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Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts

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Abstract

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the hemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patient-specific medical images to fast parameterized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier–Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parameterization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases.

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Notes

  1. The number of wall time hours needs to be multiplied by the number of processors to obtain the actual CPU time spent on the cluster. The actual CPU time is listed in Table 2 in order to have a fair comparison between the high-fidelity model (which runs in parallel on several processors) and ROM (which runs in serial).

Abbreviations

RCA:

Right coronary artery

PDA:

Posterior descending artery

PL:

Postero-lateral artery

LCA:

Main trunk of the left coronary artery

LAD:

Left anterior descending artery

Diag.:

Diagonal branch of the left anterior descending artery

LCX:

Left circumflex artery

OM:

Obtuse marginal artery

LITA:

Left internal thoracic artery

Rad.:

Radial artery bypass grafts

SVG:

Saphenous vein bypass grafts

References

  • Antiga L (2002) Patient-Specific modeling of geometry and blood flow in large arteries. PhD thesis, Dipartimento di Bioingegneria, Politecnico di Milano

  • Antiga L, Ene-Iordache B, Remuzzi A (2003) Computational geometry or patient-specific reconstruction and meshing of blood vessels from MR and CT angiography. IEEE Trans Med Imaging 22(5):674–684

    Article  Google Scholar 

  • Antiga L, Piccinelli M, Botti L, Ene-Iordache B, Remuzzi A, Steinman D (2008) An image-based modeling framework for patient-specific computational hemodynamics. Med Biol Eng Comput 46:1097–1112

    Article  Google Scholar 

  • Ballarin F (2015) Reduced-order models for patient-specific haemodynamics of coronary artery bypass grafts. PhD thesis, Department of Mathematics, Politecnico di Milano. http://hdl.handle.net/10589/102804

  • 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 315:609–628

    Article  MathSciNet  MATH  Google Scholar 

  • 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):1136–1161

    Article  MathSciNet  MATH  Google Scholar 

  • Berkooz G, Holmes P, Lumley J (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech 25(1):539–575

    Article  MathSciNet  Google Scholar 

  • Bertolotti C, Deplano V (2000) Three-dimensional numerical simulations of flow through a stenosed coronary bypass. J Biomech 33(8):1011–1022

    Article  Google Scholar 

  • Bertolotti C, Deplano V, Fuseri J, Dupouy PJ (2001) Numerical and experimental models of post-operative realistic flows in stenosed coronary bypasses. J Biomech 34(8):1049–1064

    Article  Google Scholar 

  • Bishop RL (1975) There is more than one way to frame a curve. Am Math Mon 82(3):246–251

    Article  MathSciNet  MATH  Google Scholar 

  • Bonert M, Myers JG, Fremes S, Williams J, Ross Ethier C (2002) A numerical study of blood flow in coronary artery bypass graft side-to-side anastomoses. Ann Biomed Eng 30(5):599–611

    Article  Google Scholar 

  • Boutsianis E, Dave H, Frauenfelder T, Poulikakos D, Wildermuth S, Turina M, Ventikos Y, Zund G (2004) Computational simulation of intracoronary flow based on real coronary geometry. Eur J Cardio-Thorac Surg 26(2):248–256

    Article  Google Scholar 

  • Burkardt J, Gunzburger M, Lee H-C (2006) POD and CVT-based reduced-order modeling of Navier–Stokes flows. Comput Methods Appl Mech Eng 196(1–3):337–355

    Article  MathSciNet  MATH  Google Scholar 

  • Chaichana T, Sun Z, Jewkes J (2011) Computation of hemodynamics in the left coronary artery with variable angulations. J Biomech 44(10):1869–1878

    Article  Google Scholar 

  • Chen J, Lu X-Y, Wang W (2006) Non-newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses. J Biomech 39(11):1983–1995

    Article  Google Scholar 

  • Deplano V, Bertolotti C, Boiron O (2001) Numerical simulations of unsteady flows in a stenosed coronary bypass graft. Med Biol Eng Comput 39(4):488–499

