HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

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): Mark B. Ratcliffe Permission Requests Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Ratcliffe, M. B. Articles by Wallace, A. W. Search for Related Content PubMed PubMed Citation Articles by Ratcliffe, M. B. Articles by Wallace, A. W.

J Thorac Cardiovasc Surg 1998;116:566-577
© 1998 Mosby, Inc.

SURGERY FOR ADULT CARDIOVASCULAR DISEASE

The effect of ventricular volume reduction surgery in the dilated, poorly contractile left ventricle: A simple finite element analysis

San Francisco, Calif

Supported by California Heart Association grant-in-aid 97-241.

Received for publication Nov 24, 1997. Revisions requested Jan 13, 1998; revisions received May 14, 1998. Accepted for publication May 29, 1998. Address for reprints: Mark B. Ratcliffe, MD, 112D, San Francisco Veterans Affairs Medical Center, 4150 Clement St, San Francisco, CA 94121.

	Abstract

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

 
Objectives: Ventricular volume reduction surgery has been proposed by Batista to improve cardiac function in patients with dilated cardiomyopathy. However, limited clinical data exist to determine the efficacy of this operation. A finite element simulation is therefore used to determine the effect of volume reduction surgery on left ventricular end-systolic elastance, diastolic compliance, stroke work/end-diastolic volume (preload recruitable stroke work), and stroke work/end-diastolic pressure (Starling) relationships.
Methods: End-diastole and end-systole were represented by elastic finite element models with different unloaded shapes and nonlinear material properties. End-systolic elastance, diastolic compliance, preload recruitable stroke work, and Starling relationships, as well as energy expenditure per gram of unresected myocardium, were calculated. Two different types of volume reduction surgery (apical and lateral) were simulated at 10% and 20% left ventricular mass reduction.
Results: Ventricular volume reduction surgery causes diastolic compliance to shift further to the left on the pressure-volume diagram than end-systolic elastance. Volume reduction surgery increases the slope of the preload recruitable stroke work relationship (dilated cardiomyopathy 0.006 J/mL; 20% lateral volume reduction surgery 0.009 J/mL) but decreases the slope of the Starling relationship (dilated cardiomyopathy 0.028 J/mm Hg; 20% lateral volume reduction 0.023 J/mm Hg). For a given amount of resection, lateral volume reduction has a greater effect than apical volume reduction. Ten-percent and 20% lateral volume reduction reduces energy expenditure by 7% and 17%, respectively.
Conclusion: Ventricular volume reduction surgery shifts end-systolic elastance and diastolic compliance to the left on the pressure-volume diagram. The net effect on ventricular function is mixed. Volume reduction surgery increases the slope of preload recruitable stroke work, but increased diastolic compliance causes a small decrease in the Starling relationship (3 mm Hg difference between dilated cardiomyopathy and volume reduction surgery at stroke work = 0.5 J).

	Introduction

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

 
A new surgical therapy for heart failure has recently gained attention. ^1-5 The operation, first performed by a Brazilian surgeon, Randas Batista, is known as ventricular volume reduction surgery (VVRS) and includes the resection of a viable "slice" of the lateral left ventricular (LV) wall in patients with dilated cardiomyopathy (DCM) and end-stage congestive heart failure. Although early results with this procedure in uncontrolled trials have been promising, experimental analysis of the effect of the Batista operation on LV mechanics is limited. ^6-10

The success of an operation that surgically remodels ventricular size, shape, or regional stiffness depends on how the procedure affects both end-systolic and end-diastolic pressure-volume relationships and how those changes affect ventricular function (stroke-work/end-diastolic volume; preload recruitable stroke work) [PRSW], ¹¹ and stroke-work/end-diastolic pressure relationships [Starling]). ¹² End-systolic and end-diastolic pressure-volume relationships, respectively termed end-systolic elastance and diastolic compliance, are mechanically determined by respective LV regional material properties (stiffness) and unloaded ventricular shapes. ¹³ VVRS will change the unloaded end-systolic and end-diastolic ventricular shapes and regional stiffness in and around the surgical repair site. As a consequence, postoperative ventricular elastance and compliance are altered and may shift by different absolute amounts. As a result, the stroke work/end-diastolic volume and stroke work/end-diastolic pressure relationships may shift. At present, the effect of VVRS on systolic elastance, diastolic compliance, and the resultant net effect on ventricular function is unknown.

Finite element models relate regional material properties, structural shape, and regional stress as a system of linear equations. ¹⁴ Typically a structure, in this case the LV, is composed of "elements," material properties (regional stiffness) are assigned to each element, external loads are applied (intracavitary pressure), and regional stresses and structural deformation are calculated. In this study, we describe a finite element model of the dilated LV with reduced contractility in which the effects of partial apical and lateral wall ventricular resections are simulated.

