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

The assessment of carotid plaque vulnerability is a relevant clinical information that can help prevent adverse cerebrovascular events. To this aim, in this study, we propose a patient-specific computational workflow to quantify the stress distribution in an atherosclerotic carotid artery, by means of geometric modeling and structural simulation of the plaque and vessel wall. Ten patients were involved in our study. Starting with segmentation of the lumen, calcific and lipid plaque components from computed tomography angiography images, the fibrous component and the vessel wall were semi-automatically reconstructed with an ad-hoc procedure. Finite element analyses were performed using local pressure values derived from ultrasound imaging. Simulation outputs were analyzed to assess how mechanical factors influence the stresses within the atherosclerotic wall. The developed reconstruction method was first evaluated by comparing the results obtained using the automatically generated fibrous component model and the one derived from image segmentation. The high-stress regions in the carotid artery wall around plaques suggest areas of possible rupture. In mostly lipidic and heterogeneous plaques, the highest stresses are localized at the interface between the lipidic components and the lumen, in the fibrous cap.

The mesh density has an impact on the element subsets selection corresponding to the different plaque components and CA healthy wall and consequently on the simulation results.Therefore, a preliminary mesh-convergence analysis was performed for one patient.Different meshes were created on the same CA model: a partition was used to delimit the full plaque region and the local seed size was varied to assess the difference on the estimated plaque volume from STL files and on the VM99 stress results.The local seed size was decreased with 0.1 mm step going from 0.8 mm to 0.2 mm.Plaque volume and VM99 were investigated.More specifically, concerning the plaque volume, the difference between the volume enclosed into the plaque STL files derived from CTA images (i.e., reference volume given by the sum of lipid and calcific volumes, which is 113.151mm 3 ) and the volume predicted by the lipid and calcific plaque subsets was assessed (Δvolume).For what concerns the VM99 stress instead, the difference between the results obtained using the coarser mesh and the actual mesh density was assessed (ΔVM99).The final size of the seeds was chosen when the variation of these parameters for two consecutive mesh sizes was considered negligible.Data reported in Table 1S show that the mesh refining with local seed size of 0.4 mm and 0.3 mm produced a negligible difference in the computed VM99, creating a plateau in the simulation results.Thus, since further mesh refining would dramatically increase the computational requirements without significantly improving the plaque volume estimation, we chose a final mesh size of 0.3 mm inside the plaque region (including the fibrous, lipid and calcific components).The global mesh size (outside the plaque) was instead set to 0.8 mm.

Geometric Comparison of Fibrous Components Models
3D images obtained from the mutual distance analysis between the proposed reconstructed geometry and the manually segmented geometry of the plaque fibrous components, presented in the paper for patients 1-4-7, are here provided also for the seven remaining patients in Fig. 1S.Quantitative results for all 10 patients are reported in Table 2S.It should be noted that percentage volume differences provided in Table 2S have been computed using volumes derived from geometrical models of the plaque, while volumes reported in Tables 1 and 2 in the paper have been computed on the FE models in Abaqus.For this reason, some slight differences can be observed e.g. between volume percentage differences of patients 1-4-7 in Table 2S and Table  1.Nevertheless, the plot in Fig. 2S demonstrates that volumes derived from the geometrical and FE model of the same plaque are very similar.

Sensitivity Analysis of Stress Distributions to Variations of the Fibrous Component Young's Modulus
Since the Young's moduli set for the plaque fibrous component and carotid healthy wall were quite similar (i.e.400 kPa vs. 550 kPa), a further analysis was carried out to evaluate if more significant differences could appear between the stress distributions obtained using the reference and proposed models when the Young's modulus of the fibrous component varies.The considered variations were ±10%, ±20%, ±50% of the Young's modulus initially employed (i.e.400 kPa).Analyses were carried out for patients 1-4-7.In Fig. 3S, the trend of VM99 values vs. volume is compared for all the analyzed cases in the 3 selected patients.The plots demonstrate that the same differences/similarities observed between the reference and proposed model curves for the initial Young's modulus value (400 kPa) in Figure 3 are still present even when this parameter varies.Tables 3S-4S-5S also provide VM99 values quantitatively in all the analyzed cases.Indeed, the VM99 percentage difference between the reference and proposed models for each patient doesn't show significant variations when the Young's modulus varies within the considered range.Finally, Fig. 4S compares the 2D stress distributions in the slice where the VM99 is detected.The distributions are shown for the -50% case only, as an example, since it represents the case with the greatest difference between the Young's moduli of the fibrous tissue and wall (i.e.200 kPa vs. 550 kPa) among the values considered.These plots also confirm that stress distributions for the reference and proposed models for each patient remain similar even when the Young's modulus of the fibrous plaque is 200 kPa, as observed in the initial case in Figure 4.

Fig
Fig. 1S.Pointwise distances between the reference (in transparency) and proposed models of the fibrous plaque component for patients 2, 3, 5, 6, 8, 9 and 10.The same color scale of Figure 2 has been applied.

Fig. 2S .
Fig. 2S.Comparison of volumes computed from the geometrical and FE model of the fibrous plaque for each patient (blue dots).In this case, the two volume computation approaches have been compared considering the "proposed model" of the fibrous plaque, i.e. the one obtained with our reconstruction method.

Fig. 3S .
Fig. 3S.Trend of Von Mises stress vs. cumulated volume of the fibrous elements for patients 1, 4 and 7. Differentcolors have been used for each variation of the fibrous tissue Young's modulus (±10%, ±20%, ±50%), with "Baseline" referring to the initial value (400 kPa).Dashed and solid curves refer to results obtained with the reference and proposed models, respectively.

Fig. 4S .
Fig. 4S.2D stress distributions obtained with the proposed and reference models for patients 1, 4 and 7 when employing different Young's moduli values (400 kPa and 200 kPa) for the fibrous plaque component.

Table 1S .
Mesh convergence analysis

Table 2S .
Mutual distances and volume differences between the reference and proposed fibrous plaque models.

Table 3S .
VM99 for patient 1 using different Young's moduli for the fibrous tissues

Table 4S .
VM99 for patient 4 using different Young's moduli for the fibrous tissues

Table 5S .
VM99 for patient 7 using different Young's moduli for the fibrous tissues