Asymmetric Mechanical Properties of Porcine Aortic Sinuses

Asymmetric Mechanical Properties of Porcine Aortic Sinuses Namrata Gundiah, Kimberly Kam, Peter B. Matthews, Julius Guccione, Harry A. Dwyer, David Saloner, Timothy A.M. Chuter, T. Sloane Guy, Mark B. Ratcliffe and Elaine E. Tseng Ann Thorac Surg 2008;85:1631-1638 DOI: 10.1016/j.athoracsur.2008.01.035

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The Annals of Thoracic Surgery is the official journal of The Society of Thoracic Surgeons and the Southern Thoracic Surgical Association. Copyright © 2008 by The Society of Thoracic Surgeons. Print ISSN: 0003-4975; eISSN: 1552-6259.

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Namrata Gundiah, PhD, Kimberly Kam, BS, Peter B. Matthews, BS, Julius Guccione, PhD, Harry A. Dwyer, PhD, David Saloner, PhD, Timothy A. M. Chuter, MD, T. Sloane Guy, MD, Mark B. Ratcliffe, MD, and Elaine E. Tseng, MD Departments of Surgery and Radiology, University of California at San Francisco Medical Center and San Francisco Veterans Affairs Medical Center, San Francisco, and Department of Mechanical and Aeronautic Engineering, University of California at Davis, Davis, California

Background. Aortic sinuses are crucial components of the aortic root and important for aortic valve function. Mathematical modeling of various aortic valve or root replacements requires tissue material properties, and those of the aortic sinuses are unknown. The aim of this study is to compare the biaxial mechanical properties of the individual porcine aortic sinuses. Methods. Square specimens, oriented in the longitudinal and circumferential directions, were excised from the left coronary, right coronary, and noncoronary porcine sinuses. Tissue thickness was measured, and specimens were subjected to equibiaxial mechanical testing. Stressstrain data corresponding to a 35% stretch were fitted to a Fung strain energy function. Tissue stiffness and anisotropy were compared at 0.3 strain. Results. The circumferential direction was more compliant than the longitudinal one for left coronary (183.03 ⴞ

40.78 kPa versus 231.17 ⴞ 45.38 kPa, respectively; p ⴝ 0.04) and right coronary sinuses (321.74 ⴞ 129.68 kPa versus 443.49 ⴞ 143.59 kPa, respectively; p ⴝ 0.02) at 30% strain. No such differences were noted for noncoronary sinuses (331.74 ⴞ 129.68 kPa versus 415.98 ⴞ 191.38 kPa; p ⴝ 0.19). Left coronary sinus was also significantly more compliant than right and noncoronary sinuses. There were no differences between right coronary and noncoronary sinus tissues. Conclusions. We demonstrate that the material properties of the porcine aortic sinuses are not symmetric. The left coronary sinus is significantly more compliant than the remaining sinuses. Realistic modeling of the aortic root must take into account the asymmetric differences in tissue material properties of the aortic sinuses. (Ann Thorac Surg 2008;85:1631– 8) © 2008 by The Society of Thoracic Surgeons

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testing. We quantified directional stiffness of sinus tissue and compared the compliance of each of the three sinuses. Constitutive equations were created to facilitate more accurate finite-element simulation of the aortic root. These data will better simulate in vivo heart function, providing a powerful tool for understanding disease mechanisms and developing percutaneous valves.

he aortic root, comprising the aortic valve, coronary artery ostia, and sinuses of Valsalva, extends from the aortic annulus to the sinotubular junction and joins the ascending aorta. The bulb-shaped sinuses of Valsalva are crucial for aortic valve function and coronary blood flow. New devices and techniques for aortic valve replacement involving transcatheter valves may significantly change blood flow dynamics in the aortic root and coronaries. A robust computational model of the aortic root is a prerequisite for investigating blood flow through prosthetic aortic valves. Prior models have been developed to determine the role of the sinuses in vortex formation and aortic leaflet dynamics [1–3]. These simulations have shown that asymmetric sinus geometry affects stress distribution throughout the root [4 –7]. However, computational models could better simulate the tissue’s response to stress using biaxial mechanical properties of the aortic sinuses, which are currently unknown [8]. The aim of this study is to determine material properties of each aortic sinus through biaxial stretch Accepted for publication Jan 7, 2008. Address correspondence to Dr Tseng, University of California at San Francisco, Medical Center, Division of Cardiothoracic Surgery, 500 Parnassus Ave, Suite W405, Box 0118, San Francisco, CA 94143-0118; e-mail: [email protected].

