Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1287 prodotti
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19/2020 - 12/03/2020
Stella, S.; Vergara, C.; Maines, M.; Catanzariti, D.; Africa, P.; Demattè, C.; Centonze, M.; Nobile, F.; Del Greco, M.; Quarteroni, A.
Integration of maps of activation times in computational cardiac electrophysiology | Abstract | | In this work we used the monodomain equation
in combination with the Bueno-Orovio ionic model for the prediction of the activation
times in cardiac electro-physiology. We considered four patients who suffered from Left
Bundle Branch Block (LBBB) and patient-specific maps of activation times obtained by inserting in the ventricles
electrodes located on catheters. We used activation maps acquired at the septum as input data for the model
and maps at the epicardial veins for the validation of the monodomain model
in the context of a normal excitation. In particular, a first set (half) of the latter
were used to estimate the conductivities of the patient and a second set (the remaining half) to compute
the errors of the numerical simulations. We found an excellent agreement between measures and numerical
results. Our validated
computational tool could be used to accurately predict activation times at the epicardial veins,
allowing to shorten the mapping procedure and reduce the exposition to radiations.
This could be of great interest for clinical applications, for example in the Cardiac Resynchronization
Therapy (CRT) where such mapping is commonly used to determine the best point of stimulus. |
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16/2020 - 05/03/2020
Paolucci, R.; Mazzieri, I.; Piunno, G.; Smerzini, C.; Vanini, M.; Ozcebe, A.G.
Earthquake ground motion modelling of induced seismicity in the Groningen gas field | Abstract | | A key element in the seismic hazard and risk assessment due to induced earthquakes in the Groningen gas field is a
ground motion model (GMM). Although significant efforts have been devoted to the construction of an empirical
GMM, there is a growing interest in reducing its uncertainty through data-driven approaches. In the framework of
the KEM research program launched by the Ministry of Economic Affairs and Climate Policy of the Netherlands,
the authors explored the use of 3D physics-based numerical approaches to characterize earthquake ground motion in
the Groningen area and to shed light on the potential impact of the specific geologic conditions, characterized by
irregular geologic interfaces and thick layers of soft deposits at ground surface. Within the wider scope of this
research, this paper is focused on the construction and validation of a large-scale ( 20 km × 20 km), heterogeneous
3D seismic wave propagation model for the Groningen area, based on the significant bulk of available geological,
geophysical, geotechnical and seismological data.
Results of physics-based numerical simulations are validated against the ground motion recordings of the Jan 8,
2018, ML 3.4 Zeerijp earthquake – the third largest event to date in the area. Taking advantage of suitable models of
slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found
to reproduce accurately the observed features of ground motions at short epicentral distance (Repi < 10 km), in a
broad frequency range, up to about 10 Hz. To achieve this level of accuracy, the total number of degrees-of-freedom
was up to about 1 billion, implying taking advantage of high performance computing facilities. A sensitivity analysis
is also addressed to discuss the impact of key modeling assumptions, specifically, the role of 3D underground
geological features (“tunnel valleys”), the stochastic variability of shallow seismic velocities and the amplitude and
frequency dependence of the quality factor. Amongst others, results point out crucial aspects in deriving GMMs for
induced seismicity in Groningen, such as the magnitude and distance dependence of site amplification functions
associated with 3D wave propagation features, as opposed to the standard assumption of vertically propagating
plane waves. |
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18/2020 - 05/03/2020
Fumagalli, A.; Scotti, A.; Formaggia, L.
Performances of the mixed virtual element method on complex grids for underground flow | Abstract | | The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performances of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects. |
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17/2020 - 05/03/2020
Cerroni, D.; Formaggia, L.; Scotti, A.
A control problem approach to Coulomb's friction | Abstract | | In this work we present a formulation of Coulomb's friction in a fractured elastic body as a PDE control problem where the observed quantity is the tangential stress across an internal interface, while the control parameter is the slip i.e. the displacement jump across the interface. The cost function aims at minimizing the norm of a non-linear and not everywhere differentiable
complementarity function, written in terms of the tangential stress and the slip. The interesting point of this method is that gives rise to an iterative procedure where at each iteration we solve a problem with given slip at the interface, without resorting to the use of Lagrange multipliers.
We carry out a formal derivation of the method, with some preliminary results, and a numerical experiment to verify the efficacy of the technique.
