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Ann Thorac Surg 2005;79:185-193
© 2005 The Society of Thoracic Surgeons

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Original article: Cardiovascular

Effect of Ventricular Size and Patch Stiffness in Surgical Anterior Ventricular Restoration: A Finite Element Model Study

^a School of Medicine of the University of California, San Francisco, San Francisco, California, USA
^b Department of Surgery, University of California, San Francisco, San Francisco, California, USA
^c Department of Bioengineering, University of California, San Francisco, San Francisco, California, USA
^d Department of Anesthesia, University of California, San Francisco, San Francisco, California, USA, and San Francisco Veterans Affairs Medical Center, San Francisco, California, USA
^e Department of Cardiothoracic Surgery, University of Pennsylvania, Philadelphia, Pennsylvania, USA

Accepted for publication June 4, 2004.

^* Address reprint requests to Dr Guccione, Division of Surgical Services (112D), San Francisco Veterans Affairs Medical Center, 4150 Clement St, San Francisco, CA94121 (E-mail: Julius.Guccione{at}med.va.gov).

	Abstract

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

 
BACKGROUND: Surgical anterior ventricular restoration (SAVER) has been proposed for dilated ischemic cardiomyopathy with an akinetic distal anterior left ventricular wall. We tested the hypothesis that SAVER increases stroke volume, reduces mean myofiber stress and achieves optimal results without a patch.

METHODS: A finite element model of the left ventricle (LV) with an akinetic but contractile anteroapical LV wall segment was used. Separate versions of the model with normal and dilated LV sizes were developed and used to simulate the SAVER operation with and without a patch of varying stiffness from 10 to 100 kilopascals.

RESULTS: The SAVER operation reduced myofiber stress in the akinetic infarct and infarct borderzone, but caused a reduction in the Starling relationship. In all cases, stroke volume decreased while ejection fraction increased after SAVER. The SAVER operation was more beneficial in dilated ventricles, and the reduction in stroke volume after SAVER without patch was minimal. The effect of patch stiffness was mixed as stiffer material causes a greater reduction in stress yet has the greatest negative effect on stroke volume.

CONCLUSIONS: These simulations support the use of SAVER in dilated hearts without a patch.

	Introduction

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

 
Surgical anterior ventricular restoration (SAVER) has been proposed as therapy for dilated ischemic cardiomyopathy with an akinetic distal anterior left ventricular (LV) wall [1]. Patch aneurysmorraphy, originally used to treat the LV with dyskinetic anterior wall [2], has increasingly been used to treat the LV with akinetic anterior wall [3, 4]. Given the increased incidence of dilated ischemic cardiomyopathy [5], interest in SAVER is growing. A working group has been established (RESTORE) [1], and surgical remodeling is a treatment arm of the multicenter National Institutes of Health funded Surgical Treatment of Ischemic Heart Failure (STICH) trial [6].

The effect of SAVER on LV function is difficult to anticipate. Early descriptions of SAVER exclude akinetic segments behind a Dacron patch [1] and fold the remaining myocardium over the Dacron in a "pants-over-vest" closure [1]. Currently, SAVER also refers to procedures omitting the patch and the double-layer closure. SAVER, therefore, represents a related group of operations performed on the LV with akinetic anterior LV wall.

We have previously simulated the LV with akinetic anterior LV wall using a mathematical (finite element [FE]) model [7]. The FE method is by far the most widely used mathematical tool in mechanical engineering design and analysis. Based on an anteroapical myocardial infarction (MI) in sheep that was reperfused after 1 hour, that simulation showed that unless passive infarct stiffness is greater than 285 times normal, contracting myocytes are required to prevent infarct wall dyskinesia [7]. Therefore, it is not merely possible for myocytes to survive in akinesis: contracting myocytes are obligatory. Of note, the determination of akinetic anterior wall contractile function is critically important to the mechanical analysis of the SAVER operation since exclusion of a weakly contracting anterior wall segment will clearly have a different effect than exclusion of an inert segment.

