S Jacquir
email: sjacquir@u-bourgogne.fr

S Binczak

B Xu

G Laurent

D Vandroux

P Athias

J M Bilbault

INVESTIGATION OF MICRO SPIRAL WAVES AT CELLULAR LEVEL USING A MICROELECTRODE

Keywords: Spiral wave, MicroElectrode Array (MEA) Technology, Cardiac cells, Fibrillation

During cardiac arrhythmia, functional reentries may take the form of spiral waves. The purpose of this study was to induce spiral waves by an electrical stimulation of cultured neonatal 1 rat cardiomyocytes using a microelectrode arrays technology. In basal conditions, cardiac muscle cells in monolayer culture displayed a planar wavefront propagation. External electrical impulse trains induced severe arrhythmia and spiral waves appeared. This in vitro generation of spiral wave opens a new way to test the anti-arrhythmic drugs and for strategies at microscopically scale.

Introduction

Despite abundant research, the mechanisms of cardiac arrhythmias are still poorly understood. Many studies of cardiac arrhythmia focused on the spatiotemporal propagation of the electrical waves throughout the myocardium [START_REF] Wang | Temporal relations of atrial fibrillation and congestive heart failure and their joint influence on mortality: The Framingham Heart Study[END_REF]Winfree, 1994;[START_REF] Agladze | Rotating spiral waves created by geometry[END_REF][START_REF] Gray | Mechanisms of cardiac fibrillation[END_REF][START_REF] Gray | Spatial and temporal organization during cardiac fibrillation[END_REF][START_REF] Everett | Structural atrial remodeling alters the substrate and spatiotemporal organization of atrial fibrillation: a comparison in canine models of structural and electrical atrial remodeling[END_REF]. In particular, the formation of spiral waves (SW) has been suspected to be responsible for fibrillation phenomena. Experimental evidence that functional reentrant SW are present in cardiac tissue was given by some previous reports [START_REF] Allessie | Circus movement in rabbit atrial muscle as a mechanism of tachycardia[END_REF][START_REF] Davidenko | Sustained vortex-like waves in normal isolated ventricular muscle[END_REF][START_REF] Davidenko | Stationary and drifting spiral waves of excitation in isolated cardiac muscle[END_REF][START_REF] Pertsov | Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle[END_REF]. Recent in vitro studies have suggested that maintenance of arrhythmia may depend on the periodic activity of a small number of rotors or spiral waves [START_REF] Jalife | [END_REF]Laurent et al, 2008a,b]. These SW activate the tissue substrate (atria or ventricles) at high frequencies and result in fibrillation behavior. However, the analysis and understanding of the SW appearance are very difficult for several reasons. The heart is anatomically complex, composed of different tissues and functionally instable. In particular, it is hard to maintain the heart in a stationary state (anatomical position, stable rhythm) for a long period. The whole heart imaging techniques based on the use of fluorescent dyes for the visualization of the cardiac activation waves are quite invasive, do not permit long duration observation periods and can affect tissue cells and functions. In addition, applied to heart cell cultures, the observation of the electrical activation spread with voltage-sensitive dyes is suspected to be rather cytotoxic and limited by its poor spatial resolution [START_REF] Fast | Cardiac tissue geometry as a determinant of unidirectional conduction block: assessment of microscopic excitation spread by optical mapping in patterned cell cultures and in a computer model[END_REF][START_REF] Lim | Spiral Wave Attachment to Millimeter-Sized Obstacles[END_REF][START_REF] Koura | Longitudinal to Transverse With Increasing Age Optical Mapping: Preferential Direction of Conduction Block Changes From Anisotropic Conduction Properties in Canine Atria Analyzed by High-Resolution[END_REF].

