Digital Image Correlation (DIC) systems have been used to measure surface displacement fields by tracking a pattern applied to a surface. Offering many benefits in comparison to conventional strain-measurement devices, the use of DIC has been reported in the study of tissue biomechanics and performance of joints underneath. In this study, a new method was developed to apply a quality speckle pattern on the skin of knees. Temporary tattoo paper provided a safe, easy, and quick way for pattern application to the skin without hindering its natural behavior. A pattern was developed for analyzing the knee during a squatting motion in which the field of view, system set up, and curvature of the knee were contributing factors to the development. This research is designed to prove the feasibility of using tattoo papers as patent indicators for DIC measurement. The software was able to map the entire region of the knee and measure the displacement of each area independent of other parts, thus making it easy to identify twisting and bending of the joint. Experimental results indicated that it is an effective method to accurately analyze the motion of the knee without the need of sophisticated equipment. This methodology can be used to understand how strain affects the knee during action and thus will be useful for various sports-related activities such as training and injury management.

Polycrystalline materials consist of grains (crystals) oriented at different angles resulting in a heterogeneous and anisotropic mechanical behavior at that micro-length scale. In this study, a novel method is proposed for the first time to determine the 3 D crystal orientations of grains in a 2 D domain, using solely 2 D deformation fields. The grain boundaries are assumed to be unknown and delineated from the reconstructed changes in the crystallographic orientation. Further, the constitutive equations that describe the mechanical behavior of the domain in 2 D under plane stress conditions are derived, assuming that the material is transversely isotropic in 3D. Finite element based algorithms are utilized to discretize the inverse problem. The in-house written inverse problem solver is coupled with Matlab-based optimization scripts to solve for the mechanical property distributions. The performance of this method is tested at different noise levels with synthetic displacements that were used as measured data. The reconstructions deteriorate as the noise level is increased. This work presents a first milestone in the verification of this novel technology with synthetic data.

Tomography based imaging is used in various disciplines with the most widely known as computed tomography (CT). In general, they have in common that a signal is measured on the specimen's surface and at multiple locations to reconstruct some type of a material property distribution using application specific constitutive equations. In this paper and for the first time with experimental validation, a novel tomography approach is successfully introduced based on the mechanics of solids. It utilizes the equations of equilibrium at its core embedded in an optimization framework to control the ill-posed nature of these problems. Measured signals are deformation fields obtained from a digital image correlation system with photo cameras. This work demonstrates the potential of mechanics based tomography (MBT) on a composite silicone material. This work encourages to investigate MBT as a breast tumor screening tool to visualize tumors based on their stiffness contrast. Another long-term goal could be to investigate the use of this methodology as a non-destructive testing tool for civil engineering structures such as bridges. Finally, this new methodology could potentially be miniaturized with stereoscopes and extended to map the material property distribution at the microstructure, e.g. grain length-scale.

Existing biodegradable Magnesium Alloy Stents (MAS) have several drawbacks, such as high restenosis, hasty degradation, and bulky cross-section, that limit their widespread application in a current clinical practice. To find the optimum stent with the smallest possible cross-section and adequate scaffolding ability, a 3D finite element model of 25 MAS stents of different cross-sectional dimensions were analysed while localized corrosion was underway. For the stent geometric design, a generic sine-wave ring of biodegradable magnesium alloy (AZ31) was selected. Previous studies have shown that the long-term performance of MAS was characterized by two key features: Stent Recoil Percent (SRP) and Stent Radial Stiffness (SRS). In this research, the variation with time of these two features during the corrosion phase was monitored for the 25 stents. To find the optimum profile design of the stent subjectively (without using optimization codes and with much less computational costs), radial recoil was limited to 27 % (corresponding to about 10 % probability of in-stent diameter stenosis after an almost complete degradation) and the stent with the highest radial stiffness was selected.The comparison of the recoil performance of 25 stents during the heterogeneous corrosion phase showed that four stents would satisfy the recoil criterion and among these four, the one having a width of 0.161 mm and a thickness of 0.110 mm, showed a 24 % – 49 % higher radial stiffness at the end of the corrosion phase. Accordingly, this stent, which also showed a 23.28 % mass loss, was selected as the optimum choice and it has a thinner cross-sectional profile than commercially available MAS, which leads to a greater deliverability and lower rates of restenosis.

