A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension-compression test data

A mechanobiological model for tumor spheroid evolution with application to glioblastoma: A continuum multiphysics approach

BACKGROUND

Spheroids are in vitro quasi-spherical structures of cell aggregates, eventually cultured within a hydrogel matrix, that are used, among other applications, as a technological platform to investigate tumor formation and evolution. Several interesting features can be replicated using this methodology, such as cell communication mechanisms, the effect of gradients of nutrients, or the creation of realistic 3D biological structures. The main objective of this work is to link the spheroid evolution with the mechanical activity of cells, coupled with nutrient consumption and the subsequent cell dynamics.

METHOD

We propose a continuum mechanobiological model which accounts for the most relevant phenomena that take place in tumor spheroid evolution under in vitro suspension, namely, nutrient diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. The model is qualitatively validated, after calibration of the model parameters, versus in vitro experiments of spheroids of different glioblastoma cell lines.

RESULTS

Our model is able to explain in a novel way quite different setups, such as spheroid growth (up to six times the initial configuration for U-87 MG cell line) or shrinking (almost half of the initial configuration for U-251 MG cell line); as the result of the mechanical interplay of cells driven by cellular evolution.

CONCLUSIONS

Glioblastoma tumor spheroid evolution is driven by mechanical interactions of the cell aggregate and the dynamical evolution of the cell population. All this information can be used to further investigate mechanistic effects in the evolution of tumors and their role in cancer disease.

Ogden material calibration via magnetic resonance cartography, parameter sensitivity and variational system identification

Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than [Formula: see text], we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Matrix Description of Non-Linear Properties of Materials or Structural Components-Idea and Application Examples

Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

A new type of constitutive equation for nonlinear elastic bodies. Fitting with experimental data for rubber-like materials

In this article, we develop a new implicit constitutive relation, which is based on a thermodynamic foundation that relates the Hencky strain to the Cauchy stress, by assuming a structure for the Gibbs potential based on the Cauchy stress. We study the tension/compression of a cylinder, biaxial stretching of a thin plate and simple shear within the context of our constitutive relation. We then compare the predictions of the constitutive relation that we develop and that of Ogden’s constitutive relation with the experiments of Treloar concerning tension/compression of a cylinder, and we show that the predictions of our constitutive relation provide a better description than Ogden’s model, with fewer material moduli.

Microstructure and Mechanical Properties of Carboxylated Nitrile Butadiene Rubber/Epoxy/XNBR-grafted Halloysite Nanotubes Nanocomposites

The effect of various amounts of carboxylated nitrile butadiene rubber (XNBR) functionalized halloysite nanotubes (XHNTs) on the cure characteristics, mechanical and swelling behavior of XNBR/epoxy compounds was experimentally and theoretically investigated. The morphology of the prepared XNBR/epoxy/XHNTs nanocomposites was imaged using scanning electron microscopy (SEM). The effects of various XNBR-grafted nanotubes on the damping factor of nanocomposites were evaluated by dynamic mechanical thermal analysis (DMTA). The cure behavior characterization indicated a fall in the scorch time, but a rise in the cure rate with higher loading of XHNTs into the XNBR/epoxy nanocomposites. SEM micrographs of tensile fracture surfaces were indicative of a rougher fracture surface with a uniform dispersion state of nanotubes into the polymer matrix in the XNBR/epoxy/XHNTs nanocomposites. The stress–strain behavior studies of XNBR/epoxy/XHNTs nanocomposites showed a higher tensile strength up to 40% with 7 wt % XHNTs loading. The theoretical predictions of uniaxial tensile behavior of nanocomposites using Bergström–Boyce model revealed that some of the material parameters were considerably changed with the XHNTs loading. Furthermore, the used theoretical model precisely predicted the nonlinear large strain hyperelastic behavior of nanocomposites.

Soft matter: rubber and networks

Rubber networks are important and form the basis for materials with properties ranging from rubber tires to super absorbents and contact lenses. The development of the entropy ideas of rubber deformation thermodynamics provides a powerful framework from which to understand and to use these materials. In addition, swelling of the rubber in the presence of small molecule liquids or solvents leads to materials that are very soft and 'gel' like in nature. The review covers the thermodynamics of polymer networks and gels from the perspective of the thermodynamics and mechanics of the strain energy density function. Important relationships are presented and experimental results show that the continuum ideas contained in the phenomenological thermodynamics are valid, but that the molecular bases for some of them remain to be fully elucidated. This is particularly so in the case of the entropic gels or swollen networks. The review is concluded with some perspectives on other networks, ranging from entropic polymer networks such as thermoplastic elastomers to physical gels in which cross-link points are formed by glassy or crystalline domains. A discussion is provided for other physical gels in which the network forms a spinodal-like decomposition, both in thermoplastic polymers that form a glassy network upon phase separation and for colloidal gels that seem to have a similar behavior.

Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle

Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.

