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TECHNICAL BRIEFS

Statistical Hemodynamics: A Tool for Evaluating the Effect of Fluid Dynamic Forces on Vascular Biology In Vivo

[+] Author and Article Information
Morton H. Friedman, Heather A. Himburg, Jeffrey A. LaMack

 Duke University, Department of Biomedical Engineering, Box 90281, Durham, NC 27708

J Biomech Eng 128(6), 965-968 (May 16, 2006) (4 pages) doi:10.1115/1.2354212 History: Received September 14, 2005; Revised May 16, 2006

Background. In vivo experimentation is the most realistic approach for exploring the vascular biological response to the hemodynamic stresses that are present in life. Post-mortem vascular casting has been used to define the in vivo geometry for hemodynamic simulation; however, this procedure damages or destroys the tissue and cells on which biological assays are to be performed. Method of Approach. Two statistical approaches, regional (RSH) and linear (LSH) statistical hemodynamics, are proposed and illustrated, in which flow simulations from one series of experiments are used to define a best estimate of the hemodynamic environment in a second series. As an illustration of the technique, RSH is used to compare the gene expression profiles of regions of the proximal external iliac arteries of swine exposed to different levels of time-average shear stress. Results. The results indicate that higher shears promote a more atheroprotective expression phenotype in porcine arterial endothelium. Conclusion. Statistical hemodynamics provides a realistic estimate of the hemodynamic stress on vascular tissue that can be correlated against biological response.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Consistency of shear exposure in the proximal iliac artery, based on the computed flow field in six vessels. Color coding represents the number of vessels in which a given pixel was a (a) low, (b) medium or (c) high shear site. Flow is from right to left; the flow divider is near the top of the right edge of each image. The regions from which cells were scraped, and for which the cumulative distribution functions in Fig. 3 were calculated, are delineated by black lines in the three panels.

Grahic Jump Location
Figure 2

Profiles of time-average shear stress derived from computational fluid dynamic calculations in the proximal external iliac artery along lines extending (A) circumferentially at a location halfway between the flow divider and circumflex ostium, and (B) from the flow divider distally to the level of the circumflex ostium. Fainter lines represent the shear stress profiles in the six individual arteries and the solid lines are the means of the six profiles. The inset figures are grayscale maps of shear stress, averaged among the six arteries, with arrows corresponding to the respective abscissas. The shear values in the grayscale maps were clipped at 95dyn∕cm2 for display purposes; in panel B, this clipping results in an underestimate of shear stress near the flow divider.

Grahic Jump Location
Figure 3

Cumulative distribution functions of the time average shear stress within the low, medium and high shear regions of the proximal external iliac artery from which cells were scraped. Two percent of the cells in the high shear region are expected to have been exposed to shears in excess of 95dyn∕cm2.

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