Technical Briefs

Pulse-Wave Propagation in Straight-Geometry Vessels for Stiffness Estimation: Theory, Simulations, Phantoms and In Vitro Findings

[+] Author and Article Information
Danial Shahmirzadi

 Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, NY 10025ds3031@columbia.edu

Ronny X. Li

 Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Columbia University, New York, NY 10025rxl2103@columbia.edu

Elisa E. Konofagou1

Ultrasound and Elasticity Imaging Laboratory, Department of Biomedical Engineering, Department of Radiology,  Columbia University, New York, NY 10025ek2191@columbia.edu


Corresponding author.

J Biomech Eng 134(11), 114502 (Oct 26, 2012) (6 pages) doi:10.1115/1.4007747 History: Received January 13, 2012; Revised September 13, 2012; Posted October 17, 2012; Published October 26, 2012; Online October 26, 2012

Pulse wave imaging (PWI) is an ultrasound-based method for noninvasive characterization of arterial stiffness based on pulse wave propagation. Reliable numerical models of pulse wave propagation in normal and pathological aortas could serve as powerful tools for local pulse wave analysis and a guideline for PWI measurements in vivo. The objectives of this paper are to (1) apply a fluid-structure interaction (FSI) simulation of a straight-geometry aorta to confirm the Moens-Korteweg relationship between the pulse wave velocity (PWV) and the wall modulus, and (2) validate the simulation findings against phantom and in vitro results. PWI depicted and tracked the pulse wave propagation along the abdominal wall of canine aorta in vitro in sequential Radio-Frequency (RF) ultrasound frames and estimates the PWV in the imaged wall. The same system was also used to image multiple polyacrylamide phantoms, mimicking the canine measurements as well as modeling softer and stiffer walls. Finally, the model parameters from the canine and phantom studies were used to perform 3D two-way coupled FSI simulations of pulse wave propagation and estimate the PWV. The simulation results were found to correlate well with the corresponding Moens-Korteweg equation. A high linear correlation was also established between PWV2 and E measurements using the combined simulation and experimental findings (R2  = 0.98) confirming the relationship established by the aforementioned equation.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

(a) Pulse wave imaging experimental set up. (b) Magnification at the transducer-phantom level. Red dye was injected in the fluid for leakage monitoring on the tube.

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Figure 2

(a) Half view of the full 3D aorta-fluid mesh in Abaqus. (b) Examples of a propagating wall displacement wave at multiple time points. (c) Schematic representation of a spatio-temporal map of the wall displacement wave.

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Figure 3

Spatio-temporal plots of the wall displacement obtained from PWI: (i.a) distal region on canine aorta in vitro, (ii.a) normal wall phantom, i.e., 110 kPa, (iii.a) normal wall simulation, i.e., 110 kPa; (i.b)-(iii.b) single isolated forward-traveling wave, respectively, corresponding to (i.a)–(iii.a), with the linear fit to the wave foot used for the PWV calculation.

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Figure 4

Mechanical characterization of phantom compressive modulus (E′) and threefold of the shear modulus (3G) (Appendix 6). The errorbars show the standard deviation on each measurement (n = 3). The linear fit to the defined average Young’s modulus, i.e., E=(E′+3G)/2, and the standard deviation lines are shown with the solid and dashed lines, respectively.

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Figure 5

The theoretical, i.e., Moens-Korteweg, relationship between the PWV2 versus E (based on the parameters used in the simulation) as well as the measured data from canine aortas, phantoms, and simulations, showing a high linear correlation coefficient of R2   = 0.98, combined.



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