Mechanical Behavior Of Soft Tissues Research Articles

Efficient soft tissue characterization under large deformations in medical simulations

The modeling of soft tissue behavior is essential for virtual reality (VR)-based medical simulation, providing a safe and objective medium for training of the medical personnel. This paper presents a soft tissue modeling framework including instrumentation design, in vitro organ experiments and material property characterization. As observed from the force responses measured by a force transducer, the tissue was assumed as a nonlinear, continuous, incompressible, homogeneous and isotropic material for modeling. An electromechanical indentation system to measure the mechanical behavior of soft tissues was designed, and a series harvested organ in vitro experiments were performed. The non-linear soft tissue model parameters were then extracted by matching finite element model predictions with the empirical data. The soft tissue characterization algorithm could become computationally efficient by reducing the number of parameters. The developed tissue models are suitable for computing accurate reaction forces on surgical instruments and for computing deformations of organ surfaces for the VR based medical simulation.

Scale‐dependent fiber kinematics of elastomeric electrospun scaffolds for soft tissue engineering

Electrospun poly(ester urethane)urea (PEUU) scaffolds contain complex multiscale hierarchical structures that work simultaneously to produce unique macrolevel mechanical behaviors. In this study, we focused on quantifying key multiscale scaffold structural features to elucidate the mechanisms by which these scaffolds function to emulate native tissue tensile behavior. Fiber alignment was modulated via increasing rotational velocity of the collecting mandrel, and the resultant specimens were imaged using SEM under controlled biaxial strain. From the SEM images, fiber splay, tortuosity, and diameter were quantified in the unstrained and deformed configurations. Results indicated that not only fiber alignment increased with mandrel velocity but also, paradoxically, tortuosity increased concurrently with mandrel velocity and was highly correlated with fiber orientation. At microlevel scales (1-10 mum), local scaffold deformation behavior was observed to be highly heterogeneous, while increasing the scale resulted in an increasingly homogenous strain field. From our comprehensive measurements, we determined that the transition scale from heterogenous to homogeneous-like behavior to be approximately 1 mm. Moreover, while electrospun PEUU scaffolds exhibit complex deformations at the microscale, the larger scale structural features of the fibrous network allow them to behave as long-fiber composites that deform in an affine-like manner. This study underscores the importance of understanding the structure-function relationships in elastomeric fibrous scaffolds, and in particular allowed us to link microscale deformations with mechanisms that allow them to successfully simulate soft tissue mechanical behavior.

Patient-specific finite element model of the hip muscles and bones

Hip fractures are largely considered as a major health-care problem. Several patientspecific finite element models of the isolated femur are proposed to evaluate fracture risk. However, because of their role in femur stress distribution, soft tissue covering the hip should also be considered. Such modeling is particularly complex and major difficulties are related to volumic muscle mesh generation, to specific muscles constitutive equations and numerous contacts within the structure. A method was based on deformation of a parameterized muscle mesh was proposed to get rapidly a patient-specific non distorted mesh. Based in this mesh, finite element model included bones and soft tissues, with surface contact elements between components. Hyperelastic constitutive equations, with hypothesis of incompressibility and isotropy were used to model soft tissue mechanical behavior. Preliminary simulation with quasistatic lateral compression was performed to verify the coherence of the model’s response.

A closed-form structural model of planar fibrous tissue mechanics

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress–strain law.

Patient-specific finite element model of the hip muscles and bones

Hip fractures are largely considered as a major health-care problem. Several patientspecific finite element models of the isolated femur are proposed to evaluate fracture risk. However, because of their role in femur stress distribution, soft tissue covering the hip should also be considered. Such modeling is particularly complex and major difficulties are related to volumic muscle mesh generation, to specific muscles constitutive equations and numerous contacts within the structure. A method was based on deformation of a parameterized muscle mesh was proposed to get rapidly a patient-specific non distorted mesh. Based in this mesh, finite element model included bones and soft tissues, with surface contact elements between components. Hyperelastic constitutive equations, with hypothesis of incompressibility and isotropy were used to model soft tissue mechanical behavior. Preliminary simulation with quasistatic lateral compression was performed to verify the coherence of the model’s response.

A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Dynamic finite element modeling of poroviscoelastic soft tissue

Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-β method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects.

Effects of Boundary Conditions on the Estimation of the Planar Biaxial Mechanical Properties of Soft Tissues

Evaluation and simulation of the multiaxial mechanical behavior of native and engineered soft tissues is becoming more prevalent. In spite of this growing use, testing methods have not been standardized and methodologies vary widely. The strong influence of boundary conditions were recently underscored by Waldman et al. [2002, J. Materials Science: Materials in Medicine 13, pp. 933-938] wherein substantially different experimental results were obtained using different sample gripping methods on the same specimens. As it is not possible to experimentally evaluate the effects of different biaxial test boundary conditions on specimen internal stress distributions, we conducted numerical simulations to explore these effects. A nonlinear Fung-elastic constitutive model (Sun et al., 2003, JBME 125, pp. 372-380, which fully incorporated the effects of in-plane shear, was used to simulate soft tissue mechanical behavior. Effects of boundary conditions, including varying the number of suture attachments, different gripping methods, specimen shapes, and material axes orientations were examined. Results demonstrated strong boundary effects with the clamped methods, while suture attachment methods demonstrated minimal boundary effects. Suture-based methods appeared to be best suited for biaxial mechanical tests of biological materials. Moreover, the simulations demonstrated that Saint-Venant's effects depended significantly on the material axes orientation. While not exhaustive, these comprehensive simulations provide experimentalists with additional insight into the stress-strain fields associated with different biaxial testing boundary conditions, and may be used as a rational basis for the design of biaxial testing experiments.

