Problem: Study of new techniques for the prescription of flow rate and mean pressure boundary conditions in computational fluid-dynamics Strategies: - Lagrange multipliers approach - Control based approach (minimization of a suitable functional) - Nitsche's method Applications : haemodynamics Video : Flow field in a human carotid - rigid domain - flow rate prescription with Lagrange multipliers Related publications : Veneziani A., Vergara, Flow rate defective Boundary Conditions in Haemodynamics Simulations, Int. Journ. Num. Meth. Fluids, 47, pp. 803--816, 2005. pdf Fernandez M., Moura A., Vergara C., Defective Boundary Conditions Applied to Multiscale Analysis of Blood Flow, ESAIM Proceedings & Surveys, CEMRACS 2004, 14, pp. 89-99, 2005. pdf Moura A., Vergara C., Flow rate boundary conditions and multiscale modelling of the cardiovascular system in compliant domains, in Modelling in Medicine and Biology VI, (eds. Ursino, Brebbia, Pontrelli, Magosso), pp. 351-359, related to Sixth International Conference on Modelling in Medicine and Biology, Bologna - September 7-9, 2005. pdf Veneziani A., Vergara C., Flow Rate Boundary Conditions in Fluid-Dynamics, PAMM Proceedings in Applied Mathematics and Mechanics, 6, pp. 35-38, 2006 (Proceedings of the GAMM meeting 2006, Berlin) pdf Veneziani A., Vergara C., An approximate method for solving incompressible Navier-Stokes problem with flow rate conditions, Comp. Meth. Appl. Mech. Eng., 196 (9-12), pp. 1685-1700, 2007, pdf Vergara C., Modellazione numerica di problemi con condizioni al contorno deficitarie in fluidodinamica incomprimibile, Bollettino della Unione Matematica Italiana A, 10(2), pp. 371-374, 2007 Formaggia L., Veneziani A., Vergara C., A new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics, SIAM J. Num. Anal., 46(6), pp. 2769-2794, 2008. pdf Formaggia L., Veneziani A., Vergara C., Flow rate boundary problems for an incompressible fluid in deformable domains: formulations and solution methods . Comp. Meth. Appl. Mech. Eng., 199 (9-12), pp. 677-688, 2010. pdf Vergara C., Modular algorithms for the numerical solution of the flow rate boundary value problem, Communications in Applied and Industrial Mathematics, 1(1), pp. 237-257, 2010. pdf Vergara C., Nitsche's method for defective boundary value problems in incompressibile fluid-dynamics. Journal of Scientific Computing , 46, pp. 100-123, 2011. pdf A. Porpora, P. Zunino, C. Vergara, M. Piccinelli, Numerical treatment of boundary conditions to replace lateral branches in haemodynamics. Int. J. Numer. Meth. Biomed. Eng., 28(12), pp. 1165-1183, 2012. pdf L. Formaggia and C. Vergara, Prescription of general defective boundary conditions in fluid-dynamics. Milan Journal of Mathematics, 80(2), pp. 333-350, 2012. pdf Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. Acta Numerica, 26, pp. 365-590, 2017 pdf Formaggia L., Vergara C., Defective boundary conditions for PDEs with applications in haemodynamics. In "Numerical Methods for PDEs", SEMA SIMAI Springer Series (D. Di Pietro, A. Ern, L. Formaggia eds.), 15, pp. 285-312, 2018. pdf Quarteroni A., Dede' L., Manzoni A., Vergara C., Mathematical Modelling of the Human Cardiovascular System - Data, Numerical Approximation, Clinical Applications, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2019. pdf Crugnola L., Vergara C. Inexact block LU preconditioners for incompressible fluids with flow rate conditions. arxiv, DOI:arXiv:2411.03929, 2024. pdf

Parabolic profile - Unstable flow field (by . B. Guerciotti)

Lagrange multiplier - Stable flow field (by . B. Guerciotti)

2) Numerical solution of fluid-structure interaction problem (2006-onwards)

Problem: Study and analysis of new numerical techniques for the numerical solution of the problem arising from the interaction between a fluid and a structure Strategies: - Efficient partitioned methods of implicit type - Stable and accurate partitioned methods of explicit type - Quasi-Newton methods for monolithic solution - Unfitted XFEM/DG and PolyDG approaches for an immersed thick structure and large displacements Application : vascular and cardiac haemodynamics Video : Flow field in a human carotid before the plaque removal Video : Flow field in a human carotid after the plaque removal Related publications : Nobile F., Vergara C., An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions, SIAM J. Sc. Comp., 30(2), pp. 731-763, 2008 pdf Badia S., Nobile F., Vergara C., Fluid-structure partitioned procedures based on Robin transmission conditions, J. Comp. Phys., 227, pp. 7027-7051, 2008. pdf Badia S., Nobile F., Vergara C., Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems . Comp. Meth. Appl. Mech. Eng., 198 (33-36), pp. 2768-2784, 2009. pdf Formaggia L., Veneziani A., Vergara C., Flow rate boundary problems for an incompressible fluid in deformable domains: formulations and solution methods . Comp. Meth. Appl. Mech. Eng., 199 (9-12), pp. 677-688, 2010. pdf Gerardo-Giorda L., Nobile F., Vergara C., Analysis and optimization of Robin-Robin partitioned procedures in fluid-structure interaction problems. SIAM J. Num. Anal. , 48(6), pp. 2091-2116, 2010. pdf F. Nobile, C. Vergara, Partitioned algorithms for fluid-structure interaction problems in haemodynamics. Milan Journal of Mathematics, 80(2), pp. 443-467, 2012. pdf Pozzoli M., Vergara C., Nobile F. Efficient algorithms for the solution of fluid-structure interaction problems in haemodynamic applications, Proceedings of the Conference "Numerical Methods for Hyperbolic Equations: Theory and Applications", Santiago de Compostela, pp. 355-364, 2013. pdf F. Nobile, M. Pozzoli, C. Vergara, Time accurate partitioned algorithms for the solution of fluid-structure interaction problems in haemodynamics. Computer and Fluids, 86, pp. 470-482, 2013. pdf F. Nobile, M. Pozzoli, C. Vergara, Inexact accurate partitioned algorithms for fluid-structureinteraction problems with finite elasticity in haemodynamics. Journal of Computational Physics. DOI:10.1016/j.jcp.2014.05.020. pdf Gigante G., Vergara C., Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid-structure interaction. Numer. Math., 131(2), pp. 369--404, 2015. pdf G. Gigante, C. Vergara, Optimized Schwarz method for the fluid-structure interaction with cylindrical interfaces. Domain Decomposition Methods in Science and Engineering XXII - Lecture Notes in Computational Science and Engineering - Proceedings of the 22nd International Conference on Domain Decomposition Methods, 104, pp. 521-529, 2016. pdf Zonca S., Vergara C., Formaggia L., An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach. SIAM J. Sc. Comp., 40(1), pp. B59-B84, 2018 pdf Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. Acta Numerica, 26, pp. 365-590, 2017 pdf Quarteroni A., Vergara C., Computational models for hemodynamics. Encyclopedia of Continuum Mechanics. doi:10.1007/978-3-662-53605-6_35-1, 2018. pdf Antonietti P., Verani M., Vergara C., Zonca S., Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids. Finite Elements in Analysis and Design, 159, pp. 1-14, 2019. pdf Vergara C., Zonca S., Extended Finite Elements method for fluid-structure interaction with an immersed thick non-linear structure. In "Mathematical and Numerical Modeling of the Cardiovascular System and Applications", SEMA SIMAI Springer Series (D. Boffi, L. Pavarino, G. Rozza, S. Scacchi, C. Vergara eds.), pp. 209-243, 2018. pdf Quarteroni A., Dede' L., Manzoni A., Vergara C., Mathematical Modelling of the Human Cardiovascular System - Data, Numerical Approximation, Clinical Applications, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2019. pdf Gigante G., Vergara C., On the stability of a loosely-coupled scheme based on a Robin interface condition for fluid-structure interaction. Computers and Mathematics with Applications, 96, pp. 109-119, 2021. pdf Gigante G., Sambataro G., Vergara C., Optimized Schwarz methods for spherical interfaces with application to fluid-structure interaction. SIAM J. Sc. Comp., 42(2), A751-A770, 2020. pdf Zonca S., Antonietti P.F., Vergara C. A Polygonal Discontinuous Galerkin formulation for contact mechanics in fluid-structure interaction problems. Comm. Comp. Phys., 30, pp. 1-33, 2021. pdf Gigante G., Vergara C., On the choice of interface parameters in Robin-Robin loosely coupled schemes for fluid-structure interaction. Fluids, 6(6), pp. 213-231, 2021. pdf Bucelli M., Dede' L., Quarteroni A., Vergara C., Partitioned and monolithic algorithms for the numerical solution of cardiac fluid-structure interaction. Comm. Comp. Phys. 32(5), 1217-1256, 2023. pdf Bucelli M., Geraint Gabriel M., Quarteroni A., Gigante G., Vergara C., A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction. Journal of Computational Physics, 490, 112326, 2023. pdf Fumagalli I., Vergara C., Novel approaches for the numerical solution of fluid-structure interaction in the aorta. Biomechanics of the Aorta - Modeling for Patient Care, Chapter 16, Edited by: T. Christian Gasser, Stephane Avril and John A. Elefteriades, Academic Press, 2024. pdf

