Modelling the rate-dependent mechanical behaviour of the brain tissue

A new modelling approach is employed in this work for application to the rate-dependent mechanical behaviour of the brain tissue, as an incompressible isotropic material. Extant datasets encompassing single- and multi-mode compression, tension and simple shear deformation(s) are considered, across a wide range of deformation rates from quasi-static to rates akin to blast loading conditions, in the order of 1000 s-1 . With a simple functional form and a reduced number of parameters, the model is shown to capture the considered rate-dependent behaviours favourably, including in both single- and multi-mode deformation fits, and over all range of deformation rates. The provided modelling results here are obtained from either first fitting the model to the quasi-static data, or/and predicting the behaviour at a different rate than those used for calibrating the model parameters. Given its simplicity, versatility, predictive capability and accuracy, the application of the utilised modelling framework in this work to the rate-dependent mechanical behaviour of the brain tissue is proposed.

Mechanical experimentation of the gastrointestinal tract: a systematic review

The gastrointestinal (GI) organs of the human body are responsible for transporting and extracting nutrients from food and drink, as well as excreting solid waste. Biomechanical experimentation of the GI organs provides insight into the mechanisms involved in their normal physiological functions, as well as understanding of how diseases can cause disruption to these. Additionally, experimental findings form the basis of all finite element (FE) modelling of these organs, which have a wide array of applications within medicine and engineering. This systematic review summarises the experimental studies that are currently in the literature (n = 247) and outlines the areas in which experimentation is lacking, highlighting what is still required in order to more fully understand the mechanical behaviour of the GI organs. These include (i) more human data, allowing for more accurate modelling for applications within medicine, (ii) an increase in time-dependent studies, and (iii) more sophisticated in vivo testing methods which allow for both the layer- and direction-dependent characterisation of the GI organs. The findings of this review can also be used to identify experimental data for the readers' own constitutive or FE modelling as the experimental studies have been grouped in terms of organ (oesophagus, stomach, small intestine, large intestine or rectum), test condition (ex vivo or in vivo), number of directions studied (isotropic or anisotropic), species family (human, porcine, feline etc.), tissue condition (intact wall or layer-dependent) and the type of test performed (biaxial tension, inflation-extension, distension (pressure-diameter), etc.). Furthermore, the studies that investigated the time-dependent (viscoelastic) behaviour of the tissues have been presented.

In Vivo Material Properties of Human Common Carotid Arteries: Trends and Sex Differences

INTRODUCTION

In vivo estimation of material properties of arterial tissue can provide essential insights into the development and progression of cardiovascular diseases. Furthermore, these properties can be used as an input to finite element simulations of potential medical treatments.

MATERIALS AND METHODS

This study uses non-invasively measured pressure, diameter and wall thickness of human common carotid arteries (CCAs) acquired in 103 healthy subjects. A non-linear optimization was performed to estimate material parameters of two different constitutive models: a phenomenological, isotropic model and a structural, anisotropic model. The effect of age, sex, body mass index and blood pressure on the parameters was investigated.

RESULTS AND CONCLUSION

Although both material models were able to model in vivo arterial behaviour, the structural model provided more realistic results in the supra-physiological domain. The phenomenological model predicted very high deformations for pressures above the systolic level. However, the phenomenological model has fewer parameters that were shown to be more robust. This is an advantage when only the physiological domain is of interest. The effect of stiffening with age, BMI and blood pressure was present for women, but not always for men. In general, sex had the biggest effect on the mechanical properties of CCAs. Stiffening trends with age, BMI and blood pressure were present but not very strong. The intersubject variability was high. Therefore, it can be concluded that finding a representative set of parameters for a certain age or BMI group would be very challenging. Instead, for purposes of patient-specific modelling of surgical procedures, we currently advise the use of patient-specific parameters.