The primary goal of this study is to model the effect of VVRS on end-systolic elastance, diastolic compliance, and ventricular function (stroke work/end-diastolic volume and stroke work/end-diastolic pressure [Starling] relationships). We also test the hypothesis that 2 different types of partial ventriculectomy involving either the lateral wall or apex had different effects on elastance, compliance, and ventricular function. Finally, we test the hypothesis that VVRS decreases myocardial energy expenditure.

	Methods

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

 
Overview of finite element model
A finite element model of the dilated poorly contractile LV was developed. Diastole and end-systole were represented by separate elastic models that have different unloaded shapes and material properties (Fig 1, step 1). Two types of VVRS simulations (apical VVRS and lateral VVRS) were developed (Fig 1, steps 3 and 4). Finite element meshes were created and loaded with a range of physiologic intraventricular pressures with the use of commercially available computer-assisted design and simulation software (Ideas, release 2.0, SDRC, Inc, Milford, Ohio). Nonlinear material properties were assigned and the models solved with the use of a commercially available nonlinear finite element solver (ABAQUS, Standard module, version 5.4, Hibbet, Karlson and Sorenson, Inc, Providence, RI). Finite element modeling and analysis were performed on a Unix-based workstation (SPARCsystem 10, model 40, Sun Microsystems, Inc, Mountain View, Calif).

View larger version (34K): [in this window] [in a new window]   Fig 1. Schematic of modeling process used in this study. Step 1: The unloaded diastolic LV is modeled as a thick-walled axisymmetric hemi-ellipsoid based on images of dilated human cardiomyopathic hearts. The unloaded systolic LV shape was derived from the diastolic shape. In this and subsequent steps only the right half of the axisymmetric shape is shown. Step 2: Material properties and boundary conditions are assigned. The base of the LV is fixed in both the x and y directions while the apex is fixed in the x direction only (hatched arrows). In this and the subsequent step the pre-resection shape is seen as the dashed line. Step 3: Apical VVRS: Apical resection is performed by reducing the long-axis radii, a1 and a2, while maintaining a constant wall thickness. The short-axis radii, b1 and b2, are unchanged. Step 4: Lateral VVRS: Lateral resection is performed by reducing the short-axis radii, b1 and b2, while maintaining a constant wall thickness. The long-axis radii, a1 and a2, are unchanged.

Initial unloaded end-systolic shape
The unloaded end-systolic LV shape was derived from the diastolic shape by assuming that LV wall volume and aspect ratio are constant and that average circumferential and longitudinal strains are equal to the strain of an unloaded sarcomere during contraction. End-systolic dimensions were calculated by simultaneously solving the following 4 equations (Mathematica, version 2.2, Wolfram Research Inc, Champaign, Ill):

[b²_2,ESa_2,ES - b²_1,ESa_1,ES] = [b²_2,EDa_2,ED - b²_1,EDa_1,ED]   (1)

Finite element mesh and boundary conditions
The finite element model was meshed with axisymmetric solid (continuum) elements (4 nodes, bilinear with reduced integration, element type CAX4RH, ABAQUS, standard module, version 5.4, Hibbet, Karlson and Sorenson, Inc, Providence, RI). A single axisymmetric hydrostatic fluid-filled cavity (element type FAX2, ABAQUS) was used to model the endocardial cavity. This element provides a convenient means by which endocardial cavitary pressure and volume can be calculated. Nodes at the apex along the ordinate axis were constrained to displace in the y direction (long axis) only. The base of the LV is composed primarily of fibrous tissue and was therefore constrained in all degrees of freedom (Fig 1, step 2).

Material properties
Diastolic material properties
Both diastolic and systolic material properties of the LV wall were assumed to be homogeneous and isotropic. Diastolic material properties were described by the strain energy potential constitutive equation developed by Ogden ²² to describe nonlinear isotropic rubber-like materials. The Ogden constitutive equation is shown below:

Systolic material properties
The end-systolic material properties of the LV wall were also described by means of the Ogden constitutive equation. End-systolic material stiffness parameters were empirically chosen so that the end-systolic pressure-volume relationship is approximately linear and passes through LV pressure of 120 mm Hg and LV volume of 200 mL. In general, µ_i determines the initial slope of the pressure-volume relationship and _i determines the shape of the relationship. Stiffness parameters of µ_i = 59.722 and _i = 9.5 were empirically found to produce a nearly linear pressure-volume relationship and to pass through target LV pressure and volume. These stiffness parameters are significantly less stiff than those of normal systolic myocardium. ¹³

Finally, both zero-pressure systole and zero-pressure diastole occur at lambda = 1. However, the rest length is different for systole and diastole (equations 3 and 4).