Multi-electrodes investigation is an alternative method that is devoid of the dye toxicity, but the drawback of this approach is limited by its rather rough spatial resolution in the case of the whole heart. To overcome these in vivo heart studies limitations, primary cultures of cardiac muscle cells have been developed [START_REF] Athias | Development of cardiac physiopathological models from cultured cardiomyocytes[END_REF]. This cellular preparation gives access to repeated, long term recording duration periods and to easy comparison of experimental data with those of analytical and/or computational studies. Monolayer cultures of cardiac myocytes (CM) represent thus a promising experimental model for the study of cardiac electrophysiology and arrhythmogenesis. It can be used to study the elementary phenomenon at the basis of the activation spread within cardiac muscle and at the origin of the lethal rhythm troubles, such as myocardial fibrillation, reentry with a particular interest with reentrant (spiral) waves. Extracellular recordings of electrical activity with substrateintegrated microelectrode arrays (MEA) enable non-invasive and non toxic long-term monitoring of contractile multicellular cardiac preparations [START_REF] Pillekamp | Impulse propagation in late-stage embryonic and neonatal murine ventricular slices[END_REF][START_REF] Stett | Biological application of microelectrode arrays in drug discovery and basic research[END_REF][START_REF] Banach | Develpement of electrical activity in cardiac myocyte aggregates derived from mouse embryonic stem cells[END_REF][START_REF] Hescheler | Determination of electrical properties of ES cell-derived cardiomyocytes using MEAs[END_REF]. Moreover, the MEA technology has a better spatial resolution than the fluorescence mapping procedure and is a less invasive technique than the conventional electrophysiological methods, i.e., intracellular or patch clamp technique.

In our precedent works, we have validated the use of the MEA technology for the study of the impulse propagation pattern in cardiac cell culture in the basal conditions [START_REF] Athias | Excitation spread in cardiac myocyte cultures using paired microelectrode and microelectrode array recordings[END_REF]. The purpose of the present study was to explore the basal mechanisms of cardiac arrhythmogenesis, and the possible occurrence of elementary SW at the cellular scale using neonatal rat cardiomyocytes in monolayer culture on microelectrode arrays device (MEA). Our preliminary results showed that it was possible to generate arrhythmias and SW by submitting the cell monolayer to external electrical impulse trains [Laurent et al, 2008c;[START_REF] Athias | In vitro simulation of spiral waves in cardiomyocyte networks using multi-electrode array technology[END_REF]Jacquir et al, 2009a,b], in agreement with previous reports suggesting that rapid pacing may be able to alter cardiac conduction [START_REF] Kondratyev | Dynamic changes of cardiac conduction during rapid pacing[END_REF]. Studying SW at a cellular scale may lead to a better understanding of the way by which these microscopic rotors may be able to evolute and to stabilize in the myocardial tissue substrate. It also may be useful for the development of innovative approaches for prevention, diagnosis, and treatment of cardiac arrhythmias.

This paper is organized as follows: Section (2) describes the CM culture preparation, the multielectrode array recording procedure and the stimulus generator device. Section (3) presents the experimental results and their analysis by using nonlinear dynamical system techniques such as bifurcation diagram and Poincaré maps [START_REF] Garfinkel | Quasiperiodicity and Chaos in Cardiac Fibrillation[END_REF][START_REF] Beuter | Nonlinear Dynamics in Physiology and Medecine[END_REF]. A discussion and conclusion section finishes this paper.

Materials and Methods

Cardiomyocyte culture preparation

One of the major requirement of the cell culture techniques is that all stages of the preparation and the growth must be done in strictly sterile conditions. Neonatal myocytes were prepared from 1 to 4 daysold Wistar rats by trypsin-based enzymatic dispersion as described previously [START_REF] Athias | Electrophysiological studies on heart cells in culture", The heart cells in culture[END_REF][START_REF] Grynberg | Primary rat cardiac cell culture: diet of the mother rats as a determinant parameter of cardiomyoblast production from neonates[END_REF]. The cell suspension was preplated twice in Ham's F10 medium supplemented with fetal calf serum (FCS) and penicillin/streptomycin (100 U/ml) in order to increase cardiomyocyte (CM) proportion. Cardiomyocyte-rich cultures (> 90%) were seeded at a final density of 10 5 cells per cm 2 in supplemented Ham's F10 medium. Cultures were incubated in a humidified incubator (95% air, 5% CO 2 at 37 • C) and were used after 4-5 days of growth, a step at which confluent and spontaneously beating cell monolayers were obtained. Figure 1 shows a picture of an isolated CM obtained according to this cell culture procedure. Data are acquired and analyzed with a customized platform programmed with LABVIEW (National Instruments) and MATLAB (Mathworks) in order to provide two-dimensional electrophysiological maps derived from these multisite FP recordings (Computer (D) on Fig. 3).

Multielectrode array recordings

Results

Each of the 60 microelectrodes embedded in the bottom of MEA dishes allow the long-term recordings of the extracellular electrical activity, that is, field potentials (FP), which reflects the external electrical signal resulting from CM membrane potential changes during the course of each action potential. Recorded data are classified either as normal or as abnormal signals using the continuous wavelet transform tools [Jacquir et al, 2009c]. Figure 4(a) displays an example of data resulting from this selection routine.