Fracture of the porcine aorta. Part 2: FEM modelling and inverse parameter identification

The mechanics of vascular tissue, particularly its fracture properties, are crucial in the onset and progression of vascular diseases. Vascular tissue properties are complex, and the identification of fracture mechanical properties relies on robust and efficient numerical tools. In this study, we propose a parameter identification pipeline to extract tissue properties from force-displacement and digital image correlation (DIC) data. The data has been acquired by symconCT testing porcine aorta wall specimens. Vascular tissue is modelled as a non-linear viscoelastic isotropic solid, and an isotropic cohesive zone model describes tissue fracture. The model closely replicated the experimental observations and identified the fracture energies of 1.57±0.82 kJ m^-2 and 0.96±0.34 kJ m^-2 for rupturing the porcine aortic media along the axial and circumferential directions, respectively. The identified strength was always below 350 kPa, a value significantly lower than identified through classical protocols, such as simple tension, and sheds new light on the resilience of the aorta. Further refinements to the model, such as considering rate effects in the fracture process zone and tissue anisotropy, could have improved the simulation results. STATEMENT OF SIGNIFICANCE: This paper identified porcine aorta's biomechanical properties using data acquired through a previously developed experimental protocol, the symmetry-constraint compact tension test. An implicit finite element method model mimicked the test, and a two-step approach identified the material's elastic and fracture properties directly from force-displacement curves and digital image correlation-based strain measurements. Our findings show a lower strength of the abdominal aorta as compared to the literature, which may have significant implications for the clinical evaluation of the risk of aortic rupture.

Tri-layered constitutive modelling unveils functional differences between the pig ascending and lower thoracic aorta

The arterial wall's tri-layered macroscopic and layer-specific microscopic structure determine its mechanical properties, which vary at different arterial locations. Combining layer-specific mechanical data and tri-layered modelling, this study aimed to characterise functional differences between the pig ascending (AA) and lower thoracic aorta (LTA). AA and LTA segments were obtained for n=9 pigs. For each location, circumferentially and axially oriented intact wall and isolated layer strips were tested uniaxially and the layer-specific mechanical response modelled using a hyperelastic strain energy function. Then, layer-specific constitutive relations and intact wall mechanical data were combined to develop a tri-layered model of an AA and LTA cylindrical vessel, accounting for the layer-specific residual stresses. AA and LTA behaviours were then characterised for in vivo pressure ranges while stretched axially to in vivo length. The media dominated the AA response, bearing>2/3 of the circumferential load both at physiological (100 mmHg) and hypertensive pressures (160 mmHg). The LTA media bore most of the circumferential load at physiological pressure only (57±7% at 100 mmHg), while adventitia and media load bearings were comparable at 160 mmHg. Furthermore, increased axial elongation affected the media/adventitia load-bearing only at the LTA. The pig AA and LTA presented strong functional differences, likely reflecting their different roles in the circulation. The media-dominated compliant and anisotropic AA stores large amounts of elastic energy in response to both circumferential and axial deformations, which maximises diastolic recoiling function. This function is reduced at the LTA, where the adventitia shields the artery against supra-physiological circumferential and axial loads.

Importance of experimental evaluation of structural parameters for constitutive modelling of aorta

The study compares stresses and strains in the aortic wall derived using different constitutive models for various stress-strain conditions. Structure-based constitutive models with two fibre families with (GOH) and without (HGO) dispersion of collagen fibres are compared. The constitutive models were fitted to data from equibiaxial tension tests of two separated layers of the porcine aortic wall. The initial fit was evaluated with unrestricted parameters and subsequently, the mean angles of the fibre families and the angular dispersion were fixed to the values obtained from histology. Surprisingly, none of the tested models was capable to provide a good quality fit with histologically obtained structural parameters. Fitting the HGO model to experimental data resulted in two fibre families under angles close to ±45°, while the GOH model resulted in a nearly isotropic fibre distribution. These results indicate that both of these models suffer from the absence of isotropic strain stiffening. After having modified both models with corresponding additional members based on the Yeoh model of matrix, we obtained a perfect fit to the measured data while keeping the structural histology-based parameters. Finally, significant differences in compliance and resulting stresses and strains between different models are shown by means of simulations of uniaxial tension test, equibiaxial tension tests and inflation of the aorta.