Velocity streamlines and wall displacements vectors at systole - carotid geometry (by. M. Pozzoli)

3) Geometrical multiscale modeling of the cardiovascular system (2003-onwards)

Problem: Study of coupling techniques among heterogeneous models to describe the cardiovascular system Strategies: Three dimensional/one dimensional coupling based on the total pressure Application : Haemodynamics Related publications : Balossino R., Migliavacca F., Pennati G., Dubini G., Vergara C., Formaggia L., Venenziani A., Multiscale Models of the Cardiovascular System Applied to the Study of the Flow in a Carotid Bifurcation, in Technological innovation and evaluation of medical devices for the cardiovascular system, Rapporti Istisan, 05/46, 2004. Veneziani A., Vergara, Flow rate defective Boundary Conditions in Haemodynamics Simulations, Int. Journ. Num. Meth. Fluids, 47, pp. 803--816, 2005. pdf L. Formaggia, A. Quarteroni, C. Vergara, On the physical consistency between three-dimensional and one-dimensional models in haemodynamics. Journal of Computational Physics. DOI:10.1016/j.jcp.2012.08.001. pdf Quarteroni A., Veneziani A., Vergara C., Geometric multiscale modeling of the cardiovascular system, between theory and practice. Comp. Meth. Appl. Mech. Eng., 302, pp. 193--252, 2016. pdf Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. Acta Numerica, 26, pp. 365-590, 2017 pdf Quarteroni A., Dede' L., Manzoni A., Vergara C., Mathematical Modelling of the Human Cardiovascular System - Data, Numerical Approximation, Clinical Applications, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2019. pdf Dede' L., Regazzoni F., Vergara C., Zunino P., Guglielmo M., Scrofani R., Fusini L., Cogliati C., Pontone G., Quarteroni A. Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study. Mathematical Biosciences and Engineering, 18(4), pp. 3364-3383, 2021. pdf Piersanti R., Regazzoni F., Salvador M., Corno A.F., Dede' L., Vergara C., Quarteroni A., 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics. Comp. Meth. Appl. Mech. Eng., 391, 114607, 2022. pdf Marcinno' F., Zingaro A., Fumagalli I., Dede' L., Vergara C., A computational study of blood flow dynamics in the pulmonary arteries. Vietnam Journal of Mathematics, 51, 127-149, 2023. pdf Ruffino L., Santoro A., Sparvieri, S., Regazzoni, F. Adebo D.A., Quarteroni A., Vergara C., Corno A.F., Computational analysis of cardiovascular effects of COVID- 19 infection in children. J Pediatric Adv Research, 2023. pdf Tonini A., Vergara C., Regazzoni F., Dede' L., Scrofani R., Cogliati C., Quarteroni A., A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system. Scientific Reports - Nature, 14, 8304, 2024. pdf Tonini A., Regazzoni F., Salvador M., Dede' L., Scrofani R., Fusini L., Cogliati C., Pontone G., Vergara C., Quarteroni A., Two new calibration techniques of lumped-parameter mathematical models for the cardiovascular system. Int. J. Num. Meth. Eng., 126(1), e7648, 2025. pdf Criseo E., Fumagalli I., Quarteroni A., Marianeschi S.M., Vergara C., Computational haemodynamics for pulmonary valve replacement by means of a reduced Fluid-Structure Interaction model. Int. J. Num. Meth. Biomed. Eng., 40(9), e3846, 2024. pdf

3D-0D coupling between circulatory system and electro-mechanical model (figure by Piersanti/Regazzoni)