Computational simulation of static/cyclic cell stimulations to investigate mechanical modulation of an individual mesenchymal stem cell using confocal microscopy

It has been found that cells react to mechanical stimuli, while the type and magnitude of these cells are different in various physiological and pathological conditions. These stimuli may affect cell behaviors via mechanotransduction mechanisms. The aim of this study is to evaluate mechanical responses of a mesenchymal stem cell (MSC) to a pressure loading using finite elements method (FEM) to clarify procedures of MSC mechanotransduction. The model is constructed based on an experimental set up in which statics and cyclic compressive loads are implemented on a model constructed from a confocal microscopy 3D image of a stem cell. Both of the applied compressive loads are considered in the physiological loading regimes. Moreover, a viscohyperelastic material model was assumed for the cell through which the finite elements simulation anticipates cell behavior based on strain and stress distributions in its components. As a result, high strain and stress values were captured from the viscohyperelastic model because of fluidic behavior of cytosol when compared with the obtained results through the hyperelastic models. It can be concluded that the generated strain produced by cyclic pressure is almost 8% higher than that caused by the static load and the von Mises stress distribution is significantly increased to about 150kPa through the cyclic loading. In total, the results does not only trace the efficacy of an individual 3D model of MSC using biomechanical experiments of cell modulation, but these results provide knowledge in interpretations from cell geometry. The current study was performed to determine a realistic aspect of cell behavior.

Determination and Finite Element Validation of the WYPIWYG Strain Energy of Superficial Fascia from Experimental Data

What-You-Prescribe-Is-What-You-Get (WYPIWYG) procedures are a novel and general phenomenological approach to modelling the behavior of soft materials, applicable to biological tissues in particular. For the hyperelastic case, these procedures solve numerically the nonlinear elastic material determination problem. In this paper we show that they can be applied to determine the stored energy density of superficial fascia. In contrast to the usual approach, in such determination no user-prescribed material parameters and no optimization algorithms are employed. The strain energy densities are computed solving the equilibrium equations of the set of experiments. For the case of superficial fascia it is shown that the mechanical behavior derived from such strain energies is capable of reproducing simultaneously the measured load-displacement curves of three experiments to a high accuracy.

Biomechanics of oral mucosa

The prevalence of prosthodontic treatment has been well recognized, and the need is continuously increasing with the ageing population. While the oral mucosa plays a critical role in the treatment outcome, the associated biomechanics is not yet fully understood. Using the literature available, this paper provides a critical review on four aspects of mucosal biomechanics, including static, dynamic, volumetric and interactive responses, which are interpreted by its elasticity, viscosity/permeability, apparent Poisson's ratio and friction coefficient, respectively. Both empirical studies and numerical models are analysed and compared to gain anatomical and physiological insights. Furthermore, the clinical applications of such biomechanical knowledge on the mucosa are explored to address some critical concerns, including stimuli for tissue remodelling (interstitial hydrostatic pressure), pressure–pain thresholds, tissue displaceability and residual bone resorption. Through this review, the state of the art in mucosal biomechanics and their clinical implications are discussed for future research interests, including clinical applications, computational modelling, design optimization and prosthetic fabrication.

Layer- and Direction-Specific Material Properties, Extreme Extensibility and Ultimate Material Strength of Human Abdominal Aorta and Aneurysm: A Uniaxial Extension Study

Mechanical analysis has the potential to provide complementary information to aneurysm morphology in assessing its vulnerability. Reliable calculations require accurate material properties of individual aneurysmal components. Quantification of extreme extensibility and ultimate material strength of the tissue are important if rupture is to be modelled. Tissue pieces from 11 abdomen aortic aneurysm (AAA) from patients scheduled for elective surgery and from 8 normal aortic artery (NAA) from patients who scheduled for kidney/liver transplant were collected at surgery and banked in liquid nitrogen with the use of Cryoprotectant solution to minimize frozen damage. Prior to testing, specimen were thawed and longitudinal and circumferential tissue strips were cut from each piece and adventitia, media and thrombus if presented were isolated for the material test. The incremental Young’s modulus of adventitia of NAA was direction-dependent at low stretch levels, but not the media. Both adventitia and media had a similar extreme extensibility in the circumferential direction, but the adventitia was much stronger. For aneurysmal tissues, no significant differences were found when the incremental moduli of adventitia, media or thrombus in both directions were compared. Adventitia and media from AAA had similar extreme extensibility and ultimate strength in both directions and thrombus was the weakest material. Adventitia and media from AAA were less extensible compared with those of NAA, but the ultimate strength remained similar. The material properties, including extreme extensibility and ultimate strength, of both healthy aortic and aneurysmal tissues were layer-dependent, but not direction-dependent.