Propagation of field potential in basal conditions

In first, field potential signals are recorded on basal conditions, which means that cells are not stressed and are in nutritive bath. In this case, the analysis of the spontaneous FP spikes (Fig. 4(b)) indicates that the mean frequency in the case of data presented in Fig. 4(a) corresponds to about 90 beats per minute. In addition, a moderate variability of the FP frequency between electrodes and between each period is observed, which may be due to a remodeling phenomenon of gap junctions [START_REF] Rohr | Role of gap junctions in the propagation of the cardiac action potential[END_REF], spontaneous fluctuations of the ionic channel function, or random changes in the propagation path.

This last hypothesis appears consistent with previous propagation data from intracellular recordings of the action potentials [START_REF] Athias | Excitation spread in cardiac myocyte cultures using paired microelectrode and microelectrode array recordings[END_REF]. Observing the distribution of the mean period of the FP (Fig. 5), one can conclude that the MEA system is relatively stable and robust.

The local activation time (LAT) corresponds to the FP spike appearance on each electrode in a temporal scale (see an example of FP time serie on Fig. 4(b)). Thus, the LAT is determined for each FP spike for each electrode. Then a ranking is established by ordering FP spike appearance on the 60 electrodes between each period, which leads to an activation map and enables to display the propagation path followed by the FP spikes during each period. The consecutive period to period activation maps corresponding to the signals shown in Fig. 4(a) are reported in Fig. 6. The number inserted in each colored panel corresponds to the rank of the FP spike activation (refer to Fig. 6a). From the global view of these activation maps, it can be concluded that the FP spikes propagate following a quasi-straight path, materialized by the white arrows in Figs. 6(a to h). However, the examination of the individual rank of order of FP spike activation reveals that the FP spike propagation pathway fluctuates at each period. This might mean that FP cell-to-cell propagation is not trivial, despite the fact that the overall propagation throughout the multicellular sheet is planar.

These field potential mappings confirm thus that the cultured cardiomyocytes display highly synchronous electrical activity and that the FP-derived parameters remain stable and homogeneous, as already described for conventional endocellular recordings [START_REF] Tissier | Specific electromechanical responses of cardiomyocytes to individual and combined components of ischemia[END_REF].

Field potential analysis in arrhythmia after electrical stimulation

The electrical stimulation of cultured cell stimulation requires electrical pulses with very low amplitude and a high signal to noise ratio. The stimulus generator delivers high quality pulse amplitude ranging between in 10 µV to 1 mV, with accurately adjustable frequency and duty cycle. In this case, cardiomyocytes are electrically stressed by external electrical shocks consisting in a stimulation impulse trains (burst of 200 µV at 100 Hz during 5 minutes) which are applied at one microelectrode M 1 located at the edge of the MEA (see Fig. 2(a)). The stimulation frequency is chosen purposely higher than the FP spike frequency because in order to disrupt the CM activity. This stimulation protocol causes alterations in CM electrical activity, that is depicted by the recording of irregular and disordered FP. The evolution of the FP period vs. time is given in Fig. 7 expressing a bifurcation scenario.

At first, the cells display a regular rhythm corresponding to basal conditions with a FP spikes period T = 0.667 s (cf sec.(3.1)). The stimulation is then applied at the microelectrode M 1 at t = 0 and during 5 minutes. The cells become unstable and express a chaotic state one hour after stimulation, as illustrated by event (A) on Fig. 7. Thereafter, a period doubling phenomenon is observed (event (B) for t = 3h on Fig. 7), then a transitory reversal to a stable state takes place (event (C) at t = 4h on Fig. 7), and finally a reappraisal of an unstable and disordered state can be observed.

It is well known that any system which makes a transition from order to disorder through the perioddoubling phase, whatever the exact functional nature of these systems, displays common properties. These properties found in dynamic systems can be investigated using a Poincaré map tool. In contrast to random behavior, deterministic behavior means that the present state of a system is determined by its previous states. A simple test for such a relationship is a Poincaré plot, in which each successive value of a system variable is plotted against its previous value. For a purely random system, the distribution of points on a Poincaré plot is formless, whereas for a system with significant nonrandom elements, the points often form a distinct structure. Therefore, We constructed Poincaré plots of interactivation intervals (FP period P n+1 vs. P n ). Before stimulation, in basal conditions (data of Fig. 4(a)), only stable fixed points are found in Poincaré map for each individual electrode, the number n of periods being the same for all electrodes. Data points (cross symbol in Fig. 8) can be considered as stable attractors and describe a periodic cycle in the Poincaré section. In this case, the FP frequency is regular and stable in the considered period of time.

