Model Of Biological Tissue Research Articles

Development of In Vivo Constitutive Models for Liver: Application to Surgical Simulation

Advancements in real-time surgical simulation techniques have provided the ability to utilize more complex nonlinear constitutive models for biological tissues which result in increased haptic and graphic accuracy. When developing such a model, verification is necessary to determine the accuracy of the force response as well as the magnitude of tissue deformation for tool-tissue interactions. In this study, we present an experimental device which provides the ability to obtain force-displacement information as well as surface deformation of porcine liver for in vivo probing tasks. In addition, the system is capable of accurately determining the geometry of the liver specimen. These combined attributes provide the context required to simulate the experiment with accurate boundary conditions, whereby the only variable in the analysis is the material properties of the liver specimen. During the simulation, effects of settling due to gravity have been taken into account by a technique which incorporates the proper internal stress conditions in the model without altering the geometry. Initially, an Ogden model developed from ex vivo tension and compression experimentation is run through the simulation to determine the efficacy of utilizing an ex vivo model for simulation of in vivo probing tasks on porcine liver. Subsequently, a method for improving upon the ex vivo model was developed using different hyperelastic models such that increased accuracy could be achieved for the force characteristics compared to the displacement characteristics, since changes in the force variation would be more perceptible to a user in the simulation environment, while maintaining a high correlation with the surface displacement data. Furthermore, this study also presents the probing simulation which includes the capsule surrounding the liver.

On a micro‐sphere based remodelling formulation for orthotropic soft biological tissue

AbstractAn essential property of biological tissues in vivo is the ability to adapt according to respective loading conditions‐‐for example by changing its mass, shape, or internal structure, the latter for instance being associated with fibre reorientation and often denoted as remodelling. In this contribution, a three‐dimensional micro‐sphere‐based constitutive model for anisotropic soft biological tissue is presented, which includes these fibre‐reorientation‐related remodelling effects. As a key aspect, time‐dependent remodelling effects are incorporated by introducing evolution equations for the referential orientations of the integration directions, as present in the computational micro‐sphere approach. Based on this, a remodelling formulation for the orthotropic case with two mean fibre orientations will be presented. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Stochastic Visco-hyperelastic Model of Human Placenta Tissue for Finite Element Crash Simulations

Placental abruption is the most common cause of fetal deaths in motor-vehicle crashes, but studies on the mechanical properties of human placenta are rare. This study presents a new method of developing a stochastic visco-hyperelastic material model of human placenta tissue using a combination of uniaxial tensile testing, specimen-specific finite element (FE) modeling, and stochastic optimization techniques. In our previous study, uniaxial tensile tests of 21 placenta specimens have been performed using a strain rate of 12/s. In this study, additional uniaxial tensile tests were performed using strain rates of 1/s and 0.1/s on 25 placenta specimens. Response corridors for the three loading rates were developed based on the normalized data achieved by test reconstructions of each specimen using specimen-specific FE models. Material parameters of a visco-hyperelastic model and their associated standard deviations were tuned to match both the means and standard deviations of all three response corridors using a stochastic optimization method. The results show a very good agreement between the tested and simulated response corridors, indicating that stochastic analysis can improve estimation of variability in material model parameters. The proposed method can be applied to develop stochastic material models of other biological soft tissues.

Modeling Bioheat Transport at Macroscale

Macroscale thermal models have been developed for biological tissues either by the mixture theory of continuum mechanics or by the porous-media theory. The former uses scaling-down from the global scale; the latter applies scaling-up from the microscale by the volume averaging. The used constitutive relations for heat flux density vector include the Fourier law, the Cattaneo–Vernotte (Cattaneo, C., 1958, “A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation,” Compt. Rend., 247, pp. 431–433; Vernotte, P., 1958, “Les Paradoxes de la Théorie Continue de I’equation de la Chaleur,” Compt. Rend., 246, pp. 3154–3155) theory, and the dual-phase-lagging theory. The developed models contain, for example, the Pennes (1948, “Analysis of Tissue and Arterial Blood Temperature in the Resting Human Forearm,” J. Appl. Physiol., 1, pp. 93–122), Wulff (1974, “The Energy Conservation Equation for Living Tissues,” IEEE Trans. Biomed. Eng., BME-21, pp. 494–495), Klinger (1974, “Heat Transfer in Perfused Tissue I: General Theory,” Bull. Math. Biol., 36, pp. 403–415), and Chen and Holmes (1980, “Microvascular Contributions in Tissue Heat Transfer,” Ann. N.Y. Acad. Sci., 335, pp. 137–150), thermal wave bioheat, dual-phase-lagging (DPL) bioheat, two-energy-equations, blood DPL bioheat, and tissue DPL bioheat models. We analyze the methodologies involved in these two approaches, the used constitutive theories for heat flux density vector and the developed models. The analysis shows the simplicity of the mixture theory approach and the powerful capacity of the porous-media approach for effectively developing accurate macroscale thermal models for biological tissues. Future research is in great demand to materialize the promising potential of the porous-media approach by developing a rigorous closure theory. The heterogeneous and nonisotropic nature of biological tissue yields normally a strong noninstantaneous response between heat flux and temperature gradient in nonequilibrium heat transport. Both blood and tissue macroscale temperatures satisfy the DPL-type energy equations with the same values of the phase lags of heat flux and temperature gradient that can be computed in terms of blood and tissue properties, blood-tissue interfacial convective heat transfer coefficient, and blood perfusion rate. The blood-tissue interaction leads to very sophisticated effect of the interfacial convective heat transfer, the blood velocity, the perfusion, and the metabolic reaction on blood and tissue macroscale temperature fields such as the spreading of tissue metabolic heating effect into the blood DPL bioheat equation and the appearance of the convection term in the tissue DPL bioheat equation due to the blood velocity.

