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Computational Methods for Patient-Specific Modelling

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Abstract

Patient-specific haemodynamic modelling using computational fluid dynamics approaches is a multi-stage process. Firstly, a model of the geometry of interest is created and discretised. The governing equations for the fluid must then be solved for each discretised element, and the interfaces of the domain should be treated appropriately. This chapter will describe the basic equations solved using CFD and their numerical treatment. Subsequently, the stages required in imaging the patient and converting the images into a 3D geometry will be given, followed by a brief description of discretisation (meshing). The mathematics behind lumped-parameter modelling to develop dynamic BCs will be described and a comparison with alternative BCs will be made. Finally, a brief introduction to the relevant aspects of solid modelling will be provided.

A preliminary version of the 3D-0D coupling approach developed in this Chapter was used in a study on haemodynamics in an arterio-venous fistula (Decorato et al. 2014).

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References

  • ANSYS (2011), CFX Solver Theory Guide, 14.0 edition.

    Google Scholar 

  • Patankar, S. V. (1980). Numerical heat transfer and fluid flow. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Barth, T., & Jespersen, D. (2012). The design and application of upwind schemes on unstructured meshes, in 27th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics.

    Google Scholar 

  • Bertoglio, C., Moireau, P., & Gerbeau, J.-F. (2011). Sequential parameter estimation for fluid-structure problems: Application to hemodynamics. International Journal for Numerical Methods in Biomedical Engineering, 28(4), 434–455.

    Article  MathSciNet  Google Scholar 

  • Beynon, R., Sterne, J. A. C., Wilcock, G., Likeman, M., Harbord, R. M., Astin, M., et al. (2012). Is MRI better than CT for detecting a vascular component to dementia? A systematic review and meta-analysis. BMC Neurology, 12(1), 33.

    Article  Google Scholar 

  • Brown, A. G., Shi, Y., Marzo, A., Staicu, C., Valverde, I., Beerbaum, P., et al. (2012). Accuracy vs. computational time translating aortic simulations to the clinic. Journal of Biomechanics, 45(3), 516–523.

    Article  Google Scholar 

  • Cheng, Z., Juli, C., Wood, N. B., Gibbs, R. G. J., & Xu, X. Y. (2014). Predicting flow in aortic dissection: Comparison of computational model with PC-MRI velocity measurements. Medical Engineering and Physics, 36(9), 1176–1184.

    Article  Google Scholar 

  • Chen, D., ller Eschner, M. M., von Tengg-Kobligk, H., Barber, D., Bockler, D., Hose, R., et al. (2013a). A patient-specific study of type-B aortic dissection: evaluation of true-false lumen blood exchange. BioMedical Engineering OnLine, 12, 65.

    Article  Google Scholar 

  • Chen, D., Müller-Eschner, M., Kotelis, D., Böckler, D., Ventikos, Y., & von Tengg-Kobligk, H. (2013b). A longitudinal study of Type-B aortic dissection and endovascular repair scenarios: Computational analyses. Medical Engineering and Physics, 35(9), 1321–1330.

    Article  Google Scholar 

  • Chuong, C. J., & Fung, Y. C. (1986). On residual stresses in arteries. Journal of Biomechanical Engineering, 108(2), 189–192.

    Article  Google Scholar 

  • JCS Joint Working Group (2013). Guidelines for diagnosis and treatment of aortic aneurysm and aortic dissection (JCS 2011). Circulation Journal, 77(3), 789–828.

    Google Scholar 

  • Clough, R. E., Waltham, M., Giese, D., Taylor, P. R., & Schaeffter, T. (2012). A new imaging method for assessment of aortic dissection using four-dimensional phase contrast magnetic resonance imaging. Journal of Vacscular Surgery, 55(4), 914–923.

    Article  Google Scholar 

  • Colciago, C. M., Deparis, S., & Quarteroni, A. (2014). Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics. Journal of Computational and Applied Mathematics, 265, 120–138.

    Article  MathSciNet  MATH  Google Scholar 

  • Crosetto, P., Reymond, P., Deparis, S., & Kontaxakis, D. (2011). Fluid-structure interaction simulation of aortic blood flow. Computers and Fluids, 43, 46–57.

    Article  MathSciNet  MATH  Google Scholar 

  • Decorato, I., Salsac, A.-V., Legallais, C., Alimohammadi, M., Díaz-Zuccarini, V., & Kharboutly, Z. (2014). Influence of an arterial stenosis on the hemodynamics within an arteriovenous fistula (AVF): Comparison before and after balloon-angioplasty. Cardiovascular Engineering and Technology, 5(3), 233–243.

