Search tips
Search criteria 


Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Biomech Eng. Author manuscript; available in PMC 2011 May 19.
Published in final edited form as:
PMCID: PMC3097530

Regional Left Ventricular Myocardial Contractility and Stress in a Finite Element Model of Posterobasal Myocardial Infarction


Recently, a non-invasive method for determining regional myocardial contractility, using an animal-specific finite element (FE) model-based optimization, was developed to study sheep with anteroapical infarction [1]. Using the methodology developed in the previous study [1], which incorporates tagged magnetic resonance images (MRI), three-dimensional (3D) myocardial strains, left ventricular (LV) volumes, and LV cardiac catheterization pressures, the regional myocardial contractility and stress distribution of a sheep with posterobasal infarction was investigated. Active material parameters in the noninfarcted borderzone (BZ) myocardium adjacent to the infarct (Tmax_B), in the myocardium remote from the infarct (Tmax_R), and in the infarct (Tmax_I) were estimated by minimizing the errors between FE model-predicted and experimentally measured systolic strains and LV volumes using the previously developed optimization scheme. The optimized Tmax_B was found to be significantly depressed relative to Tmax_R, while Tmax_I was found to be zero. The myofiber stress in the BZ was found to be elevated, relative to the remote region. This could cause further damage to the contracting myocytes, leading to heart failure.

Keywords: finite element modeling, numerical optimization, cardiac mechanics, tagged magnetic resonance imaging


Myocardial contractility plays a central role in the heart’s ability to pump blood efficiently into the body. When myocardial tissue becomes damaged, due to infarction, it is the job of clinicians to determine to what degree the heart is impaired. A non-invasive method for estimating regional myocardial contractility would be a beneficial tool for cardiologists to assess viable and nonviable tissue. This tool could also be used to evaluate the efficacy of surgical procedures and medical devices for treating infarction-induced heart failure. The most important benefit would be to help surgeons decide where to incise and how much of the left ventricular (LV) infarct region is impaired.

Several studies have been conducted on left ventricles with anteroapical aneurysms that employ finite element (FE) simulations, in conjunction with a manually directed pseudo-optimization, to assess the contractile function of myocardium [2, 3]. However, these studies required long computation times for each case that was evaluated. In order to overcome this deficiency, a fully automated nonlinear optimization was developed for estimating regional myocardial contractility that was at least 24 times faster than those previous studies [1, 4].

The goal of the current study is to extend the application of this formal optimization technique to examine myocardial infarction in a different region of the left ventricle. Although the previous study [1] looked at anteroapical LV aneurysm, it was found that this method is robust enough to be applied to other types of infarcts. Of particular interest is the degradation of the posterobasal region of the left ventricle, which is linked to mitral regurgitation and the advancement of heart failure [5]. The methodology described in Sun et al. [1] provided the framework for the work presented here.


The details of the experimental measurements, model generation, and optimization scheme are presented in Sun et al. [1]. A brief overview of the methodological approach, along with several key differences to the previous work, is presented in the following sections.

Experimental Measurements

A single male adult Dorsett sheep underwent posterobasal myocardial infarction as previously described [6, 7]. At 8 weeks post-myocardial infarction, a series of orthogonal short- and long-axis tagged magnetic resonance (MR) images were acquired, while ventricular pressure was continuously measured [8]. The endocardial and epicardial LV surfaces were contoured from the images, and the systolic tags were segmented for each image slice in order to compute the systolic myocardial strain at mid-wall of the LV (Figs. 1a and 1b) [9, 10]. Unlike the previous application [1], where the aneurysm wall was very thin, strain components were calculated within the infarct region in the current application. This data was used to confirm the location of the infarct due to the appearance of positive strain, which indicates that the myocardium is stretching rather than shortening during systole. This phenomenon can be seen in Fig. 1c, where the infarct strain is positive and borderzone (BZ) strain is elevated, relative to the remote region.

Figure 1
3D cardiac strain analysis from in-vivo tagged MR images. Endocardial and epicardial contours as well as segmented tag-lines were traced from (a) short-axis MR images to create a 3D geometry. (b) Each short axis slice was divided into 12 sectors and a ...