Numerical implementation of an osmo-poro-visco-hyperelastic finite element solver: application to the intervertebral disc

This work deals with the finite element (FE) implementation of a biphasic poroelastic formulation specifically developed to address the intricate behaviour of the Intervertebral Disc (IVD) and other highly hydrated soft tissues. This formulation is implemented in custom FE solver V-Biomech, being the validation performed with a lumbar IVD model, which was compared against the analogous FE model of Williams et al. and the experiments of Tyrrell et al. Good agreement with these benchmarks was achieved, meaning that V-Biomech and its novel poroelastic formulation are a viable alternative for simulation of biphasic soft tissues.

Constitutive modelling and pipeline flow of thixotropic viscoplastic wastewater sludge

Due to the inherent rheological complexity of wastewater sludges, conventional sludge pipeline design based on simplified rheological models can result in inefficient sludge transportation systems. These inefficiencies are further exacerbated by a global need for the processing of more concentrated wastewater sludges that have a more pronounced non-Newtonian character, and hence require greater energy for transportation. However, the complex rheology of these materials (typically visco-elastic and thixotropic) requires sophisticated methods for constitutive modelling that are impractical to implement for complex materials such as sewerage sludges. We address this challenge by developing a novel viscoplastic thixotropic constitutive model that exploits the separation of timescales between the thixotropic and viscoelastic processes, leading to simpler and more robust experimental methods, parameter estimation and process simulation methods. This constitutive model combines a kinetic model for thixotropic degradation and agglomeration via a classical structural parameter (λ) approach coupled nonlinearly with a Herschel-Bulkley model to yield a thixotropic viscoplastic model of sludge rheology. Experimental data for thickened digested sludge between 3 and 4.9% solids were collected to validate the assumption for the separation of viscoelastic and thixotropic responses. The fitting procedure was found to be robust and efficient, and several rheological parameters were found to be invariant with solids concentration. Simplified energy calculations for a typical sludge pipeline showed that the pumping energy could be significantly under- or overestimated without considering thixotropy. These simple and robust constitutive models and fitting methods can accurately predict (and hence design and optimise) sludge behaviour over a wide range of wastewater processes.

Comparison of porcine and human adipose tissue loading responses under dynamic compression and shear: A pilot study

Understanding the mechanical properties of human adipose tissue, and its influence on seat belt-pelvis interaction is beneficial for computational human body models that are developed for injury prediction in the vehicle crashworthiness simulations. While various studies have characterized adipose tissue, most of the studies used porcine adipose tissue as a surrogate, and none of the studies were performed at loading rates relevant for motor vehicle collisions. In this work, the mechanical response of human and porcine adipose tissue was studied. Two dynamic loading modes (compression and simple shear) were tested in adipose tissue extracted from the human abdomen and porcine back. An Ogden hyperelastic model was used to fit the loading response, and specific material parameters were obtained for each specimen. Two-sample t-tests were performed to compare the effective shear moduli and peak stresses from porcine and human samples. The material response of the human adipose tissue was consistent with previous studies. Porcine adipose tissue was found to be significantly stiffer than human adipose tissue under compression and shear loading. Also, when material model parameters were fit to only one loading mode, the predicted response in the other mode showed a poor fit.