Material and Methods Specimen Preparation Fresh porcine hearts were obtained from the local abattoir on the morning of harvest. All hearts used in the study were from large, adult pigs approximately 160 pounds. Aortic sinuses (noncoronary [NC], left coronary [LC], and right coronary [RC]) were dissected, washed, and stored at 4°C in Dulbecco’s saline solution without calcium and magnesium. Mechanical testing was completed within 24 hours of harvest. Square specimens (n ⫽ 6), approximately 1 cm2, cut from the LC, RC, and NC were generally attainable because the tissue was fresh, not fixed. Location of sample excision is depicted in Figure 1. As the exact location of the coronary ostia varies within the LC and RC sinuses of each heart, the largest sample of homogeneous thickness below or beside it was

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Abbreviations x,y f x, fy L x, L y

␭x, ␭y Txx, Tyy Exx, Eyy c, cxx, cxy, cyy F LC NC RC T W

⫽ circumferential and longitudinal directions ⫽ circumferential and longitudinal forces ⫽ length and width of test specimen (mm) ⫽ circumferential and longitudinal stretches ⫽ Cauchy stresses (kPa) ⫽ Green strains ⫽ coefficients to W ⫽ deformation gradient ⫽ left coronary sinus ⫽ noncoronary sinus ⫽ right coronary sinus ⫽ specimen thickness (mm) ⫽ Fung strain energy function

cut for testing. Sample thicknesses were measured in six places with calipers by lightly sandwiching the tissue between glass slides, and the average was used as the sample thickness. Although the sinus cavity is bulbous in shape, cut samples were planar in geometry. Principal test directions were chosen to correspond with circumferential and longitudinal axes of the cylindrical geometry of the ascending aorta (Fig 1).

Planar Biaxial Testing System A custom-built planar biaxial stretcher was used to determine the constitutive properties of the aortic sinuses (Fig 2). Details of the biaxial tensile testing methods and analyses have been previously described [9]. Briefly, three 5-0 silk sutures were sutured through each edge of the specimen and used to attach the tissue to the

Fig 1. Schematic of the aortic root showing the locations from which the tissues were excised for mechanical experiments. (L. ⫽ left; LC ⫽ left coronary sinus; NC ⫽ noncoronary sinus; R. ⫽ right; RC ⫽ right coronary sinus; x axis ⫽ circumferential; y axis ⫽ longitudinal.)

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four linear arms of the stretcher. Sample orientation is crucial in determining mechanical properties; thus, care was taken to align the circumferential and longitudinal edges of the tissue with the direction of deformation. Five black ceramic markers (MO-SCI Corp, Rolla, MO; 250 to 355 ␮m) were glued to the tissue surface using cyanoacrylate glue to create a 3-mm ⫻ 3-mm grid in the center of the specimen. The tissue was then floated in a saline bath at 20°C. Load cells (model 31/3672-02, Honeywell Sensotec Inc, Columbus, OH; 1,000 g ⫾ 0.1%), located on two orthogonal arms, were zeroed and monitored while mounting the sample to ensure that a measurement of zero force corresponded to the resting tissue length. During extension, data from the load cells were amplified (Gould Universal Amplifier, model 13-4615-58; 0.01 V; Gould Instrument Systems, Valley View, OH) and used to determine force on the sample during deformation. Real-time displacements of the marker beads on the tissue surface were obtained using a noncontacting charge-coupled device camera placed over the tissue surface (30 frames/s, model TM 9701, Pulnix Inc, Sunnyvale, CA; 0.1 pixels/mm). Images of the tissue surface during deformation were digitized, and the centroid of the pixel intensities, corresponding to each of the five black markers, was obtained based on the contrast of the surrounding tissue located within enclosed boxes. Calibration of a black circle, placed on the tissue surface before the experiment, was used to obtain the calculated marker displacements that were next converted into Green strains.

