Workshop on Mathematical and Numerical Modeling of the Cardiovascular System and Applications

New estimates on the matching problem Luigi Ambrosio Scuola Normale Superiore, Italy. The matching problem consists in finding the optimal coupling between a random distribution of N points in a d-dimensional domain and another (possibly random) distribution. There is a large literature on the asymptotic behaviour as N tends to infinity of the expectation of the minimum cost, and the results depend on the dimension d and the choice of cost, in this random optimal transport problem. In a recent work, Caracciolo, Lucibello, Parisi and Sicuro proposed an ansatz for the expansion in N of the expectation. I will illustrate how a combination of semigroup smoothing techniques and Dacorogna-Moser interpolation provide first rigorous results for this ansatz. Joint work with Federico Stra and Dario Trevisan, ArXiv:1611.04960 New trends for advanced reduced order methods in CFD: applications to parametric cardiovascular flows Francesco Ballarin Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy. We present new trends for parametric computing based on advanced reduced order methods for applications in computational fluid dynamics, with a special interest in problems related with cardiovascular flows. These problems are of particular interest due to the fact that they bring a certain complexity related with the geometry of biological structures to be reconstructed and parametrized for the simulation, medical data subject to uncertainty and noise. In addition the numerical approximation of complex nonlinear parametric systems needs proper stabilization also at the reduced order level. Few examples from real-life problems are introduced as proof-of-concept to introduce a complete computational pipeline in an advanced reduced order setting. Multi-physics is accounted in considering fluid and structure interaction between flows and arterial walls, and optimal flow control is accounted for the solution of inverse problems (defective boundary conditions, parameter estimation, data assimilation) as well as for interfacing network components. A higher-order operator-splitting method for the monodomain and bidomain models Jessica Cervi and Raymond J. Spiteri Numerical Simulation Laboratory, Department of Computer Science, University of Saskatchewan, Saskatoon, Canada. The monodomain and the bidomain models are frequently used to describe the electrical activity in myocardial tissue. They are multi-scale reaction-diffusion models that couple electrical activity at the cellular scale with the one at the tissue scale. Because of this complexity, the resulting system is demanding to solve numerically. Firstand secondorder operator-splitting methods have been successful in producing acceptable simulations for the models; however, solutions with even higher order hold the promise of increased efficiency required for real-time simulations. There have been claims in the literature that splitting methods with order higher than two are not suitable for deterministic parabolic equations because they necessarily involve backwards time integration, hence making them unstable. In this talk, we discuss the derivation and implementation of stable operatorsplitting methods with order higher than two for the monodomain and bidomain models and assess their efficiency and accuracy. In particular, we investigate the efficiency results of our method compared to various benchmarks. Kneeling and stair climbing. Numerical simulation of dynamic contact problems Peter Deuflhard Zuse Institute Berlin, Germany and Beijing Institute for Scientific and Engineering Computing, China To begin with, various methods of motion analysis of kneeling, walking, stair climbing are presented (wherein a prominent Italian collaborator enters – no, not PCF). The corresponding mathematical model is the elastodynamic contact problem. Space-time-discretization by the method of lines as well as by the method of time layers (Rothe method) will be discussed, where the latter is the method of choice here. An example of adaptive spatial mesh refinement at a knee by finite elements will be given for illustration. A class of time discretizations will be analyzed, emerging from the classical Newmark method, but with specialties that exhibit surprising features. Among them are a variant from California Institute of Technology (Caltech) and one of Zuse Institute Berlin (ZIB) (guess, which one is better!). In order to develop a fully adaptive time discretization, some deeper view into the mathematical convergence theory for the discretization is necessary. Here again surprising features occur. Finally, a realistic knee joint motion will be simulated in a numerically correct way. Engineered murine cardiac tissue for in vitro studies of electromagnetic and β-adrenergic stimulation Lorenzo Fassina, Maria Evelina Mognaschi, Giovanni Magenes, Fabio Naro Department of Electrical, Computer and Biomedical Engineering, Universitá degli