VVRS simulations
The effects of VVRS were simulated with the use of the globally dilated heart model. Apical and lateral VVRS were tested at 80% and 90% of original ventricular mass. More specifically, 10% and 20% of LV mass was removed from both the unloaded diastolic and systolic shapes. Apical resections were performed by first determining the position of a simulated apical ventriculectomy (Fig 1, step 3, exploded view: dashed line) associated with a 10% or 20% LV mass reduction. The cut edge of the ventriculectomy was parallel to y (long) axis and had y-coordinates of a_1AR and a_2AR. The cut edge of the ventricle was then moved to the midline (x = 0) (Fig 1, step 3, expanded view of apex: x) and the y-coordinates of the cut edge then became the new major semiaxes. Minor semiaxes were unchanged (Fig 1, step 3: b₁ and b₂).

Lateral resections were performed by first determining the position of a simulated lateral ventriculectomy (Fig 1, step 4) associated with a 10% or 20% LV mass reduction. The ventricle was incised parallel to the y (long) axis and the cut edges of the ventricle were apposed, creating new minor semiaxes (Fig l, step 4: b_1LR and b_2LR). The wall thickness was unchanged (b₂ – b₁ = b_2LR – b_1LR). Minor semiaxes were unchanged (Fig 1, step 4: a₁ and a₂). No attempt was made to alter material properties around the ventricular incision.

Calculation of systolic and diastolic pressure-volume relationships
Diastolic solutions were obtained at a range of diastolic intracavitary pressures (ie, 0-40 mm Hg). End-systolic solutions were obtained at a range of systolic intracavitary pressures (ie, 0-120 mm Hg). The pressure, P_ES, and volume at end-systole, V_ES, derived from the finite element model were fit to the following linear equation by means of least squares regression analysis ²⁴ (Microsoft EXCEL, Redmond, Wash):

P_ES = E_ES[V_ES - V₀]   (6)
where V0 is the volume intercept and EES is the slope of the LV elastance. The pressure, PED, and volume at end-diastole, VED, were fit to the following quadratic equation with the use of least squares regression analysis ²⁴ (Microsoft EXCEL, Redmond, Wash):

P_ED = ß₀ + ß₁V_ED + ß₂V_ED²   (7)
where ß₀, ß₁, and ß₂ are the stiffness parameters of the LV diastolic compliance.

Calculation of stroke work/P_ED (Starling) and stroke work/V_ED (PRSW) relationships
For each simulation (DCM, 10% and 20% lateral and apical VVRS), stroke work/P_ED and stroke work/V_ED relationships were calculated from the diastolic and systolic pressure-volume regressions, assuming that arterial elastance, E_A, ²⁵ was constant. E_A was calculated according to the following equation:

View larger version (27K): [in this window] [in a new window]   Fig 2. Schematic illustration of cardiac function parameters. Ea, Arterial elastance; Ees, end-systolic elastance; SW, stroke work (area ABCD); PVA, pressure-volume area (area ABCOD).

	Results

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

 
End-systolic (A) and diastolic (B) finite element meshes of the globally dilated, poorly contractile LV before and after loading are seen in Fig 3. In each panel the unloaded mesh is in green and the loaded mesh is in red. In this and subsequent examples, only the right half of the axisymmetric mesh is shown, the diastolic model is loaded with 20 mm Hg of intracavitary LV pressure, and the systolic model is loaded with 100 mm Hg of intracavitary LV pressure. End-systolic (A) and diastolic (B) finite element meshes of 20% apical VVRS before and after loading are seen in Fig 4. End-systolic (A) and diastolic (B) finite element meshes of 20% lateral VVRS before and after loading are seen in Fig 5. Unloaded and loaded LV dimensions are seen in Table I. Notice the realistic end-systolic and end-diastolic dimensions of the model of dilated cardiomyopathy. The percent wall thickness change was 26% at the equator.

View larger version (42K): [in this window] [in a new window]   Fig 3. Globally dilated, poorly contractile LV model. Systolic (A) and diastolic (B) finite element mesh before and after loading. In each panel the unloaded mesh is in green and the loaded mesh is in red. In each case only the right half of the axisymmetric mesh is shown. The diastolic model is loaded with 20 mm Hg of intracavitary LV pressure. The systolic model is loaded with 100 mm Hg of intracavitary LV pressure.

View larger version (40K): [in this window] [in a new window]   Fig 4. Apical VVRS: Systolic (A) and diastolic (B) finite element mesh before and after loading. In each panel the unloaded mesh is on the left and the loaded mesh is on the right. In each case only the right half of the axisymmetric mesh is shown. The diastolic model is loaded with 20 mm Hg of intracavitary LV pressure. The systolic model is loaded with 100 mm Hg of intracavitary LV pressure.