Data Collection and Analysis Samples were tested using equibiaxial displacement control. Each test consisted of four loading cycles of deformation using a triangular waveform at 0.5 Hz. Specimens were subjected to sequentially increasing deformations of 10%, 15%, 20%, and 35%. To ensure repeatability of the tissue’s response, each test was preceded by 10 preconditioning cycles of 10% stretch, also at 0.5 Hz. Data recorded during the first loading cycle were used to determine Cauchy stress and Green strain on the tissue during extension. Finally, effective preconditioning and consistent data measurement were evaluated. One sample from each sinus was subjected to three sequential equibiaxial tests at 35%, and the results were used as a measure of experimental repeatability. Although we have not examined the effects of strain rate on sinus tissues in this study, based on prior studies we, however, assume insensitivity of these tissues to moderate variations in strain rate [10]. Analysis of the tissue stress and strain assumes material incompressibility. Although arterial tissue is known to have heterogeneous layers and fiber alignment, the tissue was modeled as a homogeneous material, and hence global measures of stress and strain were applied [11]. The deformation gradient (F) was calculated for each recorded point of the loading cycle. The five markers within the strain region formed four nonoverlapping triangles (Fig 2). Green strain was calculated for each triangle independently to assess homogeneity of defor-

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mation, and the data from the four triangles were subsequently averaged. Components of Green strain in the circumferential (Exx) and longitudinal (Eyy) directions were calculated using the following equations: Exx ⫽ Eyy ⫽

Ⲑ

1 2 1 2

共␭x2 ⫺ 1兲

(1a)

共␭y2 ⫺ 1兲

(1b)

where ␭x and ␭y共␭i ⫽ Li Li0 , i ⫽ x, y兲 are stretches in the circumferential and longitudinal directions, representing the ratio of the deformed length to the resting tissue length after preconditioning. Planar forces (fx, fy) during deformation were converted to Cauchy stresses in the principal directions, designated as circumferential and longitudinal directions, and given by the following equations: Txx ⫽ ␭x Tyy ⫽ ␭y

fx t Ly fy t Lx

(2a) (2b)

where t is tissue thickness, and Lx and Ly are the length and the width of the samples in the two directions, respectively.

Constitutive Modeling Stress-strain data from each sinus were fit to a Fung form of strain energy function (W), given by the following equations: W⫽

c 2

Fig 2. Custom-built biaxial stretcher used in the experiments.

Convex functions are important in solving numerical problems in biomechanics using the strain energy function [13, 14]. Coefficient optimization was constrained to ensure convexity of the strain energy function. When c is greater than 0, Equation 3 is convex if and only if the following are true: cxx ⬎ 0, cyy ⬎ 0

共eQ ⫺ 1兲

2 2 Q ⫽ cxxExx ⫹ 2cxyExxEyy ⫹ cyyEyy

where c and cij, i, j, ⫽ x, y are coefficients to the model [12]. The coefficient c is a material parameter, whereas cxx and cyy are nondimensional material parameters that represent contributions in the circumferential and longitudinal directions, respectively. The cxy coefficient represents coupling in the two directions, and may be used to measure tissue anisotropy [10]. From this model, Cauchy stresses for the sinuses are given by the following equations: Txx ⫽ ␭x2c exp共Q兲共cxxExx ⫹ cxyEyy兲 Tyy ⫽ ␭y2c exp共Q兲共cxyExx ⫹ cyyEyy兲

2 and cxxcyy ⬎ cxy

(3)

(5)

Overall behavior of the tissue was quantified through tissue stiffness, the numerically determined first derivative of the modeled stress-strain response at a point during deformation. Coefficients of the strain energy function do not have real-world meaning, and hence comparing tissue stiffnesses is one method used to incorporate all coefficients and nonlinear effects. Stiffness for each principal direction was calculated at physiologic distension, corresponding to 0.3 equibiaxial strain [15]. Differences in circumferential and longitudinal stiffness were used as an index of tissue anisotropy.

