Characterizing atherosclerotic tissues: in silico analysis of mechanical properties using intravascular ultrasound and inverse finite element methods

Abstract

Atherosclerosis is a prevalent cause of acute coronary syndromes that consists of lipid deposition inside the artery wall, creating an atherosclerotic plaque. Early detection may prevent the risk of plaque rupture. Nowadays, intravascular ultrasound (IVUS) is the most common medical imaging technology for atherosclerotic plaque detection. It provides an image of the section of the coronary wall and, in combination with new techniques, can estimate the displacement or strain fields. From these magnitudes and by inverse analysis, it is possible to estimate the mechanical properties of the plaque tissues and their stress distribution. In this paper, we presented a methodology based on two approaches to characterize the mechanical properties of atherosclerotic tissues. The first approach estimated the linear behavior under particular pressure. In contrast, the second technique yielded the non-linear hyperelastic material curves for the fibrotic tissues across the complete physiological pressure range. To establish and validate this method, the theoretical framework employed in silico models to simulate atherosclerotic plaques and their IVUS data. We analyzed different materials and real geometries with finite element (FE) models. After the segmentation of the fibrotic, calcification, and lipid tissues, an inverse FE analysis was performed to estimate the mechanical response of the tissues. Both approaches employed an optimization process to obtain the mechanical properties by minimizing the error between the radial strains obtained from the simulated IVUS and those achieved in each iteration. The second methodology was successfully applied to five distinct real geometries and four different fibrotic tissues, getting median R ² of 0.97 and 0.92, respectively, when comparing the real and estimated behavior curves. In addition, the last technique reduced errors in the estimated plaque strain field by more than 20% during the optimization process, compared to the former approach. The findings enabled the estimation of the stress field over the hyperelastic plaque tissues, providing valuable insights into its risk of rupture.

Keywords: atherosclerosis; coronary; inverse finite element analysis; material characterization; optimization; vulnerability.

FIGURE 1

Five real geometries considered in the analysis (Finet et al., 2004).

FIGURE 2

Scheme of the optimization process of the first method to recover the linear elastic properties of the atherosclerotic tissues.

FIGURE 3

Scheme of the optimization process of the second method to recover the non-linear hyperelastic properties of the atherosclerotic tissues.

FIGURE 4

Scheme of the Pull-Back algorithm used to recover the Zero-Pressure geometry.

FIGURE 5

Box plot of the sr variability in the fibrotic material (left) and lipidic material (right) for the different material combinations of LHS (orange) and different geometries (red).

FIGURE 6

LHS with the differences material combinations between fibrotic-lipid elastic modulus. The left half of the circle presents the sr of the lipid core characterization and the right half for sr in fibrotic tissues. The colors range from yellow to dark red depending on how high the success rate is.

FIGURE 7

Results of the stress-stretch curves under uniaxial tensile loading obtained with the second approach over the different geometries with the material properties of calcified 1 (Table 2).

FIGURE 8

Results of the stress-stretch curves under uniaxial tensile loading obtained with the second approach over the first geometry with the calcified 1 fibrotic tissue (A), calcified 2 tissue (B), cellular tissue (C) and hypocellular tissue (D).

FIGURE 9

Comparison between the true unpressurized geometries (A) with the estimated ZP geometries (B). Fibrotic tissues are represented in reddish color, lipids in orange, and calcifications in gray.

FIGURE 10

Results of both methods over the first IVUS geometry with calcified 1 material properties. (A) Simulated radial strains after adding 20 dB of SNR to the FE results. (B) Segmentation process, where the chosen SGV to extract the lipid was $\left|▿{\epsilon }_{rr}\right|$ which is represented next to the image segmentation results. Then, the mechanical characterization used this segmentation to estimate the radial strain with linear material properties (C) or non-linear properties (D).

FIGURE 11

Max. Principal Stress distribution [kPa] at 115 mmHg in the fifth IVUS plaque taken as ground truth (A), and the resulting (σ _max) for the linear (B), and non-linear (C) approaches.