FE Model

An FE model was created based on the LV geometry at early diastole (Fig. 2a). This configuration was selected because the stress is at a minimum in the LV. The remote, BZ, and infarct regions were determined based on several factors. First, the infarct region was determined using the circumferential component of strain calculated from the MR images. In this case, positive circumferential strain was indicative of the infarct region. The geometric dimensions of this region were then confirmed with measurements of the infarct region from the excised heart of the animal. The BZ region was approximated as the transition in wall thickness between remote and infarct regions (Fig. 2b) [11]. Histological studies are currently being conducted on sheep with posterobasal infarcts, which will help characterize the size of the BZ. However, in a clinical setting histological studies will not be possible and thus other non-invasive factors will need to be assessed.

Figure 2
(a) Animal-specific finite element model used in the optimization method. The green elements represent the healthy remote region, the red elements are the borderzone, and the blue elements are the infarcted region. (b) Cross-section view of the animal-specific ...

The geometry was meshed with 8-noded trilinear brick elements, for a total of 3940 elements. Each region, remote, BZ and infarct, were assigned different material properties [1]. Cardiac myofiber angles were assigned to vary transmurally from −37° to 83° (epicardium to endocardium), relative to the circumferential direction, in the remote and BZ regions [12]. At the infarct region, fiber angles were set to 0° in order to use experimentally determined material parameters with respect to this direction [13]. Although the results from Moonly [13] were for an anteroapical infarct, it has been shown in a porcine animal model that the distribution of collagen fibers in a lateral mid-ventricular MI is primarily dominated by the circumferential direction, and is driven by the direction of highest tensile stretching [14, 15].

The_ constitutive laws for passive and active myocardium have been described previously [16, 17]. Briefly, the passive material response is given by the strain energy function, W, that is transversely isotropic with respect to the local fiber direction,


where C, bf, bt and bfs are diastolic myocardial material parameters, E11 is strain in fiber direction, E22 is cross-fiber in-plane strain, E33 is radial strain transverse to the fiber direction, and the rest are shear strains. Systolic contraction was modeled as the sum of the passive stress derived from the strain energy function and an active fiber directional component, T0 [17], which is a function of time, t, peak intracellular calcium concentration, Ca0, sarcomere length, l, and maximum isometric tension achieved at the longest sarcomere length, Tmax [18],


where Dev() is the deviatoric operator [1].

The tagged MR images were acquired during systole, which means that only systolic myocardial strains were determined. Therefore, the systolic material parameters in the remote (Tmax_R), BZ (Tmax_B), and infarct (Tmax_I) regions were computed from the optimization. The passive parameter, C, in the remote (CR) was determined such that the model-predicted end-diastolic LV volume matched the experimentally measured value. The initial search range in the optimization was set between 0 and 800 kPa for Tmax_R, between 0 and 400 kPa for Tmax_B, and between 0 and 200 kPa for Tmax_I. Although calcium concentration can vary in the region around the infarct, the contractility parameter, Tmax, was used as the single measure of change to contractile capability in the various myocardial regions.

Material Parameter Optimization

The objective function for the optimization was taken to be the mean squared error (MSE), which evaluates the difference between the computed FE and measured experimental results (end-diastolic and end-systolic volumes, and systolic strains). The goal of the optimization is to minimize the MSE. One primary difference between the previous application of the optimization [1] and the current, is the use of strain in the infarct as part of the MSE,


where n is the in-vivo strain point, N is the total number of in-vivo strain points, Eij,n is the computed FE strain at each strain point, VED and VES are the computed FE end-diastolic and end-systolic LV volumes, respectively. The overbar represents experimental in-vivo measurements. Although the end-diastolic volume does not affect the outcome of the active parameter optimization, it was included in the objective function to account for all of the constraints involved in matching the predicted outcomes to those that were experimentally measured.

The weights, defined as wn, wVED, and wVES, were used to balance the importance of each term in the MSE. In the current case, there are 4 times as many experimental strain points in the remote region than in the BZ and infarct. Thus the weights for the BZ and infarct MSE components were set to 4, while the rest were kept equal to 1. Strain in the radial direction was excluded as it cannot be measured with sufficient accuracy in the BZ region with tagged MR images [19, 20].