    Article  Google Scholar 

  • Erbel, R., Alfonso, F., Boileau, C., Dirsch, O., Eber, B., Haverich, A., et al. (2001). Diagnosis and management of aortic dissection task force on aortic dissection, european society of cardiology. European Heart Journal, 22(18), 1642–1681.

    Article  Google Scholar 

  • Formaggia, L., Veneziani, A., & Vergara, C. (2008). A new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics. SIAM Journal on Numerical Analysis, 46(6), 2769–2794.

    Article  MathSciNet  MATH  Google Scholar 

  • Formaggia, L., Veneziani, A., & Vergara, C. (2010). Comput. Methods Appl. Mech. Engrg. Computer Methods in Applied Mechanics and Engineering, 199(9–12), 677–688.

    Article  MathSciNet  MATH  Google Scholar 

  • Francois, C. J., Markl, M., Schiebler, M. L., Niespodzany, E., Landgraf, B. R., Schlensak, C., et al. (2013). Four-dimensional, flow-sensitive magnetic resonance imaging of blood flow patterns in thoracic aortic dissections. The Journal of Thoracic and Cardiovascular Surgery, 145(5), 1359–1366.

    Article  Google Scholar 

  • Fung, Y. C. (1991). What are the residual stresses doing in our blood vessels? Annals of Biomedical Engineering, 19(3), 237–249.

    Article  Google Scholar 

  • Fung, Y. (1993). Biomechanics: Mechanical properties of living tissues (2nd ed.). Heidelberg: Springer.

    Book  Google Scholar 

  • Fung, Y. (1997). Biomechanics: Circulation (2nd ed.). New York: Springer.

    Book  Google Scholar 

  • Ganten, M.-K., Weber, T. F., von Tengg-Kobligk, H., Böckler, D., Stiller, W., Geisbüsch, P., et al. (2009). Motion characterization of aortic wall and intimal flap by ECG-gated CT in patients with chronic B-dissection. European Journal of Radiology, 72(1), 146–153.

    Article  Google Scholar 

  • Gao, F., Guo, Z., Sakamoto, M., & Matsuzawa, T. (2006). Fluid-structure Interaction within a layered aortic arch model. Journal of Biological Physics, 32(5), 435–454.

    Article  Google Scholar 

  • Gasser, T. C., Ogden, R. W., & Holzapfel, G. A. (2006). Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. Journal of The Royal Society Interface, 3(6), 15–35.

    Article  Google Scholar 

  • Graham, L. S., & Kilpatrick, D. (2010). Estimation of the bidomain conductivity parameters of cardiac tissue from extracellular potential distributions initiated by point stimulation. Annals of Biomedical Engineering, 38(12), 3630–3648.

    Article  Google Scholar 

  • Grinberg, L., Anor, T., Madsen, J. R., Yakhot, A., & Karniadakis, G. E. (2009). Large-scale simulation of the human arterial tree. Clinical and Experimental Pharmacology and Physiology, 36(2), 194–205.

    Article  Google Scholar 

  • Grinberg, L., & Karniadakis, G. E. (2008). Outflow boundary conditions for arterial networks with multiple outlets. Annals of Biomedical Engineering, 36(9), 1496–1514.

    Article  Google Scholar 

  • Karmonik, C., Duran, C., Shah, D. J., Anaya-Ayala, J. E., Davies, M. G., Lumsden, A. B., et al. (2012a). Preliminary findings in quantification of changes in septal motion during follow-up of type B aortic dissections. Journal of Vacscular Surgery, 55(5), 1419.e1–1426.e1.

    Google Scholar 

  • Karmonik, C., Partovi, S., Davies, M. G., Bismuth, J., Shah, D. J., Bilecen, D., et al. (2012b). Integration of the computational fluid dynamics technique with MRI in aortic dissections. Magnetic Resonance in Medicine, 69(5), 1438–1442.

    Article  Google Scholar 

  • Kim, H. J., Vignon-Clementel, I. E., Figueroa, C. A., LaDisa, J. F., Jansen, K. E., Feinstein, J. A., et al. (2009). On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Annals of Biomedical Engineering, 37(11), 2153–2169.

    Article  Google Scholar 

  • Korakianitis, T., & Shi, Y. (2006). Numerical simulation of cardiovascular dynamics with healthy and diseased heart valves. Journal of Biomechanics, 39(11), 1964–1982.