View larger version (40K): [in this window] [in a new window]   Fig 5. Lateral VVRS: Systolic (A) and diastolic (B) finite element mesh before and after loading. In each panel the unloaded mesh is on the left and the loaded mesh is on the right. In each case only the right half of the axisymmetric mesh is shown. The diastolic model is loaded with 20 mm Hg of intracavitary LV pressure. The systolic model is loaded with 100 mm Hg of intracavitary LV pressure.

View larger version (33K): [in this window] [in a new window]   Fig 6. Elastance and compliance before and after apical VVRS. Elastance curves are to the left and compliance curves are to the right. DCM, Dilated cardiomyopathy; AR, apical VVRS. Ten-percent AR (open triangles) and 20% AR (open circles) progressively shift preresection LV elastance and compliance (asterisks) to the left. In each case note that the compliance is shifted further to the left than the elastance. Symbols (asterisk, open triangle, and open circle) represent the actual values calculated by the finite element solver.

View larger version (29K): [in this window] [in a new window]   Fig 7. Elastance and compliance before and after lateral VVRS. Elastance curves are to the left and compliance curves are to the right. DCM, Dilated cardiomyopathy; LR, lateral VVRS. Ten-percent LR (closed triangles) and 20% LR (closed circles) progressively shift pre-resection LV elastance and compliance (asterisks) to the left. In each case note that the compliance is shifted further to the left than the elastance. Note that for each amount of resected LV mass, lateral VVRS shifts compliance and elastance further to the left than apical VVRS (Fig 5). Symbols (asterisk, closed triangle, and closed circle) represent the actual values calculated by the finite element solver.

View larger version (24K): [in this window] [in a new window]   Fig 8. The effect of VVRS on the stroke work/end-diastolic volume (A) and stroke work/end-diastolic pressure (B) (Starling's law) relationship. Ten-percent AR (dash-dash), 20% AR (dot-dot), 10% LR (dash-dot-dash), and 20% LR VVRS (dash-dot-dot-dash) progressively shift stroke work/end-diastolic volume relationship to the left (A). Note that VVRS not only shifts the VED intercept to the left but increases the slope of the relationship as well (DCM 0.006 J/mL; 20% lateral VVRS 0.009 J/mL). On the other hand, VVRS progressively decreases the slope of LV Starling relationship (B) above end-diastolic pressure = 5 mm Hg. Note that these effects are increased with a larger amount of resected LV mass and are greater in lateral VVRS than apical VVRS.

The effect of VVRS on end-diastolic and end-systolic LV volume, stroke volume, and ejection fraction is seen in Table III. End-diastolic volume was obtained at 20 mm Hg and end-systolic volume was obtained at 100 mm Hg. Note that stroke volume decreases while ejection fraction increases with VVRS. Stroke volume was reduced in all cases because the decrease in diastolic compliance was not sufficiently compensated by the improvements in end-systolic elastance.

View larger version (55K): [in this window] [in a new window]   Fig 9. The effect of VVRS on the energy consumption per gram of myocardium. Note that 10% LV mass resection has an insignificant effect (1%) on myocardial energy expenditure. The 20% apical VVRS and 20% lateral VVRS reduce energy expenditure by 7% and 17%, respectively. PVA, Pressure-volume area.

	Discussion

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

VVRS causes an increase in ejection fraction while stroke volume decreases. However, ejection fraction is a poor index of ventricular function, ^27,28 and it is therefore incorrect to conclude that cardiac function has improved if VVRS increases ejection fraction.

The effects of apical and lateral VVRS on compliance, elastance, and ventricular function are qualitatively similar. The effect of 20% lateral VVRS is quantitatively largest, whereas 10% lateral VVRS is similar to 20% apical VVRS. At present, cardiac surgeons resect either an ellipse of lateral free wall myocardium or an inverted triangle or "shield," in which the wide part of the triangle or shield is toward the atrioventricular groove. However, an apical resection would be easier to surgically reconstruct and might not interfere with the papillary muscles. These results support the potential use of apical partial ventriculectomy.

VVRS causes a decrease in energy expenditure per gram of residual myocardium. Although not calculated in this study, wall stress throughout systole is also decreased. ^6,27 Both of these factors may lead to a reverse remodeling of eccentric hypertrophy and may lead to potential subacute and chronic beneficial effects from VVRS. The overall effect of VVRS must be a combination of the acute hemodynamic effects of VVRS on LV function and subacute and chronic effects of decreased energy expenditure and stress on ventricular hypertrophy.

Finite element modeling and assumptions
The accuracy of finite element analysis simulations are dependent on the accuracy of initial assumptions, including (1) the material property law, (2) the input stiffness parameters, and (3) the initial unloaded structural geometry. Given accurate initial conditions, however, finite element analysis is well suited to model the effect of LV volume reduction surgery on elastance, compliance, and ventricular function. However, the following assumptions must be recognized.

