Mechanical chest compressions with trapezoidal waveform improve haemodynamics during cardiac arrest

Mechanical chest compressions with trapezoidal waveform improve haemodynamics during cardiac arrest

Resuscitation 82 (2011) 213–218 Contents lists available at ScienceDirect Resuscitation journal homepage: www.elsevier.com/locate/resuscitation Exp...

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Resuscitation 82 (2011) 213–218

Contents lists available at ScienceDirect

Resuscitation journal homepage: www.elsevier.com/locate/resuscitation

Experimental paper

Mechanical chest compressions with trapezoidal waveform improve haemodynamics during cardiac arrest夽 Jo Kramer-Johansen a,b,∗ , Morten Pytte a,b , Ann-Elin Tomlinson a , Kjetil Sunde a,b , Elizabeth Dorph a,b , Jan Vegard H. Svendsen c , Morten Eriksen a , Tævje A. Strømme a , Lars Wik a,d a

Institute for Experimental Medical Research, Oslo University Hospital, Oslo, Norway Department of Anaesthesiology and Division of Prehospital Medicine, Oslo University Hospital, Oslo, Norway c Laerdal Medical, Stavanger, Norway d The National Competence Center for Emergency Medicine, Oslo University Hospital, Oslo, Norway b

a r t i c l e

i n f o

Article history: Received 18 June 2010 Received in revised form 15 September 2010 Accepted 4 October 2010 Keywords: Cardiopulmonary resuscitation Mechanical chest compression Swine Haemodynamics Cerebral blood flow Coronary perfusion pressure Compression waveform

a b s t r a c t Background: During manual chest compressions for cardiac arrest the waveforms of chest compressions are generally sinusoidal, whereas mechanical chest compression devices can have different waveforms, including trapezoidal. We studied the haemodynamic differences of such waveforms in a porcine model of cardiac arrest. Methods: Eight domestic pigs (weight 31 ± 3 kg) were anaesthetised and instrumented to continuously monitor aortic (AP) and right atrial pressure (RAP), carotid (CF) and cerebral cortical microcirculation blood flow (CCF). Coronary perfusion pressure (CPP) was calculated as the maximal difference between AP and RAP during diastole or decompression phase. After 4 min of electrically induced ventricular fibrillation, mechanical chest compressions were performed with four different waveforms in a factorial design, and in randomized sequence for 3 min each. Resulting differences are presented as mean with 95% confidence intervals. Results: Mean AP and RAP were higher with trapezoid than sinusoid chest compressions, difference 5.7 (0.7, 11) and 6.3 (2.1, 11) mmHg, respectively. Flow measured as CF and CCF was also improved with trapezoidal waveform, difference 14 (2.8, 26) ml/min and 11 (5.6, 17)% of baseline, respectively, with a parallel, non-significant (P = 0.08) trend for CPP. Active vs. passive decompression to zero level improved CF, but without even a trend for CPP. Conclusion: Trapezoid chest compressions and active decompression to zero level improved blood flow to the brain. The compression waveform is an additional factor to consider when comparing mechanical and manual chest compressions and when comparing different compression devices. © 2010 Elsevier Ireland Ltd. All rights reserved.

1. Introduction The purpose of external chest compressions during cardiopulmonary resuscitation (CPR) is to maintain necessary blood flow to vital organs until treatment of the underlying cause might succeed. Different compression characteristics such as compression force or depth, rate, compression part of duty cycle, and active decompression have been found to influence blood flow and short time survival in animal experiments.1–8

夽 A Spanish translated version of the abstract of this article appears as Appendix in the final online version at doi:10.1016/j.resuscitation.2010.10.009. ∗ Corresponding author at: Institute for Experimental Medical Research, Oslo University Hospital, N-0407 Oslo, Norway. Tel.: +47 23016819; fax: +47 23016799; mobile: +47 97539429. E-mail address: [email protected] (J. Kramer-Johansen). 0300-9572/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.resuscitation.2010.10.009

When retrospectively reviewing manual chest compressions recorded in our human studies,9,10 we noticed that they were generally of the same sinusoidal shape (Fig. 1a). Commercially available mechanical chest compression devices have different modes of force transduction that might give rise to different compression waveforms. We hypothesised that blood flow would be higher with more rapid onset-offset, trapezoidal compression waveforms than with the sinusoidal waveforms of manual chest compressions. Except for mathematical models11,12 the haemodynamic effects of different chest compressions waveforms have to our knowledge been only partially explored, and such knowledge can influence the design of future mechanical chest compression devices. We explored haemodynamic differences between a sinusoid (Fig. 1b) and a more trapezoidal (Fig. 1c) waveform using a custom servo controlled chest compression device in a porcine model of ventricular fibrillation (VF) The effect of active recoil to zero level was also explored in the same experiments in a factorial cross-over design.