(4)

A nonlinear regression Levenberg-Marquardt leastsquares algorithm in MATLAB (v7.0.1, Natick, MA) was used to fit the experimentally obtained stresses (Eq 2) to the corresponding theoretically calculated stresses (Eq 4). The optimization method is iterative and arrives at a solution by minimizing differences between the experimentally obtained and the calculated Cauchy stresses. Because the optimized solution may be sensitive to the starting parameters, a number of wide-ranging initial starting guesses were used to arrive at the optimum minimized solution.

Statistical Analysis One-way analysis of variance with Bonferroni comparisons was performed to test for differences between the sinus tissues in both the circumferential and longitudinal directions. Independent means paired Student’s t tests were used to independently quantify tissue anisotropy. Reported values are quoted as mean ⫾ standard deviation, and a probability value less than 0.05 was considered statistically significant. Statistical analyses were performed using the statistical toolbox in MATLAB (v 7.0, Natick, MA).

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Fig 3. Cauchy stress (Txx, Tyy) versus Green strain (Exx, Eyy) curves for the left coronary sinus (top), right coronary sinus (middle), and noncoronary sinus (bottom) tissues in the study, constructed using the coefficients to the Fung strain energy function obtained by the LevenbergMarquardt optimization method.

Results Anatomic differences were analyzed among samples taken from the three sinuses. There were no significant differences in thickness between the RC (2.11 ⫾ 0.29 mm) and the NC (1.79 ⫾ 0.48 mm; p ⫽ 0.21), or the RC and the LC (2.36 ⫾ 0.39 mm; p ⫽ 0.16). However, the LC was thicker than the NC, approaching statistical significance (p ⫽ 0.05). There were also no significant differences in sample dimensions for the RC (10.38 ⫾ 1.48 mm) as

compared with the LC (10.57 ⫾ 1.21 mm; p ⫽ 0.82), or as compared with the NC (12.08 ⫾ 1.36 mm; p ⫽ 0.07). The LC and NC were not significantly different in size (p ⫽ 0.07).

Biaxial Mechanical Response Data gathered from 35% equibiaxial stretch testing show nonlinear stress-strain behavior for the range of deformation in all three sinus groups (Fig 3). Strain in the four

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Fig 4. Sample 15 from a noncoronary sinus. The principal strains in x and y directions as well as shear strains were calculated from the four triangles. Strains were similar for all four triangles, demonstrating mostly homogeneous deformation.

triangles showed a mostly homogeneous deformation of the tissue within the central region of the sample, and the average was used to approximate the tissue’s overall response (Fig 4). Shear strain measured during deformation was in the region of one order of magnitude less than strain in the principal axes, justifying its exclusion from the strain energy function chosen. The resultant constitutive equations modeled experimental data with excellent correlation by root mean squared error. We have enforced constraint (Fig 5A) in the optimization process and have checked for constraint (Fig 5B). Averaged coefficients met both criteria for convexity for the LC and RC groups but not for the NC sinus tissues. Averaged coefficients for each sinus are shown in Table 1, representing a composite strain energy function for the tissue. Plots of the strain energy function are extrapolated to 0.5 Green strain (Fig 5) to illustrate the greater compliance of the LC in comparison wih the RC and NC, which have only a small difference in compliance. To quantify material property differences, the circumferential and longitudinal stiffness were computed using strain energy functions of the individual samples, as opposed to the composite function. Comparison of tissue stiffness was performed among the sinus groups (Fig 6A), and tissue anisotropy was examined for each sinus by comparing directional stiffness (Fig 6B). The LC is significantly stiffer in the longitudinal direction as compared with the circumferential direction (231.17 ⫾ 45.38 kPa versus 183.03 ⫾ 40.78 kPa; p ⫽ 0.04). A similar result is seen with the RC (443.49 ⫾ 143.59 kPa versus 321.74 ⫾ 129.68 kPa; p ⫽ 0.02), but not significantly in the NC (415.98 ⫾ 191.38 kPa versus 331.74 ⫾ 129.68 kPa; p ⫽ 0.19). Among the sinus groups, the LC is less stiff than the NC in the circumferential (p ⫽ 0.034) and the longitudinal (p ⫽ 0.042) directions; the LC is less stiff than the RC in the longitudinal direction (p ⫽ 0.01) and shows a trend