We used our FE model of the LV with an akinetic but contractile anterior LV wall [7] to simulate the SAVER operation. Separate versions of the model with normal and dilated LV sizes were developed and used to simulate the SAVER operation with and without patch of varying stiffness. We hypothesized that SAVER increases stroke volume (SV), reduces mean myofiber stress and that optimal results are achieved without a patch.

	Material and Methods

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

 
The three-dimensional (3-D) FE method of Costa [8] for large elastic deformations of ventricular myocardium was used, together with the mathematical descriptions for normal diastolic and systolic myocardial material properties (stress-strain relations) of Guccione [9].

Sheep Reperfused Infarct and Echocardiography
A single sheep from a group previously reported by Bowen [10] underwent anteroapical ischemia and reperfusion after 1 hour. Subdiaphragmatic two-dimensional (2-D) long-axis echocardiographs were obtained through a sterile midline laparotomy (1.8 to 4.2 MHz probe, SONOS 5500; Agilent Technologies, Andover, MA) 12 weeks postinfarction [10], and videotaped [10]. The animal model displayed significant LV remodeling at 12 weeks (infarct thickness 5.1 ± 0.3 mm; LV volume at end-systole 33 ± 6 mL) [10].

Echocardiographs at early diastolic filling (Fig 1), end-diastole, and end-systole were selected, digitized and analyzed (Findtags; Medical Imaging Lab, Johns Hopkins University, Baltimore, MD). Guided by the video echocardiogram, epicardial and endocardial contours were hand-traced, and the border between akinetic and kinetic regions identified.

View larger version (84K): [in this window] [in a new window]   Fig 1. Transesophageal echocardiogram of an ischemic ovine heart with akinetic infarct (arrows) at early diastole. (LV = left ventricle; RV = right ventricle.)

View larger version (32K): [in this window] [in a new window]   Fig 2. LV with infarct; normal size. (A) Preoperative two-dimensional mesh and three-dimensional meshes at (B) end-diastole and (C) end-systole for akinetic infarct (arrows) in normal-sized left ventricle (LV).

View larger version (38K): [in this window] [in a new window]   Fig 3. LV with infarct; dilated. (A) Preoperative two-dimensional mesh and three-dimensional meshes at (B) end-diastole and (C) end-systole for akinetic infarct (arrows) in dilated left ventricle (LV).

Material Properties
DIASTOLIC MATERIAL PROPERTIES
Diastolic and systolic material properties have been presented [9, 15]. A sharp boundary was assumed between the infarcted and noninfarcted regions. The noninfarcted region was assigned normal diastolic stiffness (C = 0.876 kPa) and systolic material properties (T_max = 200 kPa). T_max, the isometric tension achieved at the longest sarcomere length and maximum peak intracellular calcium concentration, in the noninfarcted region was chosen so that the preoperative ejection fraction (EF) approximated that in the sheep model [10].

Infarct material properties were determined as described by Dang [7]. Reduction of the infarct ability to develop active stress was accomplished by scaling T_max by a "percentage of contracting myocytes." This approach (as opposed to decreasing peak intracellular calcium concentration [16]) preserves the shape of the active stress and sarcomere length relationship. In the normal-sized model, the infarct was assigned 13.5% contracting myocytes (T_max = 27.14 kPa). In the scaled model, the infarct was assigned 15% contracting myocytes (T_max = 30.00 kPa). In both cases, the infarct was akinetic (average radial strain 0.013 [normal] to 0.003 [scaled]).

SAVER Properties
The SAVER operation was simulated by causing a constant volume deformation of the normal myocardium. Specifically, a FE model with infarct elements removed underwent an isochoric (constant volume) deformation by application of an inward force to borderzone nodes. Partial excision (40% of akinetic area) of the infarct was simulated by manually inputting nodes representing the wall thickness and shape of the infarct. Endpoints represented the greatest reduction in chamber volume with mathematically convergent solutions. With current software, further reduction in akinetic area is not feasible.