The unloaded configuration of a body without residual stresses is generally used as the starting point to compute the displacement field but may be unknown for some applications. In this paper, we propose a novel inverse formulation to identify the unloaded configuration of a deformed hyperelastic body using finite element based discretization schemes. The inverse problem consists of finding a domain that is geometrically defined by its boundary such that it deforms in a way consistent with the measurements taken on its deformed configuration. The coordinates of boundary nodes in the deformed configuration can be measured and are assumed to be known for the inverse problem. Since only the coordinates of boundary nodes in the unloaded configuration are updated in each step of the inverse analysis, re-meshing is essential to continue the optimization process. The Akin's method is employed to map the mesh used for the unloaded configuration in the previous step for the updated one. Both numerical and experimental data sets are used in 2D/3D to demonstrate the effectiveness of the proposed inverse technique. This work could have practical applications in the design of elastomeric parts or to recover the unloaded configuration of soft tissues in vivo.

In this work, we present a non-destructive approach to characterize the heterogeneous mechanical behavior of anisotropic elastic solids. This approach is based on iterative inverse algorithms using the framework of finite element discretization schemes. We test the proposed approach with several theoretical studies and observe that for a low noise level in measured displacement fields, it is possible to map the anisotropic linear elastic parameter distributions with high accuracy. We also observe that with additional displacement field measurements, the solution to the inverse problem becomes more unique. However, for higher noise levels (3%), the quality of the reconstructions deteriorates for the parameter C-12 of the orthotropic elasticity tensor. A theoretical analysis is performed and we demonstrate that this may be due to small gradients of the objective function with respect to C-12. Overall, the proposed approach has potential to characterize the anisotropic mechanical behavior of polymer based materials or tissues for pathology.

It is well known that the mechanical properties of tissues may vary spatially due to changing tissue types or due to inherent tissue disease. For example, the biomechanical properties are known to vary throughout blood vessel... | Find, read and cite all the research you need on Tech Science Press

Due to wide applications of hyper-viscoelastic material models in medicine and industry, many researchers have focused on determination of the parameters of these models. In problems for identification of material parameters of hyper-elastic and hyper-viscoelastic members, detailed information about boundary conditions is necessary. In reality, for an in vivo soft tissue or an engineering part in service, detailed information about the supports of the member may be unavailable. In such cases, assuming some kind of boundary conditions that may be far from truth will result in unacceptable solutions. In this work, for the first time, an inverse analysis-based method for the identification of hyper-viscoelastic parameters of a member with arbitrary shape under plane strain conditions is presented. The unknowns are found using displacement measurements in an elasto-dynamic loading, while details about the support of the member are unclear. The proposed algorithm minimizes the differences between measured and calculated displacements. The minimization algorithm needs some sensitivity analyses, which are performed via finite difference approximation and analytic differentiation. For modeling the hyper-viscoelastic behavior, a model consisting of some Maxwell elements in parallel with a neo-Hookean hyper-elastic spring is considered. The effectiveness of the proposed method is evaluated by presenting several numerical examples. (C) 2019 Elsevier Ltd. All rights reserved.

Identification of material properties of hyper-elastic materials such as soft tissues of the human body or rubber-like materials has been the subject of many works in recent decades. Boundary conditions generally play an important role in solving an inverse problem for material identification, while their knowledge has been taken for granted. In reality, however, boundary conditions may not be available on parts of the problem domain such as for an engineering part, e.g., a polymer that could be modeled as a hyper-elastic material, mounted on a system or an in vivo soft tissue. In these cases, using hypothetical boundary conditions will yield misleading results. In this paper, an inverse algorithm for the characterization of hyper-elastic material properties is developed, which takes into consideration unknown conditions on a part of the boundary. A cost function based on measured and calculated displacements is defined and is minimized using the Gauss-Newton method. A sensitivity analysis is carried out by employing analytic differentiation and using the finite element method (FEM). The effectiveness of the proposed method is demonstrated through numerical and experimental examples. The novel method is tested with a neo-Hookean and a Mooney-Rivlin hyper-elastic material model. In the experimental example, the material parameters of a silicone based specimen with unknown boundary condition are evaluated. In all the examples, the obtained results are verified and it is observed that the results are satisfactory and reliable.

The authors wish to correct Figures 12 and 14 in their paper published in Sensors [1], doi:10.3390/s17051075, http://www.mdpi.com/1424-8220/17/5/1075[...].

