Method of testing very soft biological tissues in compression

Mechanical properties of very soft tissues, such as brain, liver, kidney and prostate have recently joined the mainstream research topics in biomechanics. This has happened in spite of the fact that these tissues do not bear mechanical loads. The interest in the biomechanics of very soft tissues has been motivated by the developments in computer-integrated and robot-aided surgery--in particular, the emergence of automatic surgical tools and robots-as well as advances in virtual reality techniques. Mechanical testing of very soft tissues provides a formidable challenge for an experimenter. Very soft tissues are usually tested in compression using an unconfined compression set-up, which requires ascertaining that friction between sample faces and stress-strain machine platens is close to zero. In this paper a more reliable method of testing is proposed. In the proposed method top and bottom faces of a cylindrical specimen with low aspect ratio are rigidly attached to the platens of the stress-strain machine (e.g. using surgical glue). This arrangement allows using a no-slip boundary condition in the analysis of the results. Even though the state of deformation in the sample cannot be treated as orthogonal the relationships between total change of height (measured) and strain are obtained. Two important results are derived: (i) deformed shape of a cylindrical sample subjected to uniaxial compression is independent on the form of constitutive law, (ii) vertical extension in the plane of symmetry lambda(z) is proportional to the total change of height for strains as large as 30%. The importance and relevance of these results to testing procedures in biomechanics are highlighted.     

A variational constitutive model for soft biological tissues

In this paper, a fully variational constitutive model of soft biological tissues is formulated in the finite strain regime. The model includes Ogden-type hyperelasticity, finite viscosity, deviatoric and volumetric plasticity, rate and microinertia effects. Variational updates are obtained via time discretization and pre-minimization of a suitable objective function with respect to internal variables. Genetic algorithms are used for model parameter identification due to their suitability for non-convex, high dimensional optimization problems. The material behavior predicted by the model is compared to available tests on swine and human brain tissue. The ability of the model to predict a wide range of experimentally observed behavior, including hysteresis, cyclic softening, rate effects, and plastic deformation is demonstrated.     

A triaxial-measurement shear-test device for soft biological tissues

A novel shear-test device for soft biological tissue, capable of applying simple shear deformations simultaneously in two orthogonal directions while measuring the resulting forces generated in three axes, is described. We validated the device using a synthetic gel, the properties of which were ascertained from independent tensile and rotational shear tests. Material parameters for the gel were fitted using neo-Hookean analytical solutions to the independent test data, and these matched the results from the device. Preliminary results obtained with rat septal myocardium are also presented to demonstrate the feasibility of the apparatus in determining the shear characteristics of living tissue.     

A finite nonlinear hyper-viscoelastic model for soft biological tissues

Soft tissues exhibit highly nonlinear rate and time-dependent stress-strain behaviour. Strain and strain rate dependencies are often modelled using a hyperelastic model and a discrete (standard linear solid) or continuous spectrum (quasi-linear) viscoelastic model, respectively. However, these models are unable to properly capture the materials characteristics because hyperelastic models are unsuited for time-dependent events, whereas the common viscoelastic models are insufficient for the nonlinear and finite strain viscoelastic tissue responses. The convolution integral based models can demonstrate a finite viscoelastic response; however, their derivations are not consistent with the laws of thermodynamics. The aim of this work was to develop a three-dimensional finite hyper-viscoelastic model for soft tissues using a thermodynamically consistent approach. In addition, a nonlinear function, dependent on strain and strain rate, was adopted to capture the nonlinear variation of viscosity during a loading process. To demonstrate the efficacy and versatility of this approach, the model was used to recreate the experimental results performed on different types of soft tissues. In all the cases, the simulation results were well matched ($R^2⩾0.99$) with the experimental data.     