The measured end-diastolic pressure (6.1 mmHg) was applied to the endocardial wall of the FE model while the passive myocardial stiffness was varied, such that VED was accurately predicted at 104.9 mL with the measured value being 105 mL. The parameters CR and CB were calibrated to be 0.017 kPa, while CI was defined to be 10 times stiffer at 0.17 kPa. The calibrated end-diastolic state was used as the reference state for the systolic strain calculation, which was computed using a multiplicative decomposition of the deformation gradient, as described in Sun et al. [1].

The minimum MSE of 11.13, consisting of 720 systolic strain and 2 LV volume data points, was reached in 10 iterations. The optimized contractility parameters for this sheep were found to be Tmax_R = 180 kPa, Tmax_B = 115.4 kPa, and Tmax_I = 0.0 kPa. This shows a 36% decrease in contractile function in the BZ compared to the remote region, and confirms that the infarct has no contractile function. Using the measured end-systolic pressure (91.5 mmHg), the volume VES was predicted to be 67.4 mL, which is only 4.6% higher than the measured value of 64.4 mL.

The predicted systolic strains, using the optimized material parameters, were in generally good agreement with the in-vivo measured strains. Of particular interest is the agreement in the circumferential component of strain, because it aligns very closely to the fiber direction at mid-wall. The mean and standard deviation of the circumferential strain, by region, is given in Table 1 and Table 2. It can be seen that the experimental and finite element strains are within one standard deviation of each other, in each region. In fact, the difference is well below one standard deviation in the remote and BZ regions.

Table 1
Experimental circumferential strain shown by region, determined from tagged MR images.
Table 2
FE calculated circumferential strain shown by region, determined from the optimization method.

The root mean square (RMS) error for the circumferential strain component between the 116 pairs of measured and predicted strains in the remote region was 0.673, in the BZ the RMS error was 0.249 with 18 pairs of strain points, and in the infarct region the RMS was 0.167 with 10 pairs of strain points. An example of the circumferential strain agreement at a mid-ventricular slice is shown in Fig. 3a. The mean and standard deviation of the experimental strain in this slice is −0.112 ± 0.078 and for the FE strain is −0.118 ± 0.080, which are in very close agreement. An example of the longitudinal strain in the same mid-ventricular slice is shown in Fig. 3b. It can be seen that the strain is also positive in the infarct region, indicating longitudinal stretching.

Figure 3
A comparison of the experimental and finite element (a) circumferential strain and (b) longitudinal strain in a slice near mid-ventricle. On average, there is good agreement between the experimental and numerical strains in the remote, borderzone, and ...

The total stress in the myofiber direction at end-systole, as given by Equ. (2), was elevated in the BZ region relative to the remote region.. This is indicated by the peak stresses seen in Fig. 4. The region of the BZ that is most affected corresponds to sector 11 (shown in Fig. 1b). At this sector the circumferential strain is elevated relative to the remote region, which indicates that there is less shortening going on in the muscle fibers at this point (i.e. they are being extended). This stress concentration could potentially lead to further expansion of the infarct and BZ regions, through impairment of the myocytes.

Figure 4
Stress (kPa) in the myofiber direction at end-systole. The black lines represent the boundaries of the borderzone. The stress is elevated in the borderzone region, which is indicated by the red color contour.

For the optimization of 3 material parameters, 7 experimental points were selected using a D-optimal method for each iteration. The entire optimization process involving 10 iterations required about 3 hours on a Dell Precision T7400 with dual 3.2 GHz Quad Core Xeon processors.


After adapting the formal optimization method [1], it was found in this study that Tmax_B is also substantially depressed compared to Tmax_R in a posterobasal MI animal model. In addition, with improved computing power, which is now becoming more standard, the simulation time was improved by 50% compared to the previous optimization study [1].

A significant difference between the current study and initial application of the formal optimization method is the ability to compute strain in the infarct region. This is because posterobasal infarcts are thicker than anteroapical LV aneurysms (1-3 mm), and thus can be tagged during MRI. Posterobasal infarcts behave differently during remodeling, as they do not stretch as much as anteroapical infarcts. The optimization method was able to be applied to this type of infarct without any major changes to the methodology. The method should be robust enough to handle several different types of infarcts. An overview of several previous optimization studies is given in Sun et al. [1].

