Material parameter identification of arterial wall layers from homogenised stress-strain data

Multilayer structure of the artery can have significant effects on the resulting mechanical behaviour of the artery wall. Separation of the artery into individual layers is sometimes performed to identify the layer-specific parameters of constitutive model proposed by Holzapfel, Gasser and Ogden (HGO model). Inspired by this single-layer model, a double-layer model was formulated and used for identification of material parameters from homogenised stress-strain data (of non-separated artery wall). The paper demonstrates that the layer-specific parameters of the double-layer constitutive model can be identified without the need of artery separation. The resulting double-layer model can credibly describe the homogenised stress-strain behaviour of the real artery wall including large-strain stiffening effects attributed to multilayer nature of the artery.     

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

A two-layer elasto-visco-plastic rheological model for the material parameter identification of bone tissue

The ability to measure bone tissue material properties plays a major role in diagnosis of diseases and material modeling. Bone’s response to loading is complex and shows a viscous contribution to stiffness, yield and failure. It is also ductile and damaging and exhibits plastic hardening until failure. When performing mechanical tests on bone tissue, these constitutive effects are difficult to quantify, as only their combination is visible in resulting stress–strain data. In this study, a methodology for the identification of stiffness, damping, yield stress and hardening coefficients of bone from a single cyclic tensile test is proposed. The method is based on a two-layer elasto-visco-plastic rheological model that is capable of reproducing the specimens’ pre- and postyield response. The model’s structure enables for capturing the viscously induced increase in stiffness, yield, and ultimate stress and for a direct computation of the loss tangent. Material parameters are obtained in an inverse approach by optimizing the model response to fit the experimental data. The proposed approach is demonstrated by identifying material properties of individual bone trabeculae that were tested under wet conditions. The mechanical tests were conducted according to an already published methodology for tensile experiments on single trabeculae. As a result, long-term and instantaneous Young’s moduli were obtained, which were on average 3.64 GPa and 5.61 GPa, respectively. The found yield stress of 16.89 MPa was lower than previous studies suggest, while the loss tangent of 0.04 is in good agreement. In general, the two-layer model was able to reproduce the cyclic mechanical test data of single trabeculae with an root-mean-square error of 2.91 ± 1.77 MPa. The results show that inverse rheological modeling can be of great advantage when multiple constitutive contributions shall be quantified based on a single mechanical measurement.

     

Estimation of trunk mechanical properties using system identification: effects of experimental setup and modelling assumptions

The use of system identification to quantify trunk mechanical properties is growing in biomechanics research. The effects of several experimental and modelling factors involved in the system identification of trunk mechanical properties were investigated. Trunk kinematics and kinetics were measured in six individuals when exposed to sudden trunk perturbations. Effects of motion sensor positioning and properties of elements between the perturbing device and the trunk were investigated by adopting different models for system identification. Results showed that by measuring trunk kinematics at a location other than the trunk surface, the deformation of soft tissues is erroneously included into trunk kinematics and results in the trunk being predicted as a more damped structure. Results also showed that including elements between the trunk and the perturbing device in the system identification model did not substantially alter model predictions. Other important parameters that were found to substantially affect predictions were the cut-off frequency used when low-pass filtering raw data and the data window length used to estimate trunk properties.     

Estimation of trunk mechanical properties using system identification: effects of experimental setup and modelling assumptions

The use of system identification to quantify trunk mechanical properties is growing in biomechanics research. The effects of several experimental and modelling factors involved in the system identification of trunk mechanical properties were investigated. Trunk kinematics and kinetics were measured in six individuals when exposed to sudden trunk perturbations. Effects of motion sensor positioning and properties of elements between the perturbing device and the trunk were investigated by adopting different models for system identification. Results showed that by measuring trunk kinematics at a location other than the trunk surface, the deformation of soft tissues is erroneously included into trunk kinematics and results in the trunk being predicted as a more damped structure. Results also showed that including elements between the trunk and the perturbing device in the system identification model did not substantially alter model predictions. Other important parameters that were found to substantially affect predictions were the cut-off frequency used when low-pass filtering raw data and the data window length used to estimate trunk properties.     

