3D patient-specific modeling and structural finite element analysis of atherosclerotic carotid artery based on computed tomography angiography

Figure 1. Final patient-specific atherosclerotic CA wall geometries of the ten patients, obtained from the segmentation of in vivo images, with all macro-components that can be present in an atheromatous plaque, i.e. calcific (green), lipid (blue) and fibrous (orange) components.

Figure 2. Pointwise distances between the reference (in transparency) and proposed models of the fibrous plaque component for patients 1, 4 and 7.

Figure 3. VM stresses as a function of the cumulative normalized volume of the fibrous plaque elements. For each case (i.e. patients 1, 4, 7, identified by the different colors) the volume-stress plots are shown with different lines that represent simulations results using either the proposed model (solid curves) or the reference one (dotted curves). The markers highlight VM99 stress values for each simulation/patient.

Figure 4. Results of the comparative analysis for three selected cases (patient 1, 4, 7). The cross-sectional contour plots of VM stress distributions (in MPa) in the CA healthy wall and fibrous plaque, obtained from simulations of the proposed model and reference model, are shown in the figure (left and middle panels), together with the corresponding 3D model sections derived from the STL files (on the right). The lumen is denoted as Lu, while the lipid, calcific and fibrous subsets are denoted as Li, Ca, and Fi, respectively. In the plots on the right, the orange solid and dotted curves for the fibrous component refer to the proposed and reference model, respectively.

Figure 5. Contour plots of VM stress distributions (in MPa) in three example cases (patients 3, 5, 9), with the corresponding models of the vessel wall (red), and of the fibrous (orange), calcific (green) and lipid (light-blue) plaque components. The 3D views are provided on the left, while the cross-sectional views are shown on the right. A yellow dashed line has been added to the 3D views to indicate more clearly the location of the corresponding 2D transversal sections shown in the panels on the right. Since VM stress distributions are plotted both in the CA healthy wall and fibrous plaque regions, in those cases in which peak stresses are localized in the wall they are colored in gray, while the highest stress regions in the fibrous subset are always displayed in red (see color scales). Red spheres/arrows are used to mark the VM99 point location.

Figure 6. The B-mode image of the CCA on which the vessel distension waveform (in blue), computed using Esaote’s QAS modality, is shown. The QAS mode automatically detects the vessel wall average diameter tracking (in orange) and its consequent amplified movement (in green) associated to wall distension.

Figure 7. CTA axial and sagittal views for patient 10 (a), and corresponding segmentation results (b): the lumen is labelled in red, the lipid content of plaque is represented in blue and the calcific content in green. The 3D segmentation results were finally exported in STL format (c).

Figure 8. Reconstruction of the atherosclerotic wall solid and fibrous plaque component models. The final atherosclerotic wall geometry (e) is obtained as the Boolean difference between the wall inner (a) and outer (c) surfaces. Panel (b) represents the sections enlargement procedure used to include calcific and lipid components of the plaque. To obtain the fibrous plaque component (in yellow in (f)), a Boolean difference between the stenotic lumen (a) and the shrinked outer wall surface (d) is performed. Vessel geometries are shown for patient 10.

Figure 9. The figure shows a cut-view of the volumetric mesh. To display all different subsets and the corresponding section assignment used for the different components of the wall, the entire mesh was edited removing some tetrahedra. Different colors represent different material properties of components. The subset of elements representing the calcific component is shown in green, the lipid component in blue and the fibrous one in yellow. The remaining elements in red represent the healthy wall.