toward greater compliance in the circumferential direction (p ⫽ 0.059). There is no significant difference in stiffness between the RC and NC tissues in either the circumferential (p ⫽ 0.342) or longitudinal (p ⫽ 0.684) directions. Results of the repeatability trials indicate excellent consistency during experimental testing and data analysis. When sinus samples were stretched to 35% extension in three consecutive tests, the standard deviation of the calculated stiffnesses was a small percentage of the mean stiffness in both the circumferential (5.9% LC; 3.1% NC; 4.5% RC) and longitudinal directions (4.4% LC; 4.1% NC; 1.4% RC).

Comment Using equibiaxial stretch testing, we demonstrate for the first time that the aortic sinuses have significant regional asymmetry and anisotropy. At physiologic strains, the circumferential axis of the LC and RC are more compliant than the longitudinal axis, but no such difference exists in the NC. The LC is significantly more compliant than the NC in both axes and more compliant than the RC in the longitudinal but not circumferential axis; RC and NC show no difference in compliance.

Aortic Root Dynamics The highly specialized structures of the aortic root—the sinuses, annulus, and leaflets—interact in a complex, dynamic, coordinated manner [16]. The importance of aortic sinuses in creating vortices was first recognized by Leonardo da Vinci [17]. Both the sinus geometry and tissue compliance are crucial for the normal opening and closing of the aortic valve leaflets [1–3, 15, 16]. Aortic root dilation occurs before ejection and aids leaflet opening by 20% [15]. Root deformation observed in vivo is complex and asymmetric, containing elongation, compres-

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Fig 5. Composite Cauchy stress curves (Txx, Tyy) for the left coronary sinus (LC), the right coronary sinus (RC), and the noncoronary (NC) sinus tissues in the study. Each individual curve is constructed using the average value of the coefficients to the strain energy function, as shown in Table 1.

sion, shear, and torsional components [1–3, 15, 16, 18 –20]. The sinus is also known to play a role in coronary flow, which varies during the cardiac cycle and is unequally Table 1. Coefficients to Fung Strain Energy Function (Eq 3) Used To Fit Experimental Data From Sinus Tissues Variable Cxx Cxy Cyy C (kPa)

RC

NC

LC

1.4325 ⫾ 0.9545 0.5351 ⫾ 0.6560 0.3397 ⫾ 0.26 0.5870 ⫾ 0.6405 1.5129 ⫾ 0.7452 0.4235 ⫾ 0.1915 2.1321 ⫾ 0.9479 0.9518 ⫾ 0.6172 0.5395 ⫾ 0.3459 34.3346 ⫾ 22.3944 36.0552 ⫾ 24.244 96.6183 ⫾ 56.9485

C, Cxx, Cxy, and Cyy ⫽ coefficients to Fung strain energy function; LC ⫽ left coronary sinus; NC ⫽ noncoronary sinus; RC ⫽ right coronary sinus.

Fig 6. Tissue stiffness computed at a Green strain of 0.3, comparing (A) left coronary sinus (LC), the right coronary sinus (RC), and the noncoronary (NC) sinus stiffness, and (B) longitudinal versus circumferential stiffness for each sinus.

distributed between the left and right coronary arteries [21, 22]. Traditional treatment for aortic stenosis involves surgical excision of the native leaflets and replacement with a mechanical or bioprosthetic valve. However, transcatheter valves will significantly impact the geometry and compliance of the aortic root, potentially altering the dynamics of leaflet opening and flow through the root and coronaries.

Computational Modeling Earlier studies using finite-element modeling have demonstrated its value as a tool for investigating the mechan-

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ics of the aortic root [1, 2, 5–7, 23]. Increases in leaflet stress and strain, accompanied by reduced coaptation, have been shown in models of progressive root dilatation [5]. Sinus geometry has proven essential in preserving the physiologic leaflet stress patterns. The current cylindrical graft (reimplantation technique) and tailored graft (remodeling technique) valve-sparing surgeries alter these patterns, whereas pseudosinus graft geometry more closely mimics physiologic stress [6, 23]. In addition, material properties influence leaflet stresses and strains. When the aortic modulus was doubled and the root was dilated in a computational model of Marfan syndrome, stress increases ranged from 80% to 360%, and strains from 60% to 200% [7].