    Article  Google Scholar 

  • Kung, E. O., Les, A. S., Figueroa, C. A., Medina, F., Arcaute, K., Wicker, R. B., et al. (2011a). In vitro validation of finite element analysis of blood flow in deformable models. Annals of Biomedical Engineering, 39(7), 1947–1960.

    Article  Google Scholar 

  • Kung, E. O., Les, A. S., Medina, F., Wicker, R. B., McConnell, M. V., & Taylor, C. A. (2011b). In vitro validation of finite-element model of AAA hemodynamics incorporating realistic outlet boundary conditions. Journal of Biomechanical Engineering, 133(4), 041003.

    Article  Google Scholar 

  • Kung, E. O., & Taylor, C. A. (2010). Development of a physical windkessel module to re-create in vivo vascular flow impedance for in vitro experiments. Cardiovascular Engineering and Technology, 2(1), 2–14.

    Article  Google Scholar 

  • LaDisa, J. F, Jr., Dholakia, R. J., Figueroa, C. A., Vignon-Clementel, I. E., Chan, F. P., Samyn, M. M., et al. (2011). Computational simulations demonstrate altered wall shear stress in aortic coarctation patients treated by resection with end-to-end anastomosis. Congenital Heart Disease, 6(5), 432–443.

    Article  Google Scholar 

  • Layton, K. F., Kallmes, D. F., Cloft, H. J., Lindell, E. P., & Cox, V. S. (2006). Bovine aortic arch variant in humans: Clarification of a common misnomer. American Journal of Neuroradiology, 27(7), 1541–1542.

    Google Scholar 

  • Levick, J. R. (2009). An indtroduction to cardiovascular physiology (5th ed.). London: Hodder Arnold.

    Google Scholar 

  • Moghadam, M. E., Vignon-Clementel, I. E., Figliola, R., & Marsden, A. L. (2013). A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations. Journal of Computational Physics, 244(C), 63–79.

    Article  MathSciNet  Google Scholar 

  • Moireau, P., Bertoglio, C., Xiao, N., Figueroa, C. A., Taylor, C. A., Chapelle, D., et al. (2013). Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data. Biomechanics and Modeling in Mechanobiology, 12(3), 475–496.

    Article  Google Scholar 

  • Moireau, P., & Chapelle, D. (2010). Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems. ESAIM: Control Optimisation and Calculus of Variations, 17(2), 380–405.

    Article  MathSciNet  MATH  Google Scholar 

  • Moireau, P., Xiao, N., Astorino, M., Figueroa, C. A., Chapelle, D., Taylor, C. A., et al. (2011). External tissue support and fluid-structure simulation in blood flows. Biomechanics and Modeling in Mechanobiology, 11, 1–18.

    Article  Google Scholar 

  • Munson, B., Young, D., & Okiishi, T. (1994). Fundamentals of fluid mechanics (2nd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Nathan, D. P., Xu, C., Gorman, J. H, I. I. I., Fairman, R. M., Bavaria, J. E., Gorman, R. C., et al. (2011). Pathogenesis of acute aortic dissection: A finite element stress analysis. The Annals of Thoracic Surgery, 91(2), 458–463.

    Article  Google Scholar 

  • Perego, M., Veneziani, A., & Vergara, C. (2011). A variational approach for estimating the compliance of the cardiovascular tissue: An inverse fluid-structure interaction problem. SIAM Journal on Scientific Computing, 33(3), 1181–1211.

    Article  MathSciNet  MATH  Google Scholar 

  • Peterson, K. L., Tsuji, J., Johnson, A., DiDonna, J., & LeWinter, M. (1978). Diastolic left ventricular pressure-volume and stress-strain relations in patients with valvular aortic stenosis and left ventricular hypertrophy. Circulation, 58(1), 77–89.

    Article  Google Scholar 

  • Qiao, A., Yin, W., & Chu, B. (2014). Numerical simulation of fluid-structure interaction in bypassed DeBakey III aortic dissection. Computer Methods in Biomechanics and Biomedical Engineering, 18(11), 1173–1180.

    Article  Google Scholar 

  • Raghavan, M. L., & Vorp, D. A. (2000). Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: Identification of a finite strain constitutive model and evaluation of its applicability. Journal of Biomechanics, 33, 475–482.

    Article  Google Scholar 

  • Reymond, P., Crosetto, P., Deparis, S., Quarteroni, A., & Stergiopulos, N. (2013). Physiological simulation of blood flow in the aorta: Comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models. Medical Engineering and Physics, 35(6), 784–791.

