The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψ of the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψ is decoupled into volumetric and isochoric parts and the anisotropic part of Ψ is expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformation. To look at more practical appli- cations, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model).Keywords: Anisotropic, Hyperelastic, Incompressibility, Finite element, Artery, Stent Nomenclature I -identity tensor Ψ -Helmholtz free-energy (strain-energy) function Ψ vol -volumetric contribution to the free energy Ψ aniso -anisotropic contribution to the free energy Ψ iso -isotropic contribution to the isochoric free energy Ψ aniso -anisotropic contribution to the isochoric free energy σ -Cauchy stress σ -deviatoric Cauchy stress q -von Mises equivalent stress σ hyd -hydrostatic (pressure) stress F -deformation gradient J -determinant of the deformation gradient; local ratio of volume change C -right Cauchy-Green tensor I 1 -first invariant of C I 4,6 -anisotropic invariants describing the deformation of reinforcing fibres F -isochoric portion of the deformation gradient C -isochoric portion of the right Cauchy-Green deformation tensor I 1 -first invariant of C I 4,6 -isochoric anisotropic invariants a 0i , i = 4, 6 -unit vector aligned with a reinforcing fibre in the reference configuration a i , i = 4, 6 -updated (deformed) fibre direction (= Fa 0i ) κ 0 -isotropic bulk modulus µ 0 -isotropic shear modulus k i , i = 1, 2 -anisotropic material co...

The durability of bovine pericardium leaflets employed in bioprosthetic heart valves (BHVs) can significantly limit the longevity of heart valve prostheses. Collagen fibres are the dominant load bearing component of bovine pericardium, however fibre architecture within leaflet geometries is not explicitly controlled in the manufacture of commercial devices. Thus, the purpose of this study was to ascertain the influence of pre-determined collagen fibre orientation and dispersion on the mechanical performance of bovine pericardium. Three tissue groups were tested in uniaxial tension: cross-fibre tissue (XD); highly dispersed fibre-orientations (HD); or preferred-fibre tissue (PD). Both the XD and PD tissue were tested under cyclic loading at 1.5 Hz and a stress range of 2.7 MPa. The results of the static tensile experiments illustrated that collagen fibre orientation and degree of alignment significantly influenced the material's response. Whereby, there was a statistically significant decrease in material properties between the XD groups and both the PD and HD groups for ultimate tensile strength and stiffness (p<0.01). Furthermore, HD tissue had a stiffness of approximately 58% of the PD group, and XD tissue had a stiffness of approximately 18% of the PD group. The dynamic behaviour of the XD and PD groups was extremely distinct; for example a Weibull analysis indicated that the 50% probability of failure in specimens with fibres orientated perpendicular (XD) to the loading direction occurred at 375 cycles. Due to this failure, XD specimens survived less than 20% of the cycles completed by those in which fibres were aligned along the loading direction (PD). The results from this study indicate that fibre architecture is a significant factor in determining static strength and fatigue life in bovine pericardium, and thus must be incorporated in the design process to improve future device durability.

determined using SALS agreed with those found using traditional destructive techniques, however SALS has the important benefits of allowing vessel layers to remain intact, and has a fast processing time. SALS unique ability to identify load induced reorganisation in intact arterial layers offers an efficient means to gain crucial insights into arterial disease and its development over time.

The mechanisms behind in-stent restenosis, the re-narrowing of a stented artery, are poorly understood. However it is known that mechanical damage due to stent implantation plays a major role. This paper investigates the mechanism behind damage-induced cell proliferation using a coupled finite element and agent based model, assuming it is based on a) instantaneous loading, or b) cyclic loading. Furthermore the role of remnant endothelial cells in attenuating in-stent restenosis is examined. Results show that a cyclic damage model predicts a nonphysiological, overly proliferative response, whilst the instantaneous model demonstrates that lumen loss may be regulated by re-endothelialisation.

Arterial tissue is commonly assumed to be incompressible. While this assumption is convenient for both experimentalists and theorists, the compressibility of arterial tissue has not been rigorously investigated. In the current study we present an experimental-computational methodology to determine the compressibility of aortic tissue and we demonstrate that specimens excised from an ovine descending aorta are significantly compressible. Specimens are stretched in the radial direction in order to fully characterise the mechanical behaviour of the tissue ground matrix. Additionally biaxial testing is performed to fully characterise the anisotropic contribution of reinforcing fibres. Due to the complexity of the experimental tests, which entail non-uniform finite deformation of a non-linear anisotropic material, it is necessary to implement an inverse finite element analysis scheme to characterise the mechanical behaviour of the arterial tissue. Results reveal that ovine aortic tissue is highly compressible; an effective Poisson's ratio of 0.44 is determined for the ground matrix component of the tissue. It is also demonstrated that correct characterisation of material compressibility has important implications for the calibration of anisotropic fibre properties using biaxial tests. Finally it is demonstrated that correct treatment of material compressibility has significant implications for the accurate prediction of the stress state in an artery under in vivo type loading.

Collagen fibre architecture is the dominant load bearing component of arterial tissue. Remodelling of this architecture is a strain dependent process stimulated by the degradation of existing collagen. Despite this, degradation of arterial tissue and in particular, arterial collagen, is not fully understood or studied. In the current study, we identified for the first time, the strain dependent degradation response of arterial tissue, which has not been observed in other collagenous tissues in literature. We hypothesised that this unique degradation response was due to the complex structure observed in arterial tissue. Based on this hypothesis, we developed a novel numerical model capable of explaining this unique degradation response which may provide critical insights into disease development and aid in the design of interventional medical devices.

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