4) Applications to cases of clinical interest (2007-onwards)

a) Haemodynamics in the ascending aorta in presence of a bicuspid aortic valve (BAV) Problem : Comparison of the fluid-dynamics in presence of a tricuspid and a bicuspid aortic valve Clinical partner : Divisions of Cardio-surgery and Radiology, Ospedale Borgo Trento, Verona, Italy . Video : Velocity vectors in ascending aorta of a real patient with tricuspid aortic valve Video : Velocity vectors in ascending aorta of a real patient with bicuspid aortic valve Related publications : Viscardi F., Vergara C., Antiga L., Merelli S., Veneziani A., Puppini G., Faggian G., Mazzucco A., Luciani G.B., Comparative finite-element model analysis of ascending aortic flow in bicuspid and tricuspid aortic valve. Artificial Organs., 34(12), pp. 1114-1120, 2010. pdf Luciani G.B., Antiga L., Puppini G., Viscardi F., Faggian G., Mazzucco A., Vergara C.,Commissure Orientation Influences Aortic Aneurysm Morphology in Normally Functioning Bicuspid Aortic Valves: A Parametric, Computational Fluid Dynamic Study. Circulation. In: Abstracts From Scientific Sessions 2011. Orlando, USA, 13-15.11.2011, vol. 124(21 S). pdf Vergara C., Viscardi F., Antiga L., Luciani G.B., Influence of bicuspid valve geometry on ascending aortic fluid-dynamics: a parametric study. Artificial Organs , 36(4), pp 368-378, 2012. pdf E. Faggiano, L. Antiga, G. Puppini, A. Quarteroni, G.B. Luciani, C. Vergara, Helical Flows and Asymmetry of Blood Jet in Dilated Ascending Aorta with Normally Functioning Bicuspid Valve.Biomechanics and Modeling in Mechanobiology, 12(4), pp. 801-813, 2013. pdf Bonomi D., Vergara C., Faggiano E., Stevanella M., Conti C., Redaelli A., Puppini G., Faggian G., Formaggia L., Luciani G.B., Influence of the aortic valve leaflets on the fluid-dynamics in aorta in presence of a normally functioning bicuspid valve. Biomechanics and Modeling in Mechanobiology, 14(6), pp.1349--1361, 2015. pdf Kara R., Vergara C., Assessing Turbulent Effects in Ascending Aorta in Presence of Bicuspid Aortic Valve. Computer Methods in Biomechanics and Biomedical Engineering, 27, 2349-2361, 2023. pdf

Flow exiting from the left ventricle. Left: radiological image; Middle: BAV simulation; Right: Tricuspid configuration

b) Hemodynamics in the ascending and thoracic aorta for TAVI and TEVAR Problems : - Study of influence of hemodynamics on TAVI degeneration - Study of blood forces in thoracic aortic aneurysms Clinical partner : Centro Cardiologico Monzino, Milan, Italy; Divisions of Vascular-surgery and Radiology, Fondazione Ca' Granda - Policlinico di Milano, Italy Related publications : Fumagalli I., Polidori R., Renzi F., Fusini L., Quarteroni A., Pontone G., Vergara C., Fluid-structure interaction analysis of transcatheter aortic valve implantation. Int. J. Num. Meth. Biomed. Eng., 39(6), e3704, 2023. pdf Crugnola L., Vergara C., Fusini L., Fumagalli I., Luraghi G., Redaelli A., Pontone G., Computational hemodynamic indices to identify Transcatheter Aortic Valve Implantation degeneration. Computer Methods and Programs in Biomedicine, 259, 108517, 2024. pdf Duca F., Bissacco D., Crugnola L., Faitini C., Domanin M., Migliavacca F. Trimarchi S., Vergara C., Computational analysis to assess hemodynamic forces in descending thoracic aortic aneurysms. The Jouranl of Physiology, To appear. DOI: 10.1113/JP287278. pdf

Blood dynamics in ascending aorta in presence of TAVI with endograft (by L. Crugnola)

c) Haemodynamics in the abdominal aorta in presence of an aneurysm Problems : - Study of the correlation between lumen displacement (from 4D-CT images) and haemodynamic forces - Study of the transition to turbulence effects - Blood dynamics in presence of endograft Clinical partner : Divisions of Vascular-surgery and Radiology, Fondazione Ca' Granda - Policlinico di Milano, Italy Related publications : M. Piccinelli, C. Vergara, L. Antiga, L. Forzenigo, P. Biondetti, M. Domanin, Impact of hemodynamics on lumen boundary displacements in abdominal aortic aneurysms by means of dynamic computed tomography and computational fluid dynamics. Biomechanics and Modeling in Mechanobiology, 12(6), pp. 1263-1276, 2013. pdf Vergara C., Le Van D., Quadrio M., Formaggia L., Domanin M., Large Eddy Simulations of blood dynamics in abdominal aortic aneurysms. Medical Engineering & Physics , 47, pp. 38-46, 2017 pdf Domanin M., Piazzoli G., Trimarchi S., Vergara C., Image-based displacements analysis and com- putational blood dynamics after endovascular aneurysm repair. Annals of Vascular Surgery, 69, pp. 400-412, 2020. pdf

Blood dynamics in AAA with endograft (by G. Piazzoli)

d) Haemodynamics in atherosclerotic carotids Problem : - Study the effect of the plaque removal (Endarterectomy) on the fluid-dynamics - Study of the transition to turbulence effects - Modeling plaque progression Clinical partner : Divisions of Vascular-surgery and Radiology, Fondazione Ca' Granda - Policlinico di Milano, Italy Related publications : Guerciotti B., Vergara C., Azzimonti L., Forzenigo L., Buora A., Biondetti P., Domanin M., Computational study of the fluid-dynamics in carotids before and after endarterectomy. Journal of Biomechanics, 49(1), pp. 26--38, 2016. pdf Lancellotti R.M.. Vergara C., Valdettaro L., Bose S., Quarteroni A., Large Eddy Simulations for blood fluid-dynamics in real stenotic carotids. Int. J. Numer. Meth. Biomed. Eng., 33(11), e2868, 2017 pdf Domanin M., Buora A., Scardulla F., Guerciotti B., Forzenigo L., Biondetti P., Vergara C., Computational fluid-dynamic analysis of carotid bifurcations after endarterectomy: closure with patch graft versus direct suture. Annals of Vascular Surgery , 44, pp. 325 335, 2017. pdf Guerciotti B., Vergara C., Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels. In "Biomedical Technology", Lecture Notes in Applied and Computational Mechanics 84 (P. Wriggers and T. Lenarz eds.), Springer, pp. 169-183, 2018. pdf Domanin M., Vergara C., Regarding "closure technique after carotid endarterectomy influences local hemodynamics", Journal of Vascular Surgery, 63(5), p. 1409, 2016 pdf Domanin M., Bissacco D., Le Van D., Vergara C., Computational fluid-dynamic comparison between patch-based and direct suture closure techniques after carotid endarterectomy. Journal of Vascular Surgery, 67(3), pp. 887-897, 2018. pdf Domanin M., Gallo D., Vergara C., Biondetti P., Forzenigo L.V., Morbiducci U., Prediction of long term restenosis risk after surgery in the carotid bifurcation by hemodynamic and geometric analysis. Annals of Biomedical Engineering, 47(4), pp. 1129-1140, 2019. pdf Pozzi S., Vergara C., Mathematical and numerical models of atherosclerotic plaque progression in carotid arteries. In ''Numerical Mathematics and Advanced Applications ENUMATH 2019'' - Lecture Notes in Computational Science and Engineering, 139, 2021. pdf Pozzi S., Domanin M., Forzenigo L., Votta E., Zunino P., Redaelli A., Vergara C., A surrogate model for plaque modeling in carotids based on Robin conditions calibrated by cine MRI data . Int. J. Num. Meth. Biomed. Eng., 37(5), e3447, 2021. pdf Morbiducci U., Mazzi V., Domanin M., De Nisco G., Vergara C., Steinman D.A., Gallo D. Wall shear stress topological skeleton independently predicts long-term restenosis after carotid bifurcation endarterectomy. Annals of Biomedical Engineering, 48, pp. 2936 2949, 2020. pdf Pozzi S., Redaelli A., Vergara C., Votta E., Zunino P., Mathematical and numerical modeling of atherosclerotic plaque progression based on fluid-structure interaction. Journal of Mathematical Fluid Mechanics, 23, 74, 2021. pdf Bennati L., Vergara C., Domanin M., Malloggi C., Bissacco D., Trimarchi S., Silani V., Parati G., Casana R., A computational fluid structure interaction study for carotids with different atherosclerotic plaques. Journal of Biomechanical Engineering, 143(9), 091002, 2021. pdf Domanin M., Bennati L., Vergara C., Bissacco D., Malloggi C., Silani V., Parati G., Trimarchi S., Casana R., Fluid structure interaction analysis to stratify the behavior of different atheromatous carotid plaques. The Journal of Cardiovascular Surgery, 64(1), 58-56, 2023. pdf