From kinetic models of multicellular growing systems to macroscopic biological tissue models

This paper deals with the derivation of macroscopic equations of biological tissues for a class of nonlinear equations, with quadratic type nonlinearity, modeling complex multicellular systems. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis refers to the derivation of hyperbolic models focused on the influence of existence of a global equilibrium solution. The asymptotic analysis shows how the macroscopic tissue behavior can be described from the underlying cellular description and that this specific biological state modifies the structure of the models obtained by different assumptions. The approach is proposed as an alternative to the phenomenological of continuum mechanics for growing tissues.

Spatial quantification and classification of skin response following perturbation using organotypic skin cultures

For a mechanistic understanding of skin and its response to an induced perturbation, systems biology is gaining increasing attention. Unfortunately, quantitative and spatial expression data for skin, like for most other tissues, are almost not available. Integrating organotypic skin cultures, whole-slide scanning and subsequent image processing provides bioinformatics with a novel source of spatial expression data. We here used this approach to quantitatively describe the effect of treating organotypic skin cultures with sodium dodecyl sulphate in a non-corrosive concentration. We first measured the differentiation-related spatial expression gradient of Heat-Shock-Protein 27 in a time series of up to 24 h. Secondly, a multi-dimensional tissue classifier for predicting skin irritation was developed based on abstract features of these profiles. We obtained a high specificity of 0.94 and a sensitivity of 0.92 compared with manual classification. Our results demonstrate that the integration of tissue cultures, whole-slide scanning and image processing is well suited for both the standardized data acquisition for systems biological tissue models and a highly robust classification of tissue responses.

Simple two-layer reflectance model for biological tissue applications: lower absorbing layer

A simple two-layer tissue reflectance model is described. This work is a continuation of our investigations on modeling reflectance from two-layered tissues that we recently initiated. In the present article, we describe a variation of a two-layer model that assumes a lower absorbing and scattering layer and an upper scattering-only layer. This two-layer configuration is a realistic model for biological tissues in the visible and near-IR spectral ranges, where the upper layer may be an epithelial layer and the lower layer is a vascularized stroma layer. Application of the model yields estimates for tissue parameters, such as the thickness of the upper layer or the absorption properties of the lower layer. These parameters are of great interest for the noninvasive study of a wide range of epithelial biological tissues. The validity range and accuracy of the model are tested on tissue phantoms in both the forward and inverse modes of application.

Third- and fourth-order elasticities of biological soft tissues

In the theory of weakly nonlinear elasticity, Hamilton et al. [J. Acoust. Soc. Am. 116, 41-44 (2004)] identified W=muI(2)+(A/3)I(3)+DI(2) (2) as the fourth-order expansion of the strain-energy density for incompressible isotropic solids. Subsequently, much effort focused on theoretical and experimental developments linked to this expression in order to inform the modeling of gels and soft biological tissues. However, while many soft tissues can be treated as incompressible, they are not in general isotropic, and their anisotropy is associated with the presence of oriented collagen fiber bundles. Here the expansion of W is carried up to fourth order in the case where there exists one family of parallel fibers in the tissue. The results are then applied to acoustoelasticity, with a view to determining the second- and third-order nonlinear constants by employing small-amplitude transverse waves propagating in a deformed soft tissue.

A closed form solution for the uniaxial tension test of biological soft tissues

This paper concerns the modeling of biological soft tissues in the framework of anisotropic hyperelasticity. A closed form solution is proposed in the special case where uniaxial unconstrained tension loading is applied to a strip modeled by Holzapfel–Gasser–Ogden's (HGO) strain energy. The classical Cardano's formula is used to calculate the solution. This solution is investigated for different values of β which represents the angle between the collagen fibers and the circumferential direction. This study allows for the understanding of the reason why a one-to-one correspondence does not exist between the principal stretch and the fourth invariant of the right Cauchy–Green deformation tensor. It is demonstrated that the relationship becomes non-bijective when β is greater than a critical angle of 54 . 73 ∘ . The HGO model is implemented into an in-house finite element program and numerical results are in good agreement with theoretical ones.

