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Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 6, pp 1867–1881 | Cite as

Reduced-order modeling of blood flow for noninvasive functional evaluation of coronary artery disease

  • Stefano BuosoEmail author
  • Andrea Manzoni
  • Hatem Alkadhi
  • André Plass
  • Alfio Quarteroni
  • Vartan KurtcuogluEmail author
Original Paper

Abstract

We present a novel computational approach, based on a parametrized reduced-order model, for accelerating the calculation of pressure drop along blood vessels. Vessel lumina are defined by a geometric parametrization using the discrete empirical interpolation method on control points located on the surface of the vessel. Hemodynamics are then computed using a reduced-order representation of the parametrized three-dimensional unsteady Navier–Stokes and continuity equations. The reduced-order model is based on an offline–online splitting of the solution process, and on the projection of a finite volume full-order model on a low-dimensionality subspace generated by proper orthogonal decomposition of pressure and velocity fields. The algebraic operators of the hemodynamic equations are assembled efficiently during the online phase using the discrete empirical interpolation method. Our results show that with this approach calculations can be sped up by a factor of about 25 compared to the conventional full-order model, while maintaining prediction errors within the uncertainty limits of invasive clinical measurement of pressure drop. This is of importance for a clinically viable implementation of noninvasive, medical imaging-based computation of fractional flow reserve.

Keywords

FFR Coronary artery disease Computational fluid dynamics Finite volumes method Discrete empirical interpolation method Navier–Stokes Proper orthogonal decomposition Reduced basis method Reduced-order modeling 

Notes

Acknowledgements

The authors acknowledge the financial support of Mr. Joe Clark, the Swiss National Science Foundation through NCCR Kidney.CH, and the University of Zurich through the Forschungskredit Postdoc Fellowship (FK-18-043).

Compliance with ethical standards

Conflict of interest

A patent application covering parts of the technology described in the manuscript has been filed.