Vorticity before and after the plaque removal (by B. Guerciotti)

e) Hemodynamics in arteriovenous fistolae for hemodialsys Problem : Study the influence of the angle of anastomosis on the fluid-dynamic performance Clinical partner : EOC-Ente Ospedaliero Cantonale, Lugano 6900, Switzerland . Related publications : Stella S., Vergara C., Giovannacci L., Quarteroni A., Prouse G., Assessing the disturbed flow and the transition to turbulence in the arteriovenous fistula. . Journal of Biomechanical Engineering , 141(10), 101010, 2019. pdf Prouse G., Stella S., Vergara C., Quarteroni A., Engelberger S., Canevascini R., Giovannacci L., Computational Analysis of Turbulent Hemodynamics in Radiocephalic Arteriovenous Fistulas to Determine the Best Anastomotic Angles. Annals of Vascular Surgery, 68, pp. 451 459, 2020. pdf Marcinno' F., Vergara C., Giovannacci L., Quarteroni A., Prouse G., Computational fluid-structure interaction analysis of the end-to-side radio-cephalic arteriovenous fistula. Comp. Meth. & Progr. Biomed., 249, 108146, 2024. pdf

Blood dynamics in arteriovenous fistolae with different angle of anastomosis (by S. Stella)

f) Fluid-dynamics in coronaries, coronary by-passes, and cardiac perfusion Problems : - Study the relation between risk of restenosis in simple and multiple by-passes - Assess the influence of guide-wire in FFR estimates - Estimate cardiac blood flow maps Clinical partners : - Divisions of Cardio-surgery and Radiology, Ospedale Sacco, Milan, Italy - Division of Cardiology and Cardiac Imaging, Centro Cardiologico Monzino, Milan, Italy Related publications : Guerciotti B., Vergara C., Ippolito S., Quarteroni A., Antona C., Scrofani R., Computational study of the risk of restenosis in coronary bypasses. Biomechanics and Modeling in Mechanobiology. 16(1), pp. 313-332, 2017. pdf Guerciotti B., Vergara C., Ippolito S., Quarteroni A., Antona C., Scrofani R., A computational fluid-structure interaction analysis of coronary Y-grafts. Medical Engineering & Physics , 47, 117-127, 2017 pdf Guerciotti B., Vergara C., Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels. In "Biomedical Technology", Lecture Notes in Applied and Computational Mechanics 84 (P. Wriggers and T. Lenarz eds.). DOI:10.1007/978-3-319-59548-1_10, 2017. pdf Di Gregorio* S., Vergara* C., Montino Pelagi G., Baggiano A., Zunino P., Guglielmo M., Fusini L., Muscogiuri G., Rossi A., Rabbat M.G., Quarteroni A., Pontone G., Prediction of myocardial blood flow under stress conditions by means of a computational model. European Journal of Nuclear Medicine and Molecular Imaging. , 49:1894 1905, 2022. *These authors equally contributed to the work. pdf Lucca A., Fraccarollo L., Fossan F.E., Braten A.T., Pozzi S., Vergara C., Muller L.O., Impact of pressure guidewire on model-based FFR prediction. Cardiovascular Engineering and Technology, 15, 251-263, 2024. pdf Montino Pelagi G., Baggiano A., Regazzoni F., Fusini L., Ali' M., Pontone G., Valbusa G., Vergara C., Personalized pressure conditions and calibration for a predictive computational model of coronary and myocardial blood flow. Annals Biomed. Eng., 52, 1297-1312, 2024. pdf Criseo E., Baggiano A., Montino Pelagi G., Nannini G., Redaelli A., Pontone G., Vergara C., Development of a digital twin for the diagnosis of cardiac perfusion defects, medRXiv, DOI:10.1101/2025.02.04.25321638, 2024. pdf

Fluid and structure meshes of a muyltiple coronary by-pass (left). Streamlines of blood dynamics (right) (by B. Guerciotti)

g) Cardiac blood pumps Problem : Study the blood dynamics in presence of cardiac blood pumps Related publications : Scardulla S., Pasta S., D'Acquisto L., Sciacca S., Agnese V., Vergara C., Quarteroni A., Clemenza F., Bellavia D., Pilato M., Shear Stress Alterations in the Celiac Trunk of Patients with Continuous-Flow Left Ventricular Assist Device by In-Silico and In-Vitro Flow Analysis. Journal of Heart and Lung Transplantation, 36(8), pp. 906-913, 2017. pdf Martinolli M., Biasetti J.,Zonca S., Polverelli L., Vergara C., Extended Finite Element Method for Fluid-Structure Interaction in Wave Membrane Blood Pumps. Int. J. Num. Meth. Biomed. Eng., 37(7), e3467, 2021. pdf Martinolli M., Cornat F., Vergara C., Computational Fluid-Structure Interaction Study of a new Wave Membrane Blood Pump. Cardiovascular Engineering and Technology, 13, 373 392, 2022. pdf

