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 1237 prodotti
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49/2014 - 07/11/2014
Bonomi, D.; Vergara, C.; Faggiano, E.; Stevanella, M.; Conti, C.; Redaelli, A.; Puppini, G.; Faggian, G.; Formaggia, L.; Luciani, G.B.
Influence of the aortic valve leaflets on the fluid-dynamics in aorta in presence of a normally functioning bicuspid valve | Abstract | | In this work we consider the blood fluid-dynamics in the ascending aorta in presence of a normally functioning bicuspid aortic valve (BAV). In particular, we perform a computational study to assess the effect of the inclusion of the leaflets on the fluid-dynamic abnormalities characterizing BAV cases. Indeed, in previous works it has been shown that without leaflets it is possible to recover such abnormalities, in particular the strong systolic jet asymmetry, but it was not clear how the inclusion of the leaflets would have improve the results. To this aim we perform a comparison in two real geometries (a dilated and a non-dilated ones) among three scenarios which are built up for each geometry: BAV without leaflets, BAV with leaflets, and tricuspid case (TAV) with leaflets. Our results show that the inclusion of the leaflets increases the fluid-dynamics abnormalities which are quantified through the introduction of suitable synthetic indices. |
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48/2014 - 27/10/2014
Penta, R; Ambrosi, D; Shipley, R.
Effective governing equations for poroelastic growing media | Abstract | | A new mathematical model is developed for the macroscopic behaviour of a porous, linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the well-separated length scales of the material: the pores are small compared to the macroscale, with a spatially-periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and viceversa). The averaging derives a new poroelastic model, which reduces to the classical result of Burridge and Keller in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils. |
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47/2014 - 26/10/2014
Penta, R; Ambrosi, D; Quarteroni, A.
Multiscale homogenization for fluid and drug transport in vascularized malignant tissues | Abstract | | A system of differential equations for coupled fluid and drug transport in vascularized (malignant) tissues is derived by a multiscale expansion. We start from mass and momentum balance equations, stated in the physical domain, geometrically characterized by the intercapillary distance (the microscale). The Kedem-Katchalsky equations are used to account for blood and drug exchange across the capillary walls. The multiscale technique (homogenization) is used to formulate continuum equations describing the coupling of fluid and drug transport on the tumor length scale (the macroscale), under the assumption of local periodicity; macroscale variations of the microstructure account for spatial heterogeneities of the angiogenic capillary network. A double porous medium model for the uid dynamics in the tumor is obtained, where the drug dynamics is represented by a double advection-diffusion-reaction model. The homogenized equations are straightforward to approximate, as the role of the vascular geometry is recovered at an average level by solving standard cell differential problems. Fluid and drug fluxes now read as effective mass sources in the macroscale model, which upscale the interplay between blood and drug dynamics on the tissue scale. We aim to provide a theoretical setting for a better understanding of the design of effective anti-cancer therapies. |
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46/2014 - 25/10/2014
Penta, R; Ambrosi, D.
The role of the microvascular tortuosity in tumor transport phenomena | Abstract | | The role of the microvascular network geometry on transport phenomena in solid tumors and its interplay with the leakage and pressure drop across the vessels is qualitatively and quantitatively discussed. Our starting point is a multiscale homogenization, suggested by the sharp length scale separation that exists between the characteristic vessels and tumor tissue spatial scales, referred to as the microscale and the macroscale, respectively. The coupling between interstitial and capillary compartment is described by a double Darcy model on the macroscale, whereas the geometric information on the microvascular structure is encoded in the effective hydraulic conductivities, which are numerically computed solving classical differential problems on the microscale representative cell. Then, microscale information is injected into the macroscopic model, which is analytically solved in a prototypical geometry and compared with previous experimentally validated, phenomenological models. In this way, we are able to capture the role of the standard blood flow determinants in the tumor, such as the tumor radius, tissue hydraulic conductivity and vessels permeability, as well as the influence of the vascular tortuosity on fluid convection. The results quantitatively confirm that transport of blood (and, as a consequence, of any advected anti-cancer drug) can be dramatically impaired by increasing the geometrical complexity of the microvasculature. Hence, our quantitative analysis supports the argument that geometric regularization of the capillary network improve blood transport and drug delivery in the tumor mass. |
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45/2014 - 24/10/2014
Pezzuto, S.; Ambrosi,D.; Quarteroni, A.
