Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs).

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.

Collagen fibre orientation and dispersion govern ultimate tensile strength, stiffness and the fatigue performance of bovine pericardium.

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 on average 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.

The use of small angle light scattering in assessing strain induced collagen degradation in arterial tissue ex vivo.

Collagen is the predominant load bearing component in many soft tissues including arterial tissue and is therefore critical in determining the mechanical integrity of such tissues. Degradation of collagen fibres is hypothesized to be a strain dependent process whereby the rate of degradation is affected by the magnitude of strain applied to the collagen fibres. The aim of this study is to investigate the ability of small angle light scattering (SALS) imaging to identify strain dependent degradation of collagen fibres in arterial tissue ex vivo, and determine whether a strain induced protection mechanism exists in arterial tissue as observed in pure collagen and other collagenous tissues. SALS was used in combination with histological and second harmonic generation (SHG) analysis to determine the collagen fibre architecture in arterial tissue subjected to strain directed degradation. SALS alignment analysis identified statistically significant differences in fibre alignment depending on the strain magnitude applied to the tissue. These results were also observed using histology and SHG. Our findings suggest a strain protection mechanism may exist for arterial collagen at intermediate strain magnitudes between 0% and 25%. These findings may have implications for the onset and progression of arterial disease where changes in the mechanical environment of arterial tissue may lead to changes in the collagen degradation rate.

Strain mediated enzymatic degradation of arterial tissue: Insights into the role of the non-collagenous tissue matrix and collagen crimp.

Collagen fibre remodelling is a strain dependent process which is stimulated by the degradation of existing collagen. To date, literature has focussed on strain dependent degradation of pure collagen or structurally simple collagenous tissues, often overlooking degradation within more complex, heterogenous soft tissues. The aim of this study is to identify, for the first time, the strain dependent degradation behaviour and mechanical factors influencing collagen degradation in arterial tissue using a combined experimental and numerical approach. To achieve this, structural analysis was carried out using small angle light scattering to determine the fibre level response due to strain induced degradation. Next, strain dependent degradation rates were determined from stress relaxation experiments in the presence of crude and purified collagenase to determine the tissue level degradation response. Finally, a 1D theoretical model was developed, incorporating matrix stiffness and a gradient of collagen fibre crimp to decouple the mechanism behind strain dependent arterial degradation. SALS structural analysis identified a strain mediated degradation response in arterial tissue at the fibre level not dissimilar to that found in literature for pure collagen. Interestingly, two distinctly different strain mediated degradation responses were identified experimentally at the tissue level, not seen in other collagenous tissues. Our model was able to accurately predict these experimental findings, but only once the load bearing matrix, its degradation response and the gradient of collagen fibre crimp across the arterial wall were incorporated. These findings highlight the critical role that the various tissue constituents play in the degradation response of arterial tissue. STATEMENT OF SIGNIFICANCE: 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.

Collagen fibre characterisation in arterial tissue under load using SALS.

The collagen fibre architecture of arterial tissue is known to play a key role in its resultant mechanical behaviour, while maladaptive remodelling of this architecture may be linked to disease. Many of the techniques currently used to analyse collagen fibre architecture require time consuming tissue preparation procedures and are destructive in nature. The aim of this study is to fully explore Small Angle Light Scattering (SALS) as a means to non-destructively assess collagen fibre architecture in arterial tissue and subsequently gain insights into load induced reorientation. The optimised configuration of the SALS system for arterial tissue was determined using quantitative comparisons to histological analyses of porcine carotid artery as its basis. Once established, layer specific fibre orientation and the influence of tissue loading was determined for thin sections of carotid artery using SALS. This process was subsequently repeated for intact carotid artery layers. A single family of circumferentially orientated collagen fibres were found in the intima (- 0.1 ± 1.4° (5.5°)) and media (- 1.7 ± 1.9° (4.7°)) while two perpendicular families of fibres were identified in the adventitia (- 6.4 ± 0.7° (37.7°)) and (118.3 ± 2.7 (39.9°)). An increase in fibre alignment in response to a 20% circumferential strain was also identified using SALS, characterised by an increase in scattered light eccentricity. RESULTS: 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.

On the correct interpretation of measured force and calculation of material stress in biaxial tests.

