Mechanical Behavior Of Biological Tissues Research Articles

A Stretchable and Strain‐Limiting, Bio‐Inspired Nanofiber‐Reinforced Microfiber for Wearable Electronics

AbstractWith existing fiber‐based approaches for wearable electronics, devices with limited stretchability are not fully protected against large stretching when the wearer is participating in vigorous activities. A network of elastin and collagen fibers makes biological tissues elastic at low strains and strain‐limiting at high strains, showing a J‐shaped stress‐strain behavior. Stretchable systems can replicate a “J‐shaped stress‐strain/strain‐limiting” mechanical behavior of biological tissues under deformations and provide mechanical compliance and comfort to wearers. For mimicking this mechanical behavior of biological tissues, he developed a combined microfiber and nanofiber (NF)‐based approach. The soft polyurethane (PU) microfiber mimicking elastin of biological tissue is wrapped with stiff poly(vinylidene fluoride)(PVDF) NFs, mimicking collagen in tissue, and dip coated in polydimethylsiloxane (PDMS). Confocal images during stretching confirmed that the PU microfiber maintained stretchability, while the stiff PVDF NFs played a role in the strain‐limiting characteristics. By tailoring a loading ratio of the PVDF NFs on the PU microfiber, the elastic modulus is matched well with those of biological tissues. The stretchable conducting coating and temperature sensor on the bio‐inspired microfiber showed a negligible difference in a current‐time (I‐T) response during static and dynamic stretching which indicated the efficient absorption of stress by the bio‐inspired microfiber.

Characterization and modeling of a thermoplastic elastomer tissue simulant under uniaxial compression loading for a wide range of strain rates

Characterization and modeling of the mechanical behavior of biological tissues are critical to many biomedical related applications. For research and development, various soft materials have often been used as a tissue substitute. Among them, the mineral oil-based synthetic polymer styrene-ethylene-butylene-styrene (SEBS) gel has gained some popularity due to its superior mechanical and physical properties. Tissue materials or their simulants are often characterized with quasi-static loading and are treated and modeled as a nonlinear hyperelastic material. As tissues are often subjected to loadings with a wide range of strain rates, understanding of the mechanical behavior and development a predictive capability for such loadings are essential. In this work, a comprehensive study of the mechanical behavior of SEBS gels with different chemical compositions and polymer concentrations was conducted under uniaxial compression loadings over a wide range of strain rates, from 1×10−3/s to 6×103/s. In addition to experiments, a comprehensive but simple visco-pseudo-hyperelasticity model was developed. The model was demonstrated to be able to capture all the material features observed in the experiments, such as rate sensitivity, strain-induced softening, and permanent deformation after unloading. Because of its simple functional form, the model can be conveniently used for practical applications such as prediction of the rate dependence of the shear modulus.

Soft Tissue Hybrid Model for Real-Time Simulations.

In this article, a recent formulation for real-time simulation is developed combining the strain energy density of the Spring Mass Model (SMM) with the equivalent representation of the Strain Energy Density Function (SEDF). The resulting Equivalent Energy Spring Model (EESM) is expected to provide information in real-time about the mechanical response of soft tissue when subjected to uniaxial deformations. The proposed model represents a variation of the SMM and can be used to predict the mechanical behavior of biological tissues not only during loading but also during unloading deformation states. To assess the accuracy achieved by the EESM, experimental data was collected from liver porcine samples via uniaxial loading and unloading tensile tests. Validation of the model through numerical predictions achieved a refresh rate of 31 fps (31.49 ms of computation time for each frame), achieving a coefficient of determination R2 from 93.23% to 99.94% when compared to experimental data. The proposed hybrid formulation to characterize soft tissue mechanical behavior is fast enough for real-time simulation and captures the soft material nonlinear virgin and stress-softened effects with high accuracy.