In patch simulations, patches averaging 2 mm thick lined the chamber wall from the edges of the borderzone. In the absence of material properties data for surgical materials, diastolic stiffness of 10.0 kPa was considered standard. Owing to software limitations, a stiff patch was simulated as 50.0 kPa in the dilated model and as 100.0 kPa in the normal-sized model. Figure 4 summarizes the simulations run. With current software, further reduction in akinetic area and patch thickness is not feasible.

View larger version (12K): [in this window] [in a new window]   Fig 4. Outline of simulations. (LV = left ventricle.)

(1)

where ß_0,ES, and ß_1,ES, represent stiffness of the LV end-systolic elastance.

The end-diastolic pressure-volume relationship is:

(2)

where ß_0,ED, ß_1,ED, and ß_2,ED represent stiffness of the LV diastolic compliance.

Calculation of Stroke Volume/P_ED (Starling) Relationship
The SV/P_ED (Starling) relationship was calculated [12]. The arterial elastance, E_A, was calculated for a SV consistent with an end-diastolic pressure of 20 mm Hg and end-systolic pressure of 100 mm Hg [18].

The SV was obtained with the equation [19]:

(3)

and the complete SV/P_ED relationship created. This contrasts with the Myocor Myosplint where the end-systolic elastance was significantly nonlinear [12] but in line with our analysis of partial ventriculectomy [20], in which the end-systolic elastance was relatively linear and the SV/P_ED relationship reflected Sagawa's [19] view of the SV and E_A interaction.

Calculation of Diastolic and Systolic Myofiber Stress
Stress in the local muscle fiber direction was computed [8, 12]. Our method differs from Laplace's law as it accounts for myocardial material properties and transmural variation in muscle fiber orientation.

	Results

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

 
Two-dimensional early diastolic (A), and 3-D end-diastolic (B) and end-systolic (C) FE meshes of both models are shown in Figures 2 and 3. The blue wireframes represent the ventricular wall. In panels B and C, the endocardium is a red (remote myocardium) or blue (infarct) shaded surface. The diastolic model is loaded with 20 mm Hg of LV pressure and the systolic model is loaded with 100 mm Hg. Similar panels after SAVER are seen in Figures 5 and 6. In the normal-sized model, the result was a chamber volume reduction at early diastole of 17%. The dilated model had a chamber reduction of 15%. Both models reduced the infarct surface area by 40%.

View larger version (29K): [in this window] [in a new window]   Fig 5. LV with infarct; normal size; post-op SAVER. (A) Postoperative two-dimensional mesh and three-dimensional meshes at (B) end-diastole and (C) end-systole for normal-sized left ventricle (LV). Arrows identify the akinetic infarct. (SAVER = surgical anterior ventricle restoration.)

View larger version (23K): [in this window] [in a new window]   Fig 7. End-systolic elastance (squares) and compliance (circles) before (unfilled) and after (filled) a simulated surgical anterior ventricle restoration (SAVER) operation on (A) a normal-sized left ventricle (LV) and (B) a dilated LV. Diamonds = SAVER with stiff patch; triangles = SAVER without patch.

Figure 8 shows the effect of SAVER on the SV/end-diastolic pressure (Starling) relationship. The SAVER operation shifts the Starling relationship downward and rightward. However, SAVER was more beneficial in dilated ventricles. The SV reduction after patchless SAVER in the dilated ventricle was minimal. Increasing patch stiffness, C, progressively increases the shift. As described by Guccione [20], SV consistently diminished because the decreased diastolic compliance was not sufficiently compensated by the improved end-systolic elastance.

View larger version (20K): [in this window] [in a new window]   Fig 8. Stroke volume/end-diastolic pressure (Starling law) relationship before (filled) and after (unfilled) a simulated surgical anterior ventricle restoration (SAVER) operation on (A) a normal-sized left ventricle (LV) and (B) a dilated LV. Circles = preoperative simulation; triangles = SAVER without patch; squares = SAVER with compliant patch; diamonds = SAVER with stiff patch.