References

  1. Amsallem D, Zahr M, Farhat C (2012) Nonlinear model order reduction based on local reduced-order bases. Int J Numer Methods Eng 92(10):891–916MathSciNetzbMATHCrossRefGoogle Scholar
  2. Ashtekar KD, Back LH, Khoury SF, Banerjee RK (2007) In vitro quantification of guidewire flow-obstruction effect in model coronary stenoses for interventional diagnostic procedure. ASME J Med Dev 1(3):185–196CrossRefGoogle Scholar
  3. Ballarin F, Manzoni A, Quarteroni A, Rozza G (2015) Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier–Stokes equations. Int J Numer Methods Eng 102(5):1136–1161MathSciNetzbMATHCrossRefGoogle Scholar
  4. Ballarin F, Faggiano E, Ippolito S, Manzoni A, Quarteroni A, Rozza G, Scrofani R (2016) Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization. J Comput Phys 315:609–628MathSciNetzbMATHCrossRefGoogle Scholar
  5. Ballarin F, Faggiano E, Manzoni A, Quarteroni A, Rozza G, Ippolito S, Antona C, Scrofani R (2017) Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts. Biomech Model Mechanobiol 16(4):1373–1399zbMATHCrossRefGoogle Scholar
  6. Bergmann M, Bruneau CH, Iollo A (2009) Enablers for robust POD models. J Computat Phys 228(2):516–538MathSciNetzbMATHCrossRefGoogle Scholar
  7. Buljak V (2011) Inverse analyses with model reduction. Computational fluid and solid mechanics. Springer, BerlinGoogle Scholar
  8. Buoso S, Palacios R (2017) On-demand aerodynamics of integrally actuated membranes with feedback control. AIAA J 55(2):377–388CrossRefGoogle Scholar
  9. Coenen A, Lubbers MM, Kurata A, Kono A, Dedic A, Chelu RG, Dijkshoorn ML, Gijsen FJ, Ouhlous M, van Geuns RM, Nieman K (2015) Fractional flow reserve computed from noninvasive CT angiography data: diagnostic performance of an on-site clinician-operated computational fluid dynamics algorithm. Radiology 274(3):674–683CrossRefGoogle Scholar
  10. Colciago C, Deparis S, Quarteroni A (2014) Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics. J Comput Appl Math 265:20–138MathSciNetzbMATHCrossRefGoogle Scholar
  11. de Vecchi A, Clough RE, Gaddum NR, Rutten MCM, Lamata P, Schaeffter T, Nordsletten DA, Smith NP (2014) Catheter-induced errors in pressure measurements in vessels: an in-vitro and numerical study. IEEE Trans Biomed Eng 61(6):1844–1850CrossRefGoogle Scholar
  12. de Zélicourt DA, Kurtcuoglu V (2016) Patient-specific surgical planning, where do we stand? The example of the Fontan procedure. Ann Biomed Eng 44(1):174–186CrossRefGoogle Scholar
  13. Douglas PS, De Bruyne B, Pontone G, Patel MR, Norgaard BL, Byrne RA, Curzen N, Purcell I, Gutberlet M, Rioufol G, Hink U, Schuchlenz HW, Feuchtner G, Gilard M, Andreini D, Jensen JM, Hadamitzky M, Chiswell K, Cyr D, Wilk A, Wang F, Rogers C, Hlatky MA (2016) 1-Year outcomes of FFRCT-guided care in patients with suspected coronary disease. J Am Coll Cardiol 68(5):435–445CrossRefGoogle Scholar
  14. Gijsen FJ, Schuurbiers JC, van de Giessen AG, Schaap M, van der Steen AF, Wentzel JJ (2014) 3D reconstruction techniques of human coronary bifurcations for shear stress computations. J Biomech 47(1):39–43CrossRefGoogle Scholar
  15. Gould KL, Lipscomb K, Hamilton WG (1974) Physiologic basis for assessing critical coronary stenosis. Am J Cardiol 33(1):87–94CrossRefGoogle Scholar
  16. Heidenreich PA, Trogdon JG, Khavjou OA, Butler J, Dracup K, Ezekowitz MD, Finkelstein EA, Hong Y, Johnston SC, Khera A, Lloyd-Jones DM, Nelson SA, Nichol G, Orenstein D, Wilson PW, Woo YJ (2011) Forecasting the future of cardiovascular disease in the United States. Circulation 123(8):933–944CrossRefGoogle Scholar
  17. Hlatky MA, De Bruyne B, Pontone G, Patel MR, Norgaard BL, Byrne RA, Curzen N, Purcell I, Gutberlet M, Rioufol G, Hink U, Schuchlenz HW, Feuchtner G, Gilard M, Andreini D, Jensen JM, Hadamitzky M, Wilk A, Wang F, Rogers C, Douglas PS (2015) Quality-of-life and economic outcomes of assessing fractional flow reserve with computed tomography angiography. J Am Coll Cardiol 66(21):2315–2323CrossRefGoogle Scholar