Indentation of a cylinder with different shape of the base into viscoelastic half-space

During developing medical equipment and processing results of experiments on the study of biomaterials, it is necessary to describe the process of interaction of the working tool with soft tissues. With this, it is important to take into account not only the mechanical properties of the tissue under study, but also the technical characteristics of the equipment, such as the shape of the tool surface and the speed of the interaction process. For this purpose, a contact model describing the indentation of an axisymmetric rigid cylinder with different foundation surface shape into viscoelastic half-space at a constant speed was constructed. The theory of linear viscoelasticity was used to describe the mechanical behavior of the half-space. A three-parameter model of a standard viscoelastic body was chosen as a viscoelastic model that defines the type of relaxation function of the half-space material. The distribution of contact pressure under the cylinder surface and the dependence of the applied load on the depth of indentation for various forms of the contact surface of the cylinder were obtained. The influence of the shape of the cylinder base surface, the indentation speed and the relaxation properties of the half space on the characteristics of the contact interaction was studied. For describing the mechanical behavior of biological tissues, a one-dimensional model of a standard viscoelastic body was also considered. For this simplified model, the distribution of the contact pressure under the surface of cylinder with different shape of the base and the dependence of the applied load on time were also obtained. The results obtained using the continuous model and the one-dimensional model were compared. It was shown when it is more appropriate to use the simplified models to describe the interaction of an instrument with biological tissue.

Upper extremity prosthesis 3D bio-pneumatic self-adjusting clamping to non-homogeneous surfaces under the principle of communicating vessel

There are several models that emulate the mechanical behavior of biological tissues. Its automation, new materials and manufacturing techniques will enable its use in the near future. This research is based on the use of compressed air in pneumatic muscles that actuate the phalanges. The research is important because it proposes a system that adapts to the needs and economic accessibility or people with limited resources. The problem to solve is that it meets certain standards such as: stable grip and pressure and that it adapts to irregularly shaped objects with more natural movements. The principle of communicating vessels and the force exerted by a fluid on the walls of the container that is used. Consequently, the fluid exerts pressure in all directions. The prosthesis with the design of the Flexy Hand 2 is manufactured by inserting pneumatic muscles to each of the fingers connecting them by means of nylon ropes that are attached to the homemade pneumatic muscles connected to a common manifold, regulating the pressure by means of a valve and a degree of freedom. As a result of the above, it can be concluded that the prototype worked favorably.

Time-resolved in situ synchrotron-microCT: 4D deformation of bone and bone analogues using digital volume correlation

Digital volume correlation (DVC) in combination with high-resolution micro-computed tomography (microCT) imaging and in situ mechanical testing is gaining popularity for quantifying 3D full-field strains in bone and biomaterials. However, traditional in situ time-lapsed (i.e., interrupted) mechanical testing cannot fully capture the dynamic strain mechanisms in viscoelastic biological materials. The aim of this study was to investigate the time-resolved deformation of bone structures and analogues via continuous in situ synchrotron-radiation microCT (SR-microCT) compression and DVC to gain a better insight into their structure-function relationships. Fast SR-microCT imaging enabled the deformation behaviour to be captured with high temporal and spatial resolution. Time-resolved DVC highlighted the relationship between local strains and damage initiation and progression in the different biostructures undergoing plastic deformation, bending and/or buckling of their main microstructural elements. The results showed that SR-microCT continuous mechanical testing complemented and enhanced the information obtained from time-lapsed testing, which may underestimate the 3D strain magnitudes as a result of the stress relaxation occurring in between steps before image acquisition in porous biomaterials. Altogether, the findings of this study highlight the importance of time-resolved in situ experiments to fully characterise the time-dependent mechanical behaviour of biological tissues and biomaterials and to further explore their micromechanics under physiologically relevant conditions. Statement of significanceTime-resolved synchrotron X-ray tomography in combination with in situ mechanical testing provided the first four-dimensional analysis of the mechanical deformation of bone and bone analogues. To unravel the interplay of damage initiation and progression with local deformation, digital volume correlation was used to map the local strain field while microstructural changes were tracked with high temporal and spatial resolution. The results highlighted the importance of fast imaging and time-resolved in situ experiments to capture the real deformation of complex porous materials to fully characterize the local strain-damage relationship. The findings are notably improving the understanding of time-dependent mechanical behaviour of bone tissue, with the potential to be extend to highly viscoelastic biomaterials and soft tissues.