    Article  Google Scholar 

  • Desai ND, Cohen EA, Naylor CD, Fremes SE (2004) A randomized comparison of radial-artery and saphenous-vein coronary bypass grafts. N Engl J Med 351(22):2302–2309

    Article  Google Scholar 

  • Do H, Owida AA, Yang W, Morsi YS (2011) Numerical simulation of the haemodynamics in end-to-side anastomoses. Int J Numer Methods Fluids 67:638–650

    Article  MATH  Google Scholar 

  • Dur O, Coskun S, Coskun K, Frakes D, Kara L, Pekkan K (2011) Computer-aided patient-specific coronary artery graft design improvements using CFD coupled shape optimizer. Cardiovasc Eng Technol 2:35–47

    Article  Google Scholar 

  • Fedorov A, Beichel R, Kalpathy-Cramer J, Finet J, Fillion-Robin J-C, Pujol S, Bauer C, Jennings D, Fennessy F, Sonka M, Buatti J, Aylward S, Miller JV, Pieper S, Kikinis R (2012) 3D Slicer as an image computing platform for the quantitative imaging network. Magn Reson Imaging 30(9):1323–1341

    Article  Google Scholar 

  • Fei D-Y, Thomas JD, Rittgers SE (1994) The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: a numerical model study. J Biomech Eng 116(3):331–336

    Article  Google Scholar 

  • Frangi AF, Niessen WJ, Vincken KL, Viergever MA (1998) Multiscale vessel enhancement filtering. In: Wells WM, Colchester A, Delp S (eds) Medical image computing and computer-assisted interventation—MICCAI’98, vol 1496., lecture notes in computer science. Springer, Berlin Heidelberg, pp 130–137

  • Frauenfelder E, Schertler T, Husmann L, Leschka S, Poulikakos D, Marincek B, Alkadhi H (2007) Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts. Biomed Eng OnLine 6(1):35:1–35:13

    Article  Google Scholar 

  • Freshwater IJ, Morsi YS, Lai T (2006) The effect of angle on wall shear stresses in a LIMA to LAD anastomosis: numerical modelling of pulsatile flow. Proc Inst Mech Eng Part H J Eng Med 220(7):743–757

    Article  Google Scholar 

  • Ghista D, Kabinejadian F (2013) Coronary artery bypass grafting hemodynamics and anastomosis design: a biomedical engineering review. Biomed Eng Online 12(1):129:1–129:28

    Article  Google Scholar 

  • Gijsen F, Allanic E, van de Vosse F, Janssen J (1999) The influence of the non-newtonian properties of blood on the flow in large arteries: unsteady flow in a \(90^\circ \) curved tube. J Biomech 32(7):705–713

    Article  Google Scholar 

  • Giordana S, Sherwin S, Peiró J, Doorly D, Crane J, Lee K, Cheshire N, Caro C (2005) Local and global geometric influence on steady flow in distal anastomoses of peripheral bypass grafts. J Biomech Eng 127:1087

    Article  Google Scholar 

  • Go AS, Mozaffarian D, Roger VL, Benjamin EJ, Berry JD, Blaha MJ, Dai S, Ford ES et al (2014) Executive summary: heart disease and stroke statistics-2014 update: a report from the American Heart Association. Circulation 129(3):399–410

    Article  Google Scholar 

  • Guerciotti B, Vergara C, Ippolito S, Quarteroni A, Antona C, Scrofani R (2016) Computational study of the risk of restenosis in coronary bypasses. Biomech Model Mechanobiol 16(1):313–332

  • Hesthaven JS, Rozza G, Stamm B (2016) Certified reduced basis methods for parametrized partial differential equations. Springer briefs in mathematics. Springer International Publishing, New York

    Book  MATH  Google Scholar 

  • Hillis LD, Smith PK et al (2011) 2011 ACCF/AHA guideline for coronary artery bypass graft surgery—a report of the American College of Cardiology Foundation/American Heart Association task force on practice guidelines developed in collaboration with the american association for thoracic surgery, society of cardiovascular anesthesiologists, and society of thoracic surgeons. J Am Coll Cardiol 58(24):e123–e210