An orthotropic active-strain model for the myocardium mechanics and its numerical approximation | Abstract | | In the wide literature devoted to the cardiac structural mechanics, the strain energy proposed by Holzapfel and Ogden exhibits a number of interesting features: it has suitable mathematical properties and it is based on few material parameters that can, in principle, be identified by standard laboratory tests. In this work we illustrate the implementation of a numerical solver based on such a model for both the passive and active mechanics of the heart. Moreover we discuss its performance on a few tests that can be regarded as preliminary to the adoption of the Holzapfel-Ogden model for a real cardiac simulation. While the passive behavior of the cardiac muscle is modeled as an orthotropic hyperelastic material, the active contraction is here accounted for a multiplicative decomposition of the deformation gradient, yielding the so-called active strain approach, a formulation that automatically preserves the ellipticity of the stress tensor and introduces just one extra parameter in the model. We adopt the usual volumetric-isochoric decomposition of the stress tensor to obtain a mathematically consistent quasi-incompressible version of the material, then the numerical approximation applies to a classical Hu-Washizu three fields formulation. After introduction of the tangent problem, we select suitable finite element spaces for the representation of the physical fields. Boundary conditions are prescribed by introduction of a Lagrange multiplier. The robustness and performance of the numerical solver are tested versus a novel benchmark test, for which an exact solution is provided. The curvature data obtained from the free contraction of muscular thin films are used to fit the active contraction parameter. |
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44/2014 - 23/10/2014
Pezzuto, S.; Ambrosi,D.
Active contraction of the cardiac ventricle and distortion of the microstructural architecture | Abstract | | The shortening of the myocardial fibers is the microstructural engine that produces the contraction of the cardiac muscle. The complex interplay between fibers shortening and elastic macroscopic strain is functional to the ejection of blood into the pulmonary and arterial networks. Here we address the contraction of the left ventricle in a finite elasticity framework, adopting the “prolate ellipsoid” geometry and the invariants–based strain energy proposed by Holzapfel and Ogden, where the mechanical role of fibers and sheets is accounted for. We show that a microstructurally motivated mathematical model of active strain type reproduces the main indicators of normal cardiac function along the whole PV-loop without introduction of any further ad hoc law. The bare–bones mathematical model depends on one measurable parameter only, i.e. the shortening ratio of the sarcomere units, which we assume to be nearly independent on the prestretch. Strict enforcement of incompressibility and novel treatment of boundary conditions are shown to be crucial to simulate the correct muscle torsion. |
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43/2014 - 22/10/2014
Brugiapaglia, S.; Micheletti, S.; Perotto, S.
Compressed solving: a numerical approximation technique for PDEs based on compressed sensing | Abstract | | We introduce a new numerical method denoted by CORSING (COmpRessed SolvING) to approximate one-dimensional advection-diffusion-reaction problems, motivated by the recent developments in the sparse representation field, and particularly in Compressed Sensing. The object of CORSING is to lighten the computational cost characterizing a Petrov-Galerkin discretization by reducing the dimension of the test space with respect to the trial space. This choice yields an underdetermined linear system which is solved by exploiting optimization procedures, standard in Compressed Sensing, such as the l0- and l1-minimization. A Matlab implementation of the method assesses the robustness and reliability of the proposed strategy, as well as its effectiveness in reducing the computational cost of the corresponding full-sized Petrov- Galerkin problem. Finally, a preliminary extension of CORSING to the two-dimensional setting is checked on the classical Poisson problem. |
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42/2014 - 21/10/2014
Canale, A.; Vantini, S.
Constrained Functional Time Series: an Application to Demand and Supply Curves in the Italian Natural Gas Balancing Platform | Abstract | | In Italy we have assisted to the recent introduction of the natural gas balancing platform, a system in which gas operators virtually sell and buy natural gas in order to balance the common pipelines network. Basically, the operators daily submit demand bids and supply offers which are eventually sorted according to price. Demand and supply curves are hence obtained by cumulating the corresponding quantities. Motivated by market dynamic modeling in the Italian Natural Gas Balancing Platform, we propose a model to analyze time series of bounded and monotonic functions. In detail, we provide the constrained functions with a suitable pre-Hilbert structure and introduce a useful isometric bijective map associating each possible bounded and monotonic function to an unconstrained. We then introduce a functional-to-functional autoregressive model that we use to predict the entire demand/supply function. We estimate the model by minimizing the squared $L^2$ distance between functional data and functional predictions with a penalty term based on the Hilbert-Schmidt squared norm of autoregressive lagged operators. We have proved that the solution always exist, unique and that it is linear on the data with respect to the introduced geometry thus guaranteeing that the plug-in predictions of future entire demand/supply functions satisfy all required constraints. We also provide an explicit expression for estimates and predictions. The approach is of general interest and can be generalized in any situation in which one has to deal with constrained monotonic functions (strictly positive or bounded) which evolve through time (e.g., dose response functions right-censored survival curves or cumulative distribution functions). |
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