  18. Itu L, Rapaka S, Passerini T, Georgescu B, Schwemmer C, Schoebinger M, Flohr T, Sharma P, Comaniciu D (2016) A machine-learning approach for computation of fractional flow reserve from coronary computed tomography. J Appl Physiol 121:42–52CrossRefGoogle Scholar
  19. Jasak H (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. thesis, Imperial College LondonGoogle Scholar
  20. Keegan J, Gatehouse PD, Yang G-Z, Firmin DN (2004) Spiral phase velocity mapping of left and right coronary artery blood flow: correction for through-plane motion using selective fat-only excitation. J Magn Reson Imaging 20(6):953–960CrossRefGoogle Scholar
  21. Knight J, Olgac U, Saur SC, Poulikakos D, Marshall W, Cattin PC, Alkadhi H, Kurtcuoglu V (2010) Choosing the optimal wall shear parameter for the prediction of plaque location: a patient-specific computational study in human right coronary arteries. Atherosclerosis 211(2):445–450CrossRefGoogle Scholar
  22. Lassila T, Manzoni A, Quarteroni A, Rozza G (2013) A reduced computational and geometrical framework for inverse problems in haemodynamics. Int J Numer Methods Biomed Eng 29(7):741–776MathSciNetCrossRefGoogle Scholar
  23. Maday Y, Nguyen NC, Patera TA, Pau SH (2009) A general multipurpose interpolation procedure: the magic points. Commun Pure Appl Anal 8:383MathSciNetzbMATHCrossRefGoogle Scholar
  24. Mancini GBJ, Ryomoto A, Kamimura C, Yeoh E, Ramanathan K, Schulzer M, Hamburger J, Ricci D (2007) Redefining the normal angiogram using population-derived ranges for coronary size and shape: validation using intravascular ultrasound and applications in diverse patient cohorts. Int J Cardiovasc Imaging 23(4):441–453CrossRefGoogle Scholar
  25. Manzoni A (2014) An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows. ESAIM Math Model Numer Anal 48:1199–1226MathSciNetzbMATHCrossRefGoogle Scholar
  26. Manzoni A, Quarteroni A, Rozza G (2012a) Model reduction techniques for fast blood flow simulation in parametrized geometries. Int J Numer Methods Biomed Eng 28(6–7):604–625MathSciNetCrossRefGoogle Scholar
  27. Manzoni A, Quarteroni A, Rozza G (2012b) Shape optimization of cardiovascular geometries by reduced basis methods and free-form deformation techniques. Int J Numer Methods Fluids 70(5):646–670zbMATHCrossRefGoogle Scholar
  28. Moukalled F, Mangani L, Darwish M (2015) The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM and Matlab, 1st edn. Springer, BerlinzbMATHGoogle Scholar
  29. Negri F, Manzoni A, Amsallem D (2015) Efficient model reduction of parametrized systems by matrix discrete empirical interpolation. J Computat Phys 303:431–454MathSciNetzbMATHCrossRefGoogle Scholar
  30. Olgac U, Poulikakos D, Saur SC, Alkadhi H, Kurtcuoglu V (2009) Patient-specific three-dimensional simulation of LDL accumulation in a human left coronary artery in its healthy and atherosclerotic states. Am J Physiol Heart Circ Physiol 296(6):H1969–H1982CrossRefGoogle Scholar
  31. Pagani S, Manzoni A, Quarteroni A (2018) Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method. Comput Methods Appl Mech Eng 340:530–558MathSciNetCrossRefGoogle Scholar
  32. Pijls NH, van Schaardenburgh P, Manoharan G, Boersma E, Jan-Willem B, vant Veer M, Bär F, Hoorntje J, Koolen J, Wijns W, de Bruyne B (2007) Percutaneous coronary intervention of functionally nonsignificant stenosis. J Am Coll Cardiol 49(21):2105–2111CrossRefGoogle Scholar
  33. Quarteroni A, Manzoni A, Negri F (2016) Reduced basis methods for partial differential equations: an introduction. Vol. 92 of UNITEXT - La Matematica per il 3+2. Springer, BerlinCrossRefGoogle Scholar
