Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 4, pp 1373–1399 | Cite as

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

  • Francesco BallarinEmail author
  • Elena Faggiano
  • Andrea Manzoni
  • Alfio Quarteroni
  • Gianluigi Rozza
  • Sonia Ippolito
  • Carlo Antona
  • Roberto Scrofani
Original Paper


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.


Cardiovascular simulations Computational reduction strategies Coronary bypass grafts Patient-specific computing Data assimilation Geometrical parameterization 

List of symbols

Coronary arteries of the right coronary tree


Right coronary artery


Posterior descending artery


Postero-lateral artery

Coronary arteries of the left coronary tree


Main trunk of the left coronary artery


Left anterior descending artery


Diagonal branch of the left anterior descending artery


Left circumflex artery


Obtuse marginal artery

Bypass grafts


Left internal thoracic artery


Radial artery bypass grafts


Saphenous vein bypass grafts



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.

Compliance with ethical standards


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).

Conflict of Interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.MOX - Modeling and Scientific Computing, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.mathLab, Mathematics AreaSISSATriesteItaly
  3. 3.Computational Mechanics and Advanced Materials Group, Department of Civil Engineering and ArchitectureUniversity of PaviaPaviaItaly
  4. 4.CMCS - Modelling and Scientific ComputingEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  5. 5.Radiology UnitOspedale Luigi SaccoMilanItaly
  6. 6.Cardiovascular Surgery UnitOspedale Luigi SaccoMilanItaly

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