Hypoelastic soft tissues. Part I: Theory

Refinements are made to an existing hypoelastic theory developed by Freed [18, 19] for the purpose of modeling the passive response of soft, fibrous, biological tissues. Oldroyd’s [27] operators for convected differentiation and integration, which he derived from the tensor transformation law, are re-derived here from an integral equation defined in the polar configuration. Fields that obey these convected polar operators are said to be viable tensor fields, from which a new definition for strain and its rate are obtained and applied to a hypoelastic theory for tissue. Anisotropy is addressed through a material tensor, from which viable tensor fields describing fiber strain and strain rate are constructed. Material anisotropy and material constitution are handled separately for maximum flexibility. Isochoric hypoelastic models for isotropic, anisotropic, and fiber/matrix composite materials are derived. A material function is introduced to address special attributes that biological fibers impart on tissue behavior, four of which are proposed that represent various ways through which the fiber constituents might be described. Application to in-plane biaxial deformation is the focus of part II of this paper [23].     

Reversibility of electric-field-induced mechanical changes in soft tissues

Recently, ultrasound has been used to study the physiological-level electric-field-induced mechanical changes (EIMC) in general soft biological tissues. Here, we present the experimental results on the dependence of EIMC on the polarity of the applied electric field. We applied an ac voltage source to heart tissues and monitored the amplitude changes and time shifting of the ultrasound echoes. The shifting of the echoes was decomposed into a trend component and a fluctuation (feature) component. The changes in amplitude and the fluctuation component of the time shift, but not the trend component of the time shift, can be mostly reversed by reversing the polarity of the applied voltage. The polarity-dependence study reveals two different mechanisms underlying EIMC.     

Young's modulus measurements of soft tissues with application toelasticity imaging

Ultrasound elasticity imaging is a promising method that may eventually allow early detection of many tissue pathologies. However, before elasticity imaging can be applied to its numerous potential clinical applications, the quantitative accuracy of tissue elasticity measurements must be established. Simple 1-D ultrasound elasticity measurements were performed on muscle and liver and compared with independent and established mechanical measurements to investigate both the accuracy and consistency of ultrasound elasticity measurements. In addition, some interesting properties of soft tissue and aspects of the measurement process which should be considered in elasticity measurements are discussed     

Analysis of the Forming of Interlock Textile Composites Using a Hypoelastic Approach

Applied Composite Materials - Numerical simulation of the textile composites forming plays an important role in improving the manufacturing quality, reducing the manufacturing cycle, and...     

Passive elastography: shear-wave tomography from physiological-noise correlation in soft tissues

Inspired by seismic-noise correlation and time reversal, a shear-wave tomography of soft tissues using an ultrafast ultrasonic scanner is presented here. Free from the need for controlled shear-wave sources, this passive elastography is based on Green's function retrieval and takes advantage of the permanent physiological noise of the human body.     

Shear elasticity probe for soft tissues with 1-D transient elastography

Important tissue parameters such as elasticity can be deduced from the study of the propagation of low frequency shear waves. A new method for measuring the shear velocity in soft tissues is presented in this paper. Unlike conventional transient elastography in which the ultrasonic transducer and the low frequency vibrator are two separated parts, the new method relies on a probe that associates the vibrator and the transducer, which is built on the axis of the vibrator. This setup is easy to use. The low frequency shear wave is driven by the transducer itself that acts as a piston while it is used in pulse echo mode to acquire ultrasonic lines. The results obtained with the new method are in good agreement with those obtained with the conventional one.     

Absorption and attenuation in soft tissues. II. Experimental results

For pt.I see ibid., vol.35, no.2, p.242 (1988). To determine the relative contributions of ultrasonic loss mechanisms in tissues, independent measurements of total attenuation and local absorption were obtained at discrete frequencies within the range of medical diagnostic equipment, 1-13 MHz. Automation techniques were applied to aspects of experimentation where extensive averaging or curve fitting could be used to improve accuracy. Novel approaches were also implemented to calibrate focused beams for use in pulse-decay absorption measurements which covered a wider frequency range, utilizing smaller sample volumes than were previously practical. These approaches enable comparisons of the magnitude and frequency dependence of attenuation and absorption in biological media, and permit some inferences to be made as to the relative contribution of scattering to total attenuation. The results of studies on agar-gelatin phantoms, calf liver, and collagenous pig liver indicate that absorption comprises 90-100% of total attenuation in these materials. Studies on bovine brain matter and leg muscle are less definitive because complications include the inhomogeneous grey and white matter composition of brain, and fiber anisotropy in muscle. However, average results from these tissues also show a major contribution of absorption to attenuation.     

On the numerical treatment of initial strains in biological soft tissues

In this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress‐free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible ‘deformation gradient’ field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress‐free configuration, while in blood vessels the starting point is usually the load‐free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are presented to show the performance of the strategies and to quantify the errors appearing in each of them. Copyright © 2006 John Wiley & Sons, Ltd.     