Simulating Extraocular Muscle Dynamics. A Comparison between Dynamic Implicit and Explicit Finite Element Methods

The finite element method has been widely used to investigate the mechanical behavior of biological tissues. When analyzing these particular materials subjected to dynamic requests, time integration algorithms should be considered to incorporate the inertial effects. These algorithms can be classified as implicit or explicit. Although both algorithms have been used in different scenarios, a comparative study of the outcomes of both methods is important to determine the performance of a model used to simulate the active contraction of the skeletal muscle tissue. In this work, dynamic implicit and dynamic explicit solutions are presented for the movement of the eye ball induced by the extraocular muscles. Aspects such as stability, computational time and the influence of mass-scaling for the explicit formulation were assessed using ABAQUS software. Both strategies produced similar results regarding range of movement of the eye ball, total deformation and kinetic energy. Using the implicit dynamic formulation, an important amount of computational time reduction is achieved. Although mass-scaling can reduce the simulation time, the dynamic contraction of the muscle is drastically altered.

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited.This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared.The results show that the four implementation variations are very similar, with total relative errors between 10−3 and 10−15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.

Emergent structure-dependent relaxation spectra in viscoelastic fiber networks in extension

Viscoelasticity plays an important role in the mechanical behavior of biological tissues undergoing dynamic loading. Exploring viscoelastic relaxation spectra of the tissue is essential for predicting its mechanical response. Most load-bearing tissues, however, are also composed of networks of intertwined fibers and filaments of, e.g., collagen, elastin. In this work, we show how non-affine deformations within fiber networks affect the relaxation behavior of the material leading to the emergence of structure-dependent time scales in the relaxation spectra. In particular, we see two different contributions to the network relaxation process: a material contribution due to the intrinsic viscoelasticity of the fibers, and a kinematic contribution due to non-affine rearrangement of the network when different fibers relax at different rates. We also present a computational model to simulate viscoelastic relaxation of networks, demonstrating the emergent time scales and a pronounced dependence of the network relaxation behavior on whether components with different relaxation times percolate the network. Finally, we observe that the simulated relaxation spectrum for Delaunay networks is comparable to that measured experimentally for reconstituted collagen gels by others. Statement of SignificanceViscoelasticty plays an important role in the mechanical behavior of biological tissues undergoing dynamic loading. Stress relaxation tests provide a convenient way to explore the viscoelastic behavior of the material, while providing an advantage of interrogating multiple time scales in a single experiment. Most load bearing tissues, however, are composed of networks of intertwined fibers and filaments. In the present study, we analyze how the network structure can affect the viscoelastic relaxation behavior of a tissue leading to the emergence of structure-based time scales in the relaxation spectra.

An analytical poroelastic model for ultrasound elastography imaging of tumors

The mechanical behavior of biological tissues has been studied using a number of mechanical models. Due to the relatively high fluid content and mobility, many biological tissues have been modeled as poroelastic materials. Diseases such as cancers are known to alter the poroelastic response of a tissue. Tissue poroelastic properties such as compressibility, interstitial permeability and fluid pressure also play a key role for the assessment of cancer treatments and for improved therapies. At the present time, however, a limited number of poroelastic models for soft tissues are retrievable in the literature, and the ones available are not directly applicable to tumors as they typically refer to uniform tissues. In this paper, we report the analytical poroelastic model for a non-uniform tissue under stress relaxation. Displacement, strain and fluid pressure fields in a cylindrical poroelastic sample containing a cylindrical inclusion during stress relaxation are computed. Finite element simulations are then used to validate the proposed theoretical model. Statistical analysis demonstrates that the proposed analytical model matches the finite element results with less than 0.5% error. The availability of the analytical model and solutions presented in this paper may be useful to estimate diagnostically relevant poroelastic parameters such as interstitial permeability and fluid pressure, and, in general, for a better interpretation of clinically-relevant ultrasound elastography results.

Kinetics of the lower limb during two typical Tai Chi movements in the elderly

ABSTRACTTai Chi (TC) is a recommended exercise for elderly people; however, its loading on the joints of the lower limbs is unknown. This study examined the 3D kinetics of the lower limbs during two typical TC movements and walking in the elderly. Fifteen experienced TC practitioners participated. Ground reaction forces, joint moments and time-to-peak joint moment generation were analysed. Compared with walking, both TC movements generated significantly (1) smaller peak ground reaction forces in all directions, except the anterior; (2) larger hip extension, adduction and internal rotational moments, knee adduction/abduction and internal rotation moments and eversion/inversion and external/internal moments of ankle–foot; and (3) longer peak moment generation time for hip extension, adduction and internal rotation, knee extension and ankle dorsiflexion and inversion. The TC loading patterns are consistent with the mechanical behaviour of biological tissues, which could help to strengthen the lower extremities and prevent falls in the elderly.