On a coupled electro-chemomechanical model of gastric smooth muscle contraction

The stomach is a central organ in the gastrointestinal tract that performs a variety of functions, in which the spatio-temporal organisation of active smooth muscle contraction in the stomach wall (SW) is highly regulated. In the present study, a three-dimensional model of the gastric smooth muscle contraction is presented, including the mechanical contribution of the mucosal and muscular layer of the SW. Layer-specific and direction-dependent model parameters for the active and passive stress-stretch characteristics of the SW were determined experimentally using porcine smooth muscle strips. The electrical activation of the smooth muscle cells (SMC) due to the pacemaker activity of the interstitial cells of Cajal (ICC) is modelled by using FitzHugh-Nagumo-type equations, which simulate the typical ICC and SMC slow wave behaviour. The calcium dynamic in the SMC depends on the SMC membrane potential via a gaussian function, while the chemo-mechanical coupling in the SMC is modelled via an extended Hai-Murphy model. This cascade is coupled with an additional mechano-electrical feedback-mechanism, taking into account the mechanical response of the ICC and SMC due to stretch of the SW. In this way the relaxation responses of the fundus to accommodate incoming food, as well as the typical peristaltic contraction waves in the antrum for mixing and transport of the chyme, have been well replicated in simulations performed at the whole organ level. STATEMENT OF SIGNIFICANCE: In this article, a novel three-dimensional electro-chemomechanical model of the gastric smooth muscle contraction is presented. The propagating waves of electrical membrane potential in the network ofinterstitial cells of Cajal (ICC) and smooth muscle cells (SMC) lead to a global pattern of change in the calciumdynamics inside the SMC. Taking additionally into account the mechanical response of the ICC and SMC due to stretch of the stomach wall, also referred to as mechanical feedback-mechanism, the result is a complex spatio-temporal regulation of the active contraction and relaxation of the gastric smooth muscle tissue. Being a firstapproach, in future view such a three-dimensional model can give an insight into the complexload transferring system of the stomach wall, as well as into the electro-chemomechanicalcoupling process underlying smooth muscle contraction in health and disease.

A novel technique for the assessment of mechanical properties of vascular tissue

Accurate estimation of mechanical properties of the different atherosclerotic plaque constituents is important in assessing plaque rupture risk. The aim of this study was to develop an experimental set-up to assess material properties of vascular tissue, while applying physiological loading and being able to capture heterogeneity. To do so, a ring-inflation experimental set-up was developed in which a transverse slice of an artery was loaded in the radial direction, while the displacement was estimated from images recorded by a high-speed video camera. The performance of the set-up was evaluated using seven rubber samples and validated with uniaxial tensile tests. For four healthy porcine carotid arteries, material properties were estimated using ultrasound strain imaging in whole-vessel-inflation experiments and compared to the properties estimated with the ring-inflation experiment. A 1D axisymmetric finite element model was used to estimate the material parameters from the measured pressures and diameters, using a neo-Hookean and Holzapfel–Gasser–Ogden material model for the rubber and porcine samples, respectively. Reproducible results were obtained with the ring-inflation experiment for both rubber and porcine samples. Similar mean stiffness values were found in the ring-inflation and tensile tests for the rubber samples as 202 kPa and 206 kPa, respectively. Comparable results were obtained in vessel-inflation experiments using ultrasound and the proposed ring-inflation experiment. This inflation set-up is suitable for the assessment of material properties of healthy vascular tissue in vitro. It could also be used as part of a method for the assessment of heterogeneous material properties, such as in atherosclerotic plaques.

Constitutive modelling of hot deformation behaviour of a CoCrFeMnNi high-entropy alloy

Models describing the constitutive flow behaviour of a metallic material are desired for appropriate process design and realization of defect-free components. In this study, constitutive equations based on the hyperbolic-sinusoidal Arrhenius-type model have been developed to define the hot deformation characteristics of a CoCrFeMnNi high-entropy alloy. The experimental true stress-true strain data were generated over a wide temperature (1023-1423 K) and strain rates (10^-3-10 s^-1) ranges. The impact of strain rate and temperature on deformation behaviour was further characterized through a temperature compensated strain rate parameter, i.e. Zener-Hollomon parameter. Additionally, a mathematical relation was employed to express the influence of various material constants on true-strain ranging from 0.2 to 0.75. Typical third order polynomial relations were found to be appropriate to fit the true-strain dependency of these material constants. The accuracy of the developed constitutive equations was evaluated by using the average absolute relative error (AARE) and correlation coefficient (R); the obtained values were 7.63% and 0.9858, respectively, suggesting reasonable predictions. These results demonstrate that the developed constitutive equations can predict the flow stress behaviour of the alloy with a good accuracy over a wide range of temperature and strain rate conditions and for large strains.

