Christian A. J. Schulze-Bauer

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.

An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies

The current investigation addresses advanced FE analyses of intact lumbar intervertebral discs. Human disc body units basically consist of a fluid filled cavity (nucleus pulposus) approximately at the disc center and surrounding annulus tissue reinforced by collagen fibers (annulus fibrosus). For the latter component a constitutive model is presented which accounts for nonlinear anisotropic stress response. In contrast to state-of-the-art material descriptions mostly used in the literature (linear elasticity), the current approach provides numerical accuracy in the finite strain regime. Thus, local strain and stress distributions in the annulus fibrosus can properly be determined. Because of the highly nonlinear stress response of the constitutive equations, nonlinear material parameters are required. Although tensile properties of the human annulus fibrosus can already be found in the literature, these material data are not suitable for the current concept as will be shown. The entire constitutive theory is therefore based on a new experimental procedure for the determination of local, nonlinear and anisotropic stress response in annulus tissue. The constitutive model proves its applicability in representative numerical examples. In contrast to state-of-the-art FE analyses, the results do not exhibit parasitic strain (and stress) distributions in annulus tissue under physiological loading conditions. Hence, the current approach seems to be very attractive for refined spinal implant design.

Determination of constitutive equations for human arteries from clinical data

Stress-strain analyses of vessel walls require appropriate constitutive equations. Determination of constitutive equations is based on experimental data of (i) diameter and length of a vessel segment subject to internal pressure and external axial force, and (ii) the load-free reference geometry. Typical clinical data, however, provide only pressure-diameter relations in the diastolic-systolic pressure range. In order to overcome this problem, an approach is proposed allowing the determination of constitutive equations from clinical data by means of reasonable assumptions regarding in situ configurations and stress states of arterial walls. The approach is based on a two-dimensional Fung-type stored-energy function capturing the characteristic nonlinear and anisotropic responses of arteries. Examples concerning human aortas from a normotensive and a hypertensive subject illustrate the potential of the approach.

A Three-dimensional Finite Element Model for Arterial Clamping

Clamp induced injuries of the arterial wall may determine the outcome of surgical procedures. Thus, it is important to investigate the underlying mechanical effects. We present a three-dimensional finite element model, which allows the study of the mechanical response of an artery-treated as a two-layer tube-during arterial clamping. The important residual stresses, which are associated with the load-free configuration of the artery, are also considered. In particular, the finite element analysis of the deformation process of a clamped artery and the associated stress distribution is presented. Within the clamping area a zone of axial tensile peak-stresses was identified, which (may) cause intimal and medial injury. This is an additional injury mechanism, which clearly differs from the commonly assumed wall damage occurring due to compression between the jaws of the clamp. The proposed numerical model provides essential insights into the mechanics of the clamping procedure and the associated injury mechanisms. It allows detailed parameter studies on a virtual clamped artery, which can not be performed with other methodologies. This approach has the potential to identify the most appropriate clamps for certain types of arteries and to guide optimal clamp design.

Segmentation of wall and plaque in in vitro vascular MR images.

Atherosclerosis leads to heart attack and stroke, which are major killers in the western world. These cardiovascular events frequently result from local rupture of vulnerable atherosclerotic plaque. Non-invasive assessment of plaque vulnerability would dramatically change the way in which atherosclerotic disease is diagnosed, monitored, and treated. In this paper, we report a computerized method for segmentation of arterial wall layers and plaque from high-resolution volumetric MR images. The method uses dynamic programming to detect optimal borders in each MRI frame. The accuracy of the results was tested in 62 T1-weighted MR images from six vessel specimens in comparison to borders manually determined by an expert observer. The mean signed border positioning errors for the lumen, internal elastic lamina, and external elastic lamina borders were −0.1 ± 0.1, 0.0 ± 0.1, and −0.1 ± 0.1 mm, respectively. The presented wall layer segmentation approach is one of the first steps towards non-invasive assessment of plaque vulnerability in atherosclerotic subjects.

In situ tensile testing of human aortas by time- resolved small-angle X-ray scattering

The collagen diffraction patterns of human aortas under uniaxial tensile test conditions have been investigated by synchrotron small-angle X-ray scattering. Using a recently designed tensile testing device the orientation and d-spacing of the collagen fibers in the adventitial layer have been measured in situ with the macroscopic force and sample stretching under physiological conditions. The results show a direct relation between the orientation and extension of the collagen fibers on the nanoscopic level and the macroscopic stress and strain. This is attributed first to a straightening, second to a reorientation of the collagen fibers, and third to an uptake of the increasing loads by the collagen fibers.

Assessment of plaque stability by means of high-resolution MRI and finite element analyses of local stresses and strains

To date no adequate diagnostic strategy exists for the assessment of plaque stability. Current approaches focus on identification of high-risk morphological features in cross-sectional images, such as thin caps and large lipid pools. Plaque stability, however, is a 3D mechanical problem, whose solution requires information on both the geometry and the mechanical properties of the involved tissue components. This preliminary in vitro study is aimed to create multicomponent morphological and material models of human diseased arteries from cadavers. Morphological models are based on highly resolved MR images. Material models are fitted to mechanical testing data of single tissue components. Subsequent finite element analysis allows computation of local stresses and strains, whereas consideration of fracture properties provides a basis for the plaque stability assessment. Results demonstrate the complex mechanical behavior of diseased arteries, suggesting that reliable plaque stability assessment requires a combination of appropriate MR protocols, segmentation algorithms and mechanical analysis.

Vascular MR segmentation: wall and plaque

Cardiovascular events frequently result from local rupture of vulnerable atherosclerotic plaque. Non-invasive assessment of plaque vulnerability is needed to allow institution of preventive measures before heart attack or stroke occur. A computerized method for segmentation of arterial wall layers and plaque from high-resolution volumetric MR images is reported. The method uses dynamic programming to detect optimal borders in each MRI frame. The accuracy of the results was tested in 62 T1-weighted MR images from 6 vessel specimens in comparison to borders manually determined by an expert observer. The mean signed border positioning errors for the lumen, internal elastic lamina, and external elastic lamina borders were -0.12±0.14 mm, 0.04±0.12mm, and -0.15±0.13 mm, respectively. The presented wall layer segmentation approach is one of the first steps towards non-invasive assessment of plaque vulnerability in atherosclerotic subjects.