This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel ...during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development.
This study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.
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Auxetic behaviour, the unphysical transverse expansion during uniaxial tension, is a common and undesirable feature of classical anisotropic hyperelastic constitutive models for soft tissue. In this ...study we uncover the underlying mechanism of such behaviour; high levels of in-plane compaction occurs due to increasing tension in strain-stiffening fibres, leading to unphysical out-of-plane expansion. We demonstrate that auxetic behaviour is primarily influenced by the ratio of fibre to matrix stiffness, and is accentuated by strain-stiffening fibres in a constant stiffness matrix (e.g., the widely used neo-Hookean matrix with exponentially stiffening fibres). We propose a new bilinear strain stiffening fibre and matrix (BLFM) model which allows close control of the fibre-matrix stiffness ratio, thereby robustly eliminating auxetic behaviour. We demonstrate that our model provides accurate prediction of experimentally observed out-of-plane compaction, in addition to stress-stretch anisotropy, for arterial tissue subjected to uniaxial tension testing.
•The effect of fiber orientation on the notch behavior in soft tissues is thoroughly studied.•The fibers perpendicular to the notch are most effective against notch extension.•The present study ...provides a way to design artificial skin with improved toughness.
Finite element (FE) simulations are performed to investigate the effect of fiber induced anisotropy on the notch behavior in hyperelastic skin type materials. The modified anisotropic (MA) model is used to define the constitutive behavior in FE simulations through Abaqus user defined material model UMAT. A parametric study is carried out to examine the effect of fiber orientation, notch root radius and sample geometry on the stress field ahead of the notch tip. A non-dimensional parameter ξ is defined to characterize the combined effect of J energy and average anisotropic energy ϕaniso-avg on the notch behavior. It is shown that fibre orientation significantly influences the stress state and J-integral at the notch. The findings of the present study will be helpful in determining optimal constitution and orientation of skin grafts at locations of high stress and complex geometries, such as corner of eyes and lips, etc.
Regional variance in human aortic bioarchitecture responsible for the elasticity of the vessel is poorly understood. The current study quantifies the elements responsible for aortic compliance, ...namely, elastin, collagen and smooth muscle cells, using histological and stereological techniques on human tissue with a focus on regional heterogeneity. Using donated cadaveric tissue, a series of samples were excised between the proximal ascending aorta and the distal abdominal aorta, for five cadavers, each of which underwent various staining procedures to enhance specific constituents of the wall. Using polarised light microscopy techniques, the orientation of collagen fibres was studied for each location and each tunical layer of the aorta. Significant transmural and longitudinal heterogeneity in collagen fibre orientations were uncovered throughout the vessel. It is shown that a von Mises mixture model is required accurately to fit the complex collagen fibre distributions that exist along the aorta. Additionally, collagen and smooth muscle cell density was observed to increase with increasing distance from the heart, whereas elastin density decreased. Evidence clearly demonstrates that the aorta is a highly heterogeneous vessel which cannot be simplistically represented by a single compliance value. The quantification and fitting of the regional aortic bioarchitectural data, although not without its limitations, including mean cohort age of 77.6 years, facilitates the development of next‐generation finite element models that can potentially simulate the influence of regional aortic composition and microstructure on vessel biomechanics.
The microarchitecture responsible for compliance of the human aorta is quantified and shown to be highly diverse regionally. The orientation of collagen fibres is non‐symmetric and varies significantly both axially and transmurally, and the density of collagen, elastin and smooth muscle cells is also highly heterogeneous along the aortic length. The quantification of aortic bioarchitecture facilitates the development of next‐generation finite element models that can potentially simulate the influence of regional aortic composition and microstructure on vessel biomechanics.
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 deformations. To look at more practical applications, 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).
The optimum cementing technique for the tibial component in cemented primary total knee replacement (TKR) remains controversial. The technique of cementing, the volume of cement and the penetration ...are largely dependent on the operator, and hence large variations can occur. Clinical, experimental and computational studies have been performed, with conflicting results. Early implant migration is an indication of loosening. Aseptic loosening is the most common cause of failure in primary TKR and is the product of several factors. Sufficient penetration of cement has been shown to increase implant stability. This review discusses the relevant literature regarding all aspects of the cementing of the tibial component at primary TKR.
