E. Peña

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.

Mechanical behaviour of synthetic surgical meshes: Finite element simulation of the herniated abdominal wall

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall.

Assessing the Use of the “Opening Angle Method” to Enforce Residual Stresses in Patient-Specific Arteries

Numerical and analytical studies on cylindrical geometries have shown the relevance of accounting for residual stresses in arterial modeling. However, multiple difficulties, both geometrical and numerical, arise when enforcing residual stresses in patient-specific arteries. This is the reason of the few simulations that have been developed on this kind of geometries. In this paper we present a methodology that allows to include residual stresses in arbitrary geometries. Since it is not necessary to know the opened configuration of the artery, it makes it possible to take advantage of non-invasive image acquisition techniques such as CT or MRI to create customized arterial models. A simplified initial strain field showing its accuracy when applied to actual in vivo closed geometries is hypothesized from an opening angle experiment. In addition to residual stresses, the anisotropic hyperelastic and multilayered nature of the arterial tissue was accounted for the simulations of the behavior of a human coronary and iliac arteries. Results show the relevance of considering all these features for getting realistic results and the relative accuracy of using approximate solutions of residual stresses in patient-specific arterial simulations.

On modelling nonlinear viscoelastic effects in ligaments

Experiments in human ligaments revealed that the rate of stress relaxation in such materials is strain dependent. This nonlinear behavior requires therefore a modified description of the standard quasilinear viscoelasticity theory commonly used in tissue biomechanics. The goal of this study is to characterize and demonstrate the importance of the nonlinear stress-relaxation behavior of ligaments undergoing finite deformation. The structural model presented herein is based on a local additive decomposition of the stress tensor into initial and non-equilibrium parts as resulted from the assumed structure of the free energy density function that generalizes Kelvin-Voigt nonlinear viscous models. We consider different viscoelastic behavior for the matrix and the fibers and the need of considering the strain dependency of this effect is clearly demonstrated. Model parameters were fit to experimental data obtained in specimens undergoing finite deformation in two directions: longitudinal and transversal with respect to the directions of the collagen fibers. The model was then tested against several multi-axial loading situations. The strain dependent relaxation and the strain rate dependent behavior of the human medial collateral ligament were accurately predicted.

On modelling damage process in vaginal tissue.

The goal of this study was to characterize and model the damage process in prolapsed vaginal tissue undergoing finite deformations. Experiments in prolapsed vaginal tissue revealed that a softening process occurs before tissues rupture. This nonlinear damage behavior requires a continuum damage theory commonly used to describe the softening behavior of soft tissues under large deformations. The structural model here presented was built within the framework of nonlinear continuum mechanics. Tissue damage was simulated considering different damage behaviors for the matrix and the fibers. The model parameters were fit to the experimental data obtained from prolapsed vaginal tissue undergoing finite deformations in uniaxial tension tests. The tests were developed with samples cut along the longitudinal axis of the vagina. The damage model was able to predict the stress-strain behavior and the damage process accurately. The error estimations pointed to an excellent agreement between experimental results and model fittings. For all the fitted data, the normalized RMS error epsilon presented very low values and the coefficient of determination R2 was close to 1.

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.

Epicardial delivery of collagen patches with adipose-derived stem cells in rat and minipig models of chronic myocardial infarction.

Although transplantation of adipose-derived stem cells (ADSC) in chronic myocardial infarction (MI) models is associated with functional improvement, its therapeutic value is limited due to poor long-term cell engraftment and survival. Thus, the objective of this study was to examine whether transplantation of collagen patches seeded with ADSC could enhance cell engraftment and improve cardiac function in models of chronic MI. With that purpose, chronically infarcted Sprague-Dawley rats (n = 58) were divided into four groups and transplanted with media, collagen scaffold (CS), rat ADSC, or CS seeded with rat ADSC (CS-rADSC). Cell engraftment, histological changes, and cardiac function were assessed 4 months after transplantation. In addition, Göttingen minipigs (n = 18) were subjected to MI and then transplanted 2 months later with CS or CS seeded with autologous minipig ADSC (CS-pADSC). Functional and histological assessments were performed 3 months post-transplantation. Transplantation of CS-rADSC was associated with increased cell engraftment, significant improvement in cardiac function, myocardial remodeling, and revascularization. Moreover, transplantation of CS-pADSC in the pre-clinical swine model improved cardiac function and was associated with decreased fibrosis and increased vasculogenesis. In summary, transplantation of CS-ADSC resulted in enhanced cell engraftment and was associated with a significant improvement in cardiac function and myocardial remodeling.

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.

Experimental study and constitutive modeling of the viscoelastic mechanical properties of the human prolapsed vaginal tissue

In this paper, the viscoelastic mechanical properties of vaginal tissue are investigated. Using previous results of the authors on the mechanical properties of biological soft tissues and newly experimental data from uniaxial tension tests, a new model for the viscoelastic mechanical properties of the human vaginal tissue is proposed. The structural model seems to be sufficiently accurate to guarantee its application to prediction of reliable stress distributions, and is suitable for finite element computations. The obtained results may be helpful in the design of surgical procedures with autologous tissue or prostheses.

Mechanical characterization of the softening behavior of human vaginal tissue

The mechanical properties of vaginal tissue need to be characterized to perform accurate simulations of prolapse and other pelvic disorders that commonly affect women. This is also a fundamental step towards the improvement of therapeutic techniques such as surgery. In this paper, the softening behavior or Mullins effect of vaginal tissue is studied by proposing an appropriate constitutive model. This effect is an important factor after the birth, since vaginal tissue has been supporting a high load distribution and therefore does not recover its original behavior. Due to the anisotropy of the tissue, the mechanical testing of vaginal tissue, consists in loading-unloading uniaxial tension tests performed along the longitudinal and transverse axes of the vagina. A directional pseudo-elastic model was used to reproduce the inelastic behavior of the tissue. The obtained results may be helpful in the design of surgical procedures with autologous tissue or smart prostheses. A good qualitative agreement has been found between the numerical and experimental results for the vaginal tissue examples, indicating that the constitutive softening model can capture the typical stress-strain behavior observed in this kind of fibrous soft tissue.