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Ann Thorac Surg 2003;75:190-196
© 2003 The Society of Thoracic Surgeons


Original article: cardiovascular

Direct compression of the failing heart reestablishes maximal mechanical efficiency

Russell A.J. Carrington, PhDa,b*, Yifei Huang, MD, PhDa, Osamu Kawaguchi, MD, PhDa, Takeshi Yuasa, MDa, Kazuaki Shirota, MDa, Donald Martin, PhDb, Stephen N. Hunyor, MD, MTMa

a Cooperative Research Centre for Cardiac Technology and Cardiac Technology Centre, Department of Cardiology, Royal North Shore Hospital, St. Leonards, Australia
b Department of Health Sciences, University of Technology, Sydney, Australia

Accepted for publication August 2, 2002.

* Address reprint requests to Dr Carrington, c/o Dr Hunyor, Cardiac Technology Centre, Block 4, Level 3, Royal North Shore Hospital, St. Leonards (Sydney) NSW 2065, Australia
e-mail: stephenh{at}med.usyd.edu.au


    Abstract
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 
BACKGROUND: In failing hearts, homeostatic mechanisms contrive to maximize stroke work and maintain normal arterial blood pressure at the expense of energetic efficiency. In contrast dobutamine reestablishes maximal mechanical efficiency by promoting energetically optimal loading conditions. However, dobutamine also wastefully increases nonmechanical oxygen consumption. We investigated whether direct mechanical cardiac compression would reestablish maximal mechanical efficiency without the oxygen-wasting effect.

METHODS: The pressure–volume relationship and myocardial oxygen consumption were derived in sheep using left ventricular pressure and volume from manometer-tipped and conductance catheters, and coronary flow from Transonics flow probe.

RESULTS: Propranolol hydrochloride and atropine sulfate were administered to reduce ejection fraction to 21% when ventricular elastance fell to 1.35 mm Hg/mL and mechanical efficiency to 79% of maximal. Low-pressure direct mechanical compression of the failing heart restored mechanical efficiency to 94% of maximal and realigned optimal left ventricular end-systolic pressure with operating left ventricular end-systolic pressure without altering nonmechanical oxygen consumption.

CONCLUSIONS: We conclude that direct cardiac compression restores mechanical efficiency to normal maximum without wasting energy on additional nonmechanical activity.


    Introduction
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 
Normal hearts operate at optimal left ventricular end-systolic pressure (LVESP) to achieve maximal mechanical efficiency (EW/MO2) [1, 2]. In contrast, with failing hearts there are compromises in loading conditions and ventriculoarterial coupling [2] that drive the optimal LVESP below normal circulatory pressure [1]. Because homeostatic mechanisms maintain normal arterial pressure even during moderate cardiac dysfunction, the failing heart operates away from optimal LVESP and below maximal EW/MO2 [1].

After increased afterload-induced heart failure, dobutamine has been shown to restore optimal loading conditions and reestablish maximal EW/MO2 [3]. However, dobutamine also increases oxygen consumed for nonmechanical processes without improving contractile efficiency (PVA/MO2), despite its positive inotropic effect [4, 5]. This oxygen-wasting effect [5] decreases the ratio of mechanical work produced from the collective mechanical and nonmechanical energy [4, 6]. Like many ß-adrenergic agonists, dobutamine is arrhythmogenic because it increases intracellular cyclic adenosine monophosphate [1, 6] and therefore it causes excess mortality [1]. New experimental positive inotropic vasodilators eliminate the oxygen-wasting effect [6] but may also stimulate sympathetic and renin-angiotensin responses that reestablish cardiac overload and energetic inefficiency, leading ultimately to accelerated heart failure [1].

Mechanical ventricular assist potentially offers an energetically efficient alternative to positive inotropic therapy. Direct cardiac compression (DCC) has previously been implemented by means of skeletal muscle (eg, dynamic cardiomyoplasty) [7] or mechanical assist devices [811]. Unlike in-line ventricular assist devices (VAD) and total artificial hearts, which risk thromboembolism, hemolysis, and immune reactions [8], DCC avoids contact with circulating blood. The utility of DCC-VAD for resuscitation [8] and as a bridge-to-transplantation has been demonstrated [12], and recent studies show its potential for reverse remodeling [13], including in patients with dilated cardiomyopathy treated with cardiomyoplasty [14].