View larger version (25K): [in this window] [in a new window]   Fig 9. Regional myofiber stress at end-diastole and end-systole for (A, B) a normal-sized left ventricle (LV) and (C, D) a dilated LV. Connecting lines only associate simulation groups; particularly in the border zone, linear interpolation is inappropriate. Dashed line = infarct versus noninfarct; diamonds = SAVER with stiff patch; open triangles = SAVER without patch; solid circles = preoperative; solid squares = SAVER with compliant patch. (SAVER = surgical anterior ventricle restoration.)

	Comment

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

Simulations Based on Sheep Reperfused Infarct Model
The finite element model used in this study was based on an echocardiogram of a sheep with reperfused infarct rather than human imaging data for several reasons. First, in sheep, remote myocardium is uniformly normal and that greatly simplifies the mathematical simulations. That is in contrast to human SAVER patients among whom the high incidence of concomitant coronary bypass grafting (89%) [1] suggests that the remote myocardium is composed of a heterogeneous mixture of normal, ischemic, hibernating, and infarcted regions. Second, infarct and remote myocardial material properties have been previously measured in sheep [21]. However, reperfusion of an anteroapical infarct after 1 hour in sheep does not produce a dilated LV [10]. On the other hand, reperfusion after 6 hours, which does produce LV dilation, is not appropriate since the infarcted area contains few surviving myocytes [10]. While we are attempting to characterize reperfusion after 3 to 4 hours, in this study we have been forced to mathematically scale the dimensions of our baseline normal-size model in order to simulate SAVER in the dilated LV.

Reduction in Myofiber Stress
The reduction in infarct and myofiber stress with SAVER may prevent further damage and improve contractility over time [22]. As the akinetic infarct contains contracting myocytes preventing dyskinetic wall motion, residual contractile function in the infarct is probably the primary reason that a stiff patch decreases SV. Indeed, reduced myofiber stress allows the infarct myocytes to contract. However, the use of stiff patch prevents myofiber stretch during diastole and the beneficial effect of stress reduction is lost.

In our previous study, partial ventriculectomy [20] reduced mean myofiber stresses in DCM throughout the cardiac cycle. Comparison of Table 3 in Guccione [20] with Table 3 in the present study shows that SAVER decreases end-diastolic mean myofiber stresses by an amount comparable with the 20% ventricular volume reduction in DCM. Similarly, SAVER decreases end-systolic mean myofiber stresses equivalent to a 10% ventricular volume reduction in DCM.

Effect on LV Function
The reduced LV volume and wall stress with SAVER may be insufficient to improve function. Although most reports document an improvement in EF [4], the effect of SAVER on the Starling relationship remains unmeasured. The large percentage of SAVER patients with concomitant coronary bypass (89%) [1] and mitral valve repair/replacement (26%) [1] makes the clinical effect of SAVER on LV function impossible to interpret. These facts make FE simulations and animal experiments of SAVER critically important.

We had suggested that success of LV remodeling surgery depends on how it affects both end-systolic pressure-volume (elastance) and diastolic pressure-volume (compliance) relationships, and how those changes affect ventricular function (SV versus end-diastolic pressure [Starling] relationship) [23]. All simulations show that SAVER shifts diastolic compliance further to the left on the pressure volume diagram than end-systolic elastance leading to a net negative effect. This pattern of change in compliance and elastance is seen in partial ventriculectomy [20]. However, comparison of Figure 8 in the present study with prior analysis of partial ventriculectomy (Fig 4 in Guccione and associates [20]) demonstrates that SAVER without patch in the dilated LV depresses ventricular function less than partial ventriculectomy. If done without a patch in the dilated LV, the change is minimal. Complete elimination of akinetic tissue may have a more pronounced effect on the Starling relationship. Of note, EF is a misleading functional index after operations that change LV volume [23, 24].