    Article  Google Scholar 

  • Rhie, C. & Chow, W. (2012). A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. In 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics.

    Google Scholar 

  • Roy, D., Holzapfel, G. A., Kauffmann, C., & Soulez, G. (2014). Finite element analysis of abdominal aortic aneurysms: Geometrical and structural reconstruction with application of an anisotropic material model. IMA Journal of Applied Mathematics, 79(5), 1011–1026.

    Article  MathSciNet  MATH  Google Scholar 

  • Shi, Y., Lawford, P., & Hose, R. (2011). Review of Zero-D and 1-D models of blood flow in the cardiovascular system. BioMedical Engineering OnLine, 10(1), 33.

    Article  Google Scholar 

  • Speelman, L., Bosboom, E. M. H., Schurink, G. W. H., Hellenthal, F. A. M. V. I., Buth, J., Breeuwer, M., et al. (2008). Patient-specific AAA wall stress analysis: 99-percentile versus peak stress. European Journal of Vascular and Endovascular Surgery, 36(6), 668–676.

    Article  Google Scholar 

  • Stergiopulos, N., Westerhof, B. E., & Westerhof, N. (1999). Total arterial inertance as the fourth element of the windkessel model. American Journal of Physiology-Legacy Content, 276(1), H81–H88.

    Google Scholar 

  • Studwell, A. J., & Kotton, D. N. (2011). A shift from cell cultures to creatures: In vivo imaging of small animals in experimental regenerative medicine. Molecular Therapy, 19(11), 1933–1941.

    Article  Google Scholar 

  • Tan, F. P. P., Borghi, A., Mohiaddin, R. H., Wood, N. B., Thom, S., & Xu, X. Y. (2009). Analysis of flow patterns in a patient-specific thoracic aortic aneurysm model. Computers and Structures, 87(11–12), 680–690.

    Article  Google Scholar 

  • Taylor, A., Sheridan, M., McGee, S., & Halligan, S. (2005). Preoperative staging of rectal cancer by MRI; results of a UK survey. Clinical Radiology, 60, 579–586.

    Article  Google Scholar 

  • Tse, K. M., Chiu, P., Lee, H. P., & Ho, P. (2011). Investigation of hemodynamics in the development of dissecting aneurysm within patient-specific dissecting aneurismal aortas using computational fluid dynamics (CFD) simulations. Journal of Biomechanics, 44(5), 827–836.

    Article  Google Scholar 

  • Versteeg, H., & Malalasekera, W. (2007). An introduction to computational fluid dynamics (2nd ed.). Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Vignon-Clementel, I. E., Alberto Figueroa, C., Jansen, K. E., & Taylor, C. A. (2006). Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Computer Methods in Applied Mechanics and Engineering, 195(29–32), 3776–3796.

    Article  MathSciNet  MATH  Google Scholar 

  • Wesseling, P. (2000). Principles of compuational fluid dynamics. Heidelberg: Springer.

    MATH  Google Scholar 

  • Westerhof, N., Bosman, F., De Vries, C. J., & Noordergraaf, A. (1969). Analog studies of the human systemic arterial tree. Journal of Biomechanics, 2(2), 121–143.

    Article  Google Scholar 

  • Westerhof, N., Lankhaar, J.-W., & Westerhof, B. E. (2008). The arterial Windkessel. Medical and Biological Engineering and Computing, 47(2), 131–141.

    Article  Google Scholar 

  • White, F. (2011). Fluid mechanics (7th ed.). New York: McGraw-Hill.

    Google Scholar 

  • Xiao, N., Alastruey, J., & Alberto Figueroa, C. (2013). A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. International Journal for Numerical Methods in Biomedical Engineering, 30(2), 204–231.

    Article  MathSciNet  Google Scholar 

  • Yang, S., Li, X., Chao, B., Wu, L., Cheng, Z., Duan, Y., et al. (2014). Abdominal aortic intimal flap motion characterization in acute aortic dissection: Assessed with retrospective ECG-Gated thoracoabdominal aorta dual-source CT angiography. PLoS ONE, 9(2), e87664.

    Article  Google Scholar 

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Alimohammadi, M. (2018). Computational Methods for Patient-Specific Modelling. In: Aortic Dissection: Simulation Tools for Disease Management and Understanding. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-56327-5_2

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  • DOI: https://doi.org/10.1007/978-3-319-56327-5_2

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