Several medical papers have reported delamination of the coating from the stent-substrate following intravascular deployment leading to adverse outcomes for patients. However, the mechanisms of ...delamination of such polymer coatings from the surface of a stent due to large deformations during device deployment have not been studied. In this paper, a novel and in-depth investigation of the mechanisms and parameters that govern stent-coating delamination is performed, using a cohesive zone formulation to simulate the evolution of traction at the stent-coating interface. The study firstly analyses the behaviour of elastic coatings on idealised elastic stent substrates. Simulations reveal that the mode mixity of delamination is strongly dependent on the level of stent deployment at initiation. In general, peak normal tractions exceed peak shear tractions at low levels of stent deployment whereas the reverse trend is computed at high levels of stent deployment. Interface tractions increase with both increasing stent thickness and coating thickness suggesting that thinner stents and thinner coatings should be utilised for the delivery of antiproliferative drugs to reduce the risk of coating delamination. Next, the influence of stent plasticity on interface tractions and coating delamination is investigated. Even at low levels of deployment, plastic yielding occurs in the stent hinge region and the patterns of normal and shear tractions are found to be significantly more complex than those computed for the elastic stents, with both tensile and compressive regions of normal traction occurring in the stent arch. At a high level of stent deployment shear tractions at the stent-coating interface are computed to increase with decreasing strain hardening modulus. The findings of this paper provide a new insight into the stress-state at the stent-coating interface as a function of the stent design parameters and large deformation elasticity and plasticity during deployment, allowing for a more reliable assessment of the limits relating to safe implantation of coated stents.
Magnesium orthopaedic fracture fixation devices can potentially provide significant clinical benefits, such as the elimination of secondary surgeries for device removal due to in-vivo resorption and ...reduced stress shielding due to reduced device stiffness. However, development, approval, and clinical adoption of magnesium devices has been hindered by the excessively high rates of in-vivo corrosion such that the structural integrity of the device can be catastrophically reduced before fracture healing occurs. Coating of devices with calcium phosphate coatings has been shown to significantly reduce corrosion rates, while enhancing osseointegration. However, the adhesion strength between the CaP coatings and magnesium substrates has not been previously investigated. Clinical insertion of fracture fixation devices such as intramedullary nails and k-wires will impose significant shear loading on the coated surface of the implant. If the effective shear strength of the coating-device interface is not sufficiently high, the coating will be damaged and removed during device insertion. In the current study a bespoke experimental-computational approach is developed to provide a new understanding of the relationship between coating thickness, surface roughness, and effective shear strength of the CaP coating- Mg substrate interface. Nine test cases were created by adjusting either the deposition time (3 thickness values) or the surface treatment of the Mg alloy using SiC paper (3 roughness values) and double-lap shear testing was performed for these coating configurations. Strain development in the Mg substrates was monitored using strain gauges, and failure stress was determined for each configuration. Test results revealed that the effective shear strength of the coating-substrate interface is significantly higher for coatings on the rougher substrate surfaces when compared to those on smoother surfaces. Coating thickness was not found to significantly influence the effective shear strength over the range considered in this study (0.37–1.34 μm). Micro-scale finite element models of lap-shear tests were constructed using experimental profilometry data. Simulations of rough coating-substrate interfaces reveal that significant localised compression occurs at the coating-substrate interface in regions of large asperities. A novel cohesive zone formulation has been developed to simulate compression induced shear hardening, and the resultant simulations are found to accurately predict the significantly higher effective shear strength measured experimentally for rougher coatings compared to smoother Mg substrate surfaces.
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•Novel lap shear experiment studying the relationship between coating thickness, implant surface roughness and shear strength.•First cohesive zone model to incorporate shear hardening due to interface compression.•Regions of high interface compression at asperities in rough coatings, results in locally elevated interface shear strength.
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.
This tutorial paper provides a step-by-step guide to developing a comprehensive understanding of the different forms of the deformation gradient used in Abaqus, and outlines a number of key issues ...that must be considered when developing an Abaqus user defined material subroutine (UMAT) in which the Cauchy stress is computed from the deformation gradient. Firstly, we examine the “classical” forms of global and local deformation gradients. We then show that Abaqus/Standard does not use the classical form of the local deformation gradient when continuum elements are used, and we highlight the important implications for UMAT development. We outline the key steps that must be implemented in developing an anisotropic fibre-reinforced hyperelastic UMAT for use with continuum elements and local orientation systems. We also demonstrate that a classical local deformation gradient is provided by Abaqus/Standard if structural (shell and membrane) elements are used, and by Abaqus/Explicit for all element types. We emphasise, however, that the majority of biomechanical simulations rely on the use of continuum elements with a local coordinate system in Abaqus/Standard, and therefore the development of a hyperelastic UMAT requires an in-depth and precise understanding of the form of the non-classical deformation gradient provided as input by Abaqus. Several worked examples and case studies are provided for each section, so that the details and implications of the form of the deformation gradient can be fully understood. For each worked example in this tutorial paper the source files and code (Abaqus input files, UMATs, and Matlab script files) are provided, allowing the reader to efficiently explore the implications of the form of the deformation gradient in the development of a UMAT.
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