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Ann Thorac Surg 2007;83:354
© 2007 The Society of Thoracic Surgeons

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Correspondence

Are We Using the Right Fluid Mechanics Principles?

Laboratory of Biomedical Engineering, Clinical Research Institute of Montreal (IRCM), 110 Pine West Avenue, Montreal, QC, H2W 1R7 Canada

(Email: lyes.kadem{at}ircm.qc.ca; damien.garcia{at}ircm.qc.ca).

To the Editor:

We read the article of Yoshida and colleagues [1] with great interest. They showed that patients with severe aortic stenosis are inclined to type IIA von Willebrand factor (vWf) syndrome, which may be reduced by aortic valve replacement. The authors also reported that patients with valvular prosthesis mismatch may not fully benefit from a reduction in vWf abnormalities, because patient-prosthesis mismatch can lead to a residual aortic stenosis. To explain these findings, the authors stated that high shear stresses within the flow jet may cleave vWf multimers. Although the conclusion of this study is relevant, we have concerns with respect to the computations of shear stresses.

The following equation was used by Yoshida and colleagues [1] and by Vincentelli and colleagues [2]: shear stress = (4 x blood viscosity x mean velocity)/(stenosis radius). This equation is not adapted to flow through aortic stenosis. Therefore we believe that some theoretical points must be clarified.

The equation is only valid for a fully developed Hagen-Poiseuille or Womersley (in a time-averaged sense) laminar flow in a circular conduit [3]. This may justify application in the common carotid artery as in the article of Gnasso and colleagues [4]. However, an extrapolation to aortic stenosis is not appropriate, because the corresponding flow characteristics are far different from those in a tube [5].

Assuming that the aforementioned conditions are fulfilled, the equation allows computation of shear stress at the arterial wall only, but not within the flow volume.

In the equation, "mean velocity" refers to spatially averaged velocity, whereas Yoshida and colleagues [1] used the mean temporal velocity.

High shear stresses that would be prone to cleave vWf multimers in aortic stenosis are not located at the level of the vena contracta or along the wall. The jet is indeed lost in a downstream region of turbulent mixing that involves high shear stresses and significant fluid energy dissipation. An estimation of the fluid energy loss may have been more appropriate for global characterization of shear stresses [6].

Although the shear stresses computed in this study are invalid, this does not, however, affect the general conclusions of the authors. A correct application of the fundamentals of fluid mechanics would probably have resulted in higher correlations. Therefore we believe that it is important to be aware of the hypotheses and limitations of fluid mechanics equations and to be watchful when extrapolating the use of such equations.

	References

Top References

 

1. Yoshida K, Tobe S, Kawata M, Yamaguchi M. Acquired and reversible von Willebrand disease with high shear stress aortic valve stenosis Ann Thorac Surg 2006;81:490-494.[Abstract/Free Full Text]
2. Vincentelli A, Susen S, Le Tourneau T, et al. Acquired von Willebrand syndrome in aortic stenosis N Engl J Med 2003;349:343-349.[Medline]
3. Nichols WW, O’Rourke MF. Mc Donald’s blood flow in arteries. Theoretical, experimental and clinical principles. London, Philadelphia: Lea & Febiger, 1990.
4. Gnasso A, Carallo C, Irace C, et al. Association between intima-media thickness and wall shear stress in common carotid arteries in healthy male subjects Circulation 1996;94:3257-3262.[Abstract/Free Full Text]
5. Kadem L, Knapp Y, Pibarot P, et al. A new experimental technique for the determination of the effective orifice area based on the acoustical term source Exp Fluids 2005;39:1050-1060.
6. Garcia D, Pibarot P, Dumesnil JG, Sakr F, Durand LG. Assessment of aortic valve stenosis severity: a new index based on the energy loss concept Circulation 2000;101:765-771.[Abstract/Free Full Text]

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This Article 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 Permission Requests Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Kadem, L. Articles by Garcia, D. Search for Related Content PubMed PubMed Citation Articles by Kadem, L. Articles by Garcia, D. Related Collections Valve disease Related Article