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Ann Thorac Surg 2004;77:1876
© 2004 The Society of Thoracic Surgeons

Correspondence

Increased border-zone stress in bulging ventricular aneurysm

Benjamin M. Jackson, MD, Joseph H. Gorman, III, MD, Robert C. Gorman, MD

Department of Surgery, Hospital of the University of Pennsylvania, 3400 Spruce St 4 Silverstein Pavilion, Philadelphia, PA 19104, USA

e-mail: benjamin.jackson{at}uphs.upenn.edu

To the Editor:

We were intrigued with the biomechanical study of left ventricular (LV) aneurysm by Bartel and colleagues [1]. We are concerned that the physical properties of their experimental model substantially limit the validity and clinical applicability of their conclusions. Specifically, we question the use of a ventricular wall thickness of 0.3 mm. Also, given that prior descriptions of the model appear only in German, in international symposiums, and in dissertations, we wonder what are the Young modulus (Y) and the Poisson's ratio ({nu}) of the rubber model.

The authors draw two principle conclusions from their experimental data. The first is that heart rate has an effect on aneurysmal bulging. However, the authors do not explain why there might be a quadratic dependence on heart rate. Do they have any explanation for this observation? (We considered a resonance phenomenon; however, we estimate a first resonant frequency of the mechanical system of not less than approximately 400 Hz.)

The second conclusion is that stress ({sigma}) depends primarily on LV function, whereas the bulging volume of the aneurysm depends on afterload. The implication is that reduction of contractility (eg, ß-blockade) would more likely be beneficial—by a mechanism related to LV wall stress reduction—than would afterload reduction alone. However, the authors calculated {sigma} as an analytic function of afterload, bulging volume of the aneurysm, and the constant initial conditions (wall thickness and the elliptical axes of the aneurysmal defect in the ventricular wall, (r1 and r2). Therefore, but for experimental error, it is impossible for {sigma} to depend less on afterload than does aneurysmal volume.

Using typical material properties for rubber (Y = 2 x 106 Pa and {nu} = 0.5), a LV wall with an initial thickness of 0.6 cm, and boundary conditions similar to those of the model ventricle described in this study, we used two-dimensional finite element analysis (MATLAB; MathWorks, Natick, MA) to determine the regional stress field in the ventricular wall when loaded with a cavity pressure of 150 mm Hg. The resulting deformation and von Mises stress fields are represented in Figure 1.



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  		Fig 1. Displacement and von Mises stress field imposed on a two-dimensional ventricular wall by a pressure load and restraints (R) at the borders of an aneurysmal bulging. Units of stress are newtons per square centimeter.

 
This finite element analysis demonstrates that the regions of greatest LV wall stress are immediately adjacent to the aneurysm at its periphery, not in the middle of the bulging aneurysm. Therefore, the Laplacian stress calculation performed in the study of Bartel and co-workers is misdirected. It is the increased stress at the borders of the aneurysmal portion of the left ventricle that is important. In fact, increased wall stress in the nonischemic border zone of LV aneurysms in an ovine model has recently been demonstrated experimentally [2, 3]. Pathologic wall stress in the border zone region results in mechanical dysfunction and leads to ventricular remodeling and eventual congestive heart failure [4, 5].

References

  1. Bartel T., Vanheiden H., Schaar J., Mertzkirch W., Erbel R. Biomechanical modeling of hemodynamic factors determining bulging of ventricular aneurysms. Ann Thorac Surg 2002;74:1581-1588.[Abstract/Free Full Text]
  2. Jackson B.M., Gorman J.H., III, Salgo I.S., et al. Border zone geometry increases wall stress after myocardial infarction: contrast echocardiographic assessment. Am J Physiol Heart Circ Physiol 2003;284:H475-479.[Abstract/Free Full Text]
  3. Moustakidis P., Maniar H.S., Cupps B.P., et al. 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.
  4. Moulton M.J., Downing S.W., Creswell L.L., et al. Mechanical dysfunction in the border zone of an ovine model of left ventricular aneurysm. Ann Thorac Surg 1995;60:986-987.[Abstract/Free Full Text]
  5. Jackson B.M., Gorman J.H., Moainie S.L., et al. Extension of borderzone myocardium in postinfarction dilated cardiomyopathy. J Am Coll Cardiol 2002;40:1160-1171.[Abstract/Free Full Text]




This Article
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Robert C. Gorman
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