An investigation into the role of different constituents in damage accumulation in arterial tissue and constitutive model development. Biomech Model Mechanobiol. 2018;17:1757-1769. [PMID: 30058051 DOI: 10.1007/s10237-018-1054-3]

Carotid atherosclerotic plaque rupture is one of the leading causes of stroke. Treatments for atherosclerosis can induce tissue damage during the deployment of an intravascular device or through external tissue clamping during surgery. In this paper, a constituent specific study was performed to investigate the role of the ground matrix and collagen fibres of arterial tissue in response to supra-physiological loads. Cyclic mechanical tests were conducted on intact and collagenase-digested strips of porcine common carotid arteries. Using these tests, four passive damage-relevant phenomena were studied, namely (i) Mullins effect, (ii) hysteresis, (iii) permanent set and (iv) matrix failure and fibre rupture. A constitutive model was also developed to capture all of these damage-relevant phenomena using a continuum damage mechanics approach. The implemented constitutive model was fit to experimental results for both intact and digested samples. The results of this work demonstrate the important role of the ground matrix in the permanent deformation of the arterial tissue under high loads. Supra-physiological load-induced tissue damage may play a key role in vascular remodelling in arteries with atherosclerosis or following interventional procedures.

Comparison of in vivo vs. ex situ obtained material properties of sheep common carotid artery

Patient-specific biomechanical modelling can improve preoperative surgical planning. This requires patient-specific geometry as well as patient-specific material properties as input. The latter are, however, still quite challenging to estimate in vivo. This study focuses on the estimation of the mechanical properties of the arterial wall. Firstly, in vivo pressure, diameter and thickness of the arterial wall were acquired for sheep common carotid arteries. Next, the animals were sacrificed and the tissue was stored for mechanical testing. Planar biaxial tests were performed to obtain experimental stress-stretch curves. Finally, parameters for the hyperelastic Mooney-Rivlin and Gasser-Ogden-Holzapfel (GOH) material model were estimated based on the in vivo obtained pressure-diameter data as well as on the ex situ experimental stress-stretch curves. Both material models were able to capture the in vivo behaviour of the tissue. However, in the ex situ case only the GOH model provided satisfactory results. When comparing different fitting approaches, in vivo vs. ex situ, each of them showed its own advantages and disadvantages. The in vivo approach estimates the properties of the tissue in its physiological state while the ex situ approach allows to apply different loadings to properly capture the anisotropy of the tissue. Both of them could be further enhanced by improving the estimation of the stress-free state, i.e. by adding residual circumferential stresses in vivo and by accounting for the flattening effect of the tested samples ex vivo. • Competing interests: none declared • Word count: 4716.

Uncertainty quantification and sensitivity analysis of an arterial wall mechanics model for evaluation of vascular drug therapies

Quantification of the uncertainty in constitutive model predictions describing arterial wall mechanics is vital towards non-invasive assessment of vascular drug therapies. Therefore, we perform uncertainty quantification to determine uncertainty in mechanical characteristics describing the vessel wall response upon loading. Furthermore, a global variance-based sensitivity analysis is performed to pinpoint measurements that are most rewarding to be measured more precisely. We used previously published carotid diameter–pressure and intima–media thickness (IMT) data (measured in triplicate), and Holzapfel–Gasser–Ogden models. A virtual data set containing 5000 diastolic and systolic diameter–pressure points, and IMT values was generated by adding measurement error to the average of the measured data. The model was fitted to single-exponential curves calculated from the data, obtaining distributions of constitutive parameters and constituent load bearing parameters. Additionally, we (1) simulated vascular drug treatment to assess the relevance of model uncertainty and (2) evaluated how increasing the number of measurement repetitions influences model uncertainty. We found substantial uncertainty in constitutive parameters. Simulating vascular drug treatment predicted a 6% point reduction in collagen load bearing (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\mathrm {coll}$$\end{document}Lcoll), approximately 50% of its uncertainty. Sensitivity analysis indicated that the uncertainty in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll was primarily caused by noise in distension and IMT measurements. Spread in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll could be decreased by 50% when increasing the number of measurement repetitions from 3 to 10. Model uncertainty, notably that in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll, could conceal effects of vascular drug therapy. However, this uncertainty could be reduced by increasing the number of measurement repetitions of distension and wall thickness measurements used for model parameterisation.

