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Numerical Comparison and Calibration of Geometrical Multiscale Models for the Simulation of Arterial Flows

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Abstract

Arterial tree hemodynamics can be simulated by means of several models of different level of complexity, depending on the outputs of interest and the desired degree of accuracy. In this work, several numerical comparisons of geometrical multiscale models are presented with the aim of evaluating the benefits of such complex dimensionally-heterogeneous models compared to other simplified simulations. More precisely, we present flow rate and pressure wave form comparisons between three-dimensional patient-specific geometries implicitly coupled with one-dimensional arterial tree networks and (i) a full one-dimensional arterial tree model and (ii) stand-alone three-dimensional fluid–structure interaction models with boundary data taken from precomputed full one-dimensional network simulations. On a slightly different context, we also focus on the set up and calibration of cardiovascular simulations. In particular, we perform sensitivity analyses of the main quantities of interest (flow rate, pressure, and solid wall displacement) with respect to the parameters accounting for the elastic and viscoelastic responses of the tissues surrounding the external wall of the arteries. Finally, we also compare the results of geometrical multiscale models in which the boundary solid rings of the three-dimensional geometries are fixed, with respect to those where the boundary interfaces are scaled to enforce the continuity of the vessels size with the surrounding one-dimensional arteries.

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  1. http://www.lifev.org.

  2. http://simtk.org.

  3. http://www.vtk.org.

  4. http://www.vmtk.org.

  5. http://www.itk.org.

References

  1. Alastruey, J., K. H. Parker, J. Peiró, S. M. Byrd, and S. J. Sherwin. Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J. Biomech. 40(8):1794–1805, 2007.

    Article  Google Scholar 

  2. Balossino, R., G. Pennati, F. Migliavacca, L. Formaggia, A. Veneziani, M. Tuveri, and G. Dubini. Computational models to predict stenosis growth in carotid arteries: Which is the role of boundary conditions? Comput. Methods Biomech. Biomed. Eng. 12(1):113–123, 2009.

    Article  Google Scholar 

  3. Baretta, A., C. Corsini, W. Yang, I. E. Vignon-Clementel, A. L. Marsden, J. A. Feinstein, T.-Y. Hsia, G. Dubini, F. Migliavacca, and G. Pennati. Virtual surgeries in patients with congenital heart disease: a multi-scale modelling test case. Philos. Trans. R. Soc. Lond. A 369(1954):4316–4330, 2011.

    Article  Google Scholar 

  4. Bazilevs, Y., V. M. Calo, T. J. R. Hughes, and Y. Zhang. Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput. Mech. 43(1):3–37, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bertoglio, C., P. Moireau, and J.-F. Gerbeau. Sequential parameter estimation for fluid-structure problems. Application to hemodynamics. Int. J. Numer. Methods Biomed. Eng. 28(4):434–455, 2012.

    Article  MathSciNet  Google Scholar 

  6. Blanco, P. J., R. A. Feijóo, and S. A. A. Urquiza. Unified variational approach for coupling 3D–1D models and its blood flow applications. Comput. Methods Appl. Mech. Eng. 196(41–44):4391–4410, 2007.

    Article  MATH  Google Scholar 

  7. Blanco, P. J., J. S. Leiva , R. A. Feijóo, and G. C. Buscaglia. Black-box decomposition approach for computational hemodynamics: one-dimensional models. Comput. Methods Appl. Mech. Eng. 200(13–16):1389–1405, 2011.

    Article  MATH  Google Scholar 

  8. Bonnemain, J., A. C. I. Malossi, M. Lesinigo, S. Deparis, A. Quarteroni, and L. K. von Segesser. Numerical simulation of left ventricular assist device implantations: comparing the ascending and the descending aorta cannulations. Med. Eng. Phys., 2013. doi:10.1016/j.medengphy.2013.03.022.

  9. Burman, E., M. A. Fernández, and P. Hansbo. Continuous interior penalty finite element method for Oseen’s equations. SIAM J. Numer. Anal. 44(3):1248–1274, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  10. Čanić, S., K. Ravi-Chandar, Z. Krajcer, D. Mirković, and S. Lapin. Mathematical model analysis of Wallstent® and AneuRx®: dynamic responses of bare-metal endoprosthesis compared with those of stent-graft. Tex. Heart Inst. J. 34(4):502–506, 2005.

    Google Scholar 

  11. Crosetto, P. Fluid–Structure Interaction Problems in Hemodynamics: Parallel Solvers, Preconditioners, and Applications. PhD thesis, École Polytechnique Fédérale de Lausanne, 2011. http://infoscience.epfl.ch/record/166924.

  12. Crosetto, P., S. Deparis, L. Formaggia, G. Mengaldo, F. Nobile, and P. A. Tricerri. A comparative study of different nonlinear hyperelastic isotropic arterial wall models in patient-specific vascular flow simulations in the aortic arch. Submitted, 2012.