Real-time three-dimensional digital image correlation for biomedical applications.

Digital image correlation (DIC) has been successfully applied for evaluating the mechanical behavior of biological tissues. A three-dimensional (3-D) DIC system has been developed and applied to examining the motion of bones in the human foot. To achieve accurate, real-time displacement measurements, an algorithm including matching between sequential images and image pairs has been developed. The system was used to monitor the movement of markers which were attached to a precisely motorized stage. The accuracy of the proposed technique for in-plane and out-of-plane measurements was found to be ?0.25% and 1.17%, respectively. Two biomedical applications were presented. In the experiment involving the foot arch, a human cadaver lower leg and foot specimen were subjected to vertical compressive loads up to 700 N at a rate of 10??N/s and the 3-D motions of bones in the foot were monitored in real time. In the experiment involving distal tibio fibular syndesmosis, a human cadaver lower leg and foot specimen were subjected to a monotonic rotational torque up to 5 Nm at a speed of 5 deg per min and the relative displacements of the tibia and fibula were monitored in real time. Results showed that the system could reach a frequency of up to 16 Hz with 6 points measured simultaneously. This technique sheds new lights on measuring 3-D motion of bones in biomechanical studies.

Mechanical characterization of biological tissues: Experimental methods based on mathematical modeling

To illustrate a systematic procedure for mechanical characterization or mechanical behavior of biological tissues with a semi-empirical method based on mathematical models. The method is composed of a series of procedures: construction of cell elements on the specimen, image processing, continuum mechanics, hyperelasticity and so on. An element used in the method, which is similar to finite element methods, is defined by placing markers on the specimen. The change of the locations of the element during a motion is monitored to calculate the displacement for stress estimation owing to external impacts or forces. The validity of the method for mechanical characterization or mechanical behavior of biological tissues is shown through material test simulations with mathematical models, resulting in good agreement overall. A general review of mathematical modeling of biological tissues is served and a semi-empirical method, which makes good use of both finite element methods and mathematical models based on the phenomenological modeling technique, is introduced to assess the stress-strain responses of biological tissues subjected mechanical loadings.

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function--a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Evolution of the three-dimensional collagen structure in vascular walls during deformation: an in situ mechanical testing under multiphoton microscopy observation

The collagen fibers' three-dimensional architecture has a strong influence on the mechanical behavior of biological tissues. To accurately model this behavior, it is necessary to get some knowledge about the structure of the collagen network. In the present paper, we focus on the in situ characterization of the collagenous structure, which is present in porcine jugular vein walls. An observation of the vessel wall is first proposed in an unloaded configuration. The vein is then put into a mechanical tensile testing device. As the vein is stretched, three-dimensional images of its collagenous structure are acquired using multiphoton microscopy. Orientation analyses are provided for the multiple images recorded during the mechanical test. From these analyses, the reorientation of the two families of collagen fibers existing in the vein wall is quantified. We noticed that the reorientation of the fibers stops as the tissue stiffness starts decreasing, corresponding to the onset of damage. Besides, no relevant evolutions of the out of plane collagen orientations were observed. Due to the applied loading, our analysis also allowed for linking the stress relaxation within the tissue to its internal collagenous structure. Finally, this analysis constitutes the first mechanical test performed under a multiphoton microscope with a continuous three-dimensional observation of the tissue structure all along the test. It allows for a quantitative evaluation of microstructural parameters combined with a measure of the global mechanical behavior. Such data are useful for the development of structural mechanical models for living tissues.

Feasibility of using mixtures of silicone elastomers and silicone oils to model the mechanical behaviour of biological tissues.