We therefore investigated whether DCC can reestablish normal maximal mechanical efficiency in hearts with propranolol-induced failure, without causing an associated oxygen-wasting effect.


    Material and methods
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 
The study was approved by the institutional Animal Care and Ethics Committee and complied with the "Principles of Laboratory Animal Care" formulated by the National Society for Medical Research and the "Guide for the Care and Use of Laboratory Animals" published by the National Institutes of Health (National Academy Press, Washington, DC, 1996).

Experimental design
The study was performed under stable light anesthesia and autonomic nerve blockade. Direct cardiac compression–assisted beats (20 mm Hg compressing pressure) were compared with unassisted (preassisted) beats. Merino wether sheep (48.3 ± 6.4 kg, n = 6) were instrumented for mechanoenergetic (pressure-volume relationship) and MO2 measurements. At study end the sheep were killed with an intravenous bolus injection of potassium chloride (1 to 3 g), and the heart was removed and blotted dry before separating and weighing the ventricles.

Anesthesia and autonomic nerve blockade
Anesthesia was induced by 20 mg/kg thiopental sodium, and the sheep were intubated for ventilation (model 8 respirator; Bird Australia, Pty, Ltd, Sydney NSW, Australia) using 1 to 2 L/min oxygen, 2 L/min nitrous oxide, and 1.2% to 1.5% isoflurane with 400-mL to 500-mL tidal volumes. Expired carbon dioxide partial pressure was maintained between 30 and 43 mm Hg (Poet II monitor; Criticare Systems Inc, Milwaukee, WI). Maintenance fluid was provided through peripheral venous access with either Hartmann’s or Hemaccel. A 2-cm-diameter orogastric tube was passed to decompress the ruminant stomach. Autonomic nerve responses were blocked with propranolol hydrochloride (1 mg/mL multiple doses totaling <= 50 mg; Zeneca Pharmaceuticals Pty, Ltd, Sydney NSW, Australia) and atropine sulfate (0.1 mg/mL multiple doses totaling <= 4.8 mg; Astra Pharmaceuticals Pty, Ltd, Sydney NSW, Australia). Sympathetic blockade was confirmed by a lack of heart rate response to infusion of dobutamine hydrochloride (0.1 mg/mL infused at 80 to 90 mL/h; Eli-Lilly Pty, Ltd, Sydney NSW, Australia).

Left ventricular pressure-volume and general hemodynamics
The carotid artery and jugular vein were isolated through a left neck cutdown. A 5F Millar micromanometer-tipped catheter (Millar Instruments Inc, Houston, TX) and a 12-electrode 6F conductance catheter (CardioDynamics B.V., Zoetermeer, The Netherlands) were placed longitudinally in the left ventricle (LV). Their outputs were amplified (System 6, Triton Technology Inc, San Diego, CA) and processed (Sigma 5 signal conditioner-processor, CardioDynamics) to obtain instantaneous LV pressure and volume, respectively. Volumes were corrected for parallel and blood conductivity using standard injection of hypertonic saline and measurement of blood resistivity. A 22F occlusion catheter (CV 1014 Fogarty catheter; Edwards Laboratory, Santa Ana, CA) was placed in the inferior vena cava for brief occlusion. Through a left anterior thoracotomy (fifth intercostal space), a 16-mm to 20-mm flow probe (Transonic 16A/20A; Transonics Inc, Ithaca, NY) was placed around the ascending aorta to measure cardiac output.

A more complete description of pressure-volume loop theory and the various analyses used can be found in Carrington [15].

Measurement of myocardial oxygen consumption
The hemiazygos vein was ligated outside the pericardium, and a 4F venous oxygen saturation catheter (Baxter Pty, Ltd, Sydney NSW, Australia) was inserted through the hemiazygos vein into the coronary sinus for coronary venous oximetry. Two epicardial pacing electrodes were sutured to the right atrium. A 4-mm to 6-mm flow probe (Transonic 4S/6S; Transonics) was positioned on the left coronary artery to measure coronary blood flow. The venous oxygen saturation signal was transduced by a Vigilance monitor (Baxter).

