Anisotropic microsphere-based approach to damage in soft fibered tissue.

An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi-scale scheme and focusing on the directionally dependent behavior of these materials. For this purpose, a micro-structural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and discussed herein in order to test the model features. Finally, a clinical application with the material behavior obtained from actual experimental data is also presented.

A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour.

Nearly all soft tissues, among which the vascular tissue is included, present a certain degree of viscoelastic response. This behaviour may be attributed in part to fluid transport within the solid matrix, and to the friction between its fluid and solid constituents. After being preconditioned, the tissue displays highly repetitive behaviour, so that it can be considered pseudo-elastic, that is, elastic but behaving differently in loading and unloading. Because of this reason, very few constitutive laws accounting for the viscoelastic behaviour of the tissue have been developed. Nevertheless, the consideration of this inelastic effect is of crucial importance in surgeries-like vascular angioplasty-where the mentioned preconditioning cannot be considered since non-physiological deformation is applied on the vessel which, in addition, can cause damage to the tissue. A new constitutive formulation considering the particular features of the vascular tissue, such as anisotropy, together with these two inelastic phenomena is presented here and used to fit experimental stress-stretch curves from simple tension loading-unloading tests and relaxation test on porcine and ovine vascular samples.

Experimental study and constitutive modelling of the passive mechanical properties of the ovine infrarenal vena cava tissue.

The passive mechanical properties of the ovine infrarenal vena cava are analysed in this paper. In vivo stretch from 15 venae was measured in order to get data from the physiological situation before harvesting the vessel. Vena cava strips (n=64) both in longitudinal and circumferential directions were cut and subjected to simple tension tests. Results showed the strongly marked anisotropic character of the caval tissue. The maximal stretch ranges reached in both directions were very different, with the longitudinal range being much higher than the circumferential range in all cases. Three anisotropic constitutive models were used to fit the data obtained from the experiments. Advantages and drawbacks of each of these models are also discussed.

Modelling adaptative volumetric finite growth in patient-specific residually stressed arteries.

Understanding the functional performance of vascular tissue is taking a rising importance due to the increasing impact of cardiovascular diseases in developed countries. Currently available medical imaging acquisition techniques, combined with computer modelling allow patient-specific simulations of customized geometries that may help in medical diagnosis and therapeutic treatment. In this work we show methodology to develop patient-specific simulations. Particular features of arteries such as their multilayered structure, as well as the non-linear behaviour of the arterial tissue are considered. A strategy based on the decomposition of the deformation gradient tensor is followed in order to include residual stresses in the real geometry. By means of this technique, it is also possible to model the adaptative growth of the artery neglecting the developing process from the embryo state.

Biomechanical modeling of refractive corneal surgery.

The aim of refractive corneal surgery is to modify the curvature of the cornea to improve its dioptric properties. With that goal, the surgeon has to define the appropriate values of the surgical parameters in order to get the best clinical results, i.e., laser and geometric parameters such as depth and location of the incision, for each specific patient. A biomechanical study before surgery is therefore very convenient to assess quantitatively the effect of each parameter on the optical outcome. A mechanical model of the human cornea is here proposed and implemented under a finite element context to simulate the effects of some usual surgical procedures, such as photorefractive keratectomy (PRK), and limbal relaxing incisions (LRI). This model considers a nonlinear anisotropic hyperelastic behavior of the cornea that strongly depends on the physiological collagen fibril distribution. We evaluate the effect of the incision variables on the change of curvature of the cornea to correct myopia and astigmatism. The obtained results provided reasonable and useful information in the procedures analyzed. We can conclude from those results that this model reasonably approximates the corneal response to increasing pressure. We also show that tonometry measures of the IOP underpredicts its actual value after PRK or LASIK surgery.