Structure
Although more realistic than previous models, the initial end-diastolic and end-systolic shapes are approximate. This is in part because there are no experimental measurements of the normal or pathologic animal or human LV at zero left and right ventricular intracavitary pressure. Furthermore, Fung ²⁹ has demonstrated significant residual wall stress even in the absence of ventricular pressure. Residual stress has not been measured in dilated cardiomyopathy but may have a significant impact on VVRS, which in effect increases residual pre-strain and stress.

The right ventricle is not included in the model, and transseptal pressure is assumed to be the same as transmural pressure in the lateral LV wall. Right ventricular pressure has been shown to increase LV elastance and compliance, ³⁰ and the absence of the right ventricle may lead to a shift in elastance and compliance to the right.

Although finite element techniques exist that can model interaction between fluid motion in a chamber and the structure and stiffness of the chamber wall, our model does not have that capability and does not incorporate the effect of mitral regurgitation. This may be of particular importance in the interpretation of the stroke work/end-diastolic pressure curves (Fig 8, A). As above, the increase in end-diastolic pressure and corresponding increase in left atrial pressure needed to attain comparable stroke work may be effectively offset by the removal of mitral regurgitation.

The model was constructed so that average circumferential and longitudinal unloaded strains across the LV wall were equal to 0.85. This, in turn, is based on the relative change in sarcomere length between the relaxed and the contracted states. Spotnitz, Sonnenblick, and Spiro ¹⁹ measured sarcomere length in normal intact hearts and found sarcomere lengths between 1.87 and 1.95 µm in diastole and between 1.5 and 1.6 µm in systole. These values agree with values from isolated intact and skinned ventricular muscle strips. ^20,21

Material properties
Scientists have used different types of material property laws in finite element analysis models. Material property laws have ranged from Hookean (linear stress-strain relation) ³¹ to nonlinear, ¹³and both isotropic ¹³ and anisotropic (directional) ³² descriptions have been used. In addition, although an anisotropic material property law that is linked to myocardial architecture (fiber angles) is clearly preferable,3234 these descriptions are complex and knowledge of myocardial fiber angles in the dilated cardiomyopathic LV is unknown. A nonlinear isotropic material property law, such as that developed by Ogden ²² to describe nonlinear isotropic rubber-like materials, represents a reasonable first-order approximation until such structural information becomes available.

Although the incision probably undergoes stiffness changes similar to other wounds and myocardial infarction, ³⁵ stiffness in the region of the incision has not been experimentally measured. Therefore no attempt was made to alter material properties around the ventricular incision. Also, the fibrous base of the LV is assumed to be fixed in the diastolic position.

Finite element mesh
The finite elements used are 2-dimensional axisymmetric elements. Although these elements are computationally efficient, they can only be used to describe axisymmetric solids in rotation and cannot be used to describe variation in the third dimension.

VVRS in the apical position was performed by "gathering" the LV at the point of resection. True resection with linear closure in the operating room would lead to a more complex non-axisymmetric 3-dimensional shape. As above, no attempt was made to alter material properties around the ventricular incision.

Mathematical models of VVRS
There are analytic solutions that relate chamber compliance to stress and strain in simple shapes with linear material properties that undergo small deformations. An example is the linear elastic solution of an incompressible thin-walled sphere under internal pressure described by Lamé, ³⁶

Despite its shortcomings, our model in conjunction with diastolic constitutive parameters derived from actual resting stress-extension tests of canine myocardium produces realistic human pressure-volume curves. Proceeding in the other direction (ie, starting with a time varying elastance model and then characterizing stress-strain behavior by way of global wall equilibrium) could very well produce the correct trend while giving quantitatively unreliable data.

Comparison with preliminary clinical results
Early reports have documented a heterogeneous effect of VVRS on ventricular function. ^3,5 End-diastolic and end-systolic LV volumes have been consistently decreased ^4,10 and ejection fraction has consistently increased. ^4,5,7 Although most reports document a decrease in stroke volume, ^4,10 stroke volume ⁸ and cardiac index ⁵ have been noted to improve. However, because postoperative ventricular end-diastolic pressure is often decreased ^4,5 and heart rate increased, ⁴ these data are difficult to interpret.

The effects of VVRS on load-independent end-systolic and diastolic pressure-volume relationships have been measured with ventriculography, ⁹ conductance catheters, ¹⁰ and 2-dimensional echocardiography. ³ End-systolic elastance has been found to increase by twofold to threefold ^9,10 and end-diastolic compliance significantly decreases. ^3,10 Because of the heterogeneous effect of VVRS on end-systolic elastance in their study, Gorscan and associates ³ found that PRSW was not changed. The Starling relationship has not been measured. Although these preliminary results are consistent with our finite element analysis model and support the findings of this study, the effect of VVRS on ventricular function (Starling and PRSW) needs to be studied in more detail.