  34. Quarteroni A, Rozza G (2007) Numerical solution of parametrized Navier–Stokes equations by reduced basis methods. Numer Methods Partial Differ Equ 23(4):923–948MathSciNetzbMATHCrossRefGoogle Scholar
  35. Rikhtegar F, Knight JA, Olgac U, Saur SC, Poulikakos D, Marshall W, Cattin PC, Alkadhi H, Kurtcuoglu V (2012) Choosing the optimal wall shear parameter for the prediction of plaque locationa patient-specific computational study in human left coronary arteries. Atherosclerosis 221(2):432–437CrossRefGoogle Scholar
  36. Rowley CW (2011) Model reduction for fluids, using balanced proper orthogonal decomposition. Int J Bifurc Chaos 15(03):997–1013MathSciNetzbMATHCrossRefGoogle Scholar
  37. Sankaran S, Esmaily Moghadam M, Kahn AM, Tseng EE, Guccione JM, Marsden AL (2012) Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Ann Biomed Eng 40(10):2228–2242CrossRefGoogle Scholar
  38. Stabile G, Hijazi S, Mola A, Lorenzi S, Rozza G (2015) Advances in reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method. Commun Appl Ind Math 9(1):1–s21zbMATHCrossRefGoogle Scholar
  39. Stabile G, Rozza G (2018) Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier Stokes equations. Comput Fluids 173:273–284MathSciNetzbMATHCrossRefGoogle Scholar
  40. Stergiopulos N, Meister JJ, Westerhof N (1995) Evaluation of methods for estimation of total arterial compliance. Am J Physiol Heart Circ Physiol 268(4):H1540–H1548CrossRefGoogle Scholar
  41. Taylor CA, Fonte TA, Min JK (2013) Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve. J Am Coll Cardiol 61(22):2233–2241CrossRefGoogle Scholar
  42. Tonino PA, Fearon WF, Bruyne BD, Oldroyd KG, Leesar MA, Lee PNV, MacCarthy PA, van’t Veer M, Pijls NH (2010) Angiographic versus functional severity of coronary artery stenoses in the FAME study. J Am Coll Cardiol 55(25):2816–2821CrossRefGoogle Scholar
  43. Vergallo R, Papafaklis MI, Yonetsu T, Bourantas CV, Andreou I, Wang Z, Fujimoto JG, McNulty I, Lee H, Biasucci LM, Crea F, Feldman CL, Michalis LK, Stone PH, Jang I-K (2014) Endothelial shear stress and coronary plaque characteristics in humans. Circ Cardiovasc Imaging 7(6):905–911CrossRefGoogle Scholar
  44. Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12(6):620–631CrossRefGoogle Scholar
  45. Zafar H, Sharif F, Leahy MJ (2014) Measurement of the blood flow rate and velocity in coronary artery stenosis using intracoronary frequency domain optical coherence tomography: validation against fractional flow reserve. Int J Cardiol Heart Vasc Supplement C(5):68–71Google Scholar
  46. Zhang JM, Zhong L, Luo T, Lomarda AM, Huo Y, Yap J, Lim ST, Tan RS, Wong ASL, Tan JWC, Yeo KK, Fam JM, Keng FYJ, Wan M, Su B, Zhao X, Allen JC, Kassab GS, Chua TSJ, Tan SY (2016) Simplified models of non-invasive fractional flow reserve based on CT images. PLoS ONE 11(5):1–20Google Scholar
  47. Zimmermann FM, Ferrara A, Johnson NP, van Nunen LX, Escaned J, Albertsson P, Erbel R, Legrand V, Gwon H-C, Remkes WS, Stella PR, van Schaardenburgh P, Jan Willem G, De Bruyne B, Pijls NH (2015) Deferral vs. performance of percutaneous coronary intervention of functionally non-significant coronary stenosis: 15-year follow-up of the DEFER trial. Eur Heart J 36(45):3182–3188CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The Interface Group, Institute of PhysiologyUniversity of ZurichZurichSwitzerland
  2. 2.Institute of Diagnostic and Interventional Radiology, University Hospital ZurichZurichSwitzerland
  3. 3.Chair of Modeling and Scientific Computing, Mathematics Institute of Computational Science and EngineeringÉcole Fédérale Polytechnique de LausanneLausanneSwitzerland
  4. 4.Clinic for Cardiovascular Surgery, University Hospital ZurichZurichSwitzerland
  5. 5.National Center of Competence in Research, Kidney.CHZurichSwitzerland
  6. 6.Zurich Center for Integrative Human PhysiologyUniversity of ZurichZurichSwitzerland

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