Blood dynamics in a wave membrane blood pump (by M. Martinolli)

h) Cardiac blood dynamics for the study of valve diseases Problems : - Image-based atrial and ventricular CFD in moving domains with immersed valves - Systolic anterior motion and obstruction in hypertrophic cardiomyopathy - Mitral regurgitation Clinical partners : - Divisions of Cardio-surgery and Radiology, Ospedale Sacco, Milan, Italy - Divisions of Cardio-surgery and Radiology, Ospedale Borgo Trento, Verona, Italy Related publications : Nestola M.G.C., Faggiano E., Vergara C., Lancellotti R.M., Ippolito S., Filippi S., Quarteroni A., Scrofani R., Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses. Computer Methods in Biomechanics and Biomedical Engineering, 20(2), pp. 171-181, 2017. pdf Fumagalli I., Fedele M., Vergara C., Dede' L., Ippolito S., Nicolo' F., Antona C., Scrofani R., Quarteroni A., An Image-based Computational Hemodynamics Study of the Systolic Anterior Motion of the Mitral Valve. Computers in Biology and Medicine, 123, 103922, 2020. pdf Fumagalli I., Vitullo P., Vergara C., Fedele M., Corno A.F., Ippolito S., Scrofani R., Quarteroni A., Image-based computational hemodynamics analysis of systolic obstruction in hypertrophic cardiomyopathy. Frontiers in Physiology - Computational Physiology and Medicine, 12, 787082, 2022. pdf Bennati L., Vergara C., Giambruno V., Fumagalli I., Corno A.F., Quarteroni A., Puppini G., Luciani G.B., An image-based computational fluid dynamics study of mitral regurgitation in presence of prolapse. Cardiovascular Engineering and Technology, 14, 457-475, 2023. pdf Bennati L., Giambruno V., Renzi F., Di Nicola V., Maffeis C., Puppini G., Luciani G.B., Vergara C., Turbulence and blood washout in presence of mitral regurgitation: a computational fluid-dynamics study in the complete left heart. Biomech. Model. Mechanobiol., 22, 1829-1846, 2023. pdf Bennati L., Puppini G., Giambruno V., Luciani G.B., Vergara C., Image-Based Computational Fluid Dynamics to Compare Two Repair Techniques for Mitral Valve Prolapse. Annals Biomed. Eng., 52, 3295-3311, 2024. pdf Renzi F., Puppini G., Luciani G.B., Vergara C. Image-based computational hemodynamics in the right heart. Biomech. Model. Mechanobiol. To appear. pdf Renzi F., Bennati L., Fedele M., Giambruno V., Quarteroni A., Puppini G., Luciani G.B., Vergara C., From cine-MRI to computational models of blood flow within the heart. Vascular Pharmacology, 155, 107343, 2024. pdf

Atrial and ventricular blood dynamics in presence of mitral regurgitation (by L. Bennati)

i) Other publications: Corno A., Vergara C., Subramanian C., Johnson R.A., Passerini T., Veneziani A., Formaggia L., Alphonso N., Quarteroni A., Jarvis J.C., Assisted Fontan procedure: animal and in vitro models and computational fluid dynamics study , Interactive CardioVascular and Thoracic Surgery, 10, pp. 679-684, 2010 pdf Dubini G. et al., Trends in biomedical engineering: focus on Patient Specific Modeling and Life Support Systems. J. Appl. Biomater. Biomech., 9(2), pp. 109 - 117, 2011. pdf Arimon A., Balossino R., D'Angelo C., Doorly D., Dubini G., Fernandez M., Gerbeau J.F., Giordana S., Migliavacca F., Pennati G., Peiro' J., Prosi M., Sherwin S., Vergara C., Vidrascu M., Zunino P., Applications and test cases, in Cardiovascular Mathematics, Formaggia L., Quarteroni A., Veneziani A. eds., Springer, 2009. Link Tuveri M., Milani E., Marchegiani G., Landoni L., Torresani E., Capelli P., Sperandio N., D'onofrio M., Salvia R.. Vergara C., Bassi C., Hemodynamics and remodeling of the portal confluence in patients with cancer of the pancreatic head: a pilot study. Langenbeck's Archives of Surgery , 407, 143-152, 2022. pdf Tonini A., Vergara C., Regazzoni F., Dede' L., Scrofani R., Cogliati C., Quarteroni A., A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system. Scientific Reports - Nature, 14, 8304, 2024. pdf Criseo E., Fumagalli I., Quarteroni A., Marianeschi S.M., Vergara C., Computational haemodynamics for pulmonary valve replacement by means of a reduced Fluid-Structure Interaction model. Int. J. Num. Meth. Biomed. Eng., 40(9), e3846, 2024. pdf Capuano E., Regazzoni F., Maines M., Fornara S., Locatelli V., Catanzariti D., Stella S., Nobile F., Del Greco M., Vergara C., Personalized Computational Electro-mechanics Simulations to Optimize Cardiac Resynchronization Therapy. Biomech. Model. Mechanobiol., 23, 1977-2004, 2024. pdf Fumagalli I., Pagani S., Vergara C., Dede' L., Adebo D.A., Del Greco M., Frontera A., Luciani G.B., Pontone G., Scrofani R., Quarteroni A., The role of computational methods in cardiovascular medicine: a narrative review. Traslational Pediatrics, 13(1), 146-163, 2024. pdf

WSS in the portal vein and corresponding histological tumor analysis (by E. Milani)

5) Optimized Schwarz Methods (2009-onwards)

Problem: Provide convergence analyses and optimization of the generalized Schwarz method for specific interfaces Cases: Fluid-structure interaction problem, cylindrical interfaces, geometric heterogeneous coupling Related publications : L. Gerardo-Giorda, F. Nobile, C. Vergara, Analysis and optimization of Robin-Robin partitioned procedures in fluid-structure interaction problems. SIAM J. Num. Anal. , 48(6), pp. 2091-2116, 2010. pdf G. Gigante, M. Pozzoli, C. Vergara, Optimized Schwarz Methods for the diffusion-reaction problem with cylindrical interfaces . SIAM J. Num. Anal. , 51(6), pp. 3402-3420, 2013. pdf Gigante G., Vergara C., Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid-structure interaction. Numer. Math., 131(2), pp. 369--404, 2015. pdf G. Gigante, C. Vergara, Optimized Schwarz method for the fluid-structure interaction with cylindrical interfaces. Domain Decomposition Methods in Science and Engineering XXII - Lecture Notes in Computational Science and Engineering - Proceedings of the 22nd International Conference on Domain Decomposition Methods, 104, pp. 521-529, 2016. pdf Gigante G., Vergara C., Optimized Schwarz methods for the coupling of cylindrical geometries along the axial direction. Mathematical Modelling and Numerical Analysis (M2AN), 52, pp.1597-1615, 2018. pdf Gigante G., Sambataro G., Vergara C., Optimized Schwarz methods for spherical interfaces with application to fluid-structure interaction. SIAM J. Sc. Comp., 42(2), A751-A770, 2020. pdf Bucelli M., Geraint Gabriel M., Quarteroni A., Gigante G., Vergara C., A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction. Journal of Computational Physics, 490, 112326, 2023. pdf