	Conclusion and future directions

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

 
Batista's operation is an intriguing and potentially important surgical therapy for patients with DCM and congestive failure. However, although seemingly intuitive, the effect of partial ventriculectomy on ventricular function is complex. We suggest that this and all operations that surgically remodel ventricular size, shape, or regional stiffness should be analyzed by determining how the procedure affects both systolic and diastolic pressure-volume relationships and how those changes affect ventricular function.

Our finite element simulation of Batista's operation documents an acute increase in the stroke volume/end-diastolic volume relationship. However, decreased diastolic compliance causes a small decrease in the Starling relationship (3 mm Hg difference between DCM and VVRS at stroke work = 0.5 J). On the other hand, the increase in left atrial pressure needed to maintain stroke work may be effectively offset by the surgical correction of mitral regurgitation. The overall effect of VVRS is a combination of the acute hemodynamic effects of VVRS on LV function and subacute and chronic effects of decreased energy expenditure and stress on ventricular hypertrophy. This analysis suggests that VVRS may be an appropriate therapy for patients with DCM.

This model is an initial approximation. However, one of the major strengths of the finite element method is the ability to incorporate complex realistic geometry, anisotropic material properties, regional differences in material properties (ie, at the suture line), and residual stress in the unpressurized ventricle. In the future, we intend to progressively refine the model. Simulations should be repeated with varied systolic and diastolic material parameters. In addition, future directions should include the measurement of unloaded LV systolic and diastolic shapes in both the normal and pathologic heart. However, we believe that this initial approximation provides useful information provided that the assumptions incorporated in the model are clearly understood.

The finite element approach can be used to analyze the effects of any cardiac operation that surgically remodels ventricular size or shape or changes regional stiffness. Ideally, the development of such simulations will refine our understanding of operations and pathologic processes that alter ventricular shape and material properties.

	References

Top Abstract Introduction Methods Results Discussion Conclusion and future directions References

 

1. Altman L. Brazil surgeon develops a bold, promising operation for patients with heart failure. New York Times 1996 June 14; Sect A:16.
   
2. Batista RJV, Santos JLV, Takeshita N, Bocchino L, Lima PN, Cunha MA. Partial left ventriculectomy to improve left ventricular function in end-stage heart disease. J Cardiovasc Surg 1996;11:96-7.
   
3. Gorscan J, Feldman A, Kormos R, Mandarino W, Demetris A, Batista R. Heterogeneous immediate effects of partial left ventriculectomy on cardiac performance. Circulation 1998;97:839-42. [Abstract/Free Full Text]
   
4. McCarthy PM, Starling RC, Wong J, Scalia GM, Buda T, Vargo RL, et al. Early results with partial left ventriculectomy. J Thorac Cardiovasc Surg 1997;114:755-65. [Abstract/Free Full Text]
   
5. Moreira LFP, Stolf NAG, Bocchi EA, Bacal F, Giorgi MCP, Parga JR, et al. Partial left ventriculectomy with mitral preservation in the treatment of patients with dilated cardiomyopathy. J Thorac Cardiovasc Surg 1998;115:800-7. [Abstract/Free Full Text]
   
6. Wong J, Garcia MJ, Starling RC, Buda T, Vargo RL, Scalia GM, et al. Alterations in left ventricular wall stress after partial left ventriculectomy surgery. Circulation 1997;96(Suppl):I344.
   
7. Erick A, Jaques AK, Mejira LD, Smith JJ, Rastegar H, Payne D, et al. Quantitative evaluation of regional and global left ventricular shape, volume, and function using three- and two-dimensional echocardiography after ventricular remodeling surgery (Batista operation) for end-stage heart failure due to idiopathic dilated cardiomyopathy. Circulation 1997;96(Suppl):I344.
   
8. Powell K, Bernhard S, Ding X, McCarthy P, White R. Demonstration of improved ventricular function in dilated cardiomyopathy (DM) by surgical left-ventricular remodeling (LVR) using dynamic cardiac MRI. Circulation 1997;96(Suppl):I464.
   
9. Popovic Z, Miric M, Gradinac S, Neskovic AN, Jovovic AD, et al. End-systolic pressure-volume relationships and ventriculoarterial coupling following partial left ventriculectomy. Circulation 1997:96(Suppl):I198.
   
10. Kawaguchi AT, Sugimachi M, Sunagawa K, Takeshita N, Koide S, Verde JL, et al. Intraoperative left ventricular pressure-volume relationships in patients undergoing left ventricular diameter reduction. Circulation 1997;96(Suppl):I198.
    
11. Glower DD, Spratt JA, Snow ND, Kabas JS, Davis JW, Olsen CO, et al. Linearity of the Frank-Starling relationship in the intact heart: the concept of preload recruitable stroke work. Circulation 1985;71:944-1009.
    