A study of heat distribution in human skin: use of Infrared Thermography

One of the long-term objectives of this study is to be able to act quickly on body burns, to avoid propagating lesions due to heat diffusion. An experimental and numerical study is presented to better understand the thermomechanical behavior of the skin and its direct environment when exposed to strong thermal variations. The experimental step, suggested in this article, consists in placing a cooled cylindrical steel bar on the skin of a human forearm and measuring the temperature change using an infra-red camera. Blood circulation in the veins was seen to clearly influence of the heat diffusion. These experimental measurements provide a numerical model of the skin and its direct vicinity. This two-dimensional multi-layer model uses the Pennes equation to model biological tissue and the equation of heat in a fluid, to model blood. The properties of materials from the literature are validated by experimentation. The numerical model is able to simulate the experimental observations, but also to estimate blood speed in the veins.

980‐nm Laser‐Driven Photovoltaic Cells Based on Rare‐Earth Up‐Converting Phosphors for Biomedical Applications

AbstractA prerequisite for designing and constructing wireless biological nanorobots is to obtain an electrical source that is continuously available in the operational biological environment. Herein the first preparation of 980‐nm laser‐driven photovoltaic cells (980LD‐PVCs) by introducing of a film of rare‐earth up‐converting nanophosphors in conventional dye‐sensitized solar cells is reported. Under the irradiation of a 980‐nm laser with a power of 1 W, the visible up‐converting luminescence of rare‐earth nanophosphors can be efficiently absorbed by the dyes in 980LD‐PVCs so that they exhibit a maximal output power of 0.47 mW. In particular, after being covered with 1 to 6 layers of pig intestines (thickness: ca. 1 mm per layer) as a model of biological tissues, 980LD‐PVCs still possess a maximal output power of between 0.28 and 0.02 mW, which is efficient enough to drive many kinds of biodevices. This research opens up the possibility of preparing and/or developing novel electrical sources for wireless biological nanorobots and many other biodevices.

An anisotropic viscoelastic model for collagenous soft tissues at large strains – Computational aspects

AbstractThis paper focusses on computational aspects related to a recently proposed anisotropic viscoelastic model for soft biological tissues at large strains [1]. A key aspect of this model is the generalisation of micromechanically motivated one‐dimensional constitutive equations to three dimensions by numerical integration over the unit sphere. A strong effect of this procedure on the accuracy and in particular on the material symmetry of the model is observed. Finally a finite element example of an artery subject to normotensive blood pressure is presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental investigation of ovine intervertebral disc units in longitudinal loading

AbstractThe assessment of the predictive power of material models for soft biological tissues is an important issue when it comes to realistic simulations for medical applications. The determination of the model parameters needs sound experimental data. In our case we want to test the viscoelastic properties of ovine lumbar intervertebral discs (IVD's) in longitudinal loading. The complex geometry as well as the small imposed displacements combined with rather high forces are to be treated. The two vertebrae adjacent to the IVD are mounted using custom made clampings where attention is paid not to prestress the tissue. First tests were done with steel springs in order to check the suitability of the used materials testing machine. No significant compliance of the machine could be detected but a negative hysteresis that might origin from the data acquisition process. Experiments on IVD's gave us an in‐depth insight into the underlying mechanics such that we can now define appropriate protocols for future experiments. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

FDTD Modeling of Biological Tissues Cole–Cole Dispersion for 0.5–30 GHz Using Relaxation Time Distribution Samples—Novel and Improved Implementations

In this paper, novel finite-difference time-domain implementations of the Cole-Cole dispersion model for biological tissues, from 0.5 to 30 GHz, based on the sampling of the distribution of relaxation time, and the convolution integral formulation, are provided and verified. Moreover, shortcomings of the original relaxation time sampling implementation, with polarization formulation, were identified, and the improved polarization implementation is provided as well. These implementations are compared with the implementation utilizing the fractional derivative formulation. All compared implementations require storing the electric field and some related auxiliary quantities for only the previous time step. It is observed that, for a single-term Cole-Cole relation, relaxation time sampling implementations can provide accuracy, storage requirement, and simulation time comparable to the ones for the fractional derivative implementation. However, the latter does not exist for the more general multiterm Cole-Cole dispersion relation, for which the implementations based on the relaxation time sampling could be easily extended to.