Convergence set (in blue) of interface parameters for a general elliptic problem

6) Modeling the cardiac function - Electrophysiology & Electro-Mechanics (2012-onwards)

Problems: - Generation of a patient-specific Purkinje network in computational cardiology - Modeling the electro-mechanical activity in the myocardium - Study of Cardiac Resynchronization Therapy and arrhytmogenesis due to ischemia Clinical data: In-vivo measurements of the electrical activity Related publications : Vergara C., Palamara S., Catanzariti D., Pangrazzi C., Nobile F., Centonze M.,Faggiano E., Maines M., Quarteroni A., Vergara G., Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation. Medical & Biological Engineering & Computing, 52(10), pp. 813--826, 2014. pdf Palamara S., Vergara C., Catanzariti D., Faggiano E., Centonze M., Pangrazzi C., Maines M., Quarteroni A., Computational generation of the Purkinje network driven by clinical measurements: The case of pathological propagations. Int. J. Num. Meth. Biomed. Eng., 30(12), pp. 1558--1577, 2014. pdf Palamara S., Vergara C., Faggiano E., Nobile F., An effective algorithm for the generation of patient-specific Purkinje networks in computational electrocardiology. J. Comp. Phys., 283, pp. 495--517, 2015. pdf Lange M., Palamara S., Lassila T., Vergara C., Quarteroni A., Frangi A.F., Efficient Numerical Schemes for Computing Cardiac Electrical Activation over Realistic Purkinje Networks: Method and Verification, in "Functional Imaging and Modeling of the Heart", Proceedings of the 8th International Conference, FIMH 2015, Springer, pp. 430-438, 2015. pdf Vergara C., Lange M., Palamara S., Lassila T., Frangi A.F., Quarteroni A., A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network. Journal of Computational Physics, 308, pp. 218--238, 2016. pdf Lange M., Palamara S., Lassila T., Vergara C., Quarteroni A., Frangi A.F., Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks.. Int. J. Numer. Meth. Biomed. Eng., 33(6), e2835, 2017. pdf Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. Acta Numerica, 26, pp. 365-590, 2017 pdf Quarteroni A., Vergara C., Computational models for hemodynamics. Encyclopedia of Continuum Mechanics. doi:10.1007/978-3-662-53605-6_35-1, 2018. pdf Landajuela M., Vergara C., Gerbi A., Dede' L., Formaggia L., Quarteroni A., Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. Int. J. Num. Meth. Biomed. Eng., 34, e2984, 2018. pdf Quarteroni A., Vergara C., Landajuela M., Mathematical and Numerical Description of the Heart Function. In ''Imagine Math 6'' (M. Emmer and M. Abate eds.), Springer, pp. 171-177, 2018. pdf Quarteroni A., Dede' L., Manzoni A., Vergara C., Mathematical Modelling of the Human Cardiovascular System - Data, Numerical Approximation, Clinical Applications, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2019. pdf Stella S., Vergara C., Maines M., Catanzariti D., Africa P., Dematte' C., Centonze M., Nobile F., Del Greco M., Quarteroni A. Integration of activation maps of epicardial veins in computational cardiac electrophysiology . Computers in Biology and Medicine, 127, 104047, 2020. pdf Piersanti R., Africa P.C., Fedele M., Vergara C., Dede' L., Corno A.F., Quarteroni A. Modeling cardiac muscle fibers in ventricular and atrial electrophysiology simulations. Comp. Meth. Appl. Mech. Eng., 373, 113468, 2021. pdf Vergara C., Stella S., Maines M., Africa P.C., Catanzariti D., Dematte' C., Centonze M., Nobile F., Quarteroni A., Del Greco M., Computational electrophysiology of the coronary sinus branches based on electroanatomical mapping for the prediction of the latest activated region. Medical & Biological Engineering & Computing. 60, 2307 2319, 2022. pdf Piersanti R., Regazzoni F., Salvador M., Corno A.F., Dede' L., Vergara C., Quarteroni A., 3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics. Comp. Meth. Appl. Mech. Eng., 391, 114607, 2022. pdf Stella S., Regazzoni F., Vergara C., Dede' L., Quarteroni A., A fast cardiac electromechanics model coupling the Eikonal and the nonlinear mechanics equations. Mathematical Models and Methods in Applied Sciences (M3AS), 32(8), 1531--1556, 2022. pdf Quarteroni A., Dede' L., Regazzoni F., Vergara C., A mathematical model of the human heart suitable to address clinical problems. Japan Journal of Industrial and Applied Mathematics, 40, 1547-1567, 2023. pdf Botta F., Calafa' M., Africa P.C., Vergara C., Antonietti P.F., High-order Discontinuous Galerkin Methods for the Monodomain and Bidomain Models. Mathematics in Engineering, 6(6), 726-741, 2024. pdf Capuano E., Regazzoni F., Maines M., Fornara S., Locatelli V., Catanzariti D., Stella S., Nobile F., Del Greco M., Vergara C., Personalized Computational Electro-mechanics Simulations to Optimize Cardiac Resynchronization Therapy. Biomech. Model. Mechanobiol., 23, 1977-2004, 2024. pdf Corda A., Pagani S., Vergara C., Influence of acute myocardial ischemia on arrhythmogenesis: a computational study, medRXiv, DOI:10.1101/2024.11.20.24317476, 2024. pdf Brunati S., Bucelli M., Piersanti R., Dede' L., Vergara C. Coupled Eikonal problems to model cardiac reentries in Purkinje network and myocardium. arxiv, DOI: arXiv:2412.13837, 2024. pdf

7) Modeling the cardiac function - Hemodynamics & Perfusion (2018-onwards)