Planar biaxial testing of soft biological tissue using rakes: A critical analysis of protocol and fitting process

Mechanical characterization of soft biological tissue is becoming more and more prevalent. Despite the growing use of planar biaxial testing for soft tissue characterization, testing conditions and subsequent data analysis have not been standardized and vary widely. This also influences the quality of the result of the parameter fitting. Moreover, the testing conditions and data analysis are often not or incompletely reported, which impedes the proper comparison of parameters obtained from different studies. With a focus on planar biaxial tests using rakes, this paper investigates varying testing conditions and varying data analysis methods and their effect on the quality of the parameter fitting results. By means of a series of finite element simulations, aspects such as number of rakes, rakes׳ width, loading protocol, constitutive model, material stiffness and anisotropy are evaluated based on the degree of homogeneity of the stress field, and on the correlation between the experimentally obtained stress and the stress derived from the constitutive model. When calculating the aforementioned stresses, different definitions of the section width and deformation gradient are used in literature, each of which are looked into. Apart from this degree of homogeneity and correlation, also the effect on the quality of the parameter fitting result is evaluated. The results show that inhomogeneities can be reduced to a minimum for wise choices of testing conditions and analysis methods, but never completely eliminated. Therefore, a new parameter optimization procedure is proposed that corrects for the inhomogeneities in the stress field and induces significant improvements to the fitting results. Recommendations are made for best practice in rake-based planar biaxial testing of soft biological tissues and subsequent parameter fitting, and guidelines are formulated for reporting thereof in publications.

Biomechanical Analysis of Infectious Biofilms

The removal of infectious biofilms from tissues or implanted devices and their transmission through fluid transport systems depends in part of the mechanical properties of their polymeric matrix. Linking the various physical and chemical microscopic interactions to macroscopic deformation and failure modes promises to unveil design principles for novel therapeutic strategies targeting biofilm eradication, and provide a predictive capability to accelerate the development of devices, water lines, etc, that minimise microbial dispersal. Here, our current understanding of biofilm mechanics is appraised from the perspective of biophysics , with an emphasis on constitutive modelling that has been highly successful in soft matter. Fitting rheometric data to viscoelastic models has quantified linear and nonlinear stress relaxation mechanisms, how they vary between species and environments, and how candidate chemical treatments alter the mechanical response. The rich interplay between growth, mechanics and hydrodynamics is just becoming amenable to computational modelling and promises to provide unprecedented characterisation of infectious biofilms in their native state.

A constitutive model for mechanical response characterization of pumpkin peel and flesh tissues under tensile and compressive loadings

Enhancing quality of food products and reducing volume of waste during mechanical operations of food industry requires a comprehensive knowledge of material response under loadings. While research has focused on mechanical response of food material, the volume of waste after harvesting and during processing stages is still considerably high in both developing and developed countries. This research aims to develop and evaluate a constitutive model of mechanical response of tough skinned vegetables under postharvest and processing operations. The model focuses on both tensile and compressive properties of pumpkin flesh and peel tissues where the behaviours of these tissues vary depending on various factors such as rheological response and cellular structure. Both elastic and plastic response of tissue were considered in the modelling process and finite elasticity combined with pseudo elasticity theory was applied to generate the model. The outcomes were then validated using the published results of experimental work on pumpkin flesh and peel under uniaxial tensile and compression. The constitutive coefficients for peel under tensile test was α = 25.66 and β = -18.48 Mpa and for flesh α = -5.29 and β = 5.27 Mpa. under compression the constitutive coefficients were α = 4.74 and β = -1.71 Mpa for peel and α = 0.76 and β = -1.86 Mpa for flesh samples. Constitutive curves predicted the values of force precisely and close to the experimental values. The curves were fit for whole stress versus strain curve as well as a section of curve up to bio yield point. The modelling outputs had presented good agreement with the empirical values and the constructive curves exhibited a very similar pattern to the experimental curves. The presented constitutive model can be applied next to other agricultural materials under loading in future.