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Fig. 1. Different waveforms. The horizontal bar represents a time interval of 1 s, and deflection of the curve represents the compression depth on a scale from 0 to 60 mm. (a) Typical manual compression waves as recorded with HS4000SP (Laerdal Medical, Stavanger, Norway) in an out-of-hospital resuscitation episode and displayed with custom software. The presented curves have a compression depth of ∼37 mm, compression rate of 110 min−1 , and compression part of duty cycle 0.43. (b) The sinusoidal waveform used in this experimental setup; compression depth 50 mm, compression rate 100 min−1 and compression part of duty cycle 0.50. (c) The trapezoidal waveform, all other variables as in (b).

2. Material and methods 2.1. Animal preparation The experiments were conducted in accordance with “Regulations on Animal Welfare” under the Norwegian Animal Welfare Act and approved by Norwegian Animal Research Authority. Nine healthy domestic swine of either sex (4 males, 5 females), 10–12 weeks of age (mean weight 31 ± 3 kg) were fasted over night but were given free access to water. The animals were sedated with a single intramuscular injection of ketamine (∼30 mg kg−1 ) and 1 mg atropine. Peripheral venous access was then established, and anaesthesia induced with a bolus dose of propofol 3 mg kg−1 and fentanyl 0.3 mg kg−1 and continued with infusions of propofol 10–15 mg kg−1 h−1 and fentanyl 50–70 ␮g kg−1 h−1 targeted towards haemodynamic stability and non-responsiveness to painful stimuli. The animals were tracheotomised and mechanically ventilated (Servo Ventilator 900B, Siemens-Elema AB, Solna, Sweden) with ambient air. The ventilation was set with a fixed frequency of 16 min−1 and the tidal volume adjusted to maintain end expiratory fraction of CO2 at 4.5–5% as measured by a gas monitor (Datex Capnomac UltimaTM , Helsinki, Finland). Infusion of isotonic NaCl 1.5 ml kg−1 h−1 (total amount 25–30 ml kg−1 ) was maintained during preparation, but stopped during the experiment. Urine was drained continuously through a cystostoma, and the intraabdominal temperature maintained at 38–39◦ C during the experiment with an electric heating blanket placed under the animal. Instrumentation of the animals consisted of intravascular micro-tip transducer catheters (Millar Instruments, Houston, TX, USA) introduced via cut-down in the right common carotid artery to the ascending aorta and via the right external jugular vein to the right atrium. An arterial line for blood sampling was placed by cut-down into the right femoral artery and a 7.5F Swan-Ganz catheter (Baxter Healthcare Corporation, Irvine, CA, USA) for sampling of mixed venous blood was placed in the right atrium via a cut-down of the right femoral vein. An ultrasound flow probe (Transonic systems Inc., Itchaca, NY, USA) was placed on the left