Compression testing of very soft biological tissues using semi-confined configuration--a word of caution

We analyse semi-confined (i.e. using no-slip boundary conditions) compression experiment of very soft tissue sample using finite element method. We show that the assumption that the planes perpendicular to the direction of the applied force remain plane during the experiments is not satisfied for compression levels lower than previously stated in Miller [2005. Method for testing very soft biological tissues in compression. Journal of Biomechanics 38, 153-158]. Therefore, we recommend that the parameters for constitutive models of very soft tissues be determined by fitting a solution of the finite element models of the experimental set-up to the measurements obtained using semi-confined compression experiments.     

A model of fracture testing of soft viscoelastic tissues

Fracture, or tear, toughness of soft tissues can be computed from the work of fracture divided by the area of new crack surface. For soft tissues without significant plastic deformation, total work, which can be measured experimentally, is composed of the sum of fracture and viscoelastic work. In order to deduce fracture work, a method is needed to estimate viscoelastic work.Two different methods (Ph.D. Dissertation, University of Minnesota, 2000; J. Mater. Sci.: Mater. Med. 12 (2001) 327) have been proposed to estimate viscoelastic work in a fracture test of a soft tissue. The relative merits of these methods are unknown because the true viscoelastic work in an experiment is unknown. In order to characterize the accuracy of these methods, a theoretical model of crack propagation of viscoelastic soft tissue in a tensile test is presented, from which the exact viscoelastic work is calculated. The material is assumed to obey the standard linear solid model.The "exact" solution for the viscoelastic work during the fracture is computed from the model and compared with the work estimated by the two methods. It was found that both methods tend to underestimate the viscoelastic work done, and thus overestimate the fracture work and fracture toughness, although the errors were greater with the Fedewa method. It was further found that low displacement rates can give rise to a "snap" effect, where rapid crack growth can cause a disproportionate amount of viscoelastic energy to be dissipated during unloading. This modeling approach may be useful in evaluating other experimental methods of soft tissue fracture.     

Mechanical properties of soft biological tissues

Odd published data concerning the shear mechanical properties of some soft tissues in norm and pathology are reviewed.     

A strain-hardening bi-power law for the nonlinear behaviour of biological soft tissues

Biological soft tissues exhibit a strongly nonlinear viscoelastic behaviour. Among parenchymous tissues, kidney and liver remain less studied than brain, and a first goal of this study is to report additional material properties of kidney and liver tissues in oscillatory shear and constant shear rate tests. Results show that the liver tissue is more compliant but more strain hardening than kidney. A wealth of multi-parameter mathematical models has been proposed for describing the mechanical behaviour of soft tissues. A second purpose of this work is to develop a new constitutive law capable of predicting our experimental data in the both linear and nonlinear viscoelastic regime with as few parameters as possible. We propose a nonlinear strain-hardening fractional derivative model in which six parameters allow fitting the viscoelastic behaviour of kidney and liver tissues for strains ranging from 0.01 to 1 and strain rates from 0.0151 s^?1 to 0.7 s^?1.     

Non-ideal effects in indentation testing of soft tissues

Indentation has several advantages as a loading mode for determining constitutive behavior of soft, biological tissues. However, indentation induces a complex, spatially heterogeneous deformation field that creates analytical challenges for the calculation of constitutive parameters. As a result, investigators commonly assume small indentation depths and large sample thicknesses to simplify analysis and then restrict indentation depth and sample geometry to satisfy these assumptions. These restrictions limit experimental resolution in some fields, such as brain biomechanics. However, recent experimental evidence suggests that conventionally applied limits are in fact excessively conservative. We conducted a parametric study of indentation loading with various indenter geometries, surface interface conditions, sample compressibility, sample geometry and indentation depth to quantitatively describe the deviation from previous treatments that results from violation of the assumptions of small indentation depth and large sample thickness. We found that the classical solution was surprisingly robust to violation of the assumption of small strain but highly sensitive to violation of the assumption of large sample thickness, particularly if the indenter was cylindrical. The ramifications of these findings for design of indentation experiments are discussed and correction factors are presented to allow future investigators to account for these effects without recreating our finite element models.     