Three-Dimensional Structure of the Intercalated Disc Reveals Plicate Domain and Gap Junction Remodeling in Heart Failure

The intercalated disc (ICD) orchestrates electrochemical and mechanical communication between neighboring cardiac myocytes, properties that are perturbed in heart failure (HF). Although structural data from transmission electron microscopy two-dimensional images have provided valuable insights into the domains forming the ICD, there are currently no three-dimensional (3D) reconstructions for an entire ICD in healthy or diseased hearts. Here, we aimed to understand the link between changes in protein expression in an ovine tachypacing-induced HF model and ultrastructural remodeling of the ICD by determining the 3D intercalated disc architecture using serial block face scanning electron microscopy. In the failing myocardium there is no change to the number of ICDs within the left ventricle, but there is an almost doubling of the number of discs with a surface area of <1.0 × 10⁸μm² in comparison to control. The 3D reconstructions further revealed that there is remodeling of the plicate domains and gap junctions with vacuole formation around and between the contributing membranes that form the ICDs in HF. Biochemical analysis revealed upregulation of proteins involved in stabilizing the adhesive and mechanical properties consistent with the morphological changes. Our studies here have shown that in tachypacing-induced HF mechanical stresses are associated with both structural and molecular alterations. To our knowledge, these data together provide novel, to our knowledge, insights as to how remodeling at the molecular and structural levels leads to impaired intercellular communication.     

Viscoelastic properties of human mesenchymally-derived stem cells and primary osteoblasts, chondrocytes, and adipocytes

The mechanical properties of single cells play important roles in regulating cell-matrix interactions, potentially influencing the process of mechanotransduction. Recent studies also suggest that cellular mechanical properties may provide novel biological markers, or "biomarkers," of cell phenotype, reflecting specific changes that occur with disease, differentiation, or cellular transformation. Of particular interest in recent years has been the identification of such biomarkers that can be used to determine specific phenotypic characteristics of stem cells that separate them from primary, differentiated cells. The goal of this study was to determine the elastic and viscoelastic properties of three primary cell types of mesenchymal lineage (chondrocytes, osteoblasts, and adipocytes) and to test the hypothesis that primary differentiated cells exhibit distinct mechanical properties compared to adult stem cells (adipose-derived or bone marrow-derived mesenchymal stem cells). In an adherent, spread configuration, chondrocytes, osteoblasts, and adipocytes all exhibited significantly different mechanical properties, with osteoblasts being stiffer than chondrocytes and both being stiffer than adipocytes. Adipose-derived and mesenchymal stem cells exhibited similar properties to each other, but were mechanically distinct from primary cells, particularly when comparing a ratio of elastic to relaxed moduli. These findings will help more accurately model the cellular mechanical environment in mesenchymal tissues, which could assist in describing injury thresholds and disease progression or even determining the influence of mechanical loading for tissue engineering efforts. Furthermore, the identification of mechanical properties distinct to stem cells could result in more successful sorting procedures to enrich multipotent progenitor cell populations.     

In vivo characterization of the mechanical properties of human skin derived from MRI and indentation techniques

The human skin is an exceedingly complex and multi-layered material. This paper aims to introduce the application of the finite element analysis (FEA) to the in vivo characterization of the non-linear mechanical behaviour of three human skin layers. Indentation tests combined with magnetic resonance imaging (MRI) technique have been performed on the left dorsal forearm of a young man in order to reveal the mechanical behaviour of all skin layers. Using MRI images processing and a pre and post processor allows to make numerically individualized 2D model which consists of three skin layers and the muscles. FEA has been applied to simulate indentation tests. Neo-Hookean slightly compressible material model of two material constants (C(10), K) has been used to model the mechanical behaviour of the three skin layers and the muscles. The identification of material model parameters was done by applying Levenberg-Marquardt algorithm (LMA). Our methodology of identification provides a range of values for each constant. Range of values of different material properties of epidermis, dermis, hypodermis are respectively, C10(E)=0.12+/-0.06 MPa, C10(D)=1.11+/-0.09 MPa, C10(H)=0.42+/-0.05 KPa, K(E)=5.45+/-1.7 MPa, K(D)=29.6+/-1,28 MPa, K(H)=36.0+/-0.9 KPa.     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage

Abstract

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.     