In order to assess the influence of varying BZ fiber angles, a sensitivity study was conducted in which the BZ fiber angles were rotated with a 23° leftward shift, resulting in a distribution of −60° to 60° from epicardium to endocardium. It was found that Tmax_B decreased by 9% and Tmax_R increased by 6%, compared to the original optimization. This result still shows a significant depression in BZ contractility relative to the remote. The angles in the sensitivity study correspond to the in-vivo dMRI data from Wu et al. [21, 22] concerning patients with an MI in which the percentage of left-handed helical fibers (negative subepicardial fiber angles) increased from the remote zone to the BZ, and the percentage of right-handed helical fibers (positive supendocardial fiber angles) decreased from the remote zone to the BZ. Alternatively, recent ex-vivo dMRI data from infarcted rat hearts indicate that BZ helix angles are preserved [23, 24]. Thus the effect of MI on BZ fiber angle change is still unresolved.

The circumferential strain can be used as a means of non-invasively identifying the infarct region. This can be done in concert with delayed enhancement, in order to fully understand the location and depth of the infarct [25]. In many simulations, the contractility in the infarct is assumed to be zero [2, 3, 26]. In the present study, this parameter was allowed to vary during the optimization. The fact that Tmax_I was determined to be zero confirms this assumption. It is possible for an infarct not to be fully transmural. In this case the contractility would most likely be non-zero.

Due to the presence of strain in the infarct, the weights were adjusted in the objective function in order to balance the contribution of each region to the MSE. By shifting the weights, it was found that the agreement of the circumferential strain was improved, particularly in the BZ, when the weights were changed from 1 to 4 in the BZ and infarct region. In general, the weights can have a significant effect on the outcome of an optimization [27]. The influence of the weights can be explored through techniques such as the Pareto Frontier [28]. However, the weights were chosen manually in the present work.

There are several limitations in the present study. The interaction with the RV was neglected in the current study, which could explain the prediction of overstretching in the infarct compared to the experimental results. Future studies will include the RV geometry and pressure as part of the model. The quality and resolution of the experimental strain could be improved by utilizing a 3T scanner rather than a1.5T scanner, which can produce a more precise gradient of strain in the LV wall [29, 30]. Additionally, it is difficult to quantify the steep transition in the wall thickness at the BZ. Thus the BZ region was approximated using a combination of circumferential strain and a clinician’s best judgment. With further development, higher quality experimental strain may be able to help identify the BZ region more precisely.

In order to more accurately assess the degree of anisotropy in the passive response of each region in the infarcted LV, the optimization technique will be extended to evaluate diastolic material properties. In future work, this will require the acquisition of tagged MR images during the diastolic phase. Due to the robustness of this tool, the goal is to track changes in myocardial material properties of the same heart as it remodels over time. This will allow for a long term assessment of how various surgical procedures affect the mechanical response of the heart [3, 31-33].


This study was supported by NIH grants R01-HL-84431 (Dr. Ratcliffe), R01-HL-63348 (Dr. Ratcliffe), R01-HL-77921 (Dr. Guccione), and R01-HL-86400 (Dr. Guccione). This support is gratefully acknowledged.