During atrial, ventricular tachycardia (or bradycardia), interactivation intervals (FP periods) are nearly constant, but during fibrillation they become highly irregular, as shown in Fig. 7. Analyzing the time series of the FP at event (A), that is one hour after the stimulation, the arrhythmic periods indicate that the rate is irregular as compared to basal conditions (at t = 0 on Fig. 7). In this electrical shockinduced chaotic state (Fig. 9(a)), the number n of periods is different from one electrode to another and the number of attractors is different for each electrode. Attractors are not stable and move around the bissector (Fig. 9(b)). For the following events, the attractors move between two positions along the bissector which correspond to the period doubling phase (see Figs. 10(b) for event (B) of Fig. 7).

Note that this period doubling is a localized phenomenon in the CM culture. Four hours after stimu-lation, the CM spontaneous rhythm became normal again and stable (see event (C) in the bifurcation diagram (Fig. 7), the time series and the Poincaré map corresponding to this event are depicted in Fig. 11). However, CM did not stay in this state since they bifurcate afterwards again to a chaotic state (see t = 4.5h, t = 5h... in Fig. 7). These changes might mean that the cells are in a state of a sustained arrhythmia, but transitory switchs between the basal rhythm and unstable rhythms which may occur.

Our results are in accordance with [START_REF] Garfinkel | Quasiperiodicity and Chaos in Cardiac Fibrillation[END_REF], where the authors suggested that the fibrillation is a form of spatiotemporal chaos arising via a quasiperiodic transition. Our results suggest that this mechanism is present at a microscopic scale. The idea that multifrequency quasiperiodicity is inherently unstable and will degenerate into chaos was first suggested by Ruelle and Takens [START_REF] Ruelle | On the nature of turbulence[END_REF]]. The quasiperiodic scenario explains the origin of the ring lake structures seen in the Poincaré plots. The qualitative description of the functional behavior of our experimental model depicted by the Poincaré maps is confirmed using the activation maps during a period of regular rhythm and during an arrhythmic state. Activation mapping during regular rhythm reveals a planar propagation wavefront (see Fig. 6). In contrast, the activation maps reveal the occurrence of relatively stable counter-rotating micro spiral waves during a sustained induced arrhythmia episode induced by external electrical stimulation. For the visualization, a real time movie is realized and some snapshots corresponding to the evolution of one of the displayed SW at different moments are given in Fig. 12. This is an example of SW obtained from the data depicted on Fig. 9. In this case, an average of 3 ± 1 SW is observed within the surface explored by the microelectrodes array, that is 2.5 mm 2 ; due to their smallness, they are rather micro SW, and they could be a sign of a chaotic state of the system. These rotation waves appear to be random and could be submitted to period-to-period fluctuations. They are able to translocate, since they can move within or away the recording area. They have a mean radius of 400 ± 100 µm and a mean angular velocity of 300 ± 50 rotations per minute. Unstable reentrant and colliding wavefronts are also observed during an arrhythmic episode.