The anisotropic mechanical behaviour of electro-spun biodegradable polymer scaffolds: Experimental characterisation and constitutive formulation

Electro-spun biodegradable polymer fibrous structures exhibit anisotropic mechanical properties dependent on the degree of fibre alignment. Degradation and mechanical anisotropy need to be captured in a constitutive formulation when computational modelling is used in the development and design optimisation of such scaffolds. Biodegradable polyester-urethane scaffolds were electro-spun and underwent uniaxial tensile testing in and transverse to the direction of predominant fibre alignment before and after in vitro degradation of up to 28 days. A microstructurally-based transversely isotropic hyperelastic continuum constitutive formulation was developed and its parameters were identified from the experimental stress-strain data of the scaffolds at various stages of degradation. During scaffold degradation, maximum stress and strain in circumferential direction decreased from 1.02 ± 0.23 MPa to 0.38 ± 0.004 MPa and from 46 ± 11 % to 12 ± 2 %, respectively. In longitudinal direction, maximum stress and strain decreased from 0.071 ± 0.016 MPa to 0.010 ± 0.007 MPa and from 69 ± 24 % to 8 ± 2 %, respectively. The constitutive parameters were identified for both directions of the non-degraded and degraded scaffold for strain range varying between 0% and 16% with coefficients of determination r(2)>0.871. The six-parameter constitutive formulation proved versatile enough to capture the varying non-linear transversely isotropic behaviour of the fibrous scaffold throughout various stages of degradation.

Limiting extensibility constitutive model with distributed fibre orientations and ageing of abdominal aorta

The abdominal aorta is susceptible to age-related pathological changes (arteriosclerosis, atherosclerosis, aneurysm, and tortuosity). Computational biomechanics and mechanobiology provide models capable of predicting mutual interactions between a changing mechanical environment and patho-physiological processes in ageing. However, a key factor is a constitutive equation which should reflect the internal tissue architecture. Our study investigates three microstructurally-motivated invariant-based hyperelastic anisotropic models suitable for description of the passive mechanical behaviour of the human abdominal aorta at a multiaxial state of stress known from recent literature. The three adopted models have also been supplemented with a newly proposed constitutive model (limiting extensibility with fibre dispersion). All models additively decouple the mechanical response of the isotropic (elastin and smooth muscle cells represented by the neo-Hookean term) and the anisotropic (collagen) parts. Two models use exponential functions to capture large strain stiffening ascribed to the engagement of collagen fibres into the load-bearing process. The other two models are based on the concept of limiting extensibility. Perfect alignment of reinforcing fibres with two preferred directions as well as fibre dispersion are considered. Constitutive models are calibrated to the inflation-extension response adopted from the literature based on the computational model of the residually-stressed thick-walled tube. A correlation analysis of determined material parameters was performed to reveal dependence on the age. The results of the nonlinear regression suggest that limiting fibre extensibility is the concept which is suitable to be used for the constitutive description of the aorta at multiaxial stress states and is highly sensitive to ageing-induced changes in mechanical response.

Analysis of the biomechanical behaviour of gastrointestinal regions adopting an experimental and computational approach

An integrated experimental and computational procedure is provided for the evaluation of the biomechanical behaviour that characterizes the pressure-volume response of gastrointestinal regions. The experimental activity pertains to inflation tests performed on specific gastrointestinal conduct segments. Different inflation processes are performed according to progressively increasing volumes. Each inflation test is performed by a rapid liquid in-flaw, up to a prescribed volume, which is held constant for about 300s to allow the development of relaxation processes. The different tests are interspersed by 600s of rest to allow the recovery of the specimen mechanical condition. A physio-mechanical model is developed to interpret both the elastic behaviour of the sample, as the pressure-volume trend during the rapid liquid in-flaw, and the time-dependent response, as the pressure drop during the relaxation processes. The minimization of discrepancy between experimental data and model results entails the identification of the parameters that characterize the viscoelastic model adopted for the definition of the behaviour of the gastrointestinal regions. The reliability of the procedure is assessed by the characterization of the response of samples from rat small intestine.