We present for the first time the feasibility to recover the stiffness (here shear modulus) distribution of a three-dimensional heterogeneous sample using measured surface displacements and inverse algorithms without making any assumptions about local homogeneities and the stiffness distribution. We simulate experiments to create measured displacements and augment them with noise, significantly higher than anticipated measurement noise. We also test two-dimensional problems in plane strain with multiple stiff inclusions. Our inverse strategy recovers the shear modulus values in the inclusions and background well, and reveals the shape of the inclusion clearly.

A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neo-Hookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neo-Hookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neo-Hookean material model. In addition, it was observed that the inverse problem solution was inclusion size-sensitive, Consequently, an 1-D model was introduced to broaden our understanding of this issue. This 1-D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology. (C) 2018 Elsevier Ltd. All rights reserved.

We present a nondestructive approach to map the heterogeneous viscoelastic moduli from time harmonic motion via a constrained optimization strategy under the framework of finite element techniques. The adjoint equations are carefully derived to determine the gradient of the objective function with respect to the viscoelastic moduli. The feasibility of this inverse scheme is tested with simulated experiments under various driving frequencies. We observe that the overall strategy results in well-reconstructed moduli. For low frequencies, however, the mapped loss modulus is of inferior quality. To explain this observation, we analyze two simple one-dimensional (1D) models theoretically. The analysis reveals that the known displacement amplitude is less sensitive to the loss modulus value at low frequencies. Thus, we conclude that the inverse method is incapable of finding a well-reconstructed loss modulus distribution for low driving frequencies in the presence of noisy data. Overall, the inverse algorithms presented in this work are highly robust to map the storage and loss modulus with high accuracy given that a proper range of frequencies are utilized.

There are many engineering parts and natural soft members, which consist of several phases with different mechanical properties. Identification of material parameters of multi-material members is an important issue that has attracted considerable attention. In this article, a finite-element-based inverse method for identification of material parameters of a body made of several hyper-elastic materials is presented. In the presented inverse method, the unknowns are computed using a few simple displacement/length measurements in a few elasto-static experiments. The inverse analysis can be carried out without any full-field measurements. Both plane strain and plane stress conditions are considered. In the plane strain case, displacements of several sampling points on the boundary of the problem domain are used as measured data. In the plane stress case, some characteristic lengths of the member in the deformed configuration are used as measured data. A cost function in terms of the differences between calculated and measured values is defined and the Gauss–Newton method is used to minimize it. The multi-material sensitivity analysis in the optimization process is made by analytical differentiation of the weak form of the problem. Both numerical and experimental studies are made to demonstrate the effectiveness and accuracy of the proposed methods.

The mechanical properties of tissues are important indicators of tissue “health”. Diseased tissues due to cancer and other causes tend to stiffen with increase in strain, exhibiting a nonlinear stress–strain behavior. The hyperelastic mechanical behavior of soft tissues can be characterized by an exponential model with two material parameters, namely the shear modulus μ and a nonlinearity parameter γ. A variety of methods and techniques have been developed to solve inverse problems in nonlinear elasticity to determine these properties given the mechanical response of the tissues. Reconstruction of the nonlinear parameter from noisy measurements of displacement response is a difficult problem, and obtaining a well-recovered solution is challenging. This article is directed towards the improvement in the reconstruction of the nonlinear parameter, γ, by introducing a new parameter, which is a combination of γ and the first invariant of the Cauchy–Green deformation tensor. Comparative study is carried out between reconstructions of γ directly from previously existing formulations and the reconstruction of γ from the new parameter, for 2D problems. The new method is compared with previous methods using numerical experiments in terms of shape of the stiff regions, the contrast in γ and robustness under different loading conditions. We find that the new method is a considerable improvement to previous methods and could be a valuable tool in biomedical applications.

