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 1242 products
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14/2020 - 02/20/2020
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 - 02/20/2020
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 - 02/16/2020
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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11/2020 - 02/16/2020
Antonietti, P.F.; Facciola', C.; Houston, P.; Mazzieri, I.; Pennes, G.; Verani, M.
High-order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations
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10/2020 - 02/16/2020
Bonaventura, L.; Carlini, E.; Calzola, E.; Ferretti, R.
Second order fully semi-Lagrangian discretizations of advection--diffusion--reaction systems | Abstract | | We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection--diffusion--reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive terms. Standard interpolation procedures are used for the space discretization on structured and unstructured meshes.
The proposed method allows for large time steps, while avoiding the solution of large linear systems, which would be required by an implicit time discretization technique. Numerical experiments demonstrate the effectiveness of the proposed approach and its superior efficiency with respect to more conventional explicit and implicit time discretizations. |
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09/2020 - 02/16/2020
Rea, F.; Ieva, F.,; Pastorino, U.; Apolone, G.; Barni, S.; Merlino, L.; Franchi, M.; Corrao, G.
Number of lung resections performed and long-term mortality rates of patients after lung cancer surgery: evidence from an Italian investigation | Abstract | | OBJECTIVES: Although it has been postulated that patients might benefit from the centralization of high-volume specialized centres, conflicting results have been reported on the relationship between the number of lung resections performed and the long-term, all-cause mortality rates among patients who underwent surgery for lung cancer. A population-based observational study was performed to contribute to the ongoing debate.
METHODS: The 2613 patients, all residents of the Lombardy region (Italy), who underwent lung resection for lung cancer from 2012 to 2014 were entered into the cohort and were followed until 2018. The hospitals were classified according to the annual number of pulmonary resections performed. Three categories of lung resection cases were identified: low (<30), intermediate (31–95) and high (>95). The outcome of interest was all-cause death. A frailty model was used to estimate the death risk associated with the categories of numbers of lung resections performed, taking into account the multilevel structure of the data. A set of sensitivity analyses was performed to account
for sources of systematic uncertainty.
RESULTS: The 1-year and 5-year survival rates of cohort members were 90% and 63%. Patients operated on in high-volume centres were on average younger and more often women. Compared to patients operated on in a low-volume centre, the mortality risk exhibited a significant,progressive reduction as the numbers of lung resections performed increased to intermediate (-13%; 95% confidence interval +10% to -31%) and high (-26%; 0% to -45%). Sensitivity analyses revealed that the association was consistent.
CONCLUSIONS: Further evidence that the volume of lung resection cases performed strongly affects the long-term survival of lung cancer patients has been supplied. |
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08/2020 - 02/16/2020
Antonietti, P. F.; Facciolà, C.; Verani, M.
Polytopic Discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures | Abstract | | We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements with edges/faces that may be in arbitrary number (potentially unlimited) and whose measure may be arbitrarily small. Our approach is then very well suited to tame the geometrical complexity featured by most of applications in the computational geoscience field. From the modelling point of view, we adopt a reduction strategy that treats fractures as manifolds of codimension one and we employ the primal version of Darcy's law to describe the flow in both the bulk and in the fracture network. In addition, some physically consistent conditions couple the two problems, allowing for jump of pressure at their interface, and they as well prescribe the behaviour of the fluid along the intersections, imposing pressure continuity and flux conservation.
Both the bulk and fracture discretizations are obtained employing the Symmetric Interior Penalty DG method extended to the polytopic setting. The key instrument to obtain a polyDG approximation
of the problem in the fracture network is the generalization of the concepts of jump and average at the intersection, so that the contribution from all the fractures is taken into account. We prove
the well-posedness of the discrete formulation and perform an error analysis obtaining a priori hp-error estimates. All our theoretical results are validated performing preliminary numerical
tests with known analytical solution. |
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07/2020 - 01/22/2020
Fumagalli, A.; Scotti, A.
Reactive flow in fractured porous media | Abstract | | In this work we present a model reduction procedure to derive a hybrid-dimensional framework for the mathematical modeling of reactive transport in fractured porous media. Fractures are essential pathways in the underground which allow fast circulation of the fluids present in the rock matrix, often characterized by low permeability. However, due to infilling processes fractures may change their hydraulic properties and become barriers for the flow creating impervious blocks. The geometrical as well as the physical properties of the fractures require a special treatment to allow the subsequent numerical discretization to be affordable and accurate. The aim of this work is to introduce a simple yet complete mathematical model to account for such diagenetic effects where chemical reactions will occlude or empty portions of the porous media and, in particular, fractures. |
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