Experimental Study of Arrhythmia due to Mild Therapeutic Hypothermia afterResuscitation of Cardiac Arrest

B Xu1, O Pont1, G Laurent2, S Jacquir2, S Binczak2, H Yahia1

1Géostat, INRIA Bordeaux Sud-Ouest, Talence, France2CNRS UMR, Université de Bourgogne, Dijon France

Abstract

The therapeutic hypothermia (under 34 ˝C´ 32 ˝C dur-ing 12 ´ 24h) can help reduce cerebral oxygen demandand improve neurological outcomes after the cardiac ar-rest. However it can have many adverse effects. The car-diac arrhythmia generation represents an important partamong these adverse effects. In order to study the arrhyth-mia generation after therapeutic hypothermia, an exper-imental cardiomyocytes model is used. The experimentsshowed that at 35 ˝C, the acquired extracellular poten-tial of the culture are characterized by period-doublingphenomenon. Spiral waves are observed as well in thiscase. The results suggested that the global dynamics oftherapeutic hypothermia after cardiac arrest can be rep-resented by a Pitchfork bifurcation, which could explainthe different ratio of arrhythmia among the adverse effectsafter this therapy. A variable speed of cooling / rewarm-ing, especially when passing 35 ˝C, would help reduce thepost-hypothermia arrhythmia.

1. Introduction

One of the important challenges after cardiac arrest(CA) is the neurological damage of the brain. In caseof resuscitation after CA, the brain suffers the ischemiaand the inflammation from reperfusion [1]. Currently, theonly therapy available is the mild therapeutic hypother-mia (MTH) : put the patient under 34 ˝C „ 32 ˝C during12 ´ 24 hours [2–4]. In fact, the use of therapeutic hy-pothermia following cardiac arrest was reported in the late1950s [5, 6]. The results showed some benefits but uncer-tain. It was also clinically difficult to control the intervalbetween arrest and cooling which is very important. There-fore, hypothermia for cardiac arrest has waned for years.Over the past few years, the therapeutic hypothermia beganto redraw attentions of researchers, clinicians etc.. In 2003,The American Heart Association (AHA) endorsed the useof therapeutic hypothermia following cardiac arrest. Eventhough that MTH has been shown to increase the hospital

survival rate, it has many adverse effects, among which thecardiac arrhythmia generation represents an important part(up to 34%) [7, 8]. Cardiac culture in vitro provides a bet-ter spatial resolution (down to cellular level) than studiesin vivo, which could bring some insights of the mechanismof post-hypothermia arrhythmia (PHA) generation.

2. Materials and methods

Monolayer cardiac culture is prepared with cardiomy-ocytes (CM) from new-born rat (1 „ 4 days) directly on amulti-electrodes array (MEA), a system allowing real-timerecording the extracellular field potential (EFP) of the CMculture, (details of culture preparing in [9]). The CM cul-tures have the potential to reproduce in vitro a wide rangeof pathological conditions such as ischemia reperfusion,the radical stress or thermal shock, and any combinationof these conditions [9]. The EFP signals correspond tothe combination of 1st or 2nd order derivatives of actionpotential (AP). Their peaks corresponds to AP depolariza-tion (Figure 1, Right). This relationship allows to interpret-ing indirectly the results at “action potential propagation”level.

Figure 1: Left :EFP in basal conditions. Every panel cor-responding to an acquisition, placed according to their po-sition on the MEA. Right : relationship between the EFPand the action potential.

The acquired signals are then analyzed with two meth-ods from nonlinear dynamics theory : phase space recon-struction and detrended fluctuation analysis.

