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Published on: April 13, 2015
A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries
Jimena Martín Tempestti1, Saeyoung Kim2,3, Brooks D Lindsey2,3,4
1Department of Mathematics, Emory University, 400 Dowman Dr, Atlanta, 30322, GA, USA. jimena.martin@emory.edu.
Insights
A novel pseudo-spectral method accurately quantifies wall shear stress (WSS) from ultrasound Doppler data. This technique offers a more precise and computationally efficient alternative for cardiovascular disease risk assessment compared to existing methods.
Area of Science:
- Biomedical Engineering
- Medical Imaging
- Fluid Dynamics
Background:
- Wall Shear Stress (WSS) is crucial for predicting cardiovascular and coronary diseases.
- Current WSS quantification relies on Computational Fluid Dynamics (CFD) or numerical approximations from ultrasound (US) Doppler data.
- Existing methods have limitations in accuracy and computational cost.
Purpose of the Study:
- To present a novel method for quantifying WSS from 2D vector Doppler measurements.
- To improve the accuracy and efficiency of WSS estimation in patient-specific cardiovascular analysis.
Main Methods:
- Acquired in-plane velocity components using unfocused plane waves and transverse oscillation.
- Employed pseudo-spectral differentiation techniques based on Fourier approximations to compute WSS.
- Tested the Pseudo-Spectral Method (PSM) in straight and stenotic vessel phantoms under steady flow.
Main Results:
- The PSM accurately detected WSS variations in different geometries and showed reduced sensitivity to measurement noise.
- Validated against CFD simulations, the PSM demonstrated comparable accuracy to Poiseuille-based methods with noise-free data.
- Using US data, the PSM achieved 3 to 9 times lower average error in WSS compared to state-of-the-art methods.
Conclusions:
- The pseudo-spectral approach effectively controls approximation errors, especially with noisy data.
- PSM provides a more accurate and less computationally expensive alternative to CFD for WSS quantification.
- This method enhances the potential for precise cardiovascular risk assessment using readily available US data.
Purpose:
The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements.
Methods:
Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS.
Results:
Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15 mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods.
Conclusion:
The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.