Computational modelling and analysis of mechanical conditions on cell locomotion and cell–cell interaction

Between other parameters, cell migration is partially guided by the mechanical properties of its substrate. Although many experimental works have been developed to understand the effect of substrate mechanical properties on cell migration, accurate 3D cell locomotion models have not been presented yet. In this paper, we present a novel 3D model for cells migration. In the presented model, we assume that a cell follows two main processes: in the first process, it senses its interface with the substrate to determine the migration direction and in the second process, it exerts subsequent forces to move. In the presented model, cell traction forces are considered to depend on cell internal deformation during the sensing step. A random protrusion force is also considered which may change cell migration direction and/or speed. The presented model was applied for many cases of migration of the cells. The obtained results show high agreement with the available experimental and numerical data.     

Spatial distribution and orientation of dermatan sulfate in human medial collateral ligament

The proteoglycan decorin and its associated glycosaminoglycan (GAG), dermatan sulfate (DS), regulate collagen fibril formation, control fibril diameter, and have been suggested to contribute to the mechanical stability and material properties of connective tissues. The spatial distribution and orientation of DS within the tissue are relevant to these mechanical roles, but measurements of length and orientation from 2D transmission electron microscopy (TEM) are prone to errors from projection. The objectives of this study were to construct a 3D geometric model of DS GAGs and collagen fibrils, and to use the model to interpret TEM measurements of the spatial orientation and length of DS GAGs in the medial collateral ligament of the human knee. DS was distinguished from other sulfated GAGs by treating tissue with chondroitinase B, an enzyme that selectively degrades DS. An image processing pipeline was developed to analyze the TEM micrographs. The 3D model of collagen and GAGs quantified the projection error in the 2D TEM measurements. Model predictions of 3D GAG orientation were highly sensitive to the assumed GAG length distribution, with the baseline input distribution of 69+/-23 nm providing the best predictions of the angle measurements from TEM micrographs. The corresponding orientation distribution for DS GAGs was maximal at orientations orthogonal to the collagen fibrils, tapering to near zero with axial alignment. Sulfated GAGs that remained after chondroitinase B treatment were preferentially aligned along the collagen fibril. DS therefore appears more likely to bridge the interfibrillar gap than non-DS GAGs. In addition to providing quantitative data for DS GAG length and orientation in the human MCL, this study demonstrates how a 3D geometric model can be used to provide a priori information for interpretation of geometric measurements from 2D micrographs.     

Strain-energy function and three-dimensional stress distribution in esophageal biomechanics

Knowledge of the transmural stress and stretch fields in esophageal wall is necessary to quantify growth and remodeling, and the response to mechanically based clinical interventions or traumatic injury, but there are currently conflicting reports on this issue and the mechanical properties of intact esophagus have not been rigorously addressed. This paper offers multiaxial data on rabbit esophagus, warranted for proper identification of the 3D mechanical properties. The Fung-type strain-energy function was adopted to model our data for esophagus, taken as a thick-walled (1 or 2-layer) tubular structure subjected to inflation and longitudinal extension. Accurate predictions of the pressure–radius–force data were obtained using the 1-layer model, covering a broad range of extensions; the calculated material parameters indicated that intact wall was equally stiff as mucosa–submucosa, but stiffer than muscle in both principal axes, and tissue was stiffer longitudinally, concurring our histological findings (Stavropoulou et al., Journal of Biomechanics. 42 (2009) 2654–2663). Employing the material parameters of individual layers, with reference to their zero-stress state, a reasonable fit was obtained to the data for intact wall, modeled as a 2-layer tissue. Different from the stress distributions presented hitherto in the esophagus literature, consideration of residual stresses led to less dramatic homogenization of stresses under loading. Comparison of the 1- and 2-layer models of esophagus demonstrated that heterogeneity induced a more uniform distribution of residual stresses in each layer, a discontinuity in circumferential and longitudinal stresses at the interface among layers, and a considerable rise of stresses in mucosa, with a reduction in muscle.     

