The viscoelastic characteristics of in-vitro carotid plaque by Kelvin-Voigt fractional derivative modeling

Abstract

Atherosclerotic plaque with a thin fibrous cap can be ruptured by shear force. Exploiting the mechanical properties of plaques within different histological regions can help to better understand the physical mechanisms of the plaque. The association between the plaque components and viscoelasticity was studied when mapping the viscoelasticity to histological features. Eleven in-vitro carotid plaques were tested with ramp-hold relaxation nanoindentation tests. Viscoelasticity (elastic modulus E₀, fluidity α, and viscosity τ) was characterized by Kelvin-Voigt fractional derivative (KVFD) modeling. There is a significant difference (p < 0.001) on E₀, α, and τ between the collagen-rich (CR) group and the non-collagen-rich (NCR) group. In the CR group, the elastic modulus E₀ was higher but the fluidity α and viscosity τ were lower than those of the NCR group. Receiver operating characteristic (ROC) analysis revealed that combinations of E₀ and α can be used as a CR indicator with an area under the curve (AUC) of 0.770. There was a negative correlation between E₀ and the percentages of myxoid degeneration (r = -0.160, p < 0.001), necrosis (r = -0.229, p < 0.001) and inflammatory cells (r = -0.130, p < 0.001), and a positive correlation between elasticity E₀ and the percentage of foam cells (r = 0.121, p < 0.001). There was a positive correlation between fluidity α and the percentage of necrosis (r = 0.308, p < 0.001). The results confirmed the clinical evidence that the CR group with higher elasticity and lower fluidity has higher resisting ability, whereas the NCR group with lower elasticity and higher fluidity has accompanied with more myxoid degeneration, extracellular lipids and necrosis.

Keywords: Carotid plaque; Kelvin-Voigt fractional derivative (KVFD) model; Risk of vulnerability; Viscoelastic measurement.