Phase space reconstruction The basic principle of

ISSN 2325-8861 Computing in Cardiology 2013; 40:1119-1122.1119

method phase space reconstruction is to map the dynam-ical evolution of a time series into a geometrical objectembedded in an abstract representation space. This objectrepresents all possible internal states (phases) of the systemthat produced the time series. Furthermore, each dynami-cal state corresponds to a unique point, so that the recon-structed space shares the same topological properties as theoriginal phase space of the system dynamics [10]. Mathe-matically, under the approach phase space reconstruction,the system can be represented as :

~Xpτ,mq “ rxptq, xpt` τq, . . . , xpt` τpm´ 1qqs, (1)

where ~X denotes the system states and is a function ofτ and m, xptq is the time series (t “ 0, 1, 2, . . .), m is theembedding dimension and τ is the time lag. m is estimatedby the method False Nearest Neighbor (FNN) [11], whichintends to find the minimal embedding dimension. As fortime lag τ , a method based on autocorrelation function isused to find optimal values (largest one so that the resultingcoordinates for m are relatively independent) [12].

Detrended fluctuation analysis Detrended fluctuationanalysis is a method for determining the statistical self-affinity of a signal. It unmasks long-memory processes(revealing the extent of long-range correlations) in time se-ries [13]. It is more robust and less prone to artefacts than asimple period analysis. A time series xptq has N samples.It is firstly integrated, then the obtained new time seriesyptq is divided into boxes of equal length n. A least squaresline is performed for every detrended signal of length n inorder to fit to the data. The y coordinate of the straightline segments is denoted by ynptq, the local trend. Next,the integrated time series yptq is detrended by subtractingynptq, in each box. The root-mean-square fluctuation ofthis integrated and detrended time series is calculated by

F pnq “

«

1

N

Nÿ

t“1

ryptq ´ ynptqs2

ff

12

9 nα. (2)

This computation is repeated over all time scales (boxsizes) to characterize the relationship between F pnq, theaverage fluctuation, and the box size, n. Using log-logplot, a linear relationship would indicates the presence ofpower law (fractal) scaling, where the fluctuations can becharacterized by the slope of the line relating logF pnq tolog n. In other words, this scaling exponent α captures thedynamical complexity of activation signals.

3. Results

In order to simulate the MTH conditions, the experi-ments consist of two parts : culture cooling (37 ˝C Ñ

30 ˝C) and re-warming (30 ˝C Ñ 37 ˝C). Typical EFP sig-nals can be found in Figure 2. When the temperature of the

culture is decreasing, the periods of EFP signals increasein general (Figure 2 Right). Apart from T ‰ 35 ˝C, theirperiods are relatively stable. The slight variation of theseperiods could be the consequence of junction-gap remod-eling [14]. From 37 ˝C to 30 ˝C, the period is increasedfrom about 0.5 s to 1.58 s. Two period values are shownat 35 ˝C : the lower value is almost exactly the same asthe one at 37 ˝C, higher value is roughly the double (Fig-ure 2 Right). From a point view of nonlinear dynamics, thisperiod-doubling is a marker when a system is conducted tostat “chaos” [15].

Figure 2: Left : comparison of typical single period EFPsignals at different temperatures. Right : periods digram,periods-doubling at T “ 35 ˝C, black points are periodsvalues, red ones are median vales of periods at correspond-ing temperature.

These signals can be also reconstructed as an activationmap, which gives a tow-dimensional view of the signalsdynamics in the culture. When T ‰ 35 ˝C, the dynamicsof the signals is in form of plane wave propagation (Fig-ure 3). At 35 ˝C, spiral waves are observed in the activationmap which is commonly considered as a sign of cardiac ar-rhythmia (Figure 4).

Figure 3: Plane wave propagation when T ‰ 35 ˝C, fromtime (a) to (f). White arrows indicate the propagation di-rection of plane wave

From the reconstructed phase space, doubling-trajectoriesand rare tripling-trajectories are found. It implies that thegeneral dynamics of MTH could be presented as a pitch-fork bifurcation, which could explain exactly the doubling-

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Figure 4: Spiral wave propagation with clockwise rota-tion at T “ 35 ˝C, from time (a) to (f). (Images filteredfrom the original ones in order to better represent the spi-ral wave.)

trajectories and tripling-trajectories phenomena. These re-sults at cellular level agreed with other clinical studies onMTH.