We present the solution of the inverse problem for partially known elastic modulus values, e.g., the elastic modulus is known in some small region on the boundary of the domain from measurements. The inverse problem is posed as a constrained minimization problem and regularized with two different regularization types. In particular, the total variation diminishing (TVD) and the total contrast diminishing (TCD) regularizations are employed. We test both regularization strategies with theoretical diseased tissues, such as a stiff tumor surrounded by healthy background tissue and an atherosclerotic plaque having a soft inclusion surrounded by a stiff cap. In the present study, it is assumed that no traction data is available and the absolute elastic modulus distribution is calibrated from partially known elastic modulus values. We observe that this calibration fails with TVD regularization, while TCD regularization yields well-recovered absolute elastic modulus reconstructions in the presence of high noise levels in the displacement data. Finally, we investigate this problem analytically and provide an explanation for these observations. This work will advance efforts in parameter identification of heterogeneous materials as it provides a methodology to incorporate partially known parameters into the inverse problem formulation that will ultimately drive the inverse solution to an absolute and unique parameter distribution. This has great importance in classifying breast tumors based on their elastic modulus values and in planning surgical interventions of atherosclerotic plaques.

We present a non-destructive approach to sense inclusion objects embedded in a solid medium remotely from force sensors applied to the medium and boundary displacements that could be measured via a digital image correlation system using a set of cameras. We provide a rationale and strategy to uniquely identify the heterogeneous sample composition based on stiffness (here, shear modulus) maps. The feasibility of this inversion scheme is tested with simulated experiments that could have clinical relevance in diagnostic imaging (e.g., tumor detection) or could be applied to engineering materials. No assumptions are made on the shape or stiffness quantity of the inclusions. We observe that the novel inversion method using solely boundary displacements and force measurements performs well in recovering the heterogeneous material/tissue composition that consists of one and two stiff inclusions embedded in a softer background material. Furthermore, the target shear modulus value for the stiffer inclusion region is underestimated and the inclusion size is overestimated when incomplete boundary displacements on some part of the boundary are utilized. For displacements measured on the entire boundary, the shear modulus reconstruction improves significantly. Additionally, we observe that with increasing number of displacement data sets utilized in solving the inverse problem, the quality of the mapped shear moduli improves. We also analyze the sensitivity of the shear modulus maps on the noise level varied between 0.1% and 5% white Gaussian noise in the boundary displacements, force and corresponding displacement indentation. Finally, a sensitivity analysis of the recovered shear moduli to the depth, stiffness and the shape of the stiff inclusion is performed. We conclude that this approach has potential as a novel imaging modality and refer to it as Mechanics Based Tomography (MBT).

We observe that posing the inverse problem as a constrained minimization problem under regularization leads to boundary dependent solutions. In this paper, we propose a modified objective function and show with 2D examples that our method works well to reduce boundary sensitive solutions. The examples consist of two stiff inclusions embedded in a softer unit square. These inclusions could be representative of tumors, which are in general stiffer than their background tissues, thus could potentially be detected based on their stiffness contrast. We modify the objective function for the displacement correlation term by weighting it with a function that depends on the strain field. In a simplified 1D coupled model, we derive an analytical expression and observe the same trends in the reconstructions as for the 2D model. The analysis in this paper is confined to inclusions of similar size and may not overlap when projected on the horizontal axis. They may, however, vary in position along the vertical axis. Furthermore, our analysis holds for an arbitrary number of inclusions having distinct stiffness values. Finally, to increase the overall contrast of the tumors and simultaneously improve the smoothness, we solve the regularized inverse problem in a posterior step, utilizing a spatially varying regularization factor.

Blood flow plays a critical role in regulating embryonic cardiac growth and development, with altered flow leading to congenital heart disease. Progress in the field, however, is hindered by a lack of quantification of hemodynamic conditions in the developing heart. In this study, we present a methodology to quantify blood flow dynamics in the embryonic heart using subject-specific computational fluid dynamics (CFD) models. While the methodology is general, we focused on a model of the chick embryonic heart outflow tract (OFT), which distally connects the heart to the arterial system, and is the region of origin of many congenital cardiac defects. Using structural and Doppler velocity data collected from optical coherence tomography, we generated 4D (\(\hbox {3D}\,+\,\hbox {time}\)) embryo-specific CFD models of the heart OFT. To replicate the blood flow dynamics over time during the cardiac cycle, we developed an iterative inverse-method optimization algorithm, which determines the CFD model boundary conditions such that differences between computed velocities and measured velocities at one point within the OFT lumen are minimized. Results from our developed CFD model agree with previously measured hemodynamics in the OFT. Further, computed velocities and measured velocities differ by \(<\)15 % at locations that were not used in the optimization, validating the model. The presented methodology can be used in quantifications of embryonic cardiac hemodynamics under normal and altered blood flow conditions, enabling an in-depth quantitative study of how blood flow influences cardiac development.