Poroviscoelastic Two-Dimensional Anisotropic Solution with Application to Articular Cartilage Testing

The transverse anisotropic poromechanics solution for the two-dimensional Mandel-type problem geometry is extended in this paper to account for the orthotropic nature of the porous media, thus mimicking the response of articular cartilage samples when subjected to load perturbation. The anisotropic solution presented takes into account the viscoelastic and anisotropic nature of the fluid-saturated cartilage specimen sandwiched between two impermeable rigid plates and subjected to quasi-static step loading conditions; thus simulating the unconfined compressive test responses of cartilage samples in biomechanics laboratory setups. The solution addresses the stress, fluid pressure, and displacement results due to load application through exact modeling of the intrinsic nature of the orthotropic viscoelastic matrix structure as well as the compressible interstitial fluid flow responses. Poromechanical parameter characterization and modeling of biological tissues, such as cartilage, will find this analytical solution to the two-dimensional anisotropic poroviscoelastic geometry very useful. This problem will not only serve as a benchmark for validating numerical schemes and simulations but also assist in calibrating laboratory results on biological tissues, including cyclic loadings.

Microstructure based two-scale modelling of soft tissues

A technique suitable for the modelling of large deforming biological tissues with a nearly periodic microstructure is presented in this work. The proposed approach takes into account the heterogeneous material constitution and geometrical arrangement of the tissues at the microstructural level. The global material properties are described in terms of the homogenized (effective) parameters. Numerical simulations are focused on the mechanical behaviour of an arterial wall.

On the use of non‐linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals. Application to the stress analysis in fibred soft tissues

AbstractMicrosphere‐based constitutive models are a helpful tool in the modelling of materials with a micro‐structure composed of contributing elements directionally arranged. This is the case, for instance, for fibred soft tissues. In these models, the macroscopic mechanical behaviour is obtained from the integration of the micro‐structural contribution of each component (e.g. each fibre) over the surface of an underlying microsphere, which allows incorporating the mechanical features of the micro‐constituents to the macroscopic response. The combination of this sort of models and the associated numerical techniques constitutes a powerful modelling tool for which an efficient integration scheme is required. In this regard, the unit sphere discretizations proposed by Bažant and Oh (ZAMM—J Appl Math Mech Z Angew Math Mech 1986; 66(1):37–49) have been used for the integration of the microscopic contributions in isotropic materials. Nevertheless, the inclusion of anisotropy has important implications with regard to the integration scheme, since very fine discretizations are needed to perform the integration accurately, causing the integration process to be very costly. In addition, the storage of internal variables at each integration direction of every integration point is required for constitutive models based on the use of internal variables at the micro‐structural level, which renders this approach rather complex and memory demanding. In order to reduce the number of necessary integration directions, several non‐linear transformations for the integration of rotationally symmetric functions over the surface of the unit sphere are here presented. Their accuracy in the integration of the von Mises orientation distribution function is evaluated. Furthermore, a hyperelastic microsphere‐based constitutive law for the modelling of soft biological tissues is used in order to check the accuracy and computational efficiency of the proposed transformations within a Finite Element context in inhomogeneous deformation problems. Simulation results show the suitability of the proposed methodology in order to accurately approximate the value of the integrals within reasonable computational costs. Copyright © 2009 John Wiley & Sons, Ltd.

Analytical thermal-optic model for laser heating of biological tissue using the hyperbolic heat transfer equation

In this paper, we solve in an analytical way the thermal-optic coupled problem associated with a 1D model of non-perfused homogeneous biological tissue irradiated by a laser beam. We consider a laser pulse duration of 200 micros and study the temperatures of areas very close to the point of laser beam application. We consider that these values of the temporal and spatial variables mean that the problem has to be solved by means of the hyperbolic heat conduction model instead of the classic or parabolic model. We therefore obtain the solution using both models and apply the temperature profiles obtained to a specific biological tissue for comparison. Finally, we theoretically study the effect of the thermal relaxation time on the temperature profiles in the tissue for both heating and cooling phases (i.e. during and after laser application).

Model for light scattering in biological tissue and cells based on random rough nonspherical particles

A random nonspherical model for biological tissue and cells permits a better description of their optical properties. Rough surface nonspherical particles have been employed to model biological tissue and cells. The phase function, the anisotropy factor of scattering, and the reduced scattering coefficient are derived. The effect of different size distributions is also discussed. The theoretical results show good agreement with experimental data.

On a class of non-dissipative materials that are not hyperelastic

The purpose of this brief note is to develop fully Eulerian, implicit constitutive equations for the mechanical response of a class of materials that do not dissipate mechanical work in any process. We show that such materials can be modelled by obtaining a form for the Helmholtz potential as a function of the current mass density, the Cauchy stress and certain other parameters that capture anisotropic response. The resulting constitutive equations are of the form , where and are functions of the state variables of the system. The class of materials that can be obtained from such a constitutive relation is considerably more general than conventional Green-elastic hyperelastic materials. Such response functions may be suitable for the modelling of biological tissue where, due to the constant remodelling that takes place, there may be no physical meaning to a ‘reference configuration’.