[1] Sun K, Stander N, Jhun C-S, Zhang Z, Suzuki T, Saeed M, Wallace AW, Tseng EE, Baker AJ, Saloner D, Einstein DR, Ratcliffe MB, Guccione JM. A computationally efficient formal optimization of regional myocardial contractility in a sheep with left ventricular aneurysm. J Biomech Eng. 2009;131(11):111001. [PMC free article] [PubMed]
[2] Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Fata B, Hsu EW, Saloner D, Guccione JM. MRI-based finite-element analysis of left ventricular aneurysm. Am J Physiol Heart Circ Physiol. 2005;289(2):H692–700. [PubMed]
[3] Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Hsu EW, Saloner DA, Guccione JM. Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. J Thorac Cardiovasc Surg. 2008;135(5):1094–1102. e1091–1092. 1102. [PMC free article] [PubMed]
[4] Sun K, Zhang Z, Suzuki T, Wenk JF, Stander N, Einstein DR, Saloner DA, Wallace AW, Guccione JG, Ratcliffe MB. Dor procedure for dyskinetic anteroapical left ventricular aneurysm fails to improve myocardial contractility in the borderzone. J Thorac Cardiovasc Surg. 2009 doi:10.1016/j.jtcvs.2009.11.055. [PMC free article] [PubMed]
[5] Wenk JF, Zhang Z, Cheng G, Malhotra D, Acevedo-Bolton G, Burger M, Suzuki T, Saloner DA, Wallace AW, Guccione JM, Ratcliffe MB. First Finite Element Model of the Left Ventricle With Mitral Valve: Insights Into Ischemic Mitral Regurgitation. Ann Thorac Surg. 2010;89(5):1546–1553. [PMC free article] [PubMed]
[6] Llaneras MR, Nance ML, Streicher JT, Lima JAC, Savino JS, Bogen DK, Deac RFP, Ratcliffe MB, Edmunds LH. Large Animal-Model of Ischemic Mitral Regurgitation. Ann Thorac Surg. 1994;57(2):432–439. [PubMed]
[7] Llaneras MR, Nance ML, Streicher JT, Linden PL, Downing SW, Lima JAC, Deac R, Edmunds LH, Carpentier AF, Frater RW, Oury JH. Pathogenisis of Ischemic Mitral-Insufficiency. J Thorac Cardiovasc Surg. 1993;105(3):439–443. [PubMed]
[8] Guccione JM, Walker JC, Beitler JR, Moonly SM, Zhang P, Guttman MA, Ozturk C, McVeigh ER, Wallace AW, Saloner DA, Ratcliffe MB. The effect of anteroapical aneurysm plication on end-systolic three-dimensional strain in the sheep: a magnetic resonance imaging tagging study. J Thorac Cardiovasc Surg. 2006;131(3):579–586. e573. [PMC free article] [PubMed]
[9] Guttman MA, Zerhouni EA, McVeigh ER. Analysis and visualization of cardiac function from MR images. IEEE Comp Graph Appl. 1997;17(1):30–38. [PMC free article] [PubMed]
[10] Ozturk C, McVeigh ER. Four-dimensional B-spline based motion analysis of tagged MR images: introduction and in vivo validation. Phys Med Biol. 2000;45(6):1683–1702. [PMC free article] [PubMed]
[11] Moustakidis P, Maniar HS, Cupps BP, Absi T, Zheng J, Guccione JM, Sundt TM, Pasque MK. Altered left ventricular geometry changes the border zone temporal distribution of stress in an experimental model of left ventricular aneurysm: a finite element model study. Circulation. 2002;106(12 Suppl 1):I168–175. [PubMed]
[12] Omens JH, May KD, McCulloch AD. Transmural distribution of three-dimensional strain in the isolated arrested canine left ventricle. Am J Physiol Heart Circ Physiol. 1991;261(3 Pt 2):H918–928. [PubMed]
[13] Moonly S. PhD Thesis. University of California, San Francisco with University of California; Berkeley, San Francisco, CA: 2003. Experimental and computational analysis of left ventricular aneurysm mechanics.
[14] Holmes JW, Borg TK, Covell JW. Structure and mechanics of healing myocardial infarcts. Annu Rev Biomed Eng. 2005;7:223–253. [PubMed]
[15] Holmes JW, Nunez JA, Covell JW. Functional implications of myocardial scar structure. Am J Physiol Heart Circ Physiol. 1997;272(5):H2123–H2130. [PubMed]
[16] Guccione JM, McCulloch AD, Waldman LK. Passive material properties of intact ventricular myocardium determined from a cylindrical model. J Biomech Eng. 1991;113(1):42–55. [PubMed]
[17] Guccione JM, Waldman LK, McCulloch AD. Mechanics of active contraction in cardiac muscle: Part II--Cylindrical models of the systolic left ventricle. J Biomech Eng. 1993;115(1):82–90. [PubMed]