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15/2020 - 22/02/2020
Fumagalli, I.; Fedele, M.; Vergara, C.; Dede', L.; Ippolito, S.; Nicolò, F.; Antona, C.; Scrofani, R.; Quarteroni, A.
An Image-based Computational Hemodynamics Study of the Systolic Anterior Motion of the Mitral Valve | Abstract | | Systolic Anterior Motion (SAM) of the mitral valve -- often associated to Hypertrophic Obstructive Cardiomyopathy (HOCM) -- is a cardiac pathology in which, during systole, a functional subaortic stenosis is induced by the mitral leaflets partially obstructing the outflow tract of the left ventricle. Its assessment by diagnostic tests is often difficult, possibly underestimating its severity and thus increasing the risk of sudden cardiac death. In the present work, the effects of SAM on the ventricular blood flow are investigated by means of Computational Fluid Dynamics (CFD) simulations. A novel image processing pipeline is set up to integrate cine-MRI data in the numerical model. Patient-specific geometry and motion of the left ventricle are accounted for by an Arbitrary Lagrangian-Eulerian approach, and the reconstructed mitral valve is immersed in the computational domain by means of a resistive method. Clinically relevant flow and pressure indicators are assessed for different degrees of SAM severity, in order to separate the effects of SAM from those of HOCM. Our numerical results and study provide preliminary indications that help better evaluating pathological condition and the design of its surgical treatment. |
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14/2020 - 20/02/2020
Calissano, A.; Feragen, A; Vantini, S.
Populations of Unlabeled Networks: Graph Space Geometry and Geodesic Principal Components | Abstract | | Statistical analysis for populations of networks is widely applicable, but challenging as networks have strongly non-Euclidean behavior. Graph Space is an exhaustive framework for studying populations of networks which are weighted or unweighted, uni- or multi-layer, directed or undirected, labelled or unlabelled. Viewing Graph Space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is unbounded from above. Motivated by these geometric properties, we define geodesic principal components, and we introduce the Align All and Compute algorithm, which allows the computation of statistics on Graph Space. The statistics and algorithm are empirically validated on one simulated study and two real datasets, showcasing the framework’s potential utility. The whole framework is implemented in a publically available
GraphSpace Python package. |
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13/2020 - 20/02/2020
Pozzi S.; Domanin M.; Forzenigo L.; Votta E.; Zunino P.; Redaelli A.; Vergara C.
A data-driven surrogate model for fluid-structure interaction in carotid arteries with plaque | Abstract | | In this work, we propose a surrogate model for the Fluid-Structure Interaction (FSI) problem for the study of blood dynamics in carotid arteries in presence of plaque. This model is based on the integration with subject-specific data and clinical imaging. In more detail, we propose to model the atherosclerotic plaque as part of the tissues surrounding the vessel wall through the application of an elastic support boundary condition on the external surface of the structure model. In order to characterize the plaque and other surrounding tissues, such as the close-by jugular vein, the elastic parameter of the boundary condition was spatially differentiated. The values of these parameters were estimated by minimizing the discrepancies between computed vessel wall displacements and reference values obtained from CINE Magnetic Resonance Imaging (MRI) data. As a first application of the method, we considered three subjects with a degree of stenosis greater than 70%. We found that accounting for both plaque and jugular vein in the estimation of the elastic parameters increases the accuracy. In particular, in all patients, mismatches between computed and in vivo measured wall displacements were 1-2 orders of magnitude lower than the spatial resolution of the original MRI data. These results confirmed the validity of the proposed surrogate model. |
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12/2020 - 16/02/2020
Azzolin, L.; Dede', L.; Gerbi, A.; Quarteroni, A.
Effect of fibre orientation and bulk value on the electromechanical modelling of the human ventricles | Abstract | | Computational modelling has been proven to be a useful tool to simulate heart functioning and have been increasingly used in patient-specific treatments. Cardiac modelling is intricately multi-scale and multi-physics and this makes the problem really complex both to formulate and to solve. In this work, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. In this paper, we study the influence of different fibre directions and incompressibility constraint values (bulk modulus) recently proposed and validated in [Barbarotta et al., IJNMBE, 2018] on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific bi-ventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show that various fibre configurations and bulk values modify relevant clinical quantities such as stroke value, ejection fraction and ventricle contractility. It is therefore important to reconstruct subject specific fibre orientation to obtain physiological behaviors. |
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