Biomech Model Mechanobiol DOI 10.1007/s10237-017-0893-7 ORIGINAL PAPER Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts Francesco Ballarin 1,2 · Elena Faggiano 1,3 · Andrea Manzoni 4 · Alfio Quarteroni 4 · Gianluigi Rozza 2 · Sonia Ippolito 5 · Carlo Antona 6 · Roberto Scrofani 6 Received: 6 October 2016 / Accepted: 27 February 2017 © Springer-Verlag Berlin Heidelberg 2017 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 coro- nary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisi- tion 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 B Francesco Ballarin francesco.ballarin@sissa.it 1 Present Address: MOX - Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milan, Italy 2 mathLab, Mathematics Area, SISSA, via Bonomea 265, 34136 Trieste, Italy 3 Present Address: Computational Mechanics and Advanced Materials Group, Department of Civil Engineering and Architecture, University of Pavia, Via Ferrata 3, 27100 Pavia, Italy 4 CMCS - Modelling and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland 5 Radiology Unit, Ospedale Luigi Sacco, Via G. B. Grassi 74, 20157 Milan, Italy 6 Cardiovascular Surgery Unit, Ospedale Luigi Sacco, Via G. B. Grassi 74, 20157 Milan, Italy compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases. Keywords 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 RCA Right coronary artery PDA Posterior descending artery PL Postero-lateral artery Coronary arteries of the left coronary tree 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 Bypass grafts LITA Left internal thoracic artery Rad. Radial artery bypass grafts SVG Saphenous vein bypass grafts 123