A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

Characterization and assessment of hyperelastic and elastic properties of decellularized human adipose tissues

Decellularized adipose tissue (DAT) has shown potential as a regenerative scaffold for plastic and reconstructive surgery to augment or replace damaged or missing adipose tissue (e.g. following lumpectomy or mastectomy). The mechanical properties of soft tissue substitutes are of paramount importance in restoring the natural shape and appearance of the affected tissues, and mechanical mismatching can lead to unpredictable scar tissue formation and poor implant integration. The goal of this work was to assess the linear elastic and hyperelastic properties of decellularized human adipose tissue and compare them to those of normal breast adipose tissue. To assess the influence of the adipose depot source on the mechanical properties of the resultant decellularized scaffolds, we performed indentation tests on DAT samples sourced from adipose tissue isolated from the breast, subcutaneous abdominal region, omentum, pericardial depot and thymic remnant, and their corresponding force–displacement data were acquired. Elastic and hyperelastic parameters were estimated using inverse finite element algorithms. Subsequently, a simulation was conducted in which the estimated hyperelastic parameters were tested in a real human breast model under gravity loading in order to assess the suitability of the scaffolds for implantation. Results of these tests showed that in the human breast, the DAT would show similar deformability to that of native normal tissue. Using the measured hyperelastic parameters, we were able to assess whether DAT derived from different depots exhibited different intrinsic nonlinearities. Results showed that DAT sourced from varying regions of the body exhibited little intrinsic nonlinearity, with no statistically significant differences between the groups.     

Spherical indentation of soft matter beyond the Hertzian regime: numerical and experimental validation of hyperelastic models

The lack of practicable nonlinear elastic contact models frequently compels the inappropriate use of Hertzian models in analyzing indentation data and likely contributes to inconsistencies associated with the results of biological atomic force microscopy measurements. We derived and validated with the aid of the finite element method force-indentation relations based on a number of hyperelastic strain energy functions. The models were applied to existing data from indentation, using microspheres as indenters, of synthetic rubber-like gels, native mouse cartilage tissue, and engineered cartilage. For the biological tissues, the Fung and single-term Ogden models achieved the best fits of the data while all tested hyperelastic models produced good fits for the synthetic gels. The Hertz model proved to be acceptable for the synthetic gels at small deformations (strain < 0.05 for the samples tested), but not for the biological tissues. Although this finding supports the generally accepted view that many soft materials can be assumed to be linear elastic at small deformations, the nonlinear models facilitate analysis of intrinsically nonlinear tissues and large-strain indentation behavior.     

Stress-modulated collagen fiber remodeling in a human carotid bifurcation

This work concerns with the implementation of a new stress-driven remodeling model for simulating the overall structure and mechanical behavior of a human carotid bifurcation. By means of an iterative finite element based procedure collagen fiber direction and maximal principal stresses are computed. We find that the predicted fibers' architecture at the cylindrical branches and at the apex of the bifurcation correlates well with histological observations. Some insights about the mechanical response of the sinus bulb and the bifurcation apex are revealed and discussed. The results are compared with other, isotropic and orthotropic, models available in the literature.     

MRI-based experimentations of fingertip flat compression: Geometrical measurements and finite element inverse simulations to investigate material property parameters

Modeling human-object interactions is a necessary step in the ergonomic assessment of products. Fingertip finite element models can help investigating these interactions, if they are built based on realistic geometrical data and material properties. The aim of this study was to investigate the fingertip geometry and its mechanical response under compression, and to identify the parameters of a hyperelastic material property associated to the fingertip soft tissues.Fingertip compression tests in an MRI device were performed on 5 subjects at either 2 or 4 N and at 15° or 50°. The MRI images allowed to document both the internal and external fingertip dimensions and to build 5 subject-specific finite element models. Simulations reproducing the fingertip compression tests were run to obtain the material property parameters of the soft tissues.Results indicated that two ellipses in the sagittal and longitudinal plane could describe the external fingertip geometry. The internal geometries indicated an averaged maximal thickness of soft tissues of 6.4 ± 0.8 mm and a 4 ± 1 mm height for the phalanx bone. The averaged deflections under loading went from 1.8 ± 0.3 mm at 2 N, 50° to 3.1 ± 0.2 mm at 4 N, 15°. Finally, the following set of parameters for a second order hyperelastic law to model the fingertip soft tissues was proposed: C₀₁ = 0.59 ± 0.09 kPa and C₂₀ = 2.65 ± 0.88 kPa.These data should facilitate further efforts on fingertip finite element modeling.     

Structural effects of an innovative surgical technique to repair heart valve defects

The structural and functional effects of the “edge-to-edge” technique on the human mitral valve have been investigated, paying particular attention to the diastolic phase. An advanced finite element model of the valve has been developed, using a hyperelastic material schematization, suitable geometry and constraint conditions, and an effective fluidodynamic analysis. The edge-to-edge suture has been applied on this model and the diastolic phase has been simulated. The results of this calculation show that the operation increases the transvalvular pressure and the maximum stress in the leaflets, which reaches a level similar to that of the systolic phase. The influence of suture position and extension, and the mitral annulus dimension has also been investigated. The results indicate that a lateral location of the stitch is better than a central one, both regarding valve functionality (pressure level and mobility) and internal stresses level, that a longer suture worsens the valve functionality but reduces the stresses level, finally, that the dilatation of the mitral annulus does not affect the valve functionality but increases the stresses level.     

Micropipette aspiration method for characterizing biological materials with surface energy

Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration method to measure the mechanical properties of soft tissues and cells with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is taken into account by the finite element method. It is found that when the pipette radius or aspiration length is comparable to the elastocapillary length, surface energy may distinctly alter the aspiration response. Generally, both the aspiration length and the bulk normal stress decrease with increasing surface energy, and thus neglecting the surface energy would lead to an overestimation of elastic modulus. Through dimensional analysis and numerical simulations, we provide an explicit relation between the imposed pressure and the aspiration length. This method can be applied to determine the mechanical properties of soft biological tissues and organs, e.g., livers, tumors and embryos.