  13. Crosetto, P., S. Deparis, G. Fourestey, and A. Quarteroni. Parallel algorithms for fluid-structure interaction problems in haemodynamics. SIAM J. Sci. Comput. 33(4):1598–1622, 2011a

    Article  MathSciNet  MATH  Google Scholar 

  14. Crosetto, P., P. Reymond, S. Deparis, D. Kontaxakis, N. Stergiopulos, and A. Quarteroni. Fluid–structure interaction simulation of aortic blood flow. Comput. Fluids 43(1):46–57, 2011b.

    Article  MathSciNet  MATH  Google Scholar 

  15. D’Elia, M., and A. Veneziani. Uncertainty quantification for data assimilation in a steady incompressible Navier–Stokes problem. ESAIM Math. Model. Numer. Anal. 2013. doi:10.1051/m2an/2012056.

  16. Euler, L. Principia pro motu sanguinis per arterias determinando (1775). Opera Posthuma Mathematica et Physica 2:814–823, 1844.

  17. Faggiano, E., J. Bonnemain, A. Quarteroni, and S. Deparis. A patient-specific framework for the analysis of the haemodynamics in patients with ventricular assist device. Submitted, 2012.

  18. Figueroa, C. A., S. Baek, C. A. Taylor, and J. D. Humphrey. A computational framework for fluid-solid-growth modeling in cardiovascular simulations. Comput. Methods Appl. Mech. Eng. 198(45–463):3583–3601, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  19. Formaggia, L., D. Lamponi, and A. Quarteroni. One-dimensional models for blood flow in arteries. J. Eng. Math. 47(3–4):251–276, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  20. Formaggia, L., A. Moura, and F. Nobile. On the stability of the coupling of 3D and 1D fluid–structure interaction models for blood flow simulations. ESAIM Math. Model. Numer. Anal. 41(4):743–769, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  21. Formaggia, L., F. Nobile, A. Quarteroni, and A. Veneziani. Multiscale modelling of the circulatory system: a preliminary analysis. Comput. Vis. Sci. 2(2–3):75–83, 1999.

    Article  MATH  Google Scholar 

  22. Formaggia, L., A. Quarteroni, and A. Veneziani. Cardiovascular Mathematics, Vol. 1 of Modeling, Simulation & Applications. Milan: Springer, 2009.

  23. Formaggia, L., A. Veneziani, and C. Vergara. Flow rate boundary problems for an incompressible fluid in deformable domains: formulations and solution methods. Comput. Methods Appl. Mech. Eng. 199(9–12):677–688, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  24. Fung, Y. C. Biomechanics: Mechanical Properties of Living Tissues, 2nd ed. New York: Springer, 1993.

  25. Gerbeau, J.-F., M. Vidrascu, and P. Frey. Fluid–structure interaction in blood flows on geometries based on medical imaging. Comput. Struct. 83(2–3):155–165, 2005.

    Article  Google Scholar 

  26. Grinberg, L., T. Anor, J. R. Madsen, A. Yakhot, and G. E. Karniadakis. Large-scale simulation of the human arterial tree. Clin. Exp. Pharmacol. Physiol. 36(2):194–205, 2009.

    Article  Google Scholar 

  27. Holzapfel, G. A., and R. W. Ogden. Mechanics of Biological Tissue. Berlin: Springer, 2006.

  28. Holzapfel, G. A., T. C. Gasser, and R. W. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elasticity 61(1–3):1–48, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  29. Kanyanta, V., A. Ivankovic, and A. Karac. Validation of a fluid–structure interaction numerical model for predicting flow transients in arteries. J. Biomech. 42(11):1705–1712, 2009.

    Article  Google Scholar 

  30. Laganà à, K., G. Dubini, F. Migliavacca, R. Pietrabissa, G. Pennati, A. Veneziani, and A. Quarteroni. Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures. Biorheology 39(3):359–364, 2002.

    Google Scholar 

  31. Langewouters, G. J. Visco-Elasticity of the Human Aorta In Vitro in Relation to Pressure and Age. PhD thesis, Free University, Amsterdam, 1982.

  32. Li, D., and A. M. Robertson. A Structural multi-mechanism damage model for cerebral arterial tissue. J. Biomech. Eng. 131(10):101013 (8 pages), 2009.

    Google Scholar 

  33. Liu, Y., C. Dang, M. Garcia, H. Gregersen, and G. S. Kassab. Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment. Am. J. Physiol. Heart Circ. Physiol. 293(6):H3290–H3300, 2007.

    Google Scholar 

  34. Malossi, A. C. I. Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System: Models, Algorithms, and Applications. PhD thesis, École Polytechnique Fédérale de Lausanne, 2012. http://infoscience.epfl.ch/record/180639.