Discussion and conclusion

Concerning the origin of the myocardial fibrillation phenomena, and in opposition to the multiple wavelets theory [START_REF] Moe | A computer model of AF[END_REF], the SW model implies the existence of localized and stable high frequency areas. Primary cultures of cardiac cells on MEA constitute an emerging experimental model for studying cardiac electrophysiology and arrhythmia at the cellular scale and in highly controllable conditions. In addition, this model system permits to develop electrical shock-induced simulation of cardiac arrhythmia and the experimental data collected with this model may be compared with those of analytical and/or computational studies. Extracellular recordings of electrical activity with substrate-integrated MEA enable indeed true non-cytotoxic and non-invasive long-duration monitoring of spontaneously contracting sheets of cultured cardiac muscle cells. This method features a better spatial and time resolution than the optical mapping techniques and is much less hurtful than the conventional endocellular electrophysiological technique. The present data from in vitro MEA exploration confirm that monolayer cultures of cardiac muscle cells beat at very stable and regular rate and that this spontaneous electromechanical activity propagates along linear pathways throughout the cellular sheet. Laterally-imposed low-voltage electrical impulse trains cause highly disordered electrical activity and severe irregularities of the endogenous rhythm and of the propagation process, mimicking myocardial fibrillation. During these experimentally-induced arrhythmic episodes, the unprecedented observation of micro SW has been realized. They can be accurately quantified in terms of size, rotational speed, duration and displacement. These data could be related, for mechanistic and understanding purpose, to the other FP (cellular ECG) parameters, i.e. duration, rising and falling deflection speed, deflection polarity and local propagation speed. This novel in vitro model of experimentally-induced sustained arrhythmias, mimicking fibrillation patterns, may be helpful in the comprehension of cardiac arrhythmogenesis in clinical situations and may be useful to provide an experimental basis of new treatments and prevention strategies. Therefore, although it should be take into account the limitations of the model, related to its simplified 2D geometry and the absence of neural and hormonal influences, the MEA technique applied to monolayer cultures cardiac muscle cells is a new, promising and controlled experimental model that will be helpful for further study on the cellular fundamental aspects of cardiac fibrillation and defibrillation, specially for the investigation of the nonlinear inherent mechanisms in the fibrillation phenomena. A next interesting study would be to perform a mathematical modeling of the cardiac cell activities using experimental data from the MEA. Fig. 1. Cardiac myocyte of new born rat [START_REF] Athias | Development of cardiac physiopathological models from cultured cardiomyocytes[END_REF]. The blue color shows the nucleus and the red color shows the contractile sarcomeric apparatus.

  CM were grown on multi-electrode arrays allowing non-invasive synchronous multifocal field potential (FP) recordings. MEA consists of 60 substrate-integrated microelectrode arrays (8 × 8 matrix, 30 µm electrode diameter, 200 µm inter-electrode distance). Figures2(a,b,c) show the MEA supporting a cardiac cell monolayer culture used in our experiments. The MEAs give access to the cellular electrocardiogram (ECG), determined by the transmembraneous electrical changes during periodic action potentials in the cardiac muscle cell in contact with each surface microelectrode. MEA allows thus the long term, non-traumatic recording from individual and together with the simultaneous, parallel monitoring of tens of cells in the same MEA dish in an easily controlled environment. This approach permits to evaluate the multifactorial influence -including signal propagation and spatial inhomogeneity -of experimental factors such as drugs and physicochemical stress. The complete experimental setup is shown in Figure3. The 60 signals originating from the MEA are acquired with a maximum sampling rate of 50 kHz/channel with a 12 bits resolution. The amplification device containing the MEA ((A) on Fig.3) is placed inside a Faraday enclosure ((B) on Fig.3) to reduce electrical noise and interferences. A separate device ((C) on Fig.3) controls and maintains temperature at 37 • C.

Fig. 2 .

 2 Fig. 2. MEA dish with cardiac cells of newborn rats. (a) is a global view of the MEA dish, (b)

Fig. 3 .

 3 Fig. 3. Setup allowing field potential recordings from cardiac muscle cells in monolayer culture.

Fig. 4 .

 4 Fig. 4. (a) Field potential time series in the basal conditions (correct signal in blue, rejected signals in

Fig. 5 .

 5 Fig. 5. Distribution of the mean periods of the field potentials (FP) train corresponding to data

Fig. 6 .

 6 Fig. 6. Local activation maps of the field potentials. The white arrow indicates the direction of FP

Fig. 7 .

 7 Fig. 7. Bifurcation diagram of the field potential periods P for the time series given by the 60

Fig. 8 .

 8 Fig. 8. Poincaré map of the FP periods (P n+1 = f (P n )) in basal conditions (data presented in Fig.

Fig. 9 .

 9 Fig.9. Example of field potentials in a chaotic phase (event (A) in the bifurcation diagram (Fig.7)).

Fig. 10 .

 10 Fig. 10. Example of field potentials in a period doubling phase (event (B) in the bifurcation diagram

Fig. 11 .

 11 Fig. 11. Example of field potentials in a stable rhythm phase (event (C) in the bifurcation diagram

Fig. 12 .

 12 Fig. 12. Visualization of a relatively stable counter-rotating spiral wave during a sustained induced arrhythmia episode induced by external electrical stimulation (the letters ((a) -→ (b) -→ (c) -→ (d) -→ (e) -→ ( f )) indicate the clockwise rotation). Experimental data were smoothed using a cubic

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