Sketch of the behavior of a RGC, made up of an axis (described by its curvature, torsion and Frenet frame) and a contour orthogonal to the axis (described by the Fourier coefficients). The surface contains the contour . The shape of the successive contours enables the representation of stenosis as illustrated by , , and .
3D representation of blood vessel geometries obtained from RGC models. Phantoms represent a healthy vessel, (a), a stenosed vessel, , (b) and a bifurcation branching vessel, (c). In (b) and (c) the external RGC is transparent to show the external artery layers.
Flow chart illustrating the interactions between different modules (RGC, COMSOL, FIELD II) of the 3D model.
Finite element simulation of the flow and the pulsation of the stenosed cylinder . Displacement (arrows) and velocity field (grayscale) plotted at the systolic peak. The maximum flow velocity is .
Isosurface plot of the fluid velocity in frozen at the systolic peak of the pulsating inflow cycle; the greyscale represents the amplitude of the velocity. The maximum flow velocity is .
Simulated -mode of the healthy (a), the stenosed (b), and the bifurcating vessel extracted from a sequence of images, frozen during the cardiac cycle in diastole for (a) and (b), and (c).
-mode image of the straight tube simulated over a pulsating cycle. In the image the lumen area is surrounded by the arterial membrane and by tissue, each of them with different backscattering properties.
Image obtained from Fig. 7 applying denoising anisotropic filtering.
Displacement values obtained by segmentation of the wall boundary of Fig. 7 compared with the reference finite element simulation displacement.
Doppler images simulated with FIELD II at PRF (a) and velocity reference images obtained by finite element simulation (b) frozen at the same instant phase of the cardiac cycle.
Doppler-simulated velocity profile in the center of the vessel at (a) and (b) PRF, and finite element reference velocity at the same position. The location of the measured voxel is indicated by the intersection of the dashed lines in Fig. 10.
Simulated Doppler at PRF (a) and corresponding reference velocity (finite element) images (b) showing blood recirculation downstream in the stenosed area. The simulated fluid flows from left to right. The geometry of the structure is superimposed on the Doppler image on (a).
Flow streamlines obtained by finite element analysis performed on the stenosed vessel geometry. The recirculation zone posterior to the plaque and the irregular flow lines caused by narrowing are illustrated.
Mechanical parameters used in the simulations [chosen in accordance with reference values given in Fung’s papers (Refs. 20 and 27)].
Acoustic parameters used for the three-layer model.
Summary of the main features of different models.
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