Are we using the right fluid mechanics principles?

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 multim-ers. 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 ϭ (4 ϫ blood viscosity ϫ 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 …