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Ann Thorac Surg 2004;77:1876-1877
© 2004 The Society of Thoracic Surgeons

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Correspondence

Increased border-zone stress in bulging ventricular aneurysm: Reply

Division of Cardiology, Department of Internal Medicine, University of Essen, Hufelandstr 55, 45122 Essen, Germany

e-mail: thomas.bartel{at}uni-essen.de

To the Editor:

I thank Jackson and associates for their valuable remarks and their interest in our work [1]. I point out that all descriptive data regarding the model have also been published in English [2]. On the basis of the comments of Jackson and colleagues, my coauthors and I once again scrutinized our results and their implications for our understanding of the relation between bulging of a ventricular aneurysm and global hemodynamics.

Nonlinear correlation analysis revealed the relation between heart rate (HR) and the degree of bulging (bulging volume) to obey a second-order polynomial rule. A polynomial function, a trinomial in this case, does not just reflect a quadratic relationship. Each polynomial function is the sum of the various powers of the variable. Each element is multiplied by a constant. These constants express the unique character of the particular function, its minima and maxima. The present trinomial function ischaracterized by one minimum at a particular HR. To look into the issue of a possible resonance phenomenon more thoroughly, we excited the system with a unit impulse to examine its transient response. There was no evidence of any oscillation, which makes a resonance phenomenon even more unlikely. On the other hand, it is certainly justified to try to find an explanation.

I propose the following explanation: HR is inversely related to the length of diastasis and therefore to the degree of filling. Ventricular filling is directly related to bulging volume. Consequently, the higher the HR, the lower the bulging volume. However, increasing HRs not only affect filling but also lower ejection time and stroke volume, leading to worsening congestion. Congestion is associated with increased ventricular filling and therefore more bulging. Thus, we are dealing with two antagonistic processes that cause bulging to be minimal at a particular HR (calculated to be 82 beats/min in our model).

Of course, caution is in order when interpreting these results, as some features of the model ventricle are different from the working conditions of a true left ventricle. In this respect, I agree with Jackson and associates that the most important limitations are the very thin wali and the elasticity of this model ventricle. But some bulging will always be apparent within the physiologic range of HRs (between 60 and 100 beats/min).

Ventricular wall stress is another issue brought up by Jackson and coauthors. Ventricular wall stress is calculated as a function of systolic blood pressure, which is approximately the same as systolic ventricular pressure, and bulging volume. However, and this is of the utmost importance, wall stress is not calculated as a function of afterload. It is well known that afterload, which is defined as systemic vascular resistance, is calculated as a function of cardiac output and the difference between mean blood pressure and right atrial pressure [3]. In our report, the term afterload refers explicitly to systemic vascular resistance and not to systolic blood pressure.

I agree absolutely with Jackson and coauthors that this model cannot simulate the behavior of a vital aneurysmal border zone, but this problem should not be mixed up with the process of left ventricular remodeling after myocardial infarction, which is limited in time. Moreover, when a true left ventricular aneurysm eventually forms, this process is already complete. Therefore, to add a qualifier to the conclusions, the results in our study are related exclusively to the final stage of aneurysmal formation.

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. Hadland P.H., Kottmann W., Jette M., Zurmann J., Blümchen G., Mertzkirch W. The effects of simulated akinetic and dyskinetic aneurysms on left ventricular systolic function: clinical implications. Eur J Cardio-thorac Surg 1997;12:642-647.[Abstract]
3. Grossman W. Cardiac catheterization. In: Braunwald E., ed. Heart disease. A textbook of cardiovascular medicine. Philadelphia: WB Saunders, 1992:194.

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