common carotid artery. A laser-doppler flowmetry probe (Model 407, Perimed AB, Stockholm, Sweden) was placed on the surface of the left cerebral cortex after a craniotomy and duratomy approximately 10 mm anterior of the coronal suture and 15 mm lateral to the sagittal suture. Care was taken to avoid placing the probe directly over visible vessels. The probe was secured to the surface of the brain with a probe holder (Model PH 07-4, Perimed AB, Stockholm, Sweden) and dural sutures. The burr hole was sealed with bone wax. The readings are expressed in arbitrary units and give accurate measurements of flow in a small part of cerebral cortex just below the probe.13,14 Pressures and flow signals were recorded continuously with PCbased real time data acquisition hardware (DaqBoardsTM Model 200A, IOTech Inc., Cleveland, OH, USA) supported with software for DASYLab v 5.1 (Datalog, National Instruments company, Monchengladbach, Germany) and printed on a thermal array recorder (model TA 11, Gould Instruments Systems Inc., OH, USA). Arterial and mixed venous blood gases were drawn before induction of ventricular fibrillation (VF), and during the last minute of each experimental run during CPR. They were analysed with an automatic blood gas analyser (AVL OMNITM 9, AVL List GmbH Medizintechnik, Graz, Austria). Standard lead II surface ECG was monitored during the experiments by means of self-adhesive defibrillation pads (Philips Heartstart pads, Seattle, WA, USA) and a prototype defibrillator based on Heartstart 4000 (HS4000SP, Philips Medical Systems, Andover, MA, USA and Laerdal Medical, Stavanger, Norway). Chest compressions were delivered with a custom made servo controlled compression device (Pigsaver, Laerdal Medical, Stavanger, Norway). The compression rate and depth were set at 100 min−1 and 5 cm, respectively, via a software interface. The same software allowed for rapid changes between a sinusoidal and a trapezoidal compression/decompression waveform during the experiment, both with a compression part of duty cycle of 50% (Fig. 1). To enable the possibility of performing chest compressions with and without active recoil (active or passive decompression) sternum was exposed and a polyethylene compression pad secured to the sternum with screws. A locking pin could be used to attach the pad to the compression machine in order to have active recoil to zero level in the decompression phase. To allow for passive recoil, the pin was removed. 2.2. Experimental protocol After instrumentation, baseline registration of all variables was obtained. Anaesthesia and ventilation were then discontinued and VF induced by a trans-thoracic current (90 V AC for 3 s) and confirmed by ECG-changes and abrupt fall in all measured pressures and blood flow in the carotid artery and cerebral cortex. After 4 min of untreated VF, chest compressions with trapezoid waveform and passive recoil was performed for ∼30 s to allow for initial changes in chest configuration, and the vertical position of the compression piston was then adjusted to the new zero position. Four runs with the different permutations of the two waveform factors were then sequentially performed for 3 min each. A fifth run with the same method as the first served to monitor the effects of time in the model. The sequence of the methods was block-randomized to ensure that each of the four method combinations was performed twice as the first, second, third or fourth method, respectively (Table 1). Ventilations were performed with 100% oxygen at a rate of ∼10 min−1 , manually interposed between chest compressions with a self inflating bag. In all experiments the compression point was the same during the whole experiment. Registrations were made of all variables during the last minute of each run. After the experiments, autopsies were performed to verify the position of all catheters and the integrity of the mediastinal surface

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Table 2 Baseline characteristics and arterial blood gas analysis (medians and 25-, 75percentiles).

Table 1 Randomization table for the sequence of chest compression methods. T: trapezoidal waveform; S: sinusoidal waveform; A: active chest recoil; P: passive chest recoil. Pig number

Method 1

Method 2

Method 3

Method 4

(N = 8)

Baseline

1 2 3 4 5 6 7 8

TA SA TP TP TA SP SP SA

SP TA SP TA SA SA TP TP

TP SP TA SA TP TA SA SP

SA TP SA SP SP TP TA TA

Mean aortic pressure (mmHg) Mean right atrial pressure (mmHg) Mean carotid blood flow (ml/min) Mean cortical cerebral microcirculation (AU)

85 (63, 97) 5 (4, 6) 233 (173, 260) 367 (272, 458)

of the sternum and pericardium. A superficial check for pulmonary and abdominal compression injuries was also performed. 2.3. Calculations

Arterial blood gases

Baseline (FiO2 = 0.21)

During last experimental run (FiO2 = 1.0)

PO2 (kPa) PCO2 (kPa) pH Base excess (mmol/ml)

12.0 (10.6, 13,3) 4.7 (4.3, 5.2) 7.46 (7.45, 7.48) 0.9 (−1.3, 2.8)

21.7 (9.1, 67.1) 3.4 (2.3, 6.0) 7.27 (7.07, 7.35) −15 (−17, −11)

considered statistically significant. A power analysis had shown that to detect a 30% change in blood flow with the empirical knowledge of variations in our model, we needed 8 animals to have a power of ∼0.80 with an alpha of 0.05.

