Fluid-Structure Interaction Simulation of an Aortic Phantom with Uncertain Young's Modulus Using the Polynomial Chaos Expansion

Abstract:

Article Preview

To add reliability to numerical simulations, Uncertainty Quantification is considered to be a crucial tool for clinical decision making. This especially holds for risk assessment of cardiovascular surgery, for which threshold parameters computed by numerical simulations are currently being discussed. A corresponding biomechanical model includes blood flow, soft tissue deformation, as well as fluid-structure coupling. Thereby, structural material parameters have a strong impact on the dynamic behavior. In practice, however, particularly the value of the Young's modulus is rarely known in a precise way, and therefore, it reflects a natural level of uncertainty. In this work we introduce a stochastic model for representing variations in the Young's modulus and quantify its effect on the wall sheer stress and von Mises stress by means of the Polynomial Chaos method. We demonstrate the use of uncertainty quantification in this context and provide numerical results based on an aortic phantom benchmark model.

Info:

Periodical:

Edited by:

Peter F. Pelz and Peter Groche

Pages:

34-44

Citation:

J. Kratzke et al., "Fluid-Structure Interaction Simulation of an Aortic Phantom with Uncertain Young's Modulus Using the Polynomial Chaos Expansion", Applied Mechanics and Materials, Vol. 807, pp. 34-44, 2015

Online since:

November 2015

Export:

Price:

$41.00

* - Corresponding Author

[1] Hiratzka, L. F., et al., 2010 ACCF/AHA/AATS/ACR/ASA/SCA/SCAI/SIR/STS/SVM Guidelines for the Diagnosis and Management of Patients With Thoracic Aortic Disease: Executive Summary. Journal of the American College of Cardiology 55(14) (2010).

DOI: https://doi.org/10.1016/j.jacc.2010.02.010

[2] Pape, L. A., et al., Aortic diameter 5. 5 cm is not a good predictor of type a aortic dissection observations from the international registry of acute aortic dissection (irad). Circulation 116(10) (2007) 1120-1127.

DOI: https://doi.org/10.1161/circulationaha.107.702720

[3] Cozijnsen, L., Braam, R. L., Waalewijn, R. A., Schepens, M. A., Loeys, B. L., van Oosterhout, M. F., Barge-Schaapveld, D. Q., and Mulder, B. J., What is new in dilatation of the ascending aorta? review of current literature and practical advice for the cardiologist. Circulation 123(8) (2011).

DOI: https://doi.org/10.1161/circulationaha.110.949131

[4] Chung, B. and Cebral, J., CFD for evaluation and treatment planning of aneurysms: Review of proposed clinical uses and their challenges. Annals of Biomedical Engineering 43(1) (2015) 122-138.

DOI: https://doi.org/10.1007/s10439-014-1093-6

[5] Valencia, A., Burdiles, P., Ignat, M., Mura, J., Bravo, E., Rivera, R., and Sordo, J. Fluid structural analysis of human cerebral aneurysm using their own wall mechanical properties. Computational and mathematical methods in medicine, (2013).

DOI: https://doi.org/10.1155/2013/293128

[6] Damughatla, Anirudh R., et al. Quantification of aortic stiffness using MR Elastography and its comparison to MRI-based pulse wave velocity. Journal of Magnetic Resonance Imaging 41(1) (2015) 44-51.

DOI: https://doi.org/10.1002/jmri.24506

[7] Kratzke, J., Schoch, N., Weis, C., Müller-Eschner, M., Speidel, S., Farag, M., Beller, C., Heuveline, V. Enhancing 4D PC-MRI in an aortic phantom considering numerical simulations SPIE: Physics of medical imaging, 9412-47 (2015).

DOI: https://doi.org/10.1117/12.2082483

[8] Wiener, N., The homogeneous chaos. American Journal of Mathematics, 60(4) (1938) 897-936.

[9] Xiu, D. and Karniadakis, G. E., The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2) (2002) 619-644.

DOI: https://doi.org/10.1137/s1064827501387826

[10] Formaggia, L., Quarteroni, A. M., and Veneziani, A., Cardiovascular mathematics. Milan, Springer, (2009).

[11] Janela, J., Moura, A., and Sequeira, A., Absorbing boundary conditions for a 3d non-newtonian fluidstructure interaction model for blood flow in arteries. International Journal of Engineering Science 48(11) (2010) 1332 - 1349.

DOI: https://doi.org/10.1016/j.ijengsci.2010.08.004

[12] Fung, Y. C., Biomechanics: Mechanical Properties of Living Tissues, Second Edition, Springer, New York, NY, (1993).

[13] Nobile, F., Tempone, R. and Webster, C.G., A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data. SIAM J. Numer. Anal., 46(5) (2008) 2309-2345.

DOI: https://doi.org/10.1137/060663660

[14] Nichols, W., O'Rourke, M., and Vlachopoulos, C. (Eds. ). McDonald's blood flow in arteries: theoretical, experimental and clinical principles. CRC Press, (2011).

[15] Brooks, A. N. and Hughes, T. J., Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-stokes equations. Computer methods in applied mechanics and engineering 32(1) (1982).

DOI: https://doi.org/10.1016/0045-7825(82)90071-8