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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.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A n anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue A bstractInelastic phenomena such as softening and unrecoverable inelastic strains induced by loading have been observed experimentally in soft tissues such as arteries. These phenomena need to be accounted for in constitutive models of arterial tissue so that computational models can accurately predict the outcomes of interventional procedures such as balloon angioplasty and stenting that involve non-physiological loading of the tissue. In this study, a novel constitutive model is described that accounts for inelastic effects such as Mullins-type softening and permanent set in a fibre reinforced tissue. The evolution of inelasticity is governed by a set of internal variables. Softening is introduced through a typical continuum damage mechanics approach, while the inelastic residual strains are introduced through an additive split in the stress tensor. Numerical simulations of aorta and carotid arterial tissue subjected to uniaxial testing in the longitudinal, circumferential and axial directions reproduce the anisotropic inelastic behaviour of the tissue. Material parameters derived from best-fits to experimental data are provided to describe these inelastic effects for both aortic and carotid tissue.

1Understanding the mechanical behaviour of arterial tissue is vital to the development and 2 analysis of medical devices targeting diseased vessels. During angioplasty and stenting, stress 3 softening and permanent deformation of the vessel wall occur during implantation of the 4 device, however little data exists on the inelastic behaviour of cardiovascular tissue and how 5 this varies through the arterial tree. The aim of this study was to characterise the magnitude 6 of stress softening and inelastic deformations due to loading throughout the arterial tree and 7 to investigate the anisotropic inelastic behaviour of the tissue. Cyclic compression tests were 8 used to investigate the differences in inelastic behaviour for carotid, aorta, femoral and 9 coronary arteries harvested from 3-4 month old female pigs, while the anisotropic behaviour 10 of aortic and carotid tissue was determined using cyclic tensile tests in the longitudinal and 11 circumferential directions. The differences in inelastic behaviour were correlated to the ratio 12 of collagen to elastin content of the arteries. It was found that larger inelastic deformations 13 occurred in muscular arteries (coronary), which had a higher collagen to elastin ratio than 14 elastic arteries (aorta), where the smallest inelastic deformations were observed. Lower 15 magnitude inelastic deformations were observed in the circumferential tensile direction than 16 in the longitudinal tensile direction or due to radial compression. This may be as a result of 17 non-fibrous matrix or smooth muscle in the artery becoming more easily damaged than the 18 collagen fibers during loading. Stress softening was also found to be dependent on artery

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Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.

Many soft biological tissues contain collagen fibres, which act as major load bearing constituents. The orientation and the dispersion of these fibres influence the macroscopic mechanical properties of the tissue and are therefore of importance in several areas of research including constitutive model development, tissue engineering and mechanobiology. Qualitative comparisons between these fibre architectures can be made using vector plots of mean orientations and contour plots of fibre dispersion but quantitative comparison cannot be achieved using these methods. We propose a 'remodelling metric' between two angular fibre distributions, which represents the mean rotational effort required to transform one into the other. It is an adaptation of the earth mover's distance, a similarity measure between two histograms/signatures used in image analysis, which represents the minimal cost of transforming one distribution into the other by moving distribution mass around. In this paper, its utility is demonstrated by considering the change in fibre architecture during a period of plaque growth in finite element models of the carotid bifurcation. The fibre architecture is predicted using a strain-based remodelling algorithm. We investigate the remodelling metric's potential as a clinical indicator of plaque vulnerability by comparing results between symptomatic and asymptomatic carotid bifurcations. Fibre remodelling was found to occur at regions of plaque burden. As plaque thickness increased, so did the remodelling metric. A measure of the total predicted fibre remodelling during plaque growth, TRM, was found to be higher in the symptomatic group than in the asymptomatic group. Furthermore, a measure of the total fibre remodelling per plaque size, TRM/TPB, was found to be significantly higher in the symptomatic vessels. The remodelling metric may prove to be a useful tool in other soft tissues and engineered scaffolds where fibre adaptation is also present.

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