A discrete-time approach to the formulation of constitutive models for viscoelastic soft tissues

A literature review of the numerical analysis of abdominal aortic aneurysms treated with endovascular stent grafts

The purpose of this paper is to present the basic principles and relevant advances in the computational modeling of abdominal aortic aneurysms and endovascular aneurysm repair, providing the community with up-to-date state of the art in terms of numerical analysis and biomechanics. Frameworks describing the mechanical behavior of the aortic wall already exist. However, intraluminal thrombus nonhomogeneous structure and porosity still need to be well characterized. Also, although the morphology and mechanical properties of calcifications have been investigated, their effects on wall stresses remain controversial. Computational fluid dynamics usually assumes a rigid artery wall, whereas fluid-structure interaction accounts for artery compliance but is still challenging since arteries and blood have similar densities. We discuss alternatives to fluid-structure interaction based on dynamic medical images that address patient-specific hemodynamics and geometries. We describe initial stresses, elastic boundary conditions, and statistical strength for rupture risk assessment. Special emphasis is accorded to workflow development, from the conversion of medical images into finite element models, to the simulation of catheter-aorta interactions and stent-graft deployment. Our purpose is also to elaborate the key ingredients leading to virtual stenting and endovascular repair planning that could improve the procedure and stent-grafts.

Directional, regional, and layer variations of mechanical properties of esophageal tissue and its interpretation using a structure-based constitutive model

The esophagus, like other soft tissues, exhibits nonlinear and anisotropic mechanical properties. As a composite structure, the properties of the outer muscle and inner mucosal layer are different. It is expected that the complex mechanical properties will induce nonhomogeneous stress distributions in the wall and nonuniform tissue remodeling. Both are important factors which influence the function of mechanosensitive receptor located in various layers of the wall. Hence, the characterization of the mechanical properties is essential to understand the neuromuscular motion of the esophagus. In this study, the uniaxial tensile tests were conducted along two mutually orthogonal directions of porcine esophageal tissue to identify the directional (circumferential and axial), regional (abdominal, thoracic, and cervical), and layer (muscle and mucosa) variations of the mechanical properties. A structure-based constitutive model, which took the architectures of the tissue's microstructures into account, was applied to describe the mechanical behavior of the esophagus. Results showed that the constitutive model successfully described the mechanical behavior and provided robust estimates of the material parameters. In conclusion, the model was demonstrated to be a good descriptor of the mechanical properties of the esophagus and it was able to facilitate the directional, layer, and regional comparisons of the mechanical properties in terms of the associated material parameters.

Three-dimensional finite element modeling of ligaments: technical aspects

The objective of this paper is to describe strategies for addressing technical aspects of the computational modeling of ligaments with the finite element (FE) method. Strategies for FE modeling of ligament mechanics are described, differentiating between whole-joint models and models of individual ligaments. Common approaches to obtain three-dimensional ligament geometry are reviewed, with an emphasis on techniques that rely on volumetric medical image data. Considerations for the three-dimensional constitutive modeling of ligaments are reviewed in the context of ligament composition and structure. A novel approach to apply in situ strain to FE models of ligaments is described, and test problems are presented that demonstrate the efficacy of the approach. Approaches for the verification and validation of ligament FE models are outlined. The paper concludes with a discussion of future research directions.