Mechanical Properties of Patch Materials
Lee and Wilson [25] measured anisotropic mechanical properties of vascular graft materials. At a uniaxial strain of 0.025 in the much stiffer circumferential direction (Fig 1, C in Lee and Wilson [25]), these grafts are approximately 690 times stiffer than normal canine myocardium. Sachs and Choung [26] measured the orthotropic mechanical properties of chemically treated bovine pericardium. Depending on the chemical treatment and amount of equibiaxial strain (Table 2 in Sacks and Chuong [26]), the preferred fiber direction of these materials is approximately seven to 240 times stiffer than the normal canine myocardium. In our simulations, patches with stiffness consistent with chemically treated bovine pericardium showed poorer outcome than the no-patch operation. The stiffer Dacron graft should further depress Starling performance. We therefore recommend repair without a patch whenever possible.

Other Mathematical Models
Recently, Artrip and colleagues [27] used a "lumped parameter" model to compare the effects of Dor procedure, SAVER, and partial ventriculectomy on LV pressure-volume relationships. The FE method is superior to the "lumped parameter" method, given that the latter is based on linear electrical circuit design and superposition, and provides no myocardial stress data. Artrip's analysis agrees with our FE simulation of partial ventriculectomy [16, 27]. Artrip concluded that results of the SAVER operation fell midway between partial ventriculectomy and Dor [27].

Model Limitations
Our model utilizes a realistic LV geometry, diastolic myocardial material properties that are anisotropic with respect to the local muscle fiber orientation, and systolic contraction based on experimental measurements of active tension-sarcomere length relationships. The use of contractile myocytes in the akinetic regions and an isochoric deformation on a 3-D LV geometry to represent surgical remodeling make this the most realistic representation of SAVER to date. Limitations of current FE software restricted the amount of resected akinetic myocardium to a 40% reduction in area.

Another limitation is that our 3-D mesh came from 2-D ultrasonography. The orientation of muscle fibers in a man with dilated ischemic cardiomyopathy remains unknown. With regard to clinical surgery, our patch is thicker. Continuity could not simulate material thinner than 2 mm. Woven Dacron used in cardiac patch material is 0.2 mm thick; bovine pericardium is 0.6 mm. The thicker patch does not alter our main conclusions significantly as the material is passive and represents a small portion of the model.

The FE method can only assess surgery outcome from a mechanical equilibrium perspective. Intraoperative myocardial depression could produce worse than predicted results, whereas long-term recovery of function such as reversal of hibernation or reversal of LV remodeling could improve predicted results.

Conclusion and Future Directions
The SAVER operation reduces myocyte fiber stress in the akinetic infarct at the expense of a reduction in the Starling relationship. The reduction in SV after SAVER without patch in the dilated ventricle was minimal. Effects of patch stiffness were mixed. A patch made of stiffer material should cause a greater reduction in stress but also has the greatest negative effect on SV. These simulations support the use of SAVER in the dilated heart without a patch.

Future simulations will attempt to identify optimal conditions for a patch-free SAVER through an iterative approach. Three-hour reperfusion models will be explored. Finally, it will be important to know myocyte fiber angles and infarct sarcomere length.

View larger version (38K): [in this window] [in a new window]   Fig 6. LV with infarct; dilated; post-op SAVER. (A) Postoperative two-dimensional mesh and three-dimensional meshes at (B) end-diastole and (C) end-systole for dilated left ventricle (LV). Arrows = identify the akinetic infarct. (SAVER = surgical anterior ventricle restoration.)

	Acknowledgments

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

	References

Top Abstract Introduction Material and Methods Results Comment Acknowledgments References

 

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Add to Personal Folders Download to citation manager Author home page(s): Peng Zhang Robert C. Gorman Joseph H. Gorman, III Mark B. Ratcliffe Permission Requests Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Dang, A. B.C. Articles by Ratcliffe, M. B. Search for Related Content PubMed PubMed Citation Articles by Dang, A. B.C. Articles by Ratcliffe, M. B. Related Collections Congestive Heart Failure