  35. Malossi, A. C. I., P. J. Blanco, S. Deparis, and A. Quarteroni. Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows. Int. J. Numer. Methods Biomed. Eng. 27(12):2035–2057, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  36. Malossi, A. C. I., P. J. Blanco, and S. Deparis. A two-level time step technique for the partitioned solution of one-dimensional arterial networks. Comput. Methods Appl. Mech. Eng. 237–240:212–226, 2012.

    Google Scholar 

  37. Malossi, A. C. I., P. J. Blanco, P. Crosetto, S. Deparis, and A. Quarteroni. Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels. SIAM J. Multiscale Model. Simul. 11(2):474–506, 2013.

    Google Scholar 

  38. Martin, V., F. Clément, A. Decoene, and J.-F. Gerbeau. Parameter identification for a one-dimensional blood flow model. In: Proceedings of the CEMRACS: Mathematics and Applications to Biology and Medicine, Vol. 14. EASIM, 2005, pp. 174–200.

  39. Moireau, P., N. Xiao, M. Astorino, C. A. Figueroa, D. Chapelle, C.-A. Taylor, and J.-F. Gerbeau. External tissue support and fluid–structure simulation in blood flows. Biomech. Model. Mechanobiol. 11(1–2):1–18, 2012.

    Article  Google Scholar 

  40. Papadakis, G. Coupling 3D and 1D fluid–structure-interaction models for wave propagation in flexible vessels using a finite volume pressure-correction scheme. Commun. Numer. Methods Eng. 25(5):533–551, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  41. Passerini, T., M. de Luca, L. Formaggia, A. Quarteroni, A. Veneziani. A 3D/1D geometrical multiscale model of cerebral vasculature. J. Eng. Math. 64(4):319–330, 2009.

    Article  MATH  Google Scholar 

  42. Reymond, P., Y. Bohraus, F. Perren, F. Lazeyras, N. Stergiopulos. Validation of a patient-specific one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 301(3):H1173–H1182, 2011.

    Article  Google Scholar 

  43. Reymond, P., F. Merenda, F. Perren, D. Rüfenacht, N. Stergiopulos. Validation of a one-dimensional model of the systemic arterial tree. Am. J. Physiol. Heart Circ. Physiol. 297(1):H208–H222, 2009.

    Article  Google Scholar 

  44. Robertson, A. M., M. R. Hill, and D. Li. Structurally motivated damage models for arterial walls. Theory and application. In: Modeling of Physiological Flows, Vol. 5 of Modeling, Simulation & Applications. Milan: Springer, 2011, pp. 143–185.

  45. Shi, Y., P. Lawford, and R. Hose. Review of Zero-D and 1-D models of blood flow in the cardiovascular system. BioMed. Eng. OnLine 10(33):1–38, 2011.

    Google Scholar 

  46. Tezduyar, T. E., and S. Sathe. Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int. J. Numer. Methods Fluids 54(6–8):855–900, 2006.

    Google Scholar 

  47. Vignon-Clementel, I. E., C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng. 195(29–32):3776–3796, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  48. Xiao, N., J. D. Humphrey, and C. A. Figueroa. Multi-scale computational model of three-dimensional hemodynamics within a deformable full-body arterial network. J. Comput. Phys., 2013.

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Acknowledgments

A. C. I. Malossi acknowledges the Swiss Platform for High-Performance and High-Productivity Computing (HP2C). J. Bonnemain acknowledges the Swiss National Fund (SNF) grant 323630-133898. We also acknowledge the European Research Council Advanced Grant “Mathcard, Mathematical Modelling and Simulation of the Cardiovascular System”, Project ERC-2008-AdG 227058. Last but not least, we acknowledge Pablo Blanco (LNCC), Simone Deparis (CMCS, EPFL), and Alfio Quarteroni (CMCS, EPFL) for their precious support, as well as Phylippe Reymond (LHTC, EPFL) for the 3-D geometry of the aorta. All the numerical results presented in this paper have been computed using the LifeV library (http://www.lifev.org).

Conflict of interest

All authors declare that no conflicts of interest exist.

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Authors and Affiliations

  1. MATHICSE, Mathematics Institute of Computational Science and Engineering, EPFL, École Polytechnique Fédérale de Lausanne, Station 8, 1015, Lausanne, Switzerland

    A. Cristiano I. Malossi & Jean Bonnemain

  2. CHUV, Centre Hospitalier Universitaire Vaudois, Rue du Bugnon 21, 1011, Lausanne, Switzerland

    Jean Bonnemain

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  1. A. Cristiano I. Malossi
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Correspondence to A. Cristiano I. Malossi.

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Associate Editor Ajit P. Yoganathan oversaw the review of this article.

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Malossi, A.C.I., Bonnemain, J. Numerical Comparison and Calibration of Geometrical Multiscale Models for the Simulation of Arterial Flows. Cardiovasc Eng Tech 4, 440–463 (2013). https://doi.org/10.1007/s13239-013-0151-9

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