Figure 5: mean embedding dimension m vs. temperature

As shown in Figure 5, the mean embedding dimensionm initially decreases when temperature drops from 37 ˝Cto 35 ˝C. It increases then slowly up to 3.52 at 31 ˝C toanother transition point. The m increases abruptly after31 ˝C. When rewarming, the temperature returns to 37 ˝Cand m recovers its original value. This reinforces the evi-dence that a temperature around 35 ˝C contains a transitionpoint for the system. With the method DFA, a similar re-sult (Figure 6) could be obtained : Here, bimodality occurs

Figure 6: Detrended fluctuation analysis. α vs. tempera-ture. Black points are α values, red ones are main medianvales of α at corresponding temperature

at T « 35 ˝C again, further confirming it as a transitionpoint.

Attractors of trajectories in reconstructed phase spacesat different temperatures are presented in the followingFigure 7 : The trajectories in phase space have all been

Figure 7: Phase space reconstruction for typical signals atdifferent temperatures. Bifurcation / trifurcation at T «

35 ˝C. (Time lag unit: samples.)

well-formed. Apart from 35 ˝C, though the original signalsare different, the global forms of the attractors are similarwith a little variation.

Bifurcation at T « 35 ˝C also reveals in attractors them-selves. Even a rare trifurcation is found. Here arises ahypothesis : the phase transition consistent with a super-critical pitchfork bifurcation. The process could be repre-sented as in Figure 8. The bold black line denotes the sta-ble states of the system. In the dashed line, the system is inan unstable dynamic state, but it could sustainedly remainthere if quasistatic perturbations are not strong enough tomake it fall to the (dynamical) lower energy states. Thismakes that state a metastable state. From T “ 35 ˝C, thesystem enters the unstable region. For example, if the sys-tem follows the blue trajectory, it will cross twice stabilityline, which makes the period-doubling and so bifurcationin phase space will occur. If the system follows the red

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Figure 8: Illustration of Bifurcation or Trifurcation (typePitchfork) of hypothermia effect on EP.

trajectory, it will cross the stability line three times andexhibit trifurcation. Since in this region the transition be-tween stable and unstable states is fast and in most cases itis the unstable states which dominate the system dynamics,the metastable line is not always observed in practice.

4. Conclusions

In this study, the problem of arrhythmia generation af-ter MTH is studied with an experimental cardiomyocytesmodel. Here, results in vitro confirmed that arrhythmicphenomena happened around 35 ˝C, which agreed withclinical observations. In clinical trials, it is shown thatprotective hypothermia effects (below 35 ˝C) mitigate car-diac arrest. It needs also to remain above 32 ˝C: thresh-old of moderate hypothermia, leading to increased risk oforgan failure. The results suggested also that the wholeprocess of MTH consistents with supercritical pitchforkbifurcation, with the attractor dimension as order param-eter. This hypothesis can well explain the bifurcation phe-nomena observed in phase space. Depending the path thatthis process passes, the system can show either bifurcationof trajectories or trifurcation in rarer case. According tothe pitchfork bifurcation hypothesis, if the system followsthe metastable paths, it could thus avoid arrhythmogene-sis. Which means, the post-hypothermia arrhythmia couldbe avoided.

In practical hypothermia therapy, the cooling or re-warming is often under constant speed, the pitchfork bifur-cation hypothesis suggests that a variable speed would helpto reduce the rate of post-hypothermia arrhythmia. How-ever, with a faster speed passing 35 ˝C or a slower speed,it is still unclear. This needs a further study, which is oneof the objectives of an on-going project.

Acknowledgments

We acknowledge the Institute of Cardiovascular Re-search (Dijon, France) and the NVH Medicinal (Dr. DavidVANDROUX, Dijon, France) for our collaboration in the

experimental data acquisition.

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