3d Mechanical properties of the partially obstructed guinea pig small intestine

Background and aimsPartial obstruction of the small intestine results in severe hypertrophy of smooth muscle cells, dilatation and functional denervation. Hypertrophy of the small intestine is associated with alteration of the wall structure and the mechanical properties. The aims of this study were to determine three dimensional material properties of the obstructed small intestine in guinea pigs and to obtain the 3D stress–strain distributions in the small intestinal wall.MethodsPartial obstruction of mid-jejunum was created surgically in five guinea pigs that were euthanized 2 weeks after the surgery. Ten-cm-long segments proximal to the obstruction site were used for the stretch-inflation mechanical test using a tri-axial test machine. The outer diameter, longitudinal force and the luminal pressure during the test were recorded simultaneously. An anisotropic exponential pseudo-strain energy density function was used as the constitutive equation to fit the experimental loading curve and for computation of the stress–strain distribution.ResultsThe wall thickness and the wall area increased significantly in the obstructed jejunum (P<0.001). The pressure—outer radius curves in the obstructed segments were translated to the left of the normal segments, indicating wall stiffening after the obstruction. The circumferential stress and the longitudinal stress through the wall were higher in the obstructed segments (P<0.02). This was independent of whether the zero-stress state or the no-load states were used as the reference state.ConclusionThe mechanical behaviour of the obstructed small intestine can be described using a 3D constitutive model. The obstruction-induced biomechanical properties change was characterized by higher circumferential and longitudinal stresses in the wall and altered material constants in the 3D constitutive model.     

In vivo parameter identification in arteries considering multiple levels of smooth muscle activity

In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.

     

Extracellular Matrix Stiffness and Architecture Govern Intracellular Rheology in Cancer

Little is known about the complex interplay between the extracellular mechanical environment and the mechanical properties that characterize the dynamic intracellular environment. To elucidate this relationship in cancer, we probe the intracellular environment using particle-tracking microrheology. In three-dimensional (3D) matrices, intracellular effective creep compliance of prostate cancer cells is shown to increase with increasing extracellular matrix (ECM) stiffness, whereas modulating ECM stiffness does not significantly affect the intracellular mechanical state when cells are attached to two-dimensional (2D) matrices. Switching from 2D to 3D matrices induces an order-of-magnitude shift in intracellular effective creep compliance and apparent elastic modulus. However, for a given matrix stiffness, partial blocking of β1 integrins mitigates the shift in intracellular mechanical state that is invoked by switching from a 2D to 3D matrix architecture. This finding suggests that the increased cell-matrix engagement inherent to a 3D matrix architecture may contribute to differences observed in viscoelastic properties between cells attached to 2D matrices and cells embedded within 3D matrices. In total, our observations show that ECM stiffness and architecture can strongly influence the intracellular mechanical state of cancer cells.     

Identification of heterogeneous elastic properties in stenosed arteries: a numerical plane strain study

Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging. An important issue is to solve the inverse problem that consists in estimating the elastic properties inside the plaque from measured displacements. This study focuses on the identifiability of elastic parameters, e.g. on the compromise between identification time and identification accuracy. An idealised plane strain finite element (FE) model is used. The effects of the FE mesh of the a priori assumptions about the constituents, of the measurement resolution and of the data noise are numerically investigated.     

Role of physical properties of resistance vessel wall in regulating peripheral blood flow--II. Structural and mechanical behavior

In order to examine the structural and mechanical properties of the vessel wall resistance when subjected to autoregulatory flow control, a mechanical model for the vascular wall was derived from a mathematical model. The mechanical model was an analogue model which connected in series the Maxwell model (elastic modulus: K3) with the parallel elements of Hill's model (elastic modules: K2) and Hooke's elastic model (elastic modulus: K1); it was also mathematically equivalent to the Spring model (see part I). The structural and mechanical properties of the resistance vessel wall were characterized by the three elastic moduli (K1, alpha K2 and K3) [mmHg]. The parameter alpha was a modification factor of the elastic modulus K2 given by the myogenic mechanism. After a numerical analysis of the experimental data given by the mechanical model, we confirmed that the arterial pressure range for autoregulatory flow controls shifted to the upper region with an increase of the elastic modulus K1 and the flow regulation was reduced.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.