Mixtures of silicone elastomer and silicone oil were prepared and the values of their Young’s moduli, E, determined in compression. The mixtures had volume fractions, , of silicone oil in the range of 0–0.73. Measurements were made, under displacement control, for strain rates, , in the range of 0.04–3.85 s−1. The behaviour of as a function of and was investigated using a response surface model. The effects of the two variables were independent for the silicones used in this investigation. As a result, the dependence of E values (measured in MPa) on and (s−1) could be represented by . This means that these silicones can be mixed to give materials with E values in the range of about 0.02–0.57 MPa, which includes E values for many biological tissues. Thus, the mixtures can be used for making models for training health-care professionals and may be useful in some research applications as model tissues that do not exhibit biological variability.

Advanced modelling of the mechanical behaviour of biological tissues: application to 3D breast deformation

The purpose of this research was to focus on the study of the morphology of the female bust during the physical activity to improve comfort and aesthetics of bras. From a health point of view, it i...

Structural and mechanical multi-scale characterization of white New-Zealand rabbit Achilles tendon

Multi-scale characterization of structures and mechanical behavior of biological tissues are of huge importance in order to evaluate the quality of a biological tissue and/or to provide bio-inspired scaffold for functional tissue engineering. Indeed, the more information on main biological tissue structures we get, the more relevant we will be to design new functional prostheses for regenerative medicine or to accurately evaluate tissues. From this perspective, we have investigated the structures and their mechanical properties from nanoscopic to macroscopic scale of fresh ex-vivo white New-Zealand rabbit Achilles tendon using second harmonic generation (SHG) microscopy, atomic force microscopy (AFM) and tensile tests to provide a “simple” model whose parameters are relevant of its micro or nano structure. Thus, collagen fiber's crimping was identified then measured from SHG images as a plane sine wave with 28.4±5.8μm of amplitude and 141±41μm of wavelength. Young's moduli of fibrils (3.0GPa) and amorphous phases (223MPa) were obtained using TH-AFM. From these investigations, a non-linear Zener model linking a statistical Weibull's distribution of taut fibers under traction to crimp fibers were developed. This model showed that for small strain (<0.1), the amorphous inter-fibrils phase in collagen fibers is more solicited than collagen fibrils themselves. The results open the way to modeled macroscopic mechanical behavior of aligned-crimped collagen soft tissues using multi-scale tendon observations under static or dynamic solicitations.

Quasi-static and dynamic behaviour of the bone structures with fine geometric and materials modelling aspects

The principle aim of this study is to highlight the influence of velocity on mechanical responses of cortical bones. Quasi-static tests are performed on cubic samples from bovine femurs in order to highlight the anisotropic effect of cortical structure. Thanks to the Hopkinson bars technique, a set of curves will be obtained and analysed to define precisely mechanical behaviour of porosity and loading directions. Therefore, this technique combined with a precise geometrical measurement based on μCT technique is expected to provide a more accurate representation of the mechanical behaviour of biological tissues. This protocol will be applied on human tissues after validation of geometrical and material correlation in order to increase the biofidelity of human body models.

Stress distributions and material properties determined in articular cartilage from MRI-based finite strains

The noninvasive measurement of finite strains in biomaterials and tissues by magnetic resonance imaging (MRI) enables mathematical estimates of stress distributions and material properties. Such methods allow for non-contact and patient-specific modeling in a manner not possible with traditional mechanical testing or finite element techniques. Here, we employed three constitutive (i.e. linear Hookean, and nonlinear Neo-Hookean and Mooney–Rivlin) relations with known loading conditions and MRI-based finite strains to estimate stress patterns and material properties in the articular cartilage of tibiofemoral joints. Displacement-encoded MRI was used to determine two-dimensional finite strains in juvenile porcine joints, and an iterative technique estimated stress distributions and material properties with defined constitutive relations. Stress distributions were consistent across all relations, although the stress magnitudes varied. Material properties for femoral and tibial cartilage were found to be consistent with those reported in literature. Further, the stress estimates from Hookean and Neo-Hookean, but not Mooney-Rivlin, relations agreed with finite element-based simulations. A nonlinear Neo-Hookean relation provided the most appropriate model for the characterization of complex and spatially dependent stresses using two-dimensional MRI-based finite strain. These results demonstrate the feasibility of a new and computationally efficient technique incorporating MRI-based deformation with mathematical modeling to non-invasively evaluate the mechanical behavior of biological tissues and materials.