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 1251 products
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18/2012 - 04/14/2012
Formaggia, L.; Vergara, C.
Prescription of general defective boundary conditions in fluid-dynamics | Abstract | | This work reviews and extends to a more general setting some strategies
to impose defective boundary conditions to fluid-dynamic problems investigated
by the authors in the last years. We focus here to the steady Stokes
problem as a paradigm for the unsteady and non-linear cases. We show
the well posedness of the proposed approaches and discuss their relative
benefits. |
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17/2012 - 03/20/2012
Manzoni, A.; Quarteroni, A.; Gianluigi Rozza, G.
Computational reduction for parametrized PDEs: strategies and applications | Abstract | | In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models. |
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16/2012 - 03/14/2012
Cutri', E.; Zunino, P.; Morlacchi, S.; Chiastra, C.; Migliavacca, F.
Drug delivery patterns for different stenting techniques in coronary bifurcations: a comparative computational study | Abstract | | The treatment of coronary bifurcation lesions represents a challenge for the interventional cardiologists due to the lower rate of procedural success and the higher risk of restenosis. The advent of drug eluting stents (DES) has dramatically reduced restenosis and consequently the request for re-intervention. The aim of the present work is to provide further insight about the effectiveness of DES by means of a computational study that combines virtual stent implantation, fluid dynamics and drug release for
different stenting protocols currently used in the treatment of a coronary artery bifurcation. An explicit dynamic finite element model is developed in order to obtain realistic configurations of the implanted devices used to perform fluid dynamics analysis by means of a previously developed finite element method coupling the blood flow and the intramural plasma filtration in rigid arteries. To efficiently
model the drug release, a multiscale strategy is adopted, ranging from lumped parameter model
accounting for drug release, to fully 3-D models for drug transport to the artery. Differences in drug delivery to the artery are evaluated with respect to local drug dosage. This model allowed to compare alternative stenting configurations (namely, the Provisional Side Branch, the Culotte and the Inverted Culotte techniques), thus suggesting guidelines in the treatment of coronary bifurcations lesions and addressing clinical issues such as the effectiveness of drug delivery to lesions in the side branch, as well as the influence of incomplete strut apposition and overlapping stents. |
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15/2012 - 03/11/2012
Mengaldo, G.; Tricerri, P.; Crosetto,P.; Deparis, S.; Nobile, F.; Formaggia, L.
A comparative study of different nonlinear hyperelastic isotropic arterial wall models in patient-specific vascular flow simulations in the aortic arch | Abstract | | Blood flow in major arteries gives rise to a complex fluid-structure interaction (FSI) problem. The mechanical behaviour of the tissues composing the vessel wall is highly nonlinear. However, when the wall deformation is small it can be argued that the effect of the non-linearities to the flow field is small and indeed several
authors employ a linear constitutive law. In the aortic arch, however, the deformations experienced by the vessel wall during the heart beat are substantial.
In this work we have implemented different non-linear constitutive relations for the vessel wall. We compare the flow field and related quantities such as wall shear stress obtained on an anatomically realistic geometry of aortic arch
reconstructed from clinical images and using physiological data. Particular attention is also devoted to the efficiency of the algorithms employed. The fluid-structure interaction problem is solved with a fully coupled approach and using
the exact Jacobians for each different structural model to guarantee a second order convergence of the Newton method. |
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14/2012 - 03/05/2012
Fumagalli, A.;Scotti, A.
An unfitted method for two-phase flow in fractured porous media. | Abstract | | We propose an efficient computational method to simulate two-phase flow in fractured porous media.
Instead of refining the grid to capture the flow along the faults or fractures, we represent them as immersed interfaces with
reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fracture to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method for the saturation equation, with a numerical flux that yields the correct entropy solution in the case of discontinuous flux function at the interface between the fracture and the porous matrix. |
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13/2012 - 02/14/2012
Formaggia, L.; Guadagnini, A.; Imperiali, I.; Lever, V.; Porta, G.; Riva, M.; Scotti, A.; Tamellini, L.
Global Sensitivity Analysis through Polynomial Chaos Expansion of a basin-scale geochemical compaction model | Abstract | | We present a model-driven uncertainty quantification methodology based on the use of sparse grids sampling techniques in the context
of a generalized Polynomial Chaos Expansion (GPCE) approximation of a basin-scale geochemical evolution scenario. The approach is illustrated through a one-dimensional example involving the process of quartz cementation in sandstones and the resulting effects on the dynamics of the vertical distribution of porosity, pressure and
temperature. The proposed theoretical framework and computational tools allow performing an efficient and accurate Global Sensitivity Analysis (GSA) of the system states (i.e., porosity, temperature, pressure and fluxes) in the presence of uncertain key mechanical and geochemical model parameters as well as boundary conditions. GSA is grounded on the use of the variance-based Sobol indices. These allow
discriminating the relative weights of uncertain quantities on the global model variance and can be computed through the GPCE of the model response surface. Evaluation of the GPCE of the random model response is performed through the implementation of a sparse grid interpolation technique in the space of the selected uncertain
quantities. As opposed to a standard Monte Carlo sampling, the use of sparse grids polynomial interpolants renders computationally affordable and reliable evaluations of the required indices. GPCE can then be employed as a surrogate model of the system states to quantify uncertainty propagation through the model in terms of the
probability distribution (and its statistical moments) of target system states. |
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12/2012 - 02/13/2012
Guglielmi, A.; Ieva, F.; Paganoni, A.M.; Ruggeri, F.
Hospital clustering in the treatment of acute myocardial infarction patients via a Bayesian semiparametric approach | Abstract | | In this work, we develop Bayes rules for several families of loss functions for hospital report cards under a Bayesian semiparametric hierarchical
model. Moreover, we present some robustness analysis with respect to the choice of the loss function, focusing on the number of hospitals our procedure identifies as unacceptably performing . The analysis is carried out on
a case study dataset arising from MOMI2 (Month MOnitoring Myocardial Infarction in MIlan) survey on patients admitted with ST-Elevation Myocardial Infarction to the hospitals of Milan Cardiological Network. The major aim of this work is the ranking of the health care providers performances, together with the assessment of the role of patients and providers characteristics on survival outcome.
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11/2012 - 02/10/2012
Bonnemain, J.; Faggiano, E.; Quarteroni A.; Deparis S.
A Patient-Specific Framework for the Analysis of the Haemodynamics in Patients with Ventricular Assist Device | Abstract | | Nowadays ventricular assist devices play an important role in the treatment of terminal heart failure. While the devices themselves have been widely studied there are no studies of patient-specific numerical simulation in this context. This could be explained by the fact that the presence of the device induces metallic artifacts and noise in the acquired images so that conventional segmentation techniques fail. The aim of our work is to propose a robust framework for the segmentation of medical images of poor quality, the generation of high quality meshes and for the patient-specific analysis of the collected data via fluid-structure interaction (FSI) numerical simulations. First images are processed using histogram adjustment, histogram equalization, and gradient anisotropic diffusion filter. The watershed algorithm is then applied and the result is refined by the use of morphological operators. Then our framework allows the generation of two conforming meshes, one for the arterial lumen and the other for the arterial wall, ready for FSI simulations.
We also describe the numerical model and methods used to perform FSI simulations. Final results performed on two patients demonstrate the ability of our methods: the whole strategy results suitable, robust, and accurate for patient-specific data. |
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