A plate holder for non-destructive testing of mesophase crystallization assays

Here, we describe a goniometer holder to mount standard 96-well crystallization plates directly onto the goniometer head of an oscillation camera. This attachment was designed to check crystallization conditions straight from the crystallization plates under X-rays, and was proven to be useful for checking small crystals and solutions that destabilize monoolein-based lipidic cubic phase (LCP) crystallization experiments. A quick procedure for setting up LCP assays employing commercially available instruments is also reported.     

Simple shear testing of parallel-fibered planar soft tissues

The simple shear test may provide unique information regarding the material response of parallel-fibered soft tissues because it allows the elimination of the dominant fiber material response from the overall stresses. However, inhomogeneities in the strain field due to clamping and free edge effects have not been documented. The finite element method was used to study finite simple shear of simulated ligament material parallel to the fiber direction. The effects of aspect ratio, clamping prestrain, and bulk modulus were assessed using a transversely isotropic, hyperelastic material model. For certain geometries, there was a central area of uniform strain. An aspect ratio of 1:2 for the fiber to cross-fiber directions provided the largest region of uniform strain. The deformation was nearly isochoric for all bulk moduli indicating this test may be useful for isolating solid viscoelasticity from interstitial flow effects. Results suggest this test can be used to characterize the matrix properties for the type of materials examined in this study, and that planar measurements will suffice to characterize the strain. The test configuration may be useful for the study of matrix, fiber-matrix, and fiber-fiber material response in other types of parallel-fibered transversely isotropic soft tissues.     

Towards an analytical model of soft biological tissues

In the past years, soft-tissue modelling research has seen substantial developments, a significant part of which can be ascribed to the refinement of numerical techniques, such as Finite Element analysis. A large class of physico-mechanical properties can be effectively simulated and predictions can be made for a variety of phenomena. However, there is still much that can be conceptually explored by means of fundamental theoretical analysis. In the past few years, driven by our interest in articular cartilage mechanics, we have developed theoretical microstructural models for linear elasticity and permeability that accounted for the presence and arrangement of collagen fibres in cartilage. In this paper, we investigate analytically the non-linear elasticity of soft tissues with collagen fibres arranged according to a given distribution of orientation, a problem that, aside from the case of fibres aligned in a finite number of distinct directions, has been treated exclusively numerically in the literature. We show that, for the case of a tissue with complex fibre arrangement, such as articular cartilage, the theoretical framework commonly used leads to an integral expression of the elastic strain energy potential. The present model is a first attempt in the development of a unified analytical microstructural model for non-linear elasticity and permeability of hydrated, fibre-reinforced soft tissues.     

Thermal expansion measurements of frozen biological tissues at cryogenic temperatures.

Thermal expansion data are essential for analyses of cryodestruction associated with thermal stresses during cryopreservation protocols as well as during cryosurgery. The present study tests a commonly used hypothesis that the thermal expansion of frozen tissues is similar to that of pure water ice crystals. This study further provides insight into the potential effect of the presence of cryoprotectants on thermal expansion. A new apparatus for thermal strain measurements of frozen biological tissues within a cryogenic temperature range is presented. Results are presented for fresh tissue samples taken from beef muscle, chicken muscle, rabbit muscle, rabbit bone, and pig liver. Pilot studies of the effect of cryoprotectants on thermal expansion are further presented for rabbit muscle immersed in dimethyl sulphoxide (2 mols/l) and glycerol (2 mols/l), and for pig liver perfused with dimethyl sulphoxide (2 mols/l). Thermal expansion of frozen soft biological tissues was found to be similar to that of water ice crystals in the absence of cryoprotectant. Thermal expansion of the rabbit bone was found to be about one half of that of frozen soft tissues. A significant reduction in the thermal expansion at higher temperatures was observed in the presence of cryoprotectants. A rapid change of thermal strain near -100 degrees C was also observed, which is likely to be associated with the glass transition process of the cryoprotectant solutions.     

A quasi-incompressible and quasi-inextensible finite element analysis of fibrous soft biological tissues

Biomechanics and Modeling in Mechanobiology - The contribution presents an extension and application of a recently proposed finite element formulation for quasi-inextensible and...