MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1287 products
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85/2020 - 12/23/2020
Cavinato, L.; Sollini, M.; Kirienko, M.; Biroli, M.; Ricci, F.; Calderoni, L.; Tabacchi, E.; Nanni, C.; Zinzani, P. L.; Fanti, S.; Guidetti, A.; Alessi, A.; Corradini, P.; Seregni, E.; Carlo-Stella, C.; Chiti, A.; Ieva, F.;
PET radiomics-based lesions representation in Hodgkin lymphoma patients | Abstract | | As medical image analysis has been proven to entail tumor-specific in- formation, the so-called radiomics paradigm holds the promise to characterize the disease and infer long term outcomes of chemotherapy. In this work, we propose an insightful framework for disease characterization in Hodgkin lymphoma which could inform future research. Particularly, an intra-patient similarity index (ISI) was built to represent the homogeneity of the patients’ disease, while a radiomics-based fingerprint was create for local lesion description. Through descriptive statistics and classification algorithms, ISI-weighted fingerprint has been showed to be discriminatory between responders and relapsing patients. |
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84/2020 - 12/23/2020
Vergara, C.; Stella, S.; Maines, M.; Catanzariti, D.; Demattè, C.; Centonze, M.; Nobile, F.; Quarteroni, A.; Del Greco, M.
Computational electrophysiology to support the mapping of coronary sinus branches for cardiac resynchronization therapy | Abstract | | BACKGROUND
This work dealt with the assessment of a computational tool to estimate the latest electrically activated segment (LEAS) of the left ventricle during cardiac resynchronization therapy (CRT). OBJECTIVE
The aim of the work was to show that for patients with left bundle branch block (LBBB), possibly in presence of fibrosis, the proposed computational tool was able to accurately reproduce the epicardial activation maps and in particular LEAS location in the epicardial veins, often used as a target site for the left lead placement.
METHODS
We considered a computational tool based on Finite Elements used to recover the activation maps in all the myocardium. The model was calibrated by using activation times acquired in the epicardial veins with an electroanatomic mapping system (EAMS).
RESULTS
We applied our computational tool to predict LEAS in the epicardial veins of ten patients. We found an excellent accordance with LEAS measured by EAMS, the discrepancy being less than 4mm. We also calibrated our model using only the activation maps of the coronary sinus (CS), still obtaining an excellent agreement with the measured LEAS.
CONCLUSION
We showed that our computational tool is able to accurately predict the location of LEAS, even when information only at CS were used for calibration. This could be of utmost importance in view of CRT implantation, since LEAS could be determined by mapping only CS, saving time and avoiding the exposition of the patient to a deeper invasive procedure. |
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83/2020 - 12/23/2020
Hron, K.; Machalova, J.; Menafoglio, A.
Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation | Abstract | | A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former being built as the product of revised definitions of marginal densities and the latter capturing the dependence between the two random variables being studied. The developed framework opens new perspectives for dependence modelling (which is commonly performed through copulas),
and allows for the analysis of dataset of bivariate densities, in a Functional Data Analysis perspective. A spline representation for bivariate densities is also proposed, providing a computational cornerstone for the developed theory.
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82/2020 - 12/11/2020
Vismara, F; Benacchio, T.; Bonaventura, L.
A seamless, extended DG approach for hyperbolic-parabolic problems on unbounded domains | Abstract | | We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of hyperbolic-parabolic equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test functions. Numerical fluxes enable the coupling at the interface between the two subdomains in the same way as standard single domain DG interelement fluxes. A novel linear analysis on the extended DG model yields stability constraints on the finite subdomain grid size that get tighter for increasing values of the P'eclet number.
Errors due to the use of different sets of basis functions on different portions of the domain are negligible, as highlighted in numerical experiments with the linear advection-diffusion and viscous Burgers' equations. With an added damping term on the semi-infinite subdomain, the extended framework is able to efficiently simulate absorbing boundary conditions without additional conditions at the interface. A few modes in the semi-infinite subdomain are found to suffice to deal with outgoing single wave and wave train signals, thus providing an appealing model for fluid flow simulations in unbounded regions. |
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81/2020 - 12/02/2020
Antonietti, P. F.; Mascotto, L.; Verani, M.; Zonca, S.
Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems | Abstract | | We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a fluid-structure interaction problem and we numerically explore the stability properties of the method. |
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80/2020 - 11/30/2020
Zingaro, A.; Dede', L.; Menghini, F.; Quarteroni, A.
Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical model | Abstract | | In this paper, we investigate the hemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational Multiscale (VMS) model is adopted to obtain a stable formulation of the Navier-Stokes equations discretized by means of the Finite Element method and to account for turbulence modeling based on Large Eddy Simulation (LES). The aim of this paper is twofold: on one hand to improve the general understanding of blood flow in the human LA in normal conditions; on the other, to analyse the effects of VMS-LES models on a situation of blood flow which is neither laminar, nor fully turbulent, but rather transitional as in LA. Our conclusion is that the VMS-LES model is better suited to capture transitional effects than the standard SUPG stabilization method. |
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79/2020 - 11/25/2020
Regazzoni, F.; Salvador, M.; Africa, P.c.; Fedele, M.; Dede', L.; Quarteroni, A.
A cardiac electromechanics model coupled with a lumped parameters model for closed-loop blood circulation. Part I: model derivation | Abstract | | We propose an integrated electromechanical model of the human heart, with focus on the left ventricle, wherein biophysically detailed models describe the different physical phenomena concurring to the cardiac function. We model the subcellular generation of active force by means of an Artificial Neural Network, which is trained by a suitable Machine Learning algorithm from a collection of pre-computed numerical simulations of a biophysically detailed, yet computational demanding, high-fidelity model. To provide physiologically meaningful results, we couple the 3D electromechanical model with a closed-loop 0D (lumped parameters) model describing the blood circulation in the whole cardiovascular network. We prove that the 3D-0D coupling of the two models is compliant with the principle of energy conservation, which is achieved in virtue of energy-consistent boundary conditions that account for the interaction among cardiac chambers within the computational domain, pericardium and surrounding tissue. We thus derive an overall balance of mechanical energy for the 3D-0D model. This provides a quantitative insight into the energy utilization, dissipation and transfer among the different compartments of the cardiovascular network and during different stages of the heartbeat. In virtue of this new model and the energy balance, we propose a new validation tool of heart energy usage against relationships used in the daily clinical practice. Finally, we provide a mathematical formulation of an inverse problem aimed at recovering the reference configuration of one or multiple cardiac chambers, starting from the stressed configuration acquired from medical imaging. This is fundamental to correctly initialize electromechanical simulations. Numerical methods and simulations of the 3D-0D model will be detailed in Part II. |
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78/2020 - 11/25/2020
Regazzoni, F.; Salvador, M.; Africa, P.c.; Fedele, M.; Dede', L.; Quarteroni, A.
A cardiac electromechanics model coupled with a lumped parameters model for closed-loop blood circulation. Part II: numerical approximation | Abstract | | In the framework of accurate and efficient segregated schemes for 3D cardiac electromechanics and 0D cardiovascular models, we propose here a novel numerical approach to address the coupled 3D-0D problem introduced in Part I of this two-part series of papers. We combine implicit-explicit schemes to solve the different cardiac models in a multiphysics setting. We properly separate and manage the different time and space scales related to cardiac electromechanics and blood circulation. We employ a flexible and scalable intergrid transfer operator that enables to interpolate Finite Element functions among different meshes and, possibly, among different Finite Element spaces. We propose a numerical method to couple the 3D electromechanical model and the 0D circulation model in a numerically stable manner within a fully segregated fashion. No adaptations are required through the different phases of the heartbeat. We also propose a robust algorithm to reconstruct the stress-free reference configuration. Due to the computational cost associated with the numerical solution of this inverse problem, the reference configuration recovery algorithm comes along with a novel projection technique to precisely recover the unloaded geometry from a coarser representation of the computational domain. We show the convergence property of our numerical schemes by performing an accuracy study through grid refinement. To prove the biophysical accuracy of our computational model, we also address different scenarios of clinical interest in our numerical simulations by varying preload, afterload and contractility. Indeed, we simulate physiologically relevant behaviors and we reproduce meaningful results in the context of cardiac function. |
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