12. Patterson S, Starling E. On the mechanical factors which determine the output from the ventricles. J Physiol (Lond) 1914;48:357-79.
    
13. Bogen DK, Rabinowitz SA, Needleman A, McMahon TA, Abelmann WH. An analysis of the mechanical disadvantage of myocardial infarction in the canine left ventricle. Circ Res 1980;47:728-41. [Abstract/Free Full Text]
    
14. Gallagher RH. Finite element analysis: fundamentals. Englewood Cliffs [NJ]: Prentice-Hall; 1975.
    
15. Schechtem U, Sommerhoff B, Markiewicz W, White R, Cheitlin M, Higgins C. Regional left ventricular wall thickening by magnetic resonance imaging: evaluation in normal persons and patients with global and regional dysfunction. Am J Cardiol 1987;59:145-51. [Medline]
    
16. Higgins CB, Holt W, Pflugfelder P, Sechtem U. Functional evaluation of the heart with magnetic resonance imaging. Magn Reson Med 1988;6:121-39. [Medline]
    
17. Fujita M, Hartiala J, O'Sullivan M, Steiman D, Chatterjee K, Parmeley W, et al. Assessment of left ventricular diastolic function in dilated cardiomyopathy with cine magnetic resonance imaging: effect of an angiotensin converting enzyme inhibitor, benazepril. Am Heart J 1993;125:171-8. [Medline]
    
18. Feiring A, Rumberger J. Ultrafast computed tomography analysis of regional radius to wall thickness ratios in normal and volume overloaded human left ventricle. Circulation 1992;85:1423-32. [Abstract/Free Full Text]
    
19. Spotnitz HM, Sonnenblick EH, Spiro D. Relation of ultrastructure to function in the intact heart: sarcomere structure relative to pressure-volume curves of intact left ventricles of dogs. Circ Res 1966;18:49-66. [Abstract/Free Full Text]
    
20. ter Keurs H, Rijnsburger W, Van Heuningen R, Nagelsmit M. Tension development and sarcomere length in rat cardiac trabeculae. Circ Res 1980;46:703-14. [Free Full Text]
    
21. Kentish J, ter Keurs H, Ricciardi L, Bucx J, Noble M. Comparison between the sarcomere length force relations of intact and skinned trabeculae from rat right ventricle. Circ Res 1986;58:755-68. [Abstract/Free Full Text]
    
22. Ogden RW. Large deformation isotropic elasticity: on the correlation of theory and experiment for incompressible rubber-like solids. Proc R Soc Lond 1972;A326:565-84.
    
23. Needleman A, Rabinowitz SA, Bogen DK, McMahon TA. A finite element model of the infarcted left ventricle. J Biomech 1983;16:45-58. [Medline]
    
24. Kleinbaum D, Kupper L, Muller K. Applied regression analysis and other multivariable methods. Boston: PWS-Kent; 1988.
    
25. Sagawa K, Maughan WL, Suga H, Sunagawa K. Cardiac contraction and the pressure-volume relationship. New York: Oxford University Press; 1988. p. 232-98.
    
26. Suga H. Total mechanical energy of a ventricle model and cardiac oxygen consumption. Am J Physiol 1979;236:H498-505. [Abstract/Free Full Text]
    
27. Dickstein M, Spotnitz HM, Rose EZ, Burkhoff D. Heart reduction surgery: an analysis of the impact on cardiac function. J Thorac Cardiovasc Surg 1997;113:1032-40. [Abstract/Free Full Text]
    
28. Kass D, Maughan W, Guo Z, Kono A, Sunagawa K, Sagawa K. Comparative influence of load versus inotropic states on indexes of ventricular contractility: experimental and theoretical analysis based on pressure-volume relationships. Circulation 1987;76:1422-36. [Abstract/Free Full Text]
    
29. Fung YC. Biomechanics: mechanical properties of living tissues. New York: Springer-Verlag; 1981.
    
30. Slinker B, Glantz S. End-systolic and end-diastolic ventricular interaction. Am J Physiol 1986;151:H1062-75.
    
31. Pirolo JS, Creswell LL, Bresina SJ, Perman WH, Szabo BA, Myers KW, et al. Regional myocardial stress distribution from magnetic resonance image-based mathematical models. Ann Thorac Surg 1991;52:276-84. [Abstract]
    
32. Hunter PJ, Smaill BH. The analysis of cardiac function: a continuum approach. Prog Biophys Molec Biol 1988;52:101-64. [Medline]
    
33. Yin FCP, Strumpf RK, Chew PH, Zeger SL. Quantification of the mechanical properties of noncontracting myocardium under simultaneous biaxial loading. J Biomech 1987;20:577-89. [Medline]
    
