Quantifying effects of plaque structure and material properties on stress distributions in human atherosclerotic plaques using 3D FSI models

Abstract

Background: Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Methods to assess plaque vulnerability noninvasively and predict possible plaque rupture are urgently needed.

Method: MRI-based three-dimensional unsteady models for human atherosclerotic plaques with multi-component plaque structure and fluid-structure interactions are introduced to perform mechanical analysis for human atherosclerotic plaques.

Results: Stress variations on critical sites such as a thin cap in the plaque can be 300% higher than that at other normal sites. Large calcification block considerably changes stress/strain distributions. Stiffness variations of plaque components (50% reduction or 100% increase) may affect maximal stress values by 20-50%. Plaque cap erosion causes almost no change on maximal stress level at the cap, but leads to 50% increase in maximal strain value.

Conclusions: Effects caused by atherosclerotic plaque structure, cap thickness and erosion, material properties, and pulsating pressure conditions on stress/strain distributions in the plaque are quantified by extensive computational case studies and parameter evaluations. Computational mechanical analysis has good potential to improve accuracy of plaque vulnerability assessment.

Fig. 1

A cadaveric plaque sample with a large calcification block and a lipid pool. (a) Selected MR images from a 36-slice set (S ₉ – S ₃₂ are shown here, from left to right, then continued to next row.); (b) component segmentations of MR images based on histological data. Some smoothing was applied; (c) reconstructed 3D plaque geometry. The position of the vessel is rotated for better viewing.

Fig. 2

Prescribed pressure condition for the baseline model and corresponding flow rate. (a) A typical pressure profile for human internal carotid is scaled to 90–150 mm Hg and used as the upstream pressure (P _in). Down stream pressure is chosen so that flow rate will be within physiological range; (b) flow rate corresponding to the prescribed pressure conditions. It should be noted that this pressure-flow rate data is for a free-standing model such as the model presented in this paper. Realistic coronary flow rate will be affected by heart motion and contraction and will be different from the curve given here.

Fig. 3

Band plots of selected stress components from the 3D FSI baseline model on a sagittal slice and three cross-section cuts showing that the large calcification block has considerable effect on stress distributions. P _in =150 mm Hg, P _out =126 mm Hg, axial stretch=10%. (a) Position of the cut and band plot of stress-P ₁ showing calcification has higher stress level. Stress maximum occurred at a location where vessel wall is thin; (b) band plot of circumferential stress distribution. Maximum is found at the healthy side of the vessel (vessel is thin there); (c) band plot of longitudinal tensile stress; (d) stress-P ₁ on slice 4; (e) stress-P ₁ on slice 12; (f) stress-P ₁ on slice 20.

Fig. 4

Normal and critical sites are selected to track stress/strain variations. P ₁: from calcification cap; P ₂: from a thicker Ca cap; P ₃: from a thicker Ca cap; P ₄: from a thin lipid core cap (most vulnerable site); P ₅: normal point to observe stress- xx ; P ₆: normal point to observe stress-yy . (a)–(c) give locations of the six points and three slices from the plaque sample (Fig. 1).

Fig. 5

Tracking of stress components at selected locations under pulsating pressure showing critical point from the thin lipid cap has much greater stress variations. (a) Stress-P ₁ plots showing stress variation at the thin lipid core cap is much higher (400%) than that at other locations; (b) stress-xy (shear stress) plots also show that shear stress variation at the thin lipid core cap is much higher (400%) than that at other locations.

Fig. 6

Plaque with higher stenosis severity has lower stress variations. Three cases were simulated. Case 1: A human carotid plaque with 40% stenosis severity (by diameter), P _in =90–150 mm Hg as given by Fig. 3, P _out =90–145; case 2: A modified plaque with 70% stenosis severity (by diameter), pressure: same as case 1; case 3: Same plaque as in case 2, P _in =90–150 mm Hg, P _out =20 mm Hg so that flow rate is about the same as in case 1. Axial stretch=10% for all three cases. Tracking locations are indicated in (b) and (d).

Fig. 7

Simulations using in vitro models indicate that higher stenosis severity leads to lower stress variations. Nine cases were simulated with severity changed from 40% to 80% incrementally. Tube inner diameter = 8 mm, tube wall thickness (straight part) = 1 mm, tube length= 140 mm, stenosis length= 16 mm, P _in =150, P _out =145(mm Hg). (a) The in vitro stenosis model and location of tracking point; (b Stress components at the tracking point versus stenosis severity.

Fig. 8

Thinner plaque cap leads to higher stress level: quantitative study. (a) Stress-P ₁ in plaque with thicker cap; (b) maximum of stress- P ₁ appeared at the plaque cap when cap thickness was reduced to 0.02 mm; (c) maximal values of stress-P ₁ increases almost exponentially when cap thickness decreases. Eleven cases were simulated using the 70% modified plaque sample with cap thickness adjusted incrementally from 0.02 to 0.42 mm. P _in =90–150 mm Hg, P _out =20 mm Hg. Only the stress values at P _in =150 mm Hg are shown.

Fig. 9

Plaque cap erosion/weakening causes large strain increase. Maximal principal stress showed very little change (figure not shown). However, maximum of strain-P ₁ (maximal principal strain) increased about 50% when half of the cap was made 50% softer.

Fig. 10

Plots of stress-P ₁ at three selected points with different material parameters showing that material properties have considerable effect on stress distributions. For each material, material parameters in the Mooney-Rivlin model for that material were changed incrementally while parameters for the other two materials remained unchanged; nine cases were computed with case 1 being the softest and case 9 being the stiffest. Other boundary conditions: P _in =150 mm Hg, P _out =126 mm Hg, axial - stretch=10%. (a) Vessel stiffness variations: c ₁ =60,000–124,000; D ₁ =20,000–52,000; D ₂ =1.6–2.4; Ca and lipid used baseline values; (b) Ca stiffness variations: c ₁ =600,000–1,240,000; D ₁ =200,000–520,000; D ₂ =1.6–2.4; vessel and lipid used baseline values; (c) lipid core stiffness variations: c ₁ =3400–6600; D ₁ =3400–6600; D ₂ =1.1–1.9; vessel and Ca used baseline values.