A variational framework for fiber‐reinforced viscoelastic soft tissues

The mechanical properties of soft biological tissues vary depending on how the internal structure is organized. Classical examples of tissues are ligaments, tendons, skin, arteries, and annulus fibrous. The main element of such tissues is the fibers which are responsible for the tissue resistance and the main mechanical characteristic is their viscoelastic anisotropic behavior. The objective of this paper is to extend an existing model for isotropic viscoelastic materials in order to include anisotropy provided by fiber reinforcement. The incorporation of the fiber allows the mechanical behavior of these tissues to be simulated. The model is based on a variational framework in which its mechanical behavior is described by a free energy incremental potential whose local minimization provides the constraints for the internal variable updates for each load increment. The main advantage of this variational approach is the ability to represent different material models depending on the choice of suitable potential functions. Finally, the model is implemented in a finite‐element code in order to perform numerical tests to show the ability of the proposed model to represent fiber‐reinforced materials. The material parameters used in the tests were obtained through parameter identification using experimental data available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

An anisotropic discrete fiber model with dissipation for soft biological tissues

Nonlinear three-dimensional constitutive equations are developed for analyzing inelastic effects that cause dissipation in biological tissues. The model combines a structural icosahedral model of six discrete fiber bundles with a phenomenological model of the inelastic distortional deformations of the matrix containing the fibers. The inelastic response of the matrix is characterized by only three material parameters, which can be used to model both rate-independent and rate-dependent response with a smooth elastic-inelastic transition. Also, a robust, strongly objective scheme is discussed, which allows the model to be easily implemented into finite element computer codes. Examples show that the model predictions compare well with experimental data for the nonlinear, anisotropic, inelastic response of a number of tissues. Specifically, the model simulated the biaxial stretching of rabbit skin with an error of 15.7%, stress relaxation of rabbit skin with an error of 17.2%, simple shear of rat septal myocardium with an error of 21.6%, and uniaxial stress in compression of monkey liver with an error of 8.3%.     

Numerical algorithm for triphasic model of charged and hydrated soft tissues

 This paper devises an efficient numerical algorithm for solving a two-dimensional triphasic model of charged and hydrated soft tissue by using the radial basis functions. The proposed numerical method is applied directly as a simple meshless collocation algorithm to approximate the solution of the governing system of continuity, momentum, and constitutive equations for the triphasic model. Since there is no requirement on meshing, the method can easily be applied to solve problems under complicated geometry. For verification, numerical simulations of stress, strain, and fluid flow patterns for a plane strain and an axisymmetric mechano-electrochemical coupling model with real synovial joint are given respectively. Classical domain decomposition technique is also combined successfully with the proposed method for solving large scale problems with numerical verification given in solving the axisymmetric case. Received 20 November 2001 / Accepted 28 November 2001     

Hypoelastic,hyperelastic, discrete and semi-discrete approaches for textile composite reinforcement forming

The clear multi-scale structure of composite textile reinforcements leads to develop continuous and discrete approaches for their forming simulations. In this paper two continuous modelling respectively based on a hypoelastic and hyperelastic constitutive model are presented. A discrete approach is also considered in which each yarn is modelled by shell finite elements and where the contact with friction and possible sliding between the yarns are taken into account. Finally the semi-discrete approach is presented in which the shell finite element interpolation involves continuity of the displacement field but where the internal virtual work is obtained as the sum of tension, in-plane shear and bending ones of all the woven unit cells within the element. The advantages and drawbacks of the different approaches are discussed.     

Multiscale analysis of impact mitigation in soft tissues using nanotube reinforced composites

Kinetic energy of an inert projectile or its fragment can cause considerable damage to soft tissues and cause debilitating injuries or fatalities. The primary aim of threat mitigation due to kinetic energy dissipation is to provide adequate protection against projectiles or fragments in the form of body shields. Recently, novel nanocomposite materials reinforced with nanotubes are used as shields to protect the soft-tissues during impact. Soft tissues constitute an important part of human body performing various mechanical functions and a deep understanding of the behavior of soft tissue is required to characterize its response to external mechanical forces. Soft tissues are non-homogenous anisotropic materials, and their properties are dependent on the the physiological structure. In this paper, a multiscale homogenization-based analysis of the constituent properties of soft tissues and underlying endoskeleton are developed for impact mitigation using nanotube-reinforced composite shields.     

New possibilities of investigating blood flow in soft tissues of the mouth

It has been shown that the method of digital dynamic photography is an effective technique for quantitative and qualitative diagnosis of the microcirculatory state of mouth tissues. As a result of the signal processing, one can obtain information on microcirculation indices from the spectral distribution of low-frequency variations of the speckle structure. The investigated method of digital dynamic speckle photography can be used to elucidate the haemodynamic features in tissues of the oral cavity even at early stages of the disease and then at the examination and treatment stages. New possibilities of digital laser speckle technologies for tomographic investigations of the near-surface blood flow at various depths with the use of two-lens optical configurations are illustrated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 508–517, May–June, 2008.     

A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues

In this paper a generalized anisotropic hyperelastic constitutive model for fiber-reinforced materials is proposed. Collagen fiber alignment in biological tissues is taken into account by means of structural tensors, where orthotropic and transversely isotropic material symmetries appear as special cases. The model is capable to describe the anisotropic stress response of soft tissues at large strains and is applied for example to different types of arteries. The proposed strain energy function is polyconvex and coercive. This guarantees the existence of a global minimizer of the total elastic energy, which is important in the context of a boundary value problem.     

Permanent set and stress-softening constitutive equation applied to rubber-like materials and soft tissues

Many rubber-like materials present a phenomenon known as Mullins effect. It is characterized by a difference of behavior between the first and second loadings and by a permanent set after a first loading. Moreover, this phenomenon induces anisotropy in an initially isotropic material. A new constitutive equation is proposed in this paper. It relies on the decomposition of the macromolecular network into two parts: chains related together and chains related to fillers. The first part is modeled by a simple hyperelastic constitutive equation, whereas the second one is described by an evolution function introduced in the hyperelastic strain energy. It contributes to describe both the anisotropic stress softening and the permanent set. The model is finally extended to soft tissues’ mechanical behavior that present also stress softening but with an initially anisotropic behavior. The two models are successfully fitted and compared to experimental data.     

A mixed-penalty finite element formulation of the linear biphasic theory for soft tissues

Hydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed-penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six-node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six-node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six-node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed-penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.