Biaxial tests are commonly used to investigate the mechanical behaviour of soft biological tissues and polymers. In the current paper we uncover a fundamental problem associated with the calculation of material stress from measured force in standard biaxial tests. In addition to measured forces, localised unmeasured shear forces also occur at the clamps and the inability to quantify such forces has significant implications for the calculation of material stress from simplified force-equilibrium relationships. Unmeasured shear forces are shown to arise due to two distinct competing contributions: (1) negative shear force due to stretching of the orthogonal clamp, and (2) positive shear force as a result of material Poisson-effect. The clamp shear force is highly dependent on the specimen geometry and the clamp displacement ratio, as consequently, is the measured force-stress relationship. Additionally in this study we demonstrate that commonly accepted formulae for the estimation of material stress in the central region of a cruciform specimen are highly inaccurate. A reliable empirical correction factor for the general case of isotropic materials must be a function of specimen geometry and the biaxial clamp displacement ratio. Finally we demonstrate that a correction factor for the general case of non-linear anisotropic materials is not feasible and we suggest the use of inverse finite element analysis as a practical means of interpreting experimental data for such complex materials.

On the Compressibility of Arterial Tissue.

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.

A robust anisotropic hyperelastic formulation for the modelling of soft tissue.

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).

Stability enhancement of an atomic force microscope for long-term force measurement including cantilever modification for whole cell deformation.

Atomic force microscopy (AFM) is widely used in the study of both morphology and mechanical properties of living cells under physiologically relevant conditions. However, quantitative experiments on timescales of minutes to hours are generally limited by thermal drift in the instrument, particularly in the vertical (z) direction. In addition, we demonstrate the necessity to remove all air-liquid interfaces within the system for measurements in liquid environments, which may otherwise result in perturbations in the measured deflection. These effects severely limit the use of AFM as a practical tool for the study of long-term cell behavior, where precise knowledge of the tip-sample distance is a crucial requirement. Here we present a readily implementable, cost effective method of minimizing z-drift and liquid instabilities by utilizing active temperature control combined with a customized fluid cell system. Long-term whole cell mechanical measurements were performed using this stabilized AFM by attaching a large sphere to a cantilever in order to approximate a parallel plate system. An extensive examination of the effects of sphere attachment on AFM data is presented. Profiling of cantilever bending during substrate indentation revealed that the optical lever assumption of free ended cantilevering is inappropriate when sphere constraining occurs, which applies an additional torque to the cantilevers "free" end. Here we present the steps required to accurately determine force-indentation measurements for such a scenario. Combining these readily implementable modifications, we demonstrate the ability to investigate long-term whole cell mechanics by performing strain controlled cyclic deformation of single osteoblasts.

Handedness and language laterality: discrimination of handedness groups on the dichotic consonant-vowel task.

Previous studies of the performances of left and right handed S groups on the DCVT have failed to discriminate the groups. The present study examined the performance of 102 right handers and 104 left handers on the DCVT, with a free report of only one syllable per trial procedure. Results showed that, as administered, the DCVT possessed good reliability and left and right handed groups were clearly discriminated during the second half of the dichotic trials. Neither sex nor familial sinistrality factors contributed to this group discrimination. Analysis of the relationship of manual preferences for various activities (Edinburgh Handedness Inventory) with DCVT REAs showed that right hand preferences were associated with REAs across groups for most Edinburgh items during the second half of the trials. This association was shown to be strongest in the left handed Ss. In general, the results offer support for both the reliability and validity of the DCVT.

Complications after cuneiform osteotomy for moderately or severely slipped capital femoral epiphysis.

Wedge osteotomy of the femoral neck for slipped capital femoral epiphysis was performed in seventy-seven hips of seventy-one children at Gillette Children's Hospital during the period 1938 to 1973. The major complications were avascular necrosis (28.5 per cent) and cartilage necrosis (37.6 per cent). This high incidence of severe complications led to the use of an osteotomy through the base of the neck for the treatment of severely slipped capital femoral epiphysis which has given satisfactory results in six hips to date.

Deep wound sepsis following total hip arthroplasty.

After follow-ups ranging from two to five years on all but four (five hips) of 2,694 patients who had 3,215 total hip arthroplasties, deep wound infection had been demonstrated in forty-two hips (1.3 per cent). The infections among the 3,210 hips appeared during the immediate postoperative period or as long as five years after surgery. All operations were performed in conventional operating rooms. Previous operations, prolonged operating time, positive culture at operation, and unrecognized preoperative sepsis were related to the development of deep infection. In only eight of the forty-one patients (forty-two hips) was salvage of the prosthetic arthroplasty possible. The deaths of tree patients were directly attributable to the infection or its treatment.

Complications of total hip arthroplasty treated by reoperation.

In a series of 3,204 consecutive total hip arthroplasties performed on 2,684 patients at the Mayo Clinic from March 1, 1969, through February 28, 1972, reoperation for a complication was necessary in 125 hips (3.9 per cent). The complications, in order of frequency, were infection, dislocation, trochanteric problems, ectopic bone, and loosening of the femoral prosthesis. There were less frequent complications that also required further surgery. Attention to specific technical details is the most important means of avoiding a complication that requires reoperation.