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Research Papers

# A Scaling Parameter for Predicting Pressure Wave Reflection in Stented Arteries

[+] Author and Article Information
John J. Charonko

VT-WFU School of Biomedical Engineering & Sciences, Virginia Polytechnic Institute and State University, 114 Randolph Hall, Blacksburg, VA 24061john.charonko@vt.edu

Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, 333G Norris Hall, Blacksburg, VA 24061ragab@vt.edu

Pavlos P. Vlachos

Department of Mechanical Engineering, VT-WFU School of Biomedical Engineering & Sciences, Virginia Polytechnic Institute and State University, 114S Randolph Hall, Blacksburg, VA 24061pvlachos@vt.edu

J. Med. Devices 3(1), 011006 (Mar 10, 2009) (10 pages) doi:10.1115/1.3089140 History: Received June 04, 2008; Revised January 25, 2009; Published March 10, 2009

## Abstract

A one-dimensional finite-difference model was developed to predict pressure wave reflections in stented arteries, and a parametric study of variations in stent and vessel properties was performed, including stent stiffness, length, and compliance transition region, as well as vessel radius and wall thickness. The model was solved using a combination of weighted essentially nonoscillatory and Runge–Kutta methods. Over 100 cases were tested and the magnitudes of the predicted waves were less than $0.5 mm Hg$ for all cases, less than 1% of the normal pulse pressure of $40 mm Hg$. It was also shown that reasonable variations in these parameters could induce changes in reflection magnitude of up to ±50%. The relationship between each of these properties and the resulting wave reflection could be described in a simple manner, and the effect of all of them together could, in fact, be encompassed by a single nondimensional parameter titled “stent authority.” It is believed that stent authority is a novel way of relating the energy imposed upon the arterial wall by the stent to the fraction of the incident pressure energy that is reflected from the stented region. Based on these results, it is believed that stent design can have a significant effect on pressure wave reflections; however, it was concluded that their small magnitudes make clinical relevance of these waves unlikely, regardless of design.

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## Figures

Figure 1

The input pressure wave consisted of a half-sine wave pulse followed by ashorter resting period, and corresponds to a heart rate of 80 bpm

Figure 2

Results of dynamic radial stiffness testing near the distal end of an Abbott Vascular Vision stent implanted in a 3.0 mm Sylgard vessel

Figure 3

Diagram shows how the various test parameters, such as total stent length and transition length, influence the variation in stiffness along the length of the stent

Figure 4

Relative change in the magnitude of the reflected pressure wave as compared with a Cordis CS30-035 Crown stent. Each test parameter was varied independently to observe their effect on the reflected pressure waves.

Figure 5

The magnitude of the reflected pressure wave increased linearly with total stent length if maximum stiffness was held constant

Figure 6

There is a correspondence between the reflection and the effective length of the stent, but the relationship is only approximately linear

Figure 7

The pressure reflection increased with increasing vessel radius. This relationship appeared to be linear in the square root of the radius

Figure 8

The magnitude of the reflected pressure wave decreased geometrically with increasing wall thickness. Once again, the geometry appears to be related to the reflection by the exponent of 0.5.

Figure 9

Combining the inner vessel radius with the wall thickness into a single nondimensional parameter yielded a linear relationship between the reflection and the geometry of the vessel

Figure 10

The relationship between the pressure reflection and the stiffness ratio appears to be asymptotic. When plotted on a logarithmic scale, the curve closely resembles the plot of the hyperbolic tangent.

Figure 11

For a given stent length, the magnitude of the pressure reflection was observed to increase linearly with the stent authority as measured in the center of the stent. The reflection was more dependent on the stent stiffness when stent length was greater.

Figure 12

When the effect of the vessel geometry is included, every case tested collapses onto a single linear relationship between the reflection and the geometric stent authority

## Errata

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