Aortic pressure (AP), right atrial pressure (RAP), carotid blood flow (CF), and cortical cerebral microcirculation (CCF) were registered continuously (200 Hz sampling rate) with a routine in MATLAB (MATLAB 6.5, The MathWorks, Inc., Natick, MA, USA). Coronary perfusion pressure (CPP) was defined as the maximum difference between AP and RAP during the decompression. We also calculated the area between AP and RAP in the decompression phase to obtain a [coronary perfusion pressure] × [perfusion time] product (CPPT). Laser doppler flow signals are obtained as arbitrary units and CCF is therefore given as percentage of the flow signal immediately preceding the cardiac arrest (baseline). Consecutive compressions were aligned based on the compression load signal and an arithmetic average of each data sample point for the last ∼100 compressions of each experimental run was constructed for each experimental animal.

3. Results VF was obtained in all pigs. One animal was excluded because of wrong compression point on the sternum resulting in no forward flow during chest compressions and the same compression method sequence was repeated in a new experiment. None of the autopsies revealed any damage to mediastinal structures from the screws in sternum or compression damage to ribs, sternum, or viscera. The characteristics of the animals before induction of VF are summarized in Table 2. Arterial and mixed venous blood gases showed a time dependent decrease in pH, an increase in base excess (BE) and a near constant PO2 (Table 2). Table 3 summarizes the measurements during the experiments and the differences between the methods. Trapezoidal waveform gave significantly higher maximum pressures in aorta and right atrium than sinusoidal and resulted in significantly improved carotid and cortical cerebral microcirculation flows. There was a non-significant trend (P = 0.08) in favour of trapezoidal waveforms for coronary perfusion pressure. Carotid blood flow was significantly higher with active than passive chest recoil to zero position with a parallel trend for cortical cerebral flow, but not even a trend towards improved coronary perfusion pressure with active recoil. An example of intravascular pressure registrations from one ani-

2.4. Statistical analysis Primary outcome was change in haemodynamic parameters between the different methods. Descriptive data are presented as medians with 25- and 75-percentiles. Differences are presented as mean difference with 95% confidence intervals (95% CI). Each animal served as its own control and paired comparisons were made between the two compression form factors (trapezoid vs. sinusoid waveform and active vs. passive recoil) based on the factorial design (Table 1). The differences were close to normally distributed and two-sided paired t-tests were used. P-values less than 0.05 were Table 3 Haemodynamic variables. N=8

TA

TP

Arterial pressure (mmHg) Mean 38 (29, 45) 37 (31, 40) Max 91 (74, 101) 79 (69, 86) Min 5 (3, 9) 7 (4, 13) Right atrial pressure (mmHg) Mean 34 (28, 43) 31 (30, 44) Max 97 (84, 121) 90 (75, 111) Min 2 (−1, 4) 3 (0.5, 7) Coronary perfusion Pressure (mmHg) 13 (10, 22) 15 (11, 19) CPPT 6 (4, 11) 7 (5, 7) Carotid blood flow (ml/min) Mean 61 (29, 81) 52 (20, 66) Cortical cerebral microcirculation (% of baseline) Mean 51 (39, 64) 52 (20, 66) 1.2 (1.0, 1.3) 1.0 (0.9, 1.4) ET CO2 (kPa)

SA

SP

Differences T–S

P-value

Differences A–P

P-value

32 (25, 36) 64 (50, 71) 15 (12, 17)

30 (25, 32) 62 (58, 70) 13 (9, 16)

5.7 (0.7, 11) 15 (7.3, 23) −6.1 (−11, −0.3)

0.06 0.007 0.08

2.1 (−1.9, 6.3) 4.4 (−3.2, 12) 1.6 (−6.2, 9.3)

0.3 0.3 0.7

27 (21, 35) 68 (55, 99) 6 (4, 11)

28 (24, 32) 72 (61, 86) 7 (6, 10)

6.3 (2.1, 11) 19 (5.7, 31) −5.8 (−7.4, −4.3)

0.02 0.03 <0.001

1.2 (−1.8, 4.2) 5.7 (−4.3, 16) −0.8 (−1.5, −0.2)

0.5 0.3 0.05

10 (7, 16) 5 (3, 9)

11 (9, 15) 4 (3, 8)

3.6 (−0.1, 7.3) 1.4 (−0.7, 3.4)

0.09 0.2

1.1 (−3.7, 6.0) 1.0 (−2.1, 4.2)

0.7 0.5

39 (20, 52)

37 (21, 41)

14 (2.8, 26)

0.04

7.5 (0.9, 14)