Variation in the Material Property of the Sinus To our knowledge current root models do not use specific material properties of individual aortic sinuses. Using digital sonomicrometry, distensibility of the porcine aortic root has been quantified in both static pressurization and insolated working heart models [18, 19]. A circumferential strain of 33% was measured at the height of the commissures during an increase from 0 to 120 mm Hg. Although longitudinal dimensions increased by 13% between the aortic annulus and the sinotubular junction, the portion of the ascending aorta immediately distal expanded by 35% during the same increase in pressure. Because these measurements reflect strain from zero pressure to systole, as opposed to diastole to systole, they most accurately reflect data gathered during biaxial stretch testing. Therefore, we have chosen to quantify stiffness at 0.3 Green strain. The same study observed greatest compliance during the beginning of the loading cycle, corroborating our data and demonstrating characteristic nonlinearity of arterial tissue. Our current study has shown that the LC is more compliant than the RC and NC, and that the LC and RC were anisotropic, with the longitudinal direction stiffer than the circumferential direction. Using a linear, elastic, small-deformation finite-element modeling of a normal human aortic root, asymmetric distribution of stresses in the three sinuses and leaflets was observed [4]. Stresses were highest in the NC and leaflet, followed by those in the RC and then the LC leaflet system. When all three sinuses are modeled with the same modulus, strain calculations are dependent entirely on the finite-element modeling geometry and stress in that region [4]. However, material property asymmetry contributes to dilation as well and should be used as parameters for a more accurate finite-element modeling.

Study Limitations Differential stretch protocols, in addition to equibiaxial testing, are useful in characterizing coupling between two orthogonal directions [24]. The aim of our study was to compare the stiffness of aortic sinus tissue. Because equibiaxial testing is the only protocol that may be used to summarize differences in tissue stiffness in the two principal axes of strain, it was used here. Second, all experiments were conducted using a por-

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cine model. Human tissues, especially nondiseased, sexmatched and age-matched controls, are difficult to obtain. We hope to eventually obtain enough human specimens to determine whether our findings are similar in humans. Because the porcine model is frequently used as an approximation of healthy human tissues and glutaraldehyde-fixed porcine tissues are used for root replacements in humans, we hope that the findings of this study will nevertheless be useful to both researchers and surgeons [8]. Although all tissue samples were harvested from adult pigs, the exact age of the animals was not known. Arterial elastin content increases during aging, increasing tissue stiffness [25]. Because all tissues were taken from adult animals, the variability in measurements would reflect biologic differences, and the comparison would nevertheless remain valid.

Conclusions Using equibiaxial stretch testing of the aortic sinuses, we demonstrate that the aortic root has significant regional asymmetry and anisotropy. For both the LC and RC sinuses, the circumferential axis is more compliant than the longitudinal, whereas no such anisotropy exists in the NC sinus. The RC and NC are similar in compliance, but the LC is more compliant than the NC and RC. Corroborating our data, the sinus undergoing the greatest deformation in vivo is the LC, and future finite-element modeling containing regional asymmetry may further explain this observation. We also speculate that regional differences in compliance may have consequences on stress distribution on the aortic leaflets. The derived constitutive equations can be used in future modeling studies to accurately predict variations in root and coronary flow after aortic valve replacement, including percutaneous valves.

This work was supported by AHA Beginning Grant-in-Aid 0565148Y and the Northern California Institute for Research and Education.

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Asymmetric Mechanical Properties of Porcine Aortic Sinuses Namrata Gundiah, Kimberly Kam, Peter B. Matthews, Julius Guccione, Harry A. Dwyer, David Saloner, Timothy A.M. Chuter, T. Sloane Guy, Mark B. Ratcliffe and Elaine E. Tseng Ann Thorac Surg 2008;85:1631-1638 DOI: 10.1016/j.athoracsur.2008.01.035 Updated Information & Services

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