Direct cardiac compression
The heart was paced at 100 beats/min, and a cuplike prototype DCC-VAD was fitted onto the ventricular portion of the exposed heart (Fig 1) and connected to a pneumatic driver (S.T.U. Heart Inc, Salt Lake City, UT). The DCC-VAD consisted of a rigid polyurethane outer shell encasing a distensible polyurethane diaphragm (Pellethane 2363 80A Shore, Dow Corning, Pty, Ltd, Sydney NSW, Australia) in contact with the epicardium. The DCC-VAD driver was controlled by a customized instrument assembled from modules of AmLab software (software v.2.0, build 15.3; AmLab International Pty, Ltd, Sydney NSW, Australia) and implemented on an IBM-compatible Dell PC and a Minirack ADC (Amlab). The DCC-VAD was activated in synchrony with the native heart using an electrocardiographic gating signal from the epicardial leads. Direct cardiac compression at 20 mm Hg pneumatic driving pressure was applied to every third beat (1:3 ratio) for 200 ms, commencing 200 ms after the pacing signal.



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Fig 1. Schematic of experimental setup including placement of direct cardiac compression–ventricular assist device, catheters, flow probe, and right atrial epicardial electrocardiographic (ECG) leads (A) and direct cardiac compression–ventricular assist device with deflated diaphragm (B). (IVCO = inferior vena cava occlusion.)

 
At the conclusion of the studies the hearts were thoroughly examined for macroscopic signs of damage. Only small areas of superficial epicardial bruising were noted in 1 animal.

Data acquisition
All measurements were taken at end expiration. The analog pressure, volume, electrocardiographic, coronary blood flow, oximetric, and cardiac output signals were digitized at 200 Hz using a 16-channel MacLab ADC (MacLab 16/s; ADInstruments Pty, Ltd, Castle Hill, NSW, Australia.) controlled by MacLab Chart software (Chart v. 3.5.6/s; ADInstruments) through a Macintosh LC 425 PC. Data were analyzed off-line using customized software written in TurboBasic.

Data analysis
All steady-state hemodynamic variables were averaged from five to six beats. End-systolic pressure-volume relationship was assessed during transient preload reduction using inferior vena cava occlusion.

Left ventricular mechanics
Left ventricular function was assessed using LV end-systolic and end-diastolic pressure and volume as well as stroke volume (SV). Left ventricular contractility was assessed using the pressure-volume relationship [5], which is regarded as load insensitive. Both LVESP and LV end-systolic volume (LVESV) were determined for each cardiac cycle with an iterative technique. End-systolic pressure-volume relationship was then estimated using least squares linear regression fitted to these points to yield the equation:

where Ees and V0 are the slope and volume-axis intercept of end-systolic pressure-volume relationship, respectively. End-systolic elastance (Ees) was normalized for 100 g of LV. Ventriculoarterial coupling was assessed by the ratio of effective arterial elastance (Ea) to Ees, where Ea = LVESP/SV2.

Left ventricular mechanoenergetics
Pressure volume area (PVA) was used to approximate LV total mechanical energy. Pressure volume area was subdivided into potential energy (PE) and external work (EW) [5], where EW is the integral of LV pressure and volume.

Left ventricular energetics
The MO2 was determined using the Fick principle as follows:

where mCBF is coronary blood flow, AVO2 is arterial-venous oxygen difference, and HR is heart rate [16]. The AVO2, derived from the arterial–coronary sinus oxygen saturation difference and hemoglobin level, was corrected for sheep oxyhemoglobin coefficient (1.35). Inasmuch as PVA is directly related to MO2 [5], linear regression was used to determine slope ({alpha}) and MO2-axis intercept (ß) of the MO2-PVA relationship. Here ß is the unloaded or nonmechanical (PVA-independent) MO2 consumed for excitation-contraction coupling and basal metabolism, and {alpha} the oxygen cost of PVA. The inverse of {alpha} represents contractile efficiency; a measure of adenosine triphosphate production by oxidative phosphorylation and cross-bridge transduction of adenosine triphosphate into mechanical energy [1, 3, 5].