Computational analysis of cartilage implants based on an interpenetrated polymer network for tissue repairing

Interpenetrated polymer networks (IPNs), composed by two independent polymeric networks that spatially interpenetrate, are considered as valuable systems to control permeability and mechanical properties of hydrogels for biomedical applications. Specifically, poly(ethyl acrylate) (PEA)-poly(2-hydroxyethyl acrylate) (PHEA) IPNs have been explored as good hydrogels for mimicking articular cartilage. These lattices are proposed as matrix implants in cartilage damaged areas to avoid the discontinuity in flow uptake preventing its deterioration. The permeability of these implants is a key parameter that influences their success, by affecting oxygen and nutrient transport and removing cellular waste products to healthy cartilage. Experimental try-and-error approaches are mostly used to optimize the composition of such structures. However, computational simulation may offer a more exhaustive tool to test and screen out biomaterials mimicking cartilage, avoiding expensive and time-consuming experimental tests. An accurate and efficient prediction of material's permeability and internal directionality and magnitude of the fluid flow could be highly useful when optimizing biomaterials design processes. Here we present a 3D computational model based on Sussman-Bathe hyperelastic material behaviour. A fluid structure analysis is performed with ADINA software, considering these materials as two phases composites where the solid part is saturated by the fluid. The model is able to simulate the behaviour of three non-biodegradable hydrogel compositions, where percentages of PEA and PHEA are varied. Specifically, the aim of this study is (i) to verify the validity of the Sussman-Bathe material model to simulate the response of the PEA-PHEA biomaterials; (ii) to predict the fluid flux and the permeability of the proposed IPN hydrogels and (iii) to study the material domains where the passage of nutrients and cellular waste products is reduced leading to an inadequate flux distribution in healthy cartilage tissue. The obtained results show how the model predicts the permeability of the PEA-PHEA hydrogels and simulates the internal behaviour of the samples and shows the distribution and quantification of fluid flux.

Large deforming buoyant embolus passing through a stenotic common carotid artery: a computational simulation

Arterial embolism is responsible for the death of lots of people who suffers from heart diseases. The major risk of embolism in upper limbs is that the ruptured particles are brought into the brain, thus stimulating neurological symptoms or causing the stroke. We presented a computational model using fluid-structure interactions (FSI) to investigate the physical motion of a blood clot inside the human common carotid artery. We simulated transportation of a buoyant embolus in an unsteady flow within a finite length tube having stenosis. Effects of stenosis severity and embolus size on arterial hemodynamics were investigated. To fulfill realistic nonlinear property of a blood clot, a rubber/foam model was used. The arbitrary Lagrangian-Eulerian formulation (ALE) and adaptive mesh method were used inside fluid domain to capture the large structural interfacial movements. The problem was solved by simultaneous solution of the fluid and the structure equations. Stress distribution and deformation of the clot were analyzed and hence, the regions of the embolus prone to lysis were localized. The maximum magnitude of arterial wall shear stress during embolism occurred at a short distance proximal to the throat of the stenosis. Through embolism, arterial maximum wall shear stress is more sensitive to stenosis severity than the embolus size whereas role of embolus size is more significant than the effect of stenosis severity on spatial and temporal gradients of wall shear stress downstream of the stenosis and on probability of clot lysis due to clot stresses while passing through the stenosis.

Modeling, Simulation, and Optimal Initiation Planning For Needle Insertion Into the Liver

Needle insertion simulation and planning systems (SPSs) will play an important role in diminishing inappropriate insertions into soft tissues and resultant complications. Difficulties in SPS development are due in large part to the computational requirements of the extensive calculations in finite element (FE) models of tissue. For clinical feasibility, the computational speed of SPSs must be improved. At the same time, a realistic model of tissue properties that reflects large and velocity-dependent deformations must be employed. The purpose of this study is to address the aforementioned difficulties by presenting a cost-effective SPS platform for needle insertions into the liver. The study was constrained to planar (2D) cases, but can be extended to 3D insertions. To accommodate large and velocity-dependent deformations, a hyperviscoelastic model was devised to produce an FE model of liver tissue. Material constants were identified by a genetic algorithm applied to the experimental results of unconfined compressions of bovine liver. The approach for SPS involves B-spline interpolations of sample data generated from the FE model of liver. Two interpolation-based models are introduced to approximate puncture times and to approximate the coordinates of FE model nodes interacting with the needle tip as a function of the needle initiation pose; the latter was also a function of postpuncture time. A real-time simulation framework is provided, and its computational benefit is highlighted by comparing its performance with the FE method. A planning algorithm for optimal needle initiation was designed, and its effectiveness was evaluated by analyzing its accuracy in reaching a random set of targets at different resolutions of sampled data using the FE model. The proposed simulation framework can easily surpass haptic rates (>500 Hz), even with a high pose resolution level (∼30). The computational time required to update the coordinates of the node at the needle tip in the provided example was reduced from 177 s to 0.8069 ms. The planning accuracy was acceptable even with moderate resolution levels: root-mean-square and maximum errors were 1 mm and 1.2 mm, respectively, for a pose and PPT resolution levels of 17 and 20, respectively. The proposed interpolation-based models significantly improve the computational speed of needle insertion simulation and planning, based on the discretized (FE) model of the liver and can be utilized to establish a cost-effective planning platform. This modeling approach can also be extended for use in other surgical simulations.