Smooth contact strategies with emphasis on the modeling of balloon angioplasty with stenting

Abstract

SUMMARYCritical to the simulation of balloon angioplasty is the modeling of the contact between the artery wall and the medical devices. In standard approaches, the 3D contact surfaces are described by means of C 0 -continuous facet-based techniques, which may lead to numerical problems. This work introduces a novel contact algorithm where the target surfaces are described by polynomial expressions with C 2 -continuity. On the basis of uniform cubic B-splines, two different parametrization techniques are presented and compared, while the related implementation of the algorithm into a finite element analysis program is described. Two numerical examples are selected to demonstrate the special merits of the proposed contact formulation. The first example is a benchmark contact problem selected to point out the special features of the proposed strategies. The second example is concerned with the simulation of balloon angioplasty and stenting, where the contact between the balloon, the stent and the artery wall is numerically modeled. A patient-specific 3D model of a stenotic femoral artery serves as a basis. The study concludes by identifying the changes in the mechanical environment of the artery in terms of contact forces and strains by considering two different stent designs.

Experimental Studies and Numerical Analysis of the Inflation and Interaction of Vascular Balloon Catheter-Stent Systems

“…To describe the unfolding process of the balloon, and the circumferential stiffening behavior in a phenomenological way, a nonlinear anisotropic model was adopted. 27,28 The computational model for the balloon was shown to be in good agreement with the experimental results (Fig. 10).…”

“…From the above equation it is obvious that anisotropy arises only due to I 4 and I 6 : The isotropic response of the matrix material is determined through a neo-Hookean model of the form W iso ¼ lð I 1 À 3Þ, where μ > 0 is a stress-like material parameter. The anisotropic contribution W aniso to the strain-energy function is described as 27 FIGURE 9. Geometric models of the undeformed configurations of three stent products (compare with Table 1).…”

A Numerical Model to Study the Interaction of Vascular Stents with Human Atherosclerotic Lesions

“…For this purpose, a C 2 -continuous surface description is applied, which prevents numerical instabilities arising from non-smooth body discretization. 22,38 The proposed computational model also attempts to provide a deeper insight into the dominating effect of plaque fissuring and dissection during stenting. 5,27,29 This is performed by introducing two (small) initial cracks near the edges of the plaque.…”

“…It seems also that only a few studies have considered three-dimensional (3D) geometries. 16,17,22 Although simplified approaches have contributed to the current level of understanding of angioplasty mechanics, there is a need to model the actual 3D morphology and the related mechanics in a more realistic way and on a patient-specific basis. To the best of the authorsÕ knowledge, the study by Liang et al 28 was the first to incorporate the balloon in a simulation considering a stent, however, simplified, cylindrical geometries were considered.…”

A Computational Framework for Patient‐Specific Analysis of Articular Cartilage Incorporating Structural Information from DT‐MRI

“…The (discretised) cartilage was specified to remain within the cylindrical containment vessel using a frictionless rigid-deformable contact algorithm. The contact problem between the cartilage specimen and the indenter was handled using a specialised smooth contact algorithm previously developed and documented in [71].…”