Patient-Specific Wall Stress Analysis in Cerebral Aneurysms Using Inverse Shell Model

Stress analyses of patient-specific vascular structures commonly assume that the reconstructed in vivo configuration is stress free although it is in a pre-deformed state. We submit that this assumption can be obviated using an inverse approach, thus increasing accuracy of stress estimates. In this paper, we introduce an inverse approach of stress analysis for cerebral aneurysms modeled as nonlinear thin shell structures, and demonstrate the method using a patient-specific aneurysm. A lesion surface derived from medical images, which corresponds to the deformed configuration under the arterial pressure, is taken as the input. The wall stress in the given deformed configuration, together with the unstressed initial configuration, are predicted by solving the equilibrium equations as opposed to traditional approach where the deformed geometry is assumed stress free. This inverse approach also possesses a unique advantage, that is, for some lesions it enables us to predict the wall stress without accurate knowledge of the wall elastic property. In this study, we also investigate the sensitivity of the wall stress to material parameters. It is found that the in-plane component of the wall stress is indeed insensitive to the material model.

[1]  J D Humphrey,et al.  Finite strain elastodynamics of intracranial saccular aneurysms. , 1999, Journal of biomechanics.

[2]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part VII: Shell intersections with -DOF finite element formulations , 1993 .

[3]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects , 1989 .

[4]  M. L. Raghavan,et al.  Inverse method of stress analysis for cerebral aneurysms , 2008, Biomechanics and modeling in mechanobiology.

[5]  Jia Lu,et al.  Nonlinear anisotropic stress analysis of anatomically realistic cerebral aneurysms. , 2007, Journal of biomechanical engineering.

[6]  Jia Lu,et al.  Inverse formulation for geometrically exact stress resultant shells , 2008 .

[7]  J. C. Simo,et al.  On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization , 1989 .

[8]  M. L. Raghavan,et al.  Three-Dimensional Geometrical Characterization of Cerebral Aneurysms , 2004, Annals of Biomedical Engineering.

[9]  Jia Lu,et al.  Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes—Part II: Experimental Validation , 2009 .

[10]  Jia Lu,et al.  An Experimentally Derived Stress Resultant Shell Model for Heart Valve Dynamic Simulations , 2006, Annals of Biomedical Engineering.

[11]  Jay D. Humphrey,et al.  Structure, Mechanical Properties, and Mechanics of Intracranial Saccular Aneurysms , 2000 .

[12]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory , 1990 .

[13]  M. De Handbuch der Physik , 1957 .

[14]  D. Wiebers,et al.  Cerebral aneurysms. , 2006, The New England journal of medicine.

[15]  S. BRODETSKY,et al.  Theory of Plates and Shells , 1941, Nature.

[16]  J. Humphrey,et al.  Determination of a constitutive relation for passive myocardium: II. Parameter estimation. , 1990, Journal of biomechanical engineering.

[17]  M. Sacks Biaxial Mechanical Evaluation of Planar Biological Materials , 2000 .

[18]  M. L. Raghavan,et al.  Inverse elastostatic stress analysis in pre-deformed biological structures: Demonstration using abdominal aortic aneurysms. , 2007, Journal of biomechanics.

[19]  Jay D. Humphrey,et al.  Multiaxial Mechanical Behavior of Human Saccular Aneurysms , 2001 .

[20]  Jia Lu,et al.  Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes―Part I: Theoretical and Computational Developments , 2009 .

[21]  Padmanabhan Seshaiyer,et al.  A sub-domain inverse finite element characterization of hyperelastic membranes including soft tissues. , 2003, Journal of biomechanical engineering.

[22]  J D Humphrey,et al.  Further evidence for the dynamic stability of intracranial saccular aneurysms. , 2003, Journal of biomechanics.

[23]  Jia Lu,et al.  Dynamic Simulation of Bioprosthetic Heart Valves Using a Stress Resultant Shell Model , 2008, Annals of Biomedical Engineering.

[24]  J D Humphrey,et al.  The use of Laplace's equation in aneurysm mechanics. , 1996, Neurological research.

[25]  J. D. Humphrey,et al.  Further Roles of Geometry and Properties in the Mechanics of Saccular Aneurysms. , 1998, Computer methods in biomechanics and biomedical engineering.

[26]  M. L. Raghavan,et al.  Computational method of inverse elastostatics for anisotropic hyperelastic solids , 2007 .

[27]  R. Budwig,et al.  The influence of shape on the stresses in model abdominal aortic aneurysms. , 1996, Journal of biomechanical engineering.

[28]  J. G. Simmonds,et al.  The strain energy density of rubber-like shells , 1985 .

[29]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[30]  Michael S Sacks,et al.  The effects of collagen fiber orientation on the flexural properties of pericardial heterograft biomaterials. , 2005, Biomaterials.

[31]  J D Humphrey,et al.  Influence of size, shape and properties on the mechanics of axisymmetric saccular aneurysms. , 1996, Journal of biomechanics.

[32]  Wojciech Pietraszkiewicz,et al.  Theory and numerical analysis of shells undergoing large elastic strains , 1992 .

[33]  J. Humphrey,et al.  Determination of a constitutive relation for passive myocardium: I. A new functional form. , 1990, Journal of biomechanical engineering.