0.06

43 (19, 57) 1.3 (1.0, 1.5)

26 (17, 43) 1.2 (0.7, 1.5)

11 (5.6, 17) −0.1 (−0.3, 0.1)

0.005 0.4

8.5 (−3.7, 21) 0.1 (−0.1, 0.4)

0.2 0.2

Values are presented as medians (25-, 75-percentiles) from ∼100 averaged compressions for each method and mean differences (95% confidence intervals) with P-values from two-tailed paired t-tests for difference not equal to zero. CPPT was defined as the product of the difference AP–RAP during decompression phase and fraction of compression cycle with AP > RAP. Abbreviations: TA; trapezoid active recoil, TP; trapezoid passive recoil, SA; sinusoid active recoil, SP; sinusoid passive recoil. Differences: T–S; trapezoid minus sinusoid ((TA + TP)/2 − (SA + SP)/2), A–P; active recoil minus passive recoil ((TA + SA/2) − (TP + SP/2)).

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Fig. 2. The figure shows the intravascular pressure (AP; thick line, RAP; fine line, and the difference AP–RAP; punctuated line) curves for sinusoidal (left), trapezoidal (right), passive (upper), and active (lower) compressions from one of the animals. The curves show four consecutive compressions for each method.

mal is presented in Fig. 2, and aggregated curves for each method are presented in Fig. 3. 4. Discussion The present work documented higher blood flow to the brain with a non-significant parallel trend for coronary perfusion pressure with trapezoidal compared to sinusoidal chest compression waveform. We cannot exclude that the lack of a significant effect on coronary perfusion pressure is a type II statistical error as the difference in mean CPP was just below the 30% difference which the study was powered to detect. Sinusoidal compressions resemble manually performed chest compressions, whereas mechanical compression devices might be produced with different compression waveforms. It is therefore important to evaluate various compression waveforms to ensure optimal cardiac and cerebral perfusion. Several clinical studies have documented inadequate quality of CPR with too shallow chest compressions, too high compression rates and extensive time without chest compressions.9,10 The poorer results with sinusoidal than trapezoidal chest compressions add to the arguments that mechanical chest compressions can ensure better quality CPR for more than short intervals of time, unless the logistics around applying a mechanical devise has too many negative effects. Thus, although mechanical chest compressions produce better quality of CPR over time and during transportation,15,16 and better haemodynamics in experimental settings,17,18 recent clinical studies are ambiguous. Compared with manual compressions AutoPulse was found to improve19 or worsen20 survival, and one study with LUCAS has been neutral.21 Methods used, training, time to access the device, quality of

manual CPR in the control group and other circumstances may contribute to these diverging results.20,22 Characteristics of the device used, like the waveform of the compressions, may also be important. Determinants of cerebral flow and perfusion pressures in animal experiments include increased compression force,1 increased compression rate up to 120–150 min−1 ,6–8 and increased compression part of the duty cycle up to 70%.3,4 Reports of “high-impulse CPR” have shown that moderately high frequency and short duration chest compressions improve cardiac output and perfusion pressures,2,6 but a precise description of the compression waveform is lacking. A mathematical model that used computersimulated evolution of compression waveforms tended to result in rectangular waveforms when both chest and abdominal compressions were modelled.11,12 In humans chest compression force and rate have been shown to influence cardiac output as measured by excreted CO2 ,23,24 and increased average chest compression depth improved short time survival in a logistic regression.9 Our study confirms experimentally that the waveform of the chest compressions also influences blood flow. Coronary blood flow or perfusion pressures have been much studied, and maximally achieved coronary perfusion pressure has been found to correlate with short term survival in humans.25 Coronary blood flow was found to be optimal with a compression rate of ∼120 min−1 in dogs,8 and Sunde et al. found that myocardial blood flow in pigs was best with the compression part of duty cycle of 50/504 which corresponded to the best compromise waveform found in a mathematical evolution model.11 Myocardial blood flow occurs during decompression, as does refilling of the heart and thoracic capacitance vessels, which affects stroke volume. In our study chest compression rate and compression part of duty cycle were

