Martín Tempestti Jimena, Kim Saeyoung, Lindsey Brooks D, Veneziani Alessandro
Department of Mathematics, Emory University, 400 Dowman Dr, Atlanta, 30322, GA, USA.
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Dr., Atlanta, GA, 30332, USA.
Cardiovasc Eng Technol. 2024 Dec;15(6):647-666. doi: 10.1007/s13239-024-00741-2. Epub 2024 Aug 5.
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.
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.
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.
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.
壁面剪应力（WSS）是不可压缩流体中与法向应力张量边界相切的分量，一般而言，它在预测心血管疾病尤其是冠心病可能出现的不良事件方面，被认为是一个至关重要的量。在特定患者情况下，可通过基于患者几何结构进行计算流体动力学（CFD）分析来量化WSS，或者通过基于血流速度数据（如超声（US）多普勒测量）的数值近似来获取。本文提出了一种从二维矢量多普勒测量中量化WSS的新方法。
通过非聚焦平面波和横向振荡获取图像，以获取平面内的速度分量。这些速度分量使用基于导数傅里叶近似的伪谱微分技术进行处理，以计算WSS。
我们的伪谱方法（PSM）在两个血管模型（直管和狭窄管）中进行了测试，其中施加了15毫升/分钟的稳定流量。该方法已成功针对CFD模拟进行了验证，并与基于抛物线速度分布假设的现有技术进行了比较。PSM能够准确检测出与直圆柱不同几何形状中的壁面剪应力（WSS）变化，并且对测量噪声不太敏感。特别是，在圆柱几何形状上使用合成数据（无噪声，例如由CFD生成）时，基于泊肃叶定律的方法和PSM具有相当的精度；相反，当使用从超声测量中获取的数据时，PSM获得的WSS平均误差比现有技术方法获得的误差小3至9倍。
伪谱方法允许在存在噪声数据的情况下控制近似误差。这为当前标准提供了一种更准确的替代方法，并且与CFD相比计算成本更低，CFD还需要高质量数据来重建血管几何形状。
