Adam D R, Burstein P
Heart System Research Center, Julius Silver Institute, Department of Biomedical Engineering, Technion-IIT, Haifa, Israel.
Adv Exp Med Biol. 1997;430:177-85. doi: 10.1007/978-1-4615-5959-7_15.
A new method for quantitative reconstruction of a three dimensional (3D) velocity field from ultrasound color doppler mapping (USCDM) images is used here to calculate the shear stress distribution on the endothelial layer of an artery. Measurements of a few spatially unrestricted USCDM transverse cross sectional images of the artery, and of several echo-ultrasound B-mode images of the same area, are required for reconstructing the geometry of the vessel's endothelial surface. The calculation is based on assuming a physical model of flow, and solving the Continuity and the Navier-Stokes equations numerically for a steady flow of an incompressible Newtonian fluid at constant temperature within a non-flexible tube. The correct choice of the penalty parameter in the finite element method (FEM) algorithm provides proper convergence of the reconstruction. The endothelial shear stress is calculated from the gradient of the velocity field at each point of the vessel's inner surface.
本文采用一种从超声彩色多普勒映射（USCDM）图像定量重建三维（3D）速度场的新方法，来计算动脉内皮层上的剪应力分布。为了重建血管内皮表面的几何形状，需要测量动脉的一些空间无限制的USCDM横向横截面图像以及同一区域的多个超声B模式图像。该计算基于假设一个流动的物理模型，并针对不可压缩牛顿流体在非柔性管内恒温下的稳定流动，对连续性方程和纳维 - 斯托克斯方程进行数值求解。有限元法（FEM）算法中惩罚参数的正确选择可确保重建的适当收敛。内皮剪应力是根据血管内表面各点处速度场的梯度来计算的。
