Michael Stadler

A structural model for the viscoelastic behavior of arterial walls : Continuum formulation and finite element analysis

In this paper we present a two-layer structural model suitable for predicting reliably the passive (unstimulated) time-dependent three-dimensional stress and deformation states of healthy young arterial walls under various loading conditions. It extends to the viscoelastic regime a recently developed constitutive framework for the elastic strain response of arterial walls (see Holzapfel et al. (2001)). The structural model is formulated within the framework of nonlinear continuum mechanics and is well-suited for a finite element implementation. It has the special merit that it is based partly on histological information, thus allowing the material parameters to be associated with the constituents of each mechanically-relevant arterial layer. As one essential ingredient from the histological information the constitutive model requires details of the directional organization of collagen fibers as commonly observed under a microscope. We postulate a fully automatic technique for identifying the orientations of cellular nuclei, these coinciding with the preferred orientations in the tissue. The biological material is assumed to behave incompressibly so that the constitutive function is decomposed locally into volumetric and isochoric parts. This separation turns out to be advantageous in avoiding numerical complications within the finite element analysis of incompressible materials. For the description of the viscoelastic behavior of arterial walls we employ the concept of internal variables. The proposed viscoelastic model admits hysteresis loops that are known to be relatively insensitive to strain rate, an essential mechanical feature of arteries of the muscular type. To enforce incompressibility without numerical difficulties, the finite element treatment adopted is based on a three-field Hu-Washizu variational approach in conjunction with an augmented Lagrangian optimization technique. Two numerical examples are used to demonstrate the reliability and efficiency of the proposed structural model for arterial wall mechanics as a basis for large scale numerical simulations.

A Layer-Specific Three-Dimensional Model for the Simulation of Balloon Angioplasty using Magnetic Resonance Imaging and Mechanical Testing

AbstractA detailed understanding of the mechanical procedure of balloon angioplasty requires three-dimensional (3D) modeling and efficient numerical simulations. We have developed a 3D model for eight distinct arterial components associated with specific mechanical responses. The 3D geometrical model is based on in vitro magnetic resonance imaging of a human stenotic postmortem artery and is represented by nonuniform rational B-spline surfaces. Mechanical tests of the corresponding vascular tissues provide a fundamental basis for the formulation of large strain constitutive laws, which model the typical anisotropic, highly nonlinear, and inelastic mechanical characteristics under supraphysiological loadings. The 3D finite-element realization considers the balloon–artery interaction and accounts for vessel-specific axial in situ prestretches. 3D stress states of the investigated artery during balloon expansion and stent deployment were analyzed. Furthermore, we studied the changes of the 3D stress state due to model simplifications, which are characterized by neglecting axial in situ prestretch, assuming plane strain states, and isotropic material responses, as commonly utilized in previous works. Since these simplifications lead to maximum stress deviations of up to 600%—where even the stress character may interchange—the associated models are, in general, inappropriate. The proposed approach provides a tool that has the potential (i) to improve procedural protocols and the design of interventional instruments on a lesion-specific basis, and (ii) to determine postangioplasty mechanical environments, which may be correlated with restenosis responses.

Role of facet curvature for accurate vertebral facet load analysis

The curvature of vertebral facet joints may play an important role in the study of load-bearing characteristics and clinical interventions such as graded facetectomy. In previously-published finite element simulations of this procedure, the curvature was either neglected or approximated with a varying degree of accuracy. Here we study the effect of the curvature in three different load situations by using a numerical model which is able to represent the actual curvature without any loss of accuracy. The results show that previously-used approximations of the curvature lead to good results in the analysis of sagittal moment/rotation. However, for sagittal shear-force/displacement and for the contact stress distribution, previous results deviate significantly from our results. These findings are supported through related convergence studies. Hence we can conclude that in order to obtain reliable results for the analysis of sagittal shear-force/displacement and the contact stress distribution in the facet joint, the curvature must not be neglected. This is of particular importance for the numerical simulation of the spine, which may lead to improved diagnostics, effective surgical planning and intervention. The proposed method may represent a more reliable basis for optimizing the biomedical engineering design for tissue engineering or, for example, for spinal implants.

Towards a Computational Methodology for Optimizing Angioplasty Treatments with Stenting

We propose a computational methodology that allows a set of stent parameters to he varied, with the aim of evaluating the difference in the mechanical environment within the wall before and after a ...

An FPGA based diagnostic tool for jitter optimization in serial high-speed transceivers

We present an embedded jitter measurement system for on-chip diagnostics of serial high-speed interfaces. A Virtex-5 FPGA uses a 3Gbit reference signal to retrieve timing jitter distributions from a system under test (SUT). Using a recently developed fitting method, the total jitter of the system is determined, which allows for judging the quality of transmission lines, PLLs or transceiver structures. The diagnostic tool is thus able to optimize and configure the SUT without the use of an additional instrumentation device.