Using the MO2–PVA relationship, LV conventional mechanical efficiency (EW/MO2) has been expressed as a function of preload (V = LV end-diastolic volume - V0), afterload (LVESP), and contractility (Ees) [17] where

Left ventricular mechanical efficiency is maximized at an optimal LVESP such that

Statistics
Paired Student t tests (two-tailed) were performed to compare preassisted with DCC-assisted data. Probability values less than 0.05 were considered statistically significant. Data are presented as mean ± standard deviation unless otherwise stated.


    Results
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 
Figure 2 shows a representative tracing of pressure-volume loops during transient inferior vena cava occlusion in preassist and DCC assist states. Linear end-systolic pressure-volume relationships were derived from the LVESP points of iterative loops. Direct cardiac compression assist increased Ees and shifted V0 rightward.



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Fig 2. (A) Representative pressure-volume loops and end-systolic pressure-volume regressions for pre-assist and direct cardiac compression (DCC) assist beats. (B) Representative maximal oxygen consumption myocardial oxygen consumption–pressure volume area regressions for pre-assist and direct cardiac compression assist beats. (LVP = left ventricular pressure; LVV = left ventricular volume; PVA = pressure-volume area.)

 
In Table 1 the preassist beats represent a state of depressed LV systolic pump function induced by propranolol. Ejection fraction (EF) was reduced to 21% and contractility (Ees) to 1.35 ± 0.02 mm Hg/mL. Arterial elastance (4.06 ± 1.67 mm Hg/mL) was triple the LV elastance on average (Ea/Ees = 3.00 ± 1.34), indicating dysfunctional ventriculoarterial coupling. Mechanical efficiency was submaximal (79% ± 12%) because the failing heart was operating at an LVESP of 74.2 ± 7.6 mm Hg, which was 37.4 ± 10.1 mm Hg above the optimal LVESP of 36.8 ± 9.3 mm Hg (p = 0.0003; Fig 3).


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Table 1. Beat-to-Beat Left Ventricular Hemodynamics

 


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Fig 3. (A) Empirical and optimal left ventricular end-systolic pressure (LVESP) during pre-assist and direct cardiac compression (DCC) assist beats. *p < 0.05 comparing direct cardiac compression assisted beat; #p < 0.05 comparing optimal LVESP of same beat. (B) Empirical and maximal conventional mechanical efficiency (EW/MO2) for pre-assist and direct cardiac compression assist beats. *p < 0.05 comparing direct cardiac compression assisted beat; #p < 0.05 comparing maximal conventional mechanical efficiency of same beat. (C) Empirical conventional mechanical efficiency as a ratio of maximal conventional mechanical efficiency for pre-assist and direct cardiac compression assist beats.

 
Table 1 also shows the improved composite pump (native heart plus DCC) function produced by low-pressure DCC-VAD assist beats. Low-pressure DCC-VAD increased LV SV by 10.3 ± 10.0 mL (p = 0.0534) and composite EF by 12.4 ± 8.2 absolute percentage points (p = 0.0134). Composite Ees increased 80% ± 32% (p = 0.0051) above failure levels, whereas arterial elastance was reduced by 43% ± 42% (not significant). Consequently, ventriculoarterial coupling was markedly improved (p = 0.0193). The data in Table 2 show that low-pressure DCC-VAD did not alter MO2 but trended to increase PVA (by 14% ± 29%, not significant), whereas EW rose by 47% ± 13% (p = 0.0003). As a result, nonmechanical oxygen consumption was unchanged whereas contractile efficiency was improved by 14% ± 14% (p = 0.055). The maximal mechanical efficiency possible with the composite heart was 30% ± 10%, which was 31% ± 28% higher than the failing native heart alone (23% ± 7%, p = 0.043; Fig 3B). Even so, the composite heart was operating at 94% ± 24% (not significant; Fig 3C) of its maximal mechanical efficiency and was 50% ± 24% (p = 0.043) more mechanically efficient than the native heart alone. Low-pressure DCC-VAD improved the failing heart optimal LVESP (36.8 ± 9.3 mm Hg) by 20.4 ± 9.1 mm Hg (p = 0.0028) and realigned the composite optimal LVESP (57.2 ± 11.1 mm Hg) within 17 ± 16 mm Hg (not significant) of the failing native heart operating LVESP (74.2 ± 7.6 mm Hg; Fig 3A). Because the DCC-VAD applied low-pressure compression, the composite operating LVESP (75.1 ± 11.2 mm Hg) was almost identical to that of the failing native heart alone.