34. Yin FCP, Chew PH, Zeger SL. An approach to quantification of biaxial tissue stress-strain data. J Biomech 1986;19:27-37. [Medline]
    
35. Gupta KB, Ratcliffe MB, Fallert MA, Edmunds LH Jr, Bogen DK. Changes in passive mechanical stiffness of myocardial tissue with aneurysm formation. Circulation 1994;89:2315-6. [Abstract/Free Full Text]
    
36. Lamé G. Lecons sur la theorie mathematique de l'elasticite des corps solides. Paris: Bachelier; 1852.
    

This article has been cited by other articles:

				P. Zhang, J. M. Guccione, S. I. Nicholas, J. C. Walker, P. C. Crawford, A. Shamal, G. Acevedo-Bolton, M. A. Guttman, C. Ozturk, E. R. McVeigh, et al. Endoventricular patch plasty for dyskinetic anteroapical left ventricular aneurysm increases systolic circumferential shortening in sheep. J. Thorac. Cardiovasc. Surg., October 1, 2007; 134(4): 1017 - 1024.e1. [Abstract] [Full Text] [PDF]

				S. T. Wall, J. C. Walker, K. E. Healy, M. B. Ratcliffe, and J. M. Guccione Theoretical Impact of the Injection of Material Into the Myocardium: A Finite Element Model Simulation Circulation, December 12, 2006; 114(24): 2627 - 2635. [Abstract] [Full Text] [PDF]

				P. Zhang, J. M. Guccione, S. I. Nicholas, J. C. Walker, P. C. Crawford, A. Shamal, D. A. Saloner, A. W. Wallace, and M. B. Ratcliffe Left ventricular volume and function after endoventricular patch plasty for dyskinetic anteroapical left ventricular aneurysm in sheep J. Thorac. Cardiovasc. Surg., October 1, 2005; 130(4): 1032 - 1038. [Abstract] [Full Text] [PDF]

				A. B.C. Dang, J. M. Guccione, P. Zhang, A. W. Wallace, R. C. Gorman, J. H. Gorman III, and M. B. Ratcliffe Effect of Ventricular Size and Patch Stiffness in Surgical Anterior Ventricular Restoration: A Finite Element Model Study Ann. Thorac. Surg., January 1, 2005; 79(1): 185 - 193. [Abstract] [Full Text] [PDF]

				J. M. Guccione, A. Salahieh, S. M. Moonly, J. Kortsmit, A. W. Wallace, and M. B. Ratcliffe Myosplint decreases wall stress without depressing function in the failing heart: a finite element model study Ann. Thorac. Surg., October 1, 2003; 76(4): 1171 - 1180. [Abstract] [Full Text] [PDF]

				R. M. Setser, J. M. Kasper, M. L. Lieber, R. C. Starling, P. M. McCarthy, and R. D. White Persistent abnormal left ventricular systolic torsion in dilated cardiomyopathy after partial left ventriculectomy J. Thorac. Cardiovasc. Surg., July 1, 2003; 126(1): 48 - 55. [Abstract] [Full Text] [PDF]

				L. L. Mickleborough, N. Merchant, Y. Provost, S. Carson, and J. Ivanov Ventricular reconstruction for ischemic cardiomyopathy Ann. Thorac. Surg., June 1, 2003; 75(90060): S6 - 12. [Abstract] [Full Text] [PDF]

				T. Koyama, K. Nishimura, Y. Soga, O. Unimonh, K. Ueyama, and M. Komeda Importance of preserving the apex and plication of the base in left ventricular volume reduction surgery J. Thorac. Cardiovasc. Surg., March 1, 2003; 125(3): 669 - 677. [Abstract] [Full Text] [PDF]

				D. Burkhoff New heart failure therapy: The shape of things to come? J. Thorac. Cardiovasc. Surg., March 1, 2003; 125(90030): S50 - 52. [Full Text] [PDF]

				J. Hung, J. L. Guerrero, M. D. Handschumacher, G. Supple, S. Sullivan, and R. A. Levine Reverse Ventricular Remodeling Reduces Ischemic Mitral Regurgitation: Echo-Guided Device Application in the Beating Heart Circulation, November 12, 2002; 106(20): 2594 - 2600. [Abstract] [Full Text] [PDF]

				M. B. Ratcliffe Non-ischemic infarct extension: A new type of infarct enlargement and a potential therapeutic target J. Am. Coll. Cardiol., September 18, 2002; 40(6): 1168 - 1171. [Full Text] [PDF]

R. M. Kanashiro, E. Nozawa, N. Murad, L. R. Gerola, V. A. Moises, and P. J.F. Tucci Myocardial infarction scar plication in the rat: cardiac mechanics in an animal model for surgical procedures Ann. Thorac. Surg., May 1, 2002; 73(5): 1507 - 1513. [Abstract] [Full Text] [PDF]