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Active recoil mmHg

Passive recoil mmHg

Sinusoidal

Trapezoidal

120

120

100

100

80

80

60

60

40

40

20

20

0

0

-20

-20

-40

-40

120

120

100

100

80

80

60

60

40

40

20

20

0

0

-20

-20

-40

-40

Fig. 3. The figure shows the intravascular pressure (AP; thick line, RAP; fine line, and the difference AP–RAP; punctuated line) curves for sinusoidal (left), trapezoidal (right), passive (upper), and active (lower) compressions. The curves are averaged from registration of ∼100 compressions for each method from all eight animals.

kept constant, but a trend towards improved CPP was seen with trapezoidal chest compressions. Active decompression to levels above zero position improves blood flow to both brain and myocardium in porcine experimental cardiac arrest.5 In the present study carotid blood flow also improved with active vs. passive recoil to zero position, but with no effect on coronary perfusion pressure. More rapid down and up strokes during the compression decompression cycle of the trapezoidal waveform resulted in plateau levels for both depth and pressure, while there was no plateau during a sinusoidal cycle (Figs. 2 and 3). This may at least partly explain the difference in results. We speculate that different compliances of the compressible structures in the thorax may also have an effect. More rapid compressions will exaggerate the difference between highly compliant and less compliant structures. The exact position of the compression point may therefore be more important for more rapid onset waveforms and might explain the complete lack of forward blood flow in one experiment with incorrect placement of the compression pad. Evaluation of the relative effect of the down-stroke and up-stroke characteristics may elucidate the basic mechanisms of chest compressions.26 Our study has limitations in that it is an experimental pig model with only haemodynamic measures of resuscitation efficacy. The rib cage of the young pigs is differently configured and has higher viscosity than those of elderly humans, although stiffness is relatively similar.27 Active recoil may thus be relatively more important in pig CPR.5 We did not tie off the external carotid artery that

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supplies the face in the present study and carotid blood flow is thus a combination of cerebral and peripheral blood flow. The high co-variation between ipsilateral cortical cerebral microcirculation and carotid blood flows suggests that cerebral and peripheral flows changed in parallel in this setup. This may reflect the fact that no external vasopressors were administered during CPR in our protocol which would be expected to reduce peripheral blood flow. Vasopressors increase afterload and aortic pressure during the decompression phase and thus CPP. We have previously shown that the effect of adrenaline is dependent on CPR quality,28 and to avoid this possible interaction, no vasopressors were administered in our experiments. We did not find any complications such as rib fractures by autopsy in our small series of relatively young pigs. All animals were treated with all methods in sequence so no differences could be expected, but damages to the rib cage and pericardium might be more prominent with more forceful CPR with rapid decompression and in older individuals.29,30 5. Conclusion When compression duty cycle, rate and depth were kept constant, a more trapezoidal vs. sinusoidal chest compression waveform resulted in higher aortic pressure, higher carotid and cerebral cortical blood flow with a parallel non-significant trend for coronary perfusion pressure. Various waveforms must be taken into account when efficacy of mechanical chest compression devices is discussed. Contributors Wik and Kramer-Johansen contributed to the study concept and design. All authors participated in the collection of data. Strømme and Kramer-Johansen were responsible for the analysis of data. Statistical expert was provided by Kramer-Johansen. Kramer-Johansen drafted the manuscript. Funding was provided by Wik and KramerJohansen. Wik supervised the study. All authors have read the manuscript, revised it thoroughly for intellectual content, and approved of the final version. Funding The study was financed by the Laerdal Foundation for acute medicine, Norwegian Air Ambulance Foundation, and Anders Jahre Foundation for Sciences. None of the sponsors had any influence on the results or the decision to publish. Conflict of interest statement Authors Pytte, Tomlinson, Sunde, Dorph, Eriksen, and Strømme have no conflicts to declare. Kramer-Johansen and Wik have received research support from Laerdal Medical, Stavanger, Norway, and Philips Medical Systems, Andover, MA, regarding studies on quality of CPR. Svendsen was at the time of the study a full time employee of Laerdal Medical on a fixed salary. Wik has served as a medical consultant for Medtronic, Laerdal Medical, and Philips Medical Systems and is PI for a study comparing mechanical chest compressions with Manual CPR sponsored by Zoll. Acknowledgements The authors wish to thank Laerdal Medical for providing the chest compression device. We are indebted to Professor Petter Andreas Steen for good discussions and guidance and to Professor Bjørn Auestad for statistical advice. Dr. Øystein Tømte has provided valuable feedback to the paper.

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