Modelling liver tissue properties using a non-linear visco-elastic model for surgery simulation

In this work, we introduce an extension of the linear elastic tensor–mass method allowing fast computation of non-linear and visco-elastic mechanical forces and deformations for the simulation of biological soft tissue. We aim at developing a simulation tool for the planning of cryogenic surgical treatment of liver cancer. Percutaneous surgery simulation requires accurate modelling of the mechanical behaviour of soft tissue, and previous experimental characterizations have shown that linear elasticity is only a coarse approximation of the real properties of biological tissues. We first show that our model can simulate different types of non-linear and visco-elastic mechanical behaviours at speeds which are compatible with real-time applications. Then an experimental setup is presented which was used to characterize the mechanical properties of deer liver tissue under perforation by a biopsy needle. Experimental results demonstrate that a linear model is not suitable for simulating this application, while the proposed model succeeds in accurately modelling the axial load measured on the needle.

A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue.

The mechanical behavior of soft tissue demonstrates a number of complex features including nonlinearity, anisotropy, viscoelasticity, and growth. Characteristic features of the time-dependent and anisotropic behavior are related to the properties of various components of the tissue such as fibrous collagen and elastin networks, large proteins and sugars attached to these networks, and interstitial fluid. Attempts to model the elastic behavior of these tissues based on assumptions about the behavior of the underlying constituents have been reasonably successful, but the essential addition of viscoelasticity to these models has been met with varying success. Here, a new rheological network model is proposed using, as its basis, an orthotropic hyperelastic constitutive model for fibrous tissue and a viscoelastic reptation model for soft materials. The resulting model has been incorporated into numerical and computational models, and is shown to capture the mechanical behavior of soft tissue in various modes of deformation including uniaxial and biaxial tension and simple shear.

Total Hourglass Control - A Robust Finite Element Formulation for the Calculation of Organ Deformations

For use in a virtual reality based laparoscopic surgery simulator methods have been developed to model the mechanical behavior of soft tissue. Explicit Finite Element analysis turned out to be a robust basis when the approximation of hyperelastic materials is used. To reduce calculation times reduced volume integration schemes were applied, where classical hourglass control leads to drastic errors which make a simulation expanding over a long period of time impossible. Therefore, the total hourglass control scheme was developed and is presented here for several material laws. This new formulation takes the existence of the elastic potential of a hyperelastic material into account and leads to robust simulations without loss of accuracy. This is demonstrated with the off-line simulation of a model of an uterus and its adnexe.

Mechanical modeling of soft biological tissues for application in virtual reality based laparoscopy simulators

For application in a Virtual Reality (VR) based laparoscopic surgery simulator, computationally efficient algorithms for the description of the mechanical behavior of soft tissue have been developed. The explicit Finite Element Method has turned out to be a robust method for this purpose provided that absolute strain formulations are applied. Furthermore, a VR model of a uterus and its adnexe has been generated and simulation results are presented.

A recruitment-based rheological model for mechanical behavior of soft tissues

When lung tissue is subjected to finite deformations, phenomena appear that can only be described using nonlinear models. This paper considers the lung as a material composed of two elements, a continuous phase that acts uninterruptedly and a second phase composed of fiber elements that are recruited progressively into the mechanical process. Each individual fiber participates in the mechanical response of the set only when the deformation is above a certain value. A nine-parameter model was designed adopting standard viscoelastic elements both for the matrix and for each of the fibers. The mechanical behavior of the lung can be reproduced by a fitting process with standard numerical procedures in both dynamic-mechanical measurements and stress relaxation processes. Mechanical stress relaxation tests and dynamic-mechanical measurements have been carried out on subpleural parenchymal strips from rat lung. The model permits the reproduction of lung behavior in both types of measurements. The results show a recruitment ratio that decreases with deformation and the nonparticipation of the parallel matrix fraction in the lung's mechanical response so that a uniaxial transmission of force in the lung occurs via the recruited elements and the matrix series.

A new constitutive formulation for characterizing the mechanical behavior of soft tissues

We present a new constitutive formulation that combines certain desirable features of two previously used approaches (phenomenological and microstructural). Specifically, we assume that certain soft tissues can be idealized as composed of various families of noninteracting fibers and a homogeneous matrix. Both the fibers and the matrix are assumed to follow the gross deformation. Within the usual framework of pseudoelasticity, incompressibility, homogeneity, and the continuum hypothesis, a pseudostrain-energy function (W) is proposed wherein W is expressed in terms of matrix and fibrous contributions. Unlike phenomenological approaches where a W is usually chosen in an ad hoc manner, the present approach can be used to postulate reasonable forms of W based on limited structural information and multiaxial stress-strain data. Illustrative applications of the theory are discussed for visceral pleura and myocardium. Concise structurally motivated constitutive relations result, wherein load-dependent anisotropy, nonlinear material behavior, finite deformations, and incompressibility are accounted for.

A constitutive model for the mechanical behaviour of soft connective tissues

A model of the mechanical behaviour of soft connective tissue has been developed by considering the role of the collagen and glycosaminoglycan (GAG) components within the tissue in order to examine the mechanism by which a variation in the GAG components may exert a control over the mechanical properties of the tissue. It is proposed that the strain energy stored within the collagen fibrils of the loaded tissue can be transferred into a potential field created by the charged GAG components and their electrostatic interaction with the collagen fibrils. A fundamental mechanical unit is described to simulate this energy transfer and a combination of such units is used to represent the tissue. The computer implementation of the proposed tissue model shows it to reproduce many features which have been recognised in the rate dependent mechanical behaviour of soft tissues. These include the characteristic non-linearity of the force-deformation behaviour and the approximate invariance of the stress relaxation behaviour with deformation. The model is also consistent with earlier constitutive representations of tissue behaviour.