    Article  Google Scholar 

  • Idu MM, Buth J, Hop WCJ, Cuypers P, van de Pavoordt EDWM, Tordoir JMH (1999) Factors influencing the development of vein-graft stenosis and their significance for clinical management. Eur J Vasc Endovasc Surg 17(1):15–21

    Article  Google Scholar 

  • Inzoli F, Migliavacca F, Pennati G (1996) Numerical analysis of steady flow in aorto-coronary bypass 3-D model. J Biomech Eng 118(2):172–179

    Article  Google Scholar 

  • Ishida N, Sakuma H, Cruz BP, Shimono T, Tokui T, Yada I, Takeda K, Higgins CB (2001) MR flow measurement in the internal mammary artery-to-coronary artery bypass graft: comparison with graft stenosis at radiographic angiography. Radiology 220(2):441–447

    Article  Google Scholar 

  • Jackson ZS, Ishibashi H, Gotlieb AI, Langille BL (2001) Effects of anastomotic angle on vascular tissue responses at end-to-side arterial grafts. J Vasc Surg 34(2):300–307

    Article  Google Scholar 

  • Kabinejadian F, Chua L, Ghista D, Sankaranarayanan M, Tan Y (2010) A novel coronary artery bypass graft design of sequential anastomoses. Ann Biomed Eng 38(10):3135–3150

    Article  Google Scholar 

  • Kabinejadian F, Ghista DN (2012) Compliant model of a coupled sequential coronary arterial bypass graft: effects of vessel wall elasticity and non-Newtonian rheology on blood flow regime and hemodynamic parameters distribution. Med Eng Phys 34(7):860–872

    Article  Google Scholar 

  • 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):953–960

    Article  Google Scholar 

  • Keynton RS, Shu MCS, Rittgers SE (1991) The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: an in vitro model study. J Biomech Eng 113(4):458–463

    Article  Google Scholar 

  • Kim HJ, Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2010) Developing computational methods for three-dimensional finite element simulations of coronary blood flow. Finite Elements Anal Des 46(6):514–525

    Article  MathSciNet  Google Scholar 

  • Kirk BS, Peterson JW, Stogner RH, Carey GF (2006) libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations. Eng Comput 22(3–4):237–254

    Article  Google Scholar 

  • Kirklin JW, Barratt-Boyes BG (1988) Cardiac surgery: morphology, diagnostic criteria, natural history, techniques, results, and indications. Churchill Livingstone, New York

    Google Scholar 

  • Kleinstreuer C, Nazemi M, Archie JP (1991) Hemodynamics analysis of a stenosed carotid bifurcation and its plaque-mitigating design. J Biomech Eng 113(3):330–335

    Article  Google Scholar 

  • Knezevic DJ, Peterson JW (2011) A high-performance parallel implementation of the certified reduced basis method. Comput Methods Appl Mech Eng 200(13–16):1455–1466

    Article  MATH  Google Scholar 

  • Ku DN, Giddens DP, Zarins CK, Glagov S (1985) Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arterioscler Thromb Vasc Biol 5(3):293–302

    Article  Google Scholar 

  • Kute SM, Vorp DA (2001) The effect of proximal artery flow on the hemodynamics at the distal anastomosis of a vascular bypass graft: computational study. J Biomech Eng 123(3):277–283

    Article  Google Scholar 

  • Lei M, Archie JP, Kleinstreuer C (1997) Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis. J Vasc Surg 25(4):637–646

    Article  Google Scholar 

  • Lei M, Giddens DP, Jones SA, Loth F, Bassiouny H (2000) Pulsatile flow in an end-to-side vascular graft model: comparison of computations with experimental data. J Biomech Eng 123(1):80–87

    Article  Google Scholar 

  • Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3d surface construction algorithm. Comput Graph 21(4):163–169

