. 12 (5), 1867–1881. Poolos, N.P., Mauk, M.D., Kocsis, J.D., 1987. Activity-evoked increases in extracellular potassium modulate presynaptic excitability in the CA1 region of the hippocampus. J. Neurophysiol. 58 (2), 404–416. Poulsen, F.R., Jahnsen, H., Blaabjerg, M., Zimmer, J., 2002. Pilocarpine-induced seizure-like activity with increased BNDF and neuropeptide Y expression in organotypic hippocampal slice cultures. Brain Res. 950 (1–2), 103–118. Salazar, P., Tapia, R., Rogawski, M.A., 2003. Effects of neurosteroids on epileptiform activity induced by picrotoxin and 4-aminopyridine in the rat hippocampal slice. Epilepsy Res. 55, 71–82. Staley, K.J., Longacher, M., Bains, J.S., Yee, A., 1998. Presynaptic modulation of CA3 network activity. Nat. Neurosci. 1, 201–209. Thiébaud, J.P., Beuret, C., Koudelka-Hep, M., Bove, M., Martinoia, S., Grattarola, M., Jahnsen, H., Rebaudo, R., Balestrino, M., Zimmer, J., Dupont, Y., 1999. Biosens Bioelectr. 14, 61–65. Traub, R.D., Miles, R., Jefferys, J.G., 1993. Synaptic and intrinsic conductances shape picrotoxin-induced synchronized after-discharges in the guinea-pig hippocampal slice. J. Physiol. 461, 525–547. Vajda, I., van Pelt, J., Wolters, P., Chiappalone, M., Martinoia, S., van Someren, E., van Ooyen, A., 2008. Low-frequency stimulation induces stable transitions in stereotypical activity in cortical networks. Biophys. J. 94 (12), 5028–5039. www.neurospec.org accessed on Aug 6, 2010.