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 1249 prodotti
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48/2016 - 23/11/2016
Scardulla, S.; Pasta, S.; D’Acquisto, L.; Sciacca, S.; Agnese, V.; Vergara, C.; Quarteroni, A.; Clemenza, F.; Bellavia, D.; Pilato, M.
Shear Stress Alterations in the Celiac Trunk of Patients with Continuous-Flow Left Ventricular Assist Device by In-Silico and In-Vitro Flow Analysis | Abstract | | Background: The use of left ventricular assist device (LVAD) to treat advanced cardiac heart failure is constantly increasing, although this device leads to high risk for gastrointestinal.
Methods: Using in-silico flow analysis, we quantified hemodynamic alterations due to continuous-flow LVAD (HeartWare Inc, Framingham, MA, USA) in the celiac trunk and major branches of the abdominal aorta and then explored the relationship between wall shear stress (WSS) and celiac trunk orientation. To assess outflow from aortic branch, a 3D printed patient-specific model of the celiac trunk reconstructed from a LVAD-supported patient was used to estimate echocardiographic outflow velocities under continuous-flow conditions and then to calibrate computational simulations. Moreover, flow pattern and resulting WSS were computed on 5 patients with LVAD implantation.
Results: Peak WSSs were estimated on the three branches of celiac trunk and the LVAD cannula. Mean values of WSS demonstrated that the left gastric artery experiences the greatest WSS of 9.08±5.45 Pa with an average flow velocity of 0.57±0.25 m/s when compared to that of other vessel districts. The common hepatic artery had the less critical WSS of 4.58±1.77 Pa. A positive correlation was found between the celiac trunk angulation and the WSS stress just distal the ostium of celiac trunk (R=0.9), and this may increase to vulnerability of this vessel to bleeding.
Conclusions: Although further studies are warranted to confirm these findings in a larger patient cohort, computational flow simulations may enhance the information of clinical image data and may have an application in clinical investigations of hemodynamic changes in LVAD-supported patients. |
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47/2016 - 17/11/2016
Canuto, C.; Nochetto, R. H.; Stevenson R.; Verani, M.
On p-Robust Saturation for hp-AFEM | Abstract | | For the Poisson problem in two dimensions,
we consider the standard adaptive finite element loop solve, estimate, mark, refine, with
estimate being implemented using the $p$-robust equilibrated flux estimator, and, mark being Dorfler marking.
As a refinement strategy we employ $p$-refinement. We investigate the question by which amount the local polynomial degree on any marked patch has to be increase in order to achieve a p-independent error reduction.
The resulting adaptive method can be turned into an instance optimal $hp$-adaptive method by the addition of a coarsening routine. |
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46/2016 - 17/11/2016
Lila, E.; Aston, J.A.D.; Sangalli, L.M.
Smooth Principal Component Analysis over two-dimensional manifolds with an application to Neuroimaging | Abstract | | Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For this purpose a regularization approach is adopted, introducing a smoothing penalty coherent with the geodesic distance over the manifold. The model introduced can be applied to any manifold topology, can naturally handle missing data and functional
samples evaluated in different grids of points. We approach the discretization task by means of finite element analysis and propose an efficient iterative algorithm for its resolution. We compare the performances of the proposed algorithm with other approaches classically adopted in literature. We finally apply the proposed method to resting state functional magnetic resonance imaging data from the Human Connectome
Project, where the method shows substantial differential variations between
brain regions that were not apparent with other approaches. |
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45/2016 - 08/11/2016
Bukac, M.; Yotov, I.; Zunino, P.
DIMENSIONAL MODEL REDUCTION FOR FLOW THROUGH FRACTURES IN POROELASTIC MEDIA | Abstract | | We study the interaction between a poroelastic medium and a fracture filled with fluid. The flow in the fracture is described by the Brinkman equations for an incompressible fluid and the poroelastic medium by the quasi-static Biot model. The two models are fully coupled via the kinematic and dynamic conditions. The Brinkman equations are then averaged over the cross-sections, giving rise to a reduced flow model on the fracture midline. We derive suitable interface and closure conditions between the Biot system and the dimensionally reduced Brinkman model that guarantee solvability of the resulting coupled problem. We design and analyze a numerical discretization scheme based on finite elements in space and the Backward Euler in time, and perform numerical experiments to compare the behavior of the reduced model to the full-dimensional formulation and study the response of the model with respect to its parameters. |
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44/2016 - 08/11/2016
Notaro, D.; Cattaneo, L.; Formaggia, L.; Scotti, A.; Zunino, P.
A Mixed Finite Element Method for Modeling the Fluid Exchange between Microcirculation and Tissue Interstitium | Abstract | | Thanks to dimensional (or topological) model reduction techniques, small inclusions in a three-dimensional (3D) continuum can be described as one-dimensional (1D) concentrated sources, in order to reduce the computational cost of simulations. However, concentrated sources lead to singular solutions that still require compu- tationally expensive graded meshes to guarantee accurate approximation. The main computational barrier consists in the ill-posedness of restriction operators (such as the trace operator) applied on manifolds with co-dimension larger than one. We overcome the computational challenges of approximating PDEs on manifolds with high dimensionality gap by means of nonlocal restriction operators that combine standard traces with mean values of the solution on low dimensional manifolds