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Table 2. Beat-to-Beat Mechanoenergetics and Energetics

 

    Comment
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 
This study examined the efficiency of energy transfer to EW in propranolol-induced failing hearts after low-pressure DCC-VAD. It demonstrates that this form of DCC-VAD reestablishes energetically optimal loading conditions and maximizes mechanical efficiency levels, without incurring the oxygen-wasting effect found with dobutamine.

We used pressure-volume and mechanoenergetic (MO2-PVA, EW/MO2) relationships to predict benefits of low-pressure DCC-VAD on energy transfer to EW. Our data indicate improvement in contractile efficiency and conventional mechanical efficiency in propranolol-induced failing hearts in vivo. This was reflected in a decreased slope of the MO2-PVA relation and increased ratio of external work to myocardial oxygen consumption (EW/MO2). These results confirm enhanced mechanical work in the face of unaltered myocardial oxygen supply—indicative of an oxygen-sparing effect in the failing heart. The empiric end-systolic pressure-volume relationship and MO2-PVA relations were linear in accord with previously reported mechanoenergetic principles [5].

Previously titration of propranolol has been used to produce heart-failure (HF) [18]. In the current experiment finite bolus doses of propranolol produced LV systolic contractile and hemodynamic dysfunction equivalent to previous reports in sheep with coronary microembolization-induced HF [19] and in humans with congestive HF [2, 14]. Both coronary microembolization [20] and bolus propranolol infusion [5] have been shown to generate a parallel downward shift in MO2-PVA relation, confirming a similar effect on MO2 despite their different causes. Notably our empiric HF Ees, EF, Ea and Ea/Ees matched previously reported HF levels: EF 26% ± 5% [19]; Ees 1.3 ± 0.5 mm Hg/mL [19]; Ea 2.7 ± 0.6 mm Hg/mL [2]; and Ea/Ees2.56 ± 2.03 [2]. Experimentally, the autonomic blockade was validated when the failing heart was unresponsive to bolus infusion of dobutamine.

Although nonmechanical MO2 is reduced with propranolol-induced HF [21] and coronary microembolization-induced HF in dogs [20], the contractile efficiency generally remains normal (30% to 50%, [5]). In this way the experimentally induced HF conforms with human congestive HF, which has also demonstrated normal contractile efficiency [16]. Comparatively, our preassist contractile efficiency of 56% ± 19% was above expectation. Although pacing and coronary perfusion [21] are both known to alter contractile efficiency, our elevated contractile efficiency was most likely related to a girdling effect from the DCC-VAD, similar to that attributed to cardiomyoplasty [7, 14]. The passive VAD girdling effect appeared to have minimal impact on the failing energy transfer to EW, because the conventional mechanical efficiency of our preassist beats was equivalent to previously reported human congestive HF [1, 2] and coronary occlusion-induced ischemic HF in sheep [22]. Moreover, the native heart was operating well above optimal LVESP and at only 79% ± 22% of its maximal mechanical efficiency, both characteristic of suboptimal energetics defined in human HF [1]. Apart from their initial effects, pacing rate, coronary flow, propranolol, and girdling were not altered during our protocol; therefore, we are confident that the beat-to-beat changes reported in the current study are caused by low-pressure DCC-VAD enhancement of acute HF alone.

In terms of mechanoenergetic transfer, our DCC-VAD reestablished optimal loading conditions (LVESP) and in the process normalized and maximized mechanical efficiency. The DCC-VAD achieved this effect through a mechanical interaction with the physiologic system only, without exploiting or augmenting the physiologic energy supply (MO2). For this reason mechanoenergetic assis-tance delivered by a nonbiologic device must be treated differently from that delivered by a biologic assist technique (eg, cardiomyoplasty) because the latter reappropriates physiologic energy to produce DCC.

