Effects of Calcification Modulus and Geometry on Stress in Models of Calcified Atherosclerotic Plaque

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Cardiovascular Engineering and Technology





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Large calcifications often develop in advanced atherosclerotic plaques. Prior computational studies showed these macrocalcifications to stabilize arterial wall stress with calcification moduli (Ecalc) of 2.5 MPa. However, recent nanoindentation studies measured Ecalc as 10-25 GPa, suggesting underestimation by up to 104 in previous models. This study investigated the effects of Ecalc and calcification geometry on stress in models of atherosclerotic plaque, with the modifying factor of fibrous component constitutive relation.

Stress was calculated in idealized plane-strain finite element models of pressurized coronary arteries containing calcified lesions. Lesions were modeled as arc-shaped, circular, and elliptical regions with varying lumen separation, length, and thickness. Ecalc varied from 1.0 MPa to 10 GPa. Various orthotropic and hyperelastic constitutive relations for arterial wall and fibrous plaque were assigned, representing a range of literature values.

In all models, stress concentration at the calcification-fibrous plaque interface increased with increasing Ecalc, with highest stresses in orthotropic models for higher Poisson’s ratios and lower radial and circumferential moduli. This effect was more pronounced in arc-shaped calcifications, and was highly sensitive to geometry, with peak stress dependent on calcification distance from the lumen, and increasing dramatically with increased length and decreased thickness.


This study indicates the importance of using accurate material properties and geometries in models of atherosclerotic arteries. Results suggest calcification geometry, rather than calcification area, is a better predictor of high stresses in the arterial cross section and that some macrocalcifications, instead of providing a stabilizing influence, may predispose a plaque to rupture at the calcified interface.

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