Inelasticity of Human Carotid Atherosclerotic Plaque

Abstract

Little mechanical test data exists regarding the inelastic behavior of atherosclerotic plaques. As a result finite element (FE) models of stenting procedures commonly use hyperelastic material models to describe the soft tissue response thus limiting the accuracy of the model to the expansion stage of stent implantation and leave them unable to predict the lumen gain. In this study, cyclic mechanical tests were performed to characterize the inelastic behavior of fresh human carotid atherosclerotic plaque tissue due to radial compressive loading. Plaques were classified clinically as either mixed (M), calcified (Ca), or echolucent (E). An approximately linear increase in the plastic deformation was observed with increases in the peak applied strain for all plaque types. While calcified plaques generally appeared stiffest, it was observed that the clinical classification of plaques had no significant effect on the magnitude of permanent deformation on unloading. The test data was characterized using a constitutive model that accounts for both permanent deformation and stress softening to describe the compressive plaque behavior on unloading. Material constants are reported for individual plaques as well as mean values for each plaque classification. This data can be considered as a first step in characterizing the inelastic behavior of atherosclerotic plaques and could be used in combination with future mechanical data to improve the predictive capabilities of FE models of angioplasty and stenting procedures particularly in relation to lumen gain.

An anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue

“…tissues as isotropic (Delfino et al, 1997;Maher et al, 2011). The anisotropic components are exponential functions of the invariants and :…”

“…Another phenomenon that occurs as a result of non-physiological loading is the presence of residual inelastic strains (or permanent set) on unloading. Both stress softening and permanent set have been observed for other soft tissues: such as skin, brain, venous and vaginal tissue (Ehret and Itskov, 2009;Franceschini et al, 2006;Peña, 2011); as well as arterial tissue (Calvo et al, 2007;Pena et al, 2010) and atherosclerotic plaque (Maher et al, 2011).…”

“…A number of models have been proposed to describe stress softening in biological tissues. These models are often based on continuum damage mechanics theory; where a reduction factor (Simo and Ju, 1987a;Simo and Ju, 1987b) related to the evolution of irreversible internal variables is applied to model damage to either isotropic (Hokanson and Yazdani, 1997;Maher et al, 2011) or anisotropic models (Alastrué et al, 2007;Balzani et al, 2006;Calvo et al, 2007;Pena and Doblare, 2009). In anisotropic models of soft tissue, damage can either be isolated to the anisotropic fibrous component (Balzani et al, 2006) or applied to both the isotropic matrix and fibrous components separately (Calvo et al, 2007).…”

“…Relatively few constitutive models have been proposed to describe permanent set (Ehret and Itskov, 2009;Franceschini et al, 2006;Gasser, 2011;Gasser and Holzapfel, 2002;Maher et al, 2011;Peña, 2011;Tanaka and Yamada, 1990 (2011) used a formulation based on the evolution of internal variables to introduce inelastic softening to the anisotropic components of the model. Franceschini et al (2006) adapted a pseudoelastic formulation for particle filled rubbers (Dorfmann and Ogden, 2004;Ogden and Roxburgh, 1999) to model softening and permanent set for brain tissue.…”

“…Franceschini et al (2006) adapted a pseudoelastic formulation for particle filled rubbers (Dorfmann and Ogden, 2004;Ogden and Roxburgh, 1999) to model softening and permanent set for brain tissue. Other models have also used a pseudo-elastic based approach to describe inelastic strains in carotid plaque (Maher et al, 2011).…”