Problems: - Multiscale modeling of the cardiac perfusion - Image-based ventricular and atrial blood dynamics Clinical data: Dynamic atrial and ventricular images Related publications : Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. Acta Numerica, 26, pp. 365-590, 2017 pdf Quarteroni A., Vergara C., Computational models for hemodynamics. Encyclopedia of Continuum Mechanics. doi:10.1007/978-3-662-53605-6_35-1, 2018. pdf Quarteroni A., Dede' L., Manzoni A., Vergara C., Mathematical Modelling of the Human Cardiovascular System - Data, Numerical Approximation, Clinical Applications, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2019. pdf Di Gregorio S., Fedele M., Pontone G., Corno A.F., Zunino P., Vergara C., Quarteroni A., A computational model applied to myocardial perfusion in the human heart: From large coronaries to microvasculature. Journal of Computational Physics, 424, 109836, 2021. pdf Fumagalli I., Fedele M., Vergara C., Dede' L., Ippolito S., Nicolo' F., Antona C., Scrofani R., Quarteroni A., An Image-based Computational Hemodynamics Study of the Systolic Anterior Motion of the Mitral Valve. Computers in Biology and Medicine, 123, 103922, 2020. pdf Dede' L., Regazzoni F., Vergara C., Zunino P., Guglielmo M., Scrofani R., Fusini L., Cogliati C., Pontone G., Quarteroni A. Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study. Mathematical Biosciences and Engineering, 18(4), pp. 3364-3383, 2021. pdf Barnafi N., Di Gregorio S., Dede' L., Zunino P., Vergara C., Quarteroni, A., A multiscale poromechanics model integrating myocardial perfusion and the epicardial coronary vessels. SIAM J. Appl. Math.. 82(4), 1167--1193, 2022. pdf Bucelli M., Dede' L., Quarteroni A., Vergara C., Partitioned and monolithic algorithms for the numerical solution of cardiac fluid-structure interaction. Comm. Comp. Phys. 32(5), 1217-1256, 2023. pdf Bennati L., Vergara C., Giambruno V., Fumagalli I., Corno A.F., Quarteroni A., Puppini G., Luciani G.B., An image-based computational fluid dynamics study of mitral regurgitation in presence of prolapse. Cardiovascular Engineering and Technology, 14, 457-475, 2023 pdf Bucelli M., Geraint Gabriel M., Quarteroni A., Gigante G., Vergara C., A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction. Journal of Computational Physics, 490, 112326, 2023. pdf Quarteroni A., Dede' L., Regazzoni F., Vergara C., A mathematical model of the human heart suitable to address clinical problems. Japan Journal of Industrial and Applied Mathematics, 40, 1547-1567, 2023. pdf Bennati L., Giambruno V., Renzi F., Di Nicola V., Maffeis C., Puppini G., Luciani G.B., Vergara C., Turbulence and blood washout in presence of mitral regurgitation: a computational fluid-dynamics study in the complete left heart. Biomech. Model. Mechanobiol., 22, 1829-1846, 2023. pdf Zingaro A., Vergara C., Dede' L., Regazzoni F., Quarteroni A., A comprehensive mathematical model for cardiac perfusion. Scientific Reports - Nature, 13, 14220, 2023. pdf Renzi F., Vergara C., Fedele M., Giambruno V., Quarteroni A., Puppini G., Luciani G.B., Accurate Reconstruction of Right Heart Shape and Motion from Cine-MRI for Image-Driven Computational Hemodynamics. Int. J. Num. Meth. Biomed. Eng., 41(1), e3891, 2025. pdf . Montino Pelagi G., Baggiano A., Regazzoni F., Fusini L., Ali' M., Pontone G., Valbusa G., Vergara C., Personalized pressure conditions and calibration for a predictive computational model of coronary and myocardial blood flow. Annals Biomed. Eng., 52, 1297-1312, 2024. pdf Montino Pelagi G., Regazzoni F., Huyghe J.M., Baggiano A., Ali' M., Bertoluzza S., Valbusa G., Pontone G., Vergara C., Modeling cardiac microcirculation for the simulation of coronary flow and 3D myocardial perfusion. Biomech. Model. Mechanobiol., 23, 1863-1888, 2024. pdf Bennati L., Crispino A., Vergara C. Computational modeling of cardiac hemodynamics including chordae tendineae, papillaries, and valves dynamics. Computers in Biology and Medicine, 186, 109658, 2025. pdf Renzi F., Puppini G., Luciani G.B., Vergara C. Image-based computational hemodynamics in the right heart. Biomech. Model. Mechanobiol. To appear. pdf Renzi F., Bennati L., Fedele M., Giambruno V., Quarteroni A., Puppini G., Luciani G.B., Vergara C., From cine-MRI to computational models of blood flow within the heart. Vascular Pharmacology, 155, 107343, 2024. pdf

8) Finite Elements methods for unfitted meshes (2016-onwards)

Problem: Developing Finite Elements methods for non matching grids Strategies: Extended Finite Elements - Discontinuos Galerkin methods for meshes with arbitrary polygons Application: Fluid-structure interaction Related publications : Zonca S., Vergara C., Formaggia L., An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach. SIAM J. Sc. Comp., 40(1), pp. B59-B84, 2018 pdf Formaggia L., Vergara C., Zonca S., Unfitted Extended Finite Elements for composite grids. Computers and Mathematics with Applications, 76(4), pp. 893-904, 2018. pdf Antonietti P., Verani M., Vergara C., Zonca S., Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids. Finite Elements in Analysis and Design, 159, pp. 1-14, 2019. pdf Vergara C., Zonca S., Extended Finite Elements method for fluid-structure interaction with an immersed thick non-linear structure. In "Mathematical and Numerical Modeling of the Cardiovascular System and Applications", SEMA SIMAI Springer Series (D. Boffi, L. Pavarino, G. Rozza, S. Scacchi, C. Vergara eds.). In press. pdf Zonca S., Antonietti P.F., Vergara C. A Polygonal Discontinuous Galerkin formulation for contact mechanics in fluid-structure interaction problems. Comm. Comp. Phys., 30, pp. 1-33, 2021. pdf Martinolli M., Biasetti J.,Zonca S., Polverelli L., Vergara C., Extended Finite Element Method for Fluid-Structure Interaction in Wave Membrane Blood Pumps. Int. J. Num. Meth. Biomed. Eng., 37(7), e3467, 2021. pdf Martinolli M., Cornat F., Vergara C., Computational Fluid-Structure Interaction Study of a new Wave Membrane Blood Pump. Cardiovascular Engineering and Technology, 13, 373 392, 2022. pdf Criseo E., Fumagalli I., Quarteroni A., Marianeschi S.M., Vergara C., Computational haemodynamics for pulmonary valve replacement by means of a reduced Fluid-Structure Interaction model. Int. J. Num. Meth. Biomed. Eng., 40(9), e3846, 2024. pdf

Fluid velocity magnitude (on the background) and structure displacement on a slice - 3D Fluid structure interaction simulation (by S. Zonca)

9) Parameter estimation for cardiovascular problems (2009-onwards)