We have shown that the mechanical energy transfer of the composite heart was equivalent to a normal human heart [1, 3]. These conditions could potentially promote reverse remodeling of the assisted failing heart, which, although not generating the total PVA or EW on its own, is subject to energetically optimized loads and increased SV without increasing MO2. Contrary to the oxygen-wasting effect of dobutamine, low-pressure DCC-VAD did not increase nonmechanical MO2 but instead conserved MO2 by increasing contractile efficiency. Like the mechanical energy transfer, the pressure-volume variables produced by low-pressure DCC-VAD were equivalent to PVA and EW values reported for normal sheep [22]. However, apart from achieving SV equivalent to that seen in normal sheep [19], most hemodynamic responses to low-pressure DCC-VAD remained subnormal. Thus, it lifted EF from levels seen in severe human HF [2] and microembolized HF sheep [19] to those encountered in milder forms of human HF. Assisted EF and LVESP were subnormal compared with previous reports in sheep [19]. Previously, subnormal hemodynamic responses have been reported even with higher pressure DCC-VAD using cuff-type VADs in coronary microembolization-induced acute HF in dogs [9]. Here the shortfall was attributed to limited ventricular filling rather than deficient contractile assistance during DCC [9].

Measurements of mechanical efficiency are critically dependent on coronary perfusion pressure and MO2, with both varying owing to blood flow heterogeneities within and across myocardial layers [23]. The MO2 and coronary perfusion pressure are directly affected by wall stress and motion, which have been shown to change with DCC implemented as cardiomyoplasty [24, 25]. Apart from global blood flow and MO2 measurements, the effect of DCC-VAD on local myocardial perfusion and MO2 heterogeneity was beyond the scope of the current experiments. Importantly though, DCC-VAD was shown to preserve blood flow and high-energy phosphate supply [8] to various regions of the heart providing the VAD diaphragm was fabricated from a suitably distensible biomaterial [26]. The diaphragm in our device was constructed from Pellethane2363, 80A Shore rather than silicone rubber and tended to create small pockets separated by folds or grooves during inflation. The direct compression resulting from our DCC-VAD does not faithfully mimic the wringing and shortening action of native myocardium. The impact of this irregular contraction profile and resulting geometric cavity distortion on local blood flow, perfusion pressure, and wall stress, as well as the cylindrical conductance volumetry model, was not measured, but may exert some influence on beat-to-beat mechanoenergetics.

In the current study conductance volumetry was not scaled by an electrical field inhomogeneity gain factor ({alpha}) because empiric SV measurements were realistic only for {alpha} = 1. Empiric volumes were corrected for parallel conductance ({alpha}Vc) measured before inferior vena cava occlusion and not on a beat-to-beat basis, because previously unpublished work by our own group showed no change in {alpha}Vc between fitting the DCC-VAD passively and using it to actively assist the heart. Potential variations in {alpha} and {alpha}Vc owing to inferior vena cava occlusion and DCC-VAD–related changes in chamber geometry were ignored as being insignificant in comparison to the overall beat-to-beat volume change caused by DCC-VAD. The MO2 was derived from coronary blood flow and arterial and coronary sinus oxygen content difference. We also recognize that measurement of beat-to-beat blood oxygen content is complicated by device response time, streaming and mixing, and the blood transit time through the heart. Therefore, measured coronary sinus oxygen saturation may relate to flow that is out of synchrony. Thus a limitation of our study is the use of average coronary sinus oxygen content although other variables were measured on a beat-to-beat basis.

In summary, in the failing sheep heart, low-pressure DCC-VAD reestablished optimal loading conditions (LVESP) and maximized mechanical efficiency, without an oxygen-wasting effect. Mechanical energy transfer of the composite heart was equivalent to a normal human heart, creating conditions that may promote reverse remodeling of the failing ventricle.


    Acknowledgments
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 
We acknowledge the technical assistance of Marie Pryor, Serguei Plekhanov, PhD, Alfredo Martinez-Coll, PhD, Gabrial Gomes, Ray Kearns, Janelle Young, and Peter Darge. This research was performed under a PhD scholarship from the Australian Government’s Cooperative Research Centers (CRC) Scheme in the CRC for Cardiac Technology with PhD candidature at the University of Technology, Sydney, Australia.


    References
 Top
 Abstract
 Introduction
 Material and methods
 Results
 Comment
 Acknowledgments
 References
 

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