Studi di Pavia, Italy Department of Anatomical, Histological, Forensic and Orthopaedic Sciences, Università degli Studi di Roma ”La Sapienza”, Roma, Italy In a model of murine cardiac tissue in vitro, we have studied the inotropic effects of electromagnetic stimulation (frequency, 75 Hz), isoproterenol administration (10 M), and their combination. In particular, we have performed an image processing analysis to evaluate the kinematics and the dynamics of beating syncytia starting from the video registration of their contraction movement. We have found that the electromagnetic stimulation is able to counteract the β-adrenergic effect of isoproterenol and to elicit an anti-hypertrophic response. This work suggests a potential application of the electromagnetic stimulus in the treatment of arrhythmias and hypertrophy. In particular, a weakening of the β-adrenergic sensibility can be significant in the ischemia-reperfusion injuries, where an abnormal depolarization could arise outside the normal conduction tissue causing life-threatening arrhythmias. Computational analysis of the possibile causes of coronary artery bypass grafts failure Bruno Guerciotti, Roberto Scrofani, Sonia Ippolito, Alfio Quarteroni, Christian Vergara MOX, Dipartimento di Matematica, Politecnico di Milano, Italy Cardio-surgery Unit, Ospedale L.Sacco, Milan, Italy Radiology unit, Ospedale L.Sacco, Milan, Italy MATHICSE CMCS, École polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland Coronary artery disease is one of the leading causes of death worldwide. For high-risk patients, the stenotic coronary vessels are generally treated with coronary artery bypass grafts (CABG), which can be either arterial (internal mammary artery, radial artery) or venous (saphenous vein). Despite overall excellent patency rates, bypasses may fail due to restenosis. In particular, the clinical outcome of CABG in terms of risk of restenosis and subsequent graft failure is thought to be influenced by the degree of the native coronary stenosis and by the mechanical properties of the graft (arterial vs venous). In this context, we performed numerical simulations in patient-specific geometries with the aim of better understanding the influence of the stenosis degree and the bypass mechanical properties on the risk of graft failure. Our results show that low degrees of coronary stenosis produce a more disturbed fluid dynamics in the graft, resulting in hemodynamic conditions that may promote a higher risk of graft failure. Furthermore, the use of a venous bypass results in a more disturbed flow field at the anastomosis and in higher stresses in the vessel wall with respect to the arterial one, thus possibly explaining the better long-term patency of the arterial bypasses experienced in the clinical practice. Epicardial kinematic parameters computed from video of in situ beating heart Michele Miragoli, Lorenzo Fassina, Giacomo Rozzi, Stefano Rossi, Simone Scacchi, Fabrizio Del Bianco, Piero Colli Franzone, Giuseppe Petrilli, Giuseppe Faggian Dipartimento di Medicina Clinica e Sperimentale, Università degli Studi di Parma and Humanitas Clinical and Research Center, Dipartimento di Ingegneria Industriale e dellInformazione, Università degli Studi di Pavia, Dipartimento di Matematica, Università degli Studi di Milano Dipartimento di Matematica, Università degli Studi di Pavia, Dipartimento di Cardiochirurgia, Università degli Studi di Verona Rationale: Cardiac mechanical function during open-chest cardiac surgery is monitored by echocardiographic techniques. However, little is known about local kinematics, particularly for the right ventricle and for the reperfused regions after an ischemic event. Objective: We report a novel imaging modality, which extracts local and global kinematic parameters from videos of in situ beating hearts and displays data during open-chest clinical procedure. Methods and Results: a custom algorithm, following the X-Y movement of appropriated selected video-markers, which returned cardiac frequency, contraction/relaxation trajectory, contraction displacement and velocity, acceleration, and kinetic energy, analyzes all video frames. We characterized the kinematic parameters in silico, using computational modeling of cardiac ischemia and beating human hearts before and after coronary arterybypass graft surgery (CABG). By virtually selecting the markers onto the ischemic and reperfused regions on the video, we measured the aforementioned parameters together with the conventional prognostic ones assessed by transesophageal echocardiography. We observed a significant decrement of our kinematics parameters, acquired by high-resolution camera, in ischemic rat hearts and the subsequent significant increment in the same regions after reperfusion. We detected similar behavior for operated CABG patients except one, recommended for extra intensive care. We also validated the increment of kinetic energy by analyzing the local Frank-Starling effect following atrioventricular blocks in