Problem: Estimation through the solution of inverse problems of some parameters characterizing cardiovascular problems Strategies: Minimization in a variational framework of a suitable functional. Direct search methods for application to clinical data Applications: - Plaque characterization in carotid arteries by using CINE MRI data - Estimation conduction velocities in cardiac electrophysiology by using activation time measures - Calibration of cardiac perfusion model parameters - Calibration of lumped parameter models Related publications : Perego M., Veneziani A., Vergara C., A variational approach for estimating the compliance of the cardiovascular tissue: An Inverse fluid-structure interaction problem. SIAM J. Sc. Comp , 33(3), pp. 1181-1211, 2011. pdf D'Elia M., Mirabella L.,Passerini T., Perego M., Piccinelli M., Vergara C., Veneziani A., Applications of variational data assimilation in computational hemodynamics, in Modeling of Physiological Flows, Ambrosi D., Quarteroni A., Rozza G. eds., Springer, 2011. Link Veneziani A., Vergara C., Inverse problems in Cardiovascular Mathematics: toward patient-specific data assimilation and optimization, Editorial of the special issue "Inverse Problems in Cardiovascular Mathematics", International Journal for Numerical Methods in Biomedical Engineering, 29(7), pp. 7 23-725, 2013. pdf Quarteroni A., Manzoni A., Vergara C., The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications. Acta Numerica, 26, pp. 365-590, 2017 pdf Quarteroni A., Dede' L., Manzoni A., Vergara C., Mathematical Modelling of the Human Cardiovascular System - Data, Numerical Approximation, Clinical Applications, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, 2019. pdf Pozzi S., Domanin M., Forzenigo L., Votta E., Zunino P., Redaelli A., Vergara C., A surrogate model for plaque modeling in carotids based on Robin conditions calibrated by cine MRI data . Int. J. Num. Meth. Biomed. Eng., 37(5), e3447, 2021. pdf Stella S., Vergara C., Maines M., Catanzariti D., Africa P., Dematte' C., Centonze M., Nobile F., Del Greco M., Quarteroni A. Integration of activation maps of epicardial veins in computational cardiac electrophysiology . Computers in Biology and Medicine, 127, 104047, 2020. pdf Di Gregorio* S., Vergara* C., Montino Pelagi G., Baggiano A., Zunino P., Guglielmo M., Fusini L., Muscogiuri G., Rossi A., Rabbat M.G., Quarteroni A., Pontone G., Prediction of myocardial blood flow under stress conditions by means of a computational model. European Journal of Nuclear Medicine and Molecular Imaging. , 49:1894 1905, 2022. *These authors equally contributed to the work. pdf Vergara C., Stella S., Maines M., Africa P.C., Catanzariti D., Dematte' C., Centonze M., Nobile F., Quarteroni A., Del Greco M., Computational electrophysiology of the coronary sinus branches based on electroanatomical mapping for the prediction of the latest activated region. Medical & Biological Engineering & Computing. 60, 2307 2319, 2022. pdf Tonini A., Regazzoni F., Salvador M., Dede' L., Scrofani R., Fusini L., Cogliati C., Pontone G., Vergara C., Quarteroni A., Two new calibration techniques of lumped-parameter mathematical models for the cardiovascular system. Int. J. Num. Meth. Eng., 126(1), e7648, 2025. pdf Capuano E., Regazzoni F., Maines M., Fornara S., Locatelli V., Catanzariti D., Stella S., Nobile F., Del Greco M., Vergara C., Personalized Computational Electro-mechanics Simulations to Optimize Cardiac Resynchronization Therapy. Biomech. Model. Mechanobiol., 23, 1977-2004, 2024. pdf Montino Pelagi G., Regazzoni F., Huyghe J.M., Baggiano A., Ali' M., Bertoluzza S., Valbusa G., Pontone G., Vergara C., Modeling cardiac microcirculation for the simulation of coronary flow and 3D myocardial perfusion. Biomech. Model. Mechanobiol., 23, 1863-1888, 2024. pdf Criseo E., Baggiano A., Montino Pelagi G., Nannini G., Redaelli A., Pontone G., Vergara C., Development of a digital twin for the diagnosis of cardiac perfusion defects, medRXiv, DOI:10.1101/2025.02.04.25321638, 2024. pdf

Characterization of tissues: plaque (yellow), jugular vein (blue, light blue and violet), healthy vessel (white) (by S. Pozzi)

10) Estimation of the flow rate in haemodynamic measures (2005-2010)

Problem: Estimation of the flow rate in vascular districts by the knowledge of the maximum velocity measured with the Doppler techniques Strategies: Proposal of suitable laws linking the mean and the maximum valocities with parameters suitably tuned Related publications : Ponzini R., Vergara C., Redaelli A., Veneziani A., Reliable CFD-based estimation of flow rate in haemodynamics measures, Ultrasound in Med. and Biol., 32 (10), pp. 1545--1555, 2006. pdf Ponzini R., Vergara C., Veneziani A., Redaelli A., Design of new reliable CFD-based estimation of flow rate in haemodynamics measures, Journal of Biomechanics (41), Supplement 1, page S214, 2008. pdf Ponzini R., Vergara C., Veneziani A., Redaelli A., Design of new reliable CFD-based estimation of flow rate: Early in-vivo results, Computers in Cardiology, pp. 953-955, 2008. pdf Ponzini R., Rizzo G., Vergara C., Veneziani A., Morbiducci U., Montevecchi F.M., Redaelli A., Computational modeling of local hemodynamics phenomena: Methods, tools and clinical applications , Nuovo Cimento C della Societa' Italiana di Fisica - Colloquia on Physics, 32(2), pp. 77-80, 2009 Ponzini R., Vergara C., Rizzo G., Veneziani A., Redaelli A., Vanzulli A., Parodi O., Computational fluid dynamics-based estimation of blood flow rate in Doppler analsys: in vivo validation by means of phase contrast magnetic resonance imaging, Proceedings of the ASME summer conference, pp. 227-228, 2009. pdf Vergara C., Ponzini R., Veneziani A., Redaelli A., Neglia D., Parodi O., Womersley number-based estimation of flow rate with Doppler Ultrasound: Sensitivity analysis and first clinical application . Computer Methods and Programs in Biomedicine, 98(2), pp. 151-160, 2010. pdf Ponzini R., Vergara C., Rizzo G., Veneziani A., Roghi A., Vanzulli A., Parodi O., Redaelli A., Womersley number-based estimates of blood flow rate in Doppler analysis: In vivo validation by means of Phase Contrast Magnetic Resonance Imaging. IEEE Transaction on Biomedical Engineering, 57 (7), pp. 1807-1815, 2010. pdf

Velocity profiles measured with PC-MRI. Top: abdominal aorta; Middle: carotid; Bottom: brachial artery (by R. Ponzini)

11) Drug release from medical stents (2006-2008)

Problem: Numerical modeling of the release of drug in medical stents Strategies: Coupling of a Darcy problem for the fluid advection and of a diffuzion-reaction problem for the drug release Related publications : Vergara C., Zunino P., Multiscale modeling and simulation of drug release from cardiovascular stents, SIAM Multiscale Modeling and Simulation, 7(2), pp. 565-588, 2008. pdf Zunino P., D'Angelo C., Petrini L., Vergara C., Capelli C., Migliavacca F. Numerical simulation of drug eluting coronary stents: mechanics, fluid dynamics and drug release . Comp. Meth. Appl. Mech. Eng., 198(45-46), pp. 3633-3644, 2009. pdf