[18] Tozeren A. Continuum rheology of muscle contraction and its application to cardiac contractility. Biophys J. 1985;47(3):303–309. [PubMed]
[19] Declerck J, Denney TS, Ozturk C, O’Dell W, McVeigh ER. Left ventricular motion reconstruction from planar tagged MR images: a comparison. Phys Med Biol. 2000;45(6):1611–1632. [PMC free article] [PubMed]
[20] Denney TS, Jr., Gerber BL, Yan L. Unsupervised reconstruction of a three-dimensional left ventricular strain from parallel tagged cardiac images. Magn Reson Med. 2003;49(4):743–754. [PubMed]
[21] Wu MT, Su MYM, Huang YL, Chiou KR, Yang PC, Pan HB, Reese TG, Wedeen VJ, Tseng WYI. Sequential Changes of Myocardial Microstructure in Patients Postmyocardial Infarction by Diffusion-Tensor Cardiac MR Correlation With Left Ventricular Structure and Function. Circ Cardiovasc Imaging. 2009;2(1):32–40. [PubMed]
[22] Wu MT, Tseng WYI, Su MYM, Liu CP, Chiou KR, Wedeen VJ, Reese TG, Yang CF. Diffusion tensor magnetic resonance imaging mapping the fiber architecture remodeling in human myocardium after infarction - Correlation with viability and wall motion. Circulation. 2006;114(10):1036–1045. [PubMed]
[23] Sosnovik DE, Wang RP, Dai GP, Reese TG, Wedeen VJ. Diffusion MR tractography of the heart. J Cardiovasc Magn Reson. 2009;11 [PMC free article] [PubMed]
[24] Sosnovik DE, Wang RP, Dai GP, Wang T, Aikawa E, Novikov M, Rosenzweig A, Gilbert RJ, Wedeen VJ. Diffusion Spectrum MRI Tractography Reveals the Presence of a Complex Network of Residual Myofibers in Infarcted Myocardium. Circ Cardiovasc Imaging. 2009;2(3):206–212. [PMC free article] [PubMed]
[25] Saeed M, Weber O, Lee R, Do L, Martin A, Saloner D, Ursell P, Robert P, Corot C, Higgins CB. Discrimination of Myocardial Acute and Chronic (Scar) Infarctions on Delayed Contrast Enhanced Magnetic Resonance Imaging With Intravascular Magnetic Resonance Contrast Media. J Am Coll Cardiol. 2006;48:1961–1968. [PubMed]
[26] Guccione JM, Moonly SM, Moustakidis P, Costa KD, Moulton MJ, Ratcliffe MB, Pasque MK. Mechanism underlying mechanical dysfunction in the border zone of left ventricular aneurysm: a finite element model study. Ann Thorac Surg. 2001;71(2):654–662. [PubMed]
[27] Wenk JF, Wall S, Peterson RC, Helgerson SL, Sabbah HN, Burger M, Stander N, Ratcliffe MB, Guccione JM. A Method for Automatically Optimizing Medical Devices for Treating Heart Failure: Designing Polymeric Injection Patterns. J Biomech Eng. 2009;131(12):121011. [PubMed]
[28] Stander N, Roux W, Eggleston T, Craig K. LS-OPT user’s manual version 3.2. 2007.
[29] Liu Y, Wen H, Gorman RC, Pilla JJ, Gorman JH, 3rd, Buckberg G, Teague SD, Kassab GS. Reconstruction of myocardial tissue motion and strain fields from displacement-encoded MR imaging. Am J Physiol Heart Circ Physiol. 2009;297(3):H1151–1162. [PubMed]
[30] Xu C, Pilla JJ, Isaac G, Gorman JH, 3rd, Blom AS, Gorman RC, Ling Z, Dougherty L. Deformation analysis of 3D tagged cardiac images using an optical flow method. J Cardiovasc Magn Reson. 2010;12(1):19. [PMC free article] [PubMed]
[31] Dang AB, Guccione JM, Zhang P, Wallace AW, Gorman RC, Gorman JH, 3rd, Ratcliffe MB. Effect of ventricular size and patch stiffness in surgical anterior ventricular restoration: a finite element model study. Ann Thorac Surg. 2005;79(1):185–193. [PubMed]
[32] Wall ST, Walker JC, Healy KE, Ratcliffe MB, Guccione JM. Theoretical impact of the injection of material into the myocardium: a finite element model simulation. Circulation. 2006;114(24):2627–2635. [PubMed]
[33] Zhang P, Guccione JM, Nicholas SI, Walker JC, Crawford PC, Shamal A, Acevedo-Bolton G, Guttman MA, Ozturk C, McVeigh ER, Saloner DA, Wallace AW, Ratcliffe MB. Endoventricular patch plasty for dyskinetic anteroapical left ventricular aneurysm increases systolic circumferential shortening in sheep. J Thorac Cardiovasc Surg. 2007;134(4):1017–1024. [PMC free article] [PubMed]