    Article  Google Scholar 

  • Loth F, Fischer PF, Bassiouny HS (2008) Blood flow in end-to-side anastomoses. Annu Rev Fluid Mech 40:367–393

    Article  MathSciNet  MATH  Google Scholar 

  • 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 48:1199–1226

    Article  MathSciNet  MATH  Google Scholar 

  • Marsden AL (2014) Optimization in cardiovascular modeling. Annu Rev Fluid Mech 46(1):519–546

    Article  MathSciNet  MATH  Google Scholar 

  • Marsden AL, Feinstein JA, Taylor CA (2008) A computational framework for derivative-free optimization of cardiovascular geometries. Comput Methods Appl Mech Eng 197(21–24):1890–1905

    Article  MathSciNet  MATH  Google Scholar 

  • Migliavacca F, Dubini G (2005) Computational modeling of vascular anastomoses. Biomech Model Mechanobiol 3(4):235–250

    Article  Google Scholar 

  • Moran SV, Baeza R, Guarda E, Zalaquett R, Irarrazaval MJ, Marchant E, Deck C (2001) Predictors of radial artery patency for coronary bypass operations. Ann Thorac Surg 72(5):1552–1556

    Article  Google Scholar 

  • Nicolini F, Agostinelli A, Spaggiari I, Vezzani A, Benassi F, Maestri F, Gherli T (2014) Current trends in surgical revascularization of multivessel coronary artery disease with arterial grafts. Int Heart J 55(5):381–385

    Article  Google Scholar 

  • Nordgaard H, Swillens A, Nordhaug D, Kirkeby-Garstad I, Van Loo D, Vitale N, Segers P, Haaverstad R, Lovstakken L (2010) Impact of competitive flow on wall shear stress in coronary surgery: computational fluid dynamics of a LIMA-LAD model. Cardiovasc Res 88(3):512–519

    Article  Google Scholar 

  • Owida AA, Do H, Morsi YS (2012) Numerical analysis of coronary artery bypass grafts: an over view. Comput Methods Program Biomed 108(2):689–705

    Article  Google Scholar 

  • Pagni S, Storey J, Ballen J, Montgomery W, Qaqish NK, Etoch S, Spence PA (1997) Factors affecting internal mammary artery graft survival: how is competitive flow from a patent native coronary vessel a risk factor? J Surg Res 71(2):172–178

    Article  Google Scholar 

  • Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639

    Article  Google Scholar 

  • Politis AK, Stavropoulos GP, Christolis MN, Panagopoulos PG, Vlachos NS, Markatos NC (2008) Numerical modelling of simulated blood flow in idealized composite arterial coronary grafts: transient flow. J Biomech 41(1):25–39

    Article  Google Scholar 

  • Probst M, Lülfesmann M, Nicolai M, Bücker HM, Behr M, Bischof CH (2010) Sensitivity of optimal shapes of artificial grafts with respect to flow parameters. Comput Methods Appl Mech Eng 199(17–20):997–1005

    Article  MathSciNet  MATH  Google Scholar 

  • Puskas JD, Lazar HL, Mack MJ, Sabik JF III, Taggart DP (2014) State-of-the-art coronary artery bypass graft. Semin Thorac Cardiovasc Surg 26(1):76–94

    Article  Google Scholar 

  • Qiao A, Liu Y (2006) Influence of graft-host diameter ratio on the hemodynamics of CABG. Bio-Med Mater Eng 16(3):189–201

    Google Scholar 

  • Quarteroni A, Manzoni A, Negri F (2016) Reduced Basis Methods for partial differential equations. An introduction, volume 92 of unitext. Springer, New York

    MATH  Google Scholar 

  • Ramachandra AB, Kahn AM, Marsden AL (2016) Patient-specific simulations reveal significant differences in mechanical stimuli in venous and arterial coronary grafts. J Cardiovasc Transl Res 9(4):279–290

    Article  Google Scholar 

  • Ravindran S (2000) A reduced-order approach for optimal control of fluids using proper orthogonal decomposition. Int J Numer Methods Fluids 34:425–448

    Article  MathSciNet  MATH  Google Scholar 

  • Ross Ethier C, Steinman DA, Zhang X, Karpik S, Ojha M (1998) Flow waveform effects on end-to-side anastomotic flow patterns. J Biomech 31(7):609–617

    Article  Google Scholar 

  • Rowe GG, Thomsen JH, Stenlund RR, Mckenna DH, Sialer S, Corliss RJ (1969) A study of hemodynamics and coronary blood flow in man with coronary artery disease. Circulation 39(1):139–148

    Article  Google Scholar 

  • Rozza G, Huynh DBP, Manzoni A (2013) Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants. Numer Math 125(1):115–152

    Article  MathSciNet  MATH  Google Scholar 

  • Sabik JF III, Blackstone EH (2008) Coronary artery bypass graft patency and competitive flow. J Am Coll Cardiol 51(2):126–128

    Article  Google Scholar 

  • Sabik JF III, Lytle BW, Blackstone EH, Houghtaling PL, Cosgrove DM (2005) Comparison of saphenous vein and internal thoracic artery graft patency by coronary system. Ann Thorac Surg 79(2):544–551

    Article  Google Scholar 

  • Sabik JF III, Lytle BW, Blackstone EH, Khan M, Houghtaling PL, Cosgrove DM (2003) Does competitive flow reduce internal thoracic artery graft patency? Ann Thorac Surg 76(5):1490–1497

    Article  Google Scholar 

  • Sankaran S, Esmaily Moghadam M, Kahn A, Tseng E, Guccione J, Marsden A (2012) Patient-specific multiscale modeling of blood flow for coronary artery bypass graft surgery. Ann Biomed Eng 40:2228–2242

    Article  Google Scholar 

  • Sankaran S, Kim HJ, Choi G, Taylor CA (2016) Uncertainty quantification in coronary blood flow simulations: impact of geometry, boundary conditions and blood viscosity. J Biomech 49(12):2540–2547 (Cardiovascular Biomechanics in Health and Disease)

    Article  Google Scholar 

  • Sankaran S, Marsden AL (2010) The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow. Phys Fluids 22(12):1–16

    Article  Google Scholar 

  • Schiavazzi D, Doostan A, Iaccarino G, Marsden A (2017) A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling. Comput Methods Appl Mech Eng 314:196–221

    Article  MathSciNet  Google Scholar 

  • Sherwin SJ, Doorly DJ (2003) Flow dynamics within model distal arterial bypass grafts. Adv Fluid Mech 34:327–374

    Google Scholar 

  • Sherwin SJ, Shah O, Doorly DJ, Peiro J, Papaharilaou Y, Watkins N, Caro CG, Dumoulin CL (1999) The influence of out-of-plane geometry on the flow within a distal end-to-side anastomosis. J Biomech Eng 122(1):86–95

    Article  Google Scholar 

  • Si H (2015) Tetgen, a delaunay-based quality tetrahedral mesh generator. ACM Trans Math Softw 41(2):11:1–11:36

    Article  MathSciNet  MATH  Google Scholar 

  • Staalsen N-H, Ulrich M, Winther J, Pedersen EM, How T, Nygaard H (1995) The anastomosis angle does change the flow fields at vascular end-to-side anastomoses in vivo. J Vasc Surg 21(3):460–471

    Article  Google Scholar 

  • Swillens A, De Witte M, Nordgaard H, Løvstakken L, Van Loo D, Trachet B, Vierendeels J, Segers P (2012) Effect of the degree of LAD stenosis on “competitive flow” and flow field characteristics in LIMA-to-LAD bypass surgery. Med Biol Eng Comput 50(8):839–849

    Article  Google Scholar 

  • Taylor CA, Draney MT (2004) Experimental and computational methods in cardiovascular fluid mechanics. Ann Rev Fluid Mech 36:197–231

    Article  MathSciNet  MATH  Google Scholar 

  • Towne JB, Schmitt DD, Seabrook GR, Bandyk DF (1991) The effect of vein diameter on patency of in situ grafts. J Cardiovasc Surg 32(2):192–196

    Google Scholar 

  • Tran JS, Schiavazzi DE, Ramachandra AB, Kahn AM, Marsden AL (2017) Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations. Comput Fluids 142:128–138

    Article  MathSciNet  Google Scholar 

  • Wen J, Zheng T, Jiang W, Deng X, Fan Y (2011) A comparative study of helical-type and traditional-type artery bypass grafts: numerical simulation. Am Soc Artif Intern Organs J 57(5):399–406

    Article  Google Scholar 

  • Xiong FL, Chong CK (2008) A parametric numerical investigation on haemodynamics in distal coronary anastomoses. Med Eng Phys 30(3):311–320

    Article  Google Scholar 

  • Yie K, Na C-Y, Oh SS, Kim J-H, Shinn S-H, Seo H-J (2008) Angiographic results of the radial artery graft patency according to the degree of native coronary stenosis. Eur J Cardio-Thorac Surg 33(3):341–348

    Article  Google Scholar 

  • Zhang J-M, Chua LP, Ghista DN, Yu SCM, Tan YS (2008) Numerical investigation and identification of susceptible sites of atherosclerotic lesion formation in a complete coronary artery bypass model. Med Biol Eng Comput 46(7):689–699

    Article  Google Scholar 

  • Zhang J-M, Luo T, Tan SY, Lomarda AM, Wong ASL, Keng FYJ, Allen JC, Huo Y, Su B, Zhao X, Wan M, Kassab GS, Tan RS, Zhong L (2015) Hemodynamic analysis of patient-specific coronary artery tree. Int J Numer Methods Biomed Eng 31(4):1–16

    Article  MathSciNet  Google Scholar 

  • Zhang J-M, 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):1–20

    Google Scholar 

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Acknowledgements

We acknowledge the use of CINECA supercomputing facilities within the projects “Convenzione di Ateneo” agreement between Politecnico di Milano and CINECA, and “COGESTRA” between SISSA and CINECA, and Istituto Nazionale di Fisica Nucleare, within the project SUMA. We acknowledge the use of a customized version of the library rbOOmit within libMesh (Knezevic and Peterson 2011; Kirk et al. 2006) for the numerical simulations, and of the Vascular Modelling Toolkit vmtk (Antiga et al. 2008) and 3DSlicer (Fedorov et al. 2012) for the medical imaging pipeline.

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  1. Francesco Ballarin

    Present address: MOX - Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133, Milan, Italy

  2. Elena Faggiano

    Present address: Computational Mechanics and Advanced Materials Group, Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100, Pavia, Italy

Authors and Affiliations

  1. MOX - Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133, Milan, Italy

    Elena Faggiano

  2. mathLab, Mathematics Area, SISSA, via Bonomea 265, 34136, Trieste, Italy

    Francesco Ballarin & Gianluigi Rozza

  3. CMCS - Modelling and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015, Lausanne, Switzerland

    Andrea Manzoni & Alfio Quarteroni

  4. Radiology Unit, Ospedale Luigi Sacco, Via G. B. Grassi 74, 20157, Milan, Italy

    Sonia Ippolito

  5. Cardiovascular Surgery Unit, Ospedale Luigi Sacco, Via G. B. Grassi 74, 20157, Milan, Italy

    Carlo Antona & Roberto Scrofani

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Correspondence to Francesco Ballarin.

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Francesco Ballarin and Elena Faggiano acknowledge the support of the PRIN project “Mathematical and numerical modeling of the cardiovascular system, and their clinical applications”. Gianluigi Rozza acknowledges the SISSA Excellence Grant NOFYSAS “Computational and Geometrical Reduction Strategies for the simulation, control and optimization of complex systems”. We also acknowledge ERC Advanced Grant Mathcard (Number 227058).

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Ballarin, F., Faggiano, E., Manzoni, A. et al. Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts. Biomech Model Mechanobiol 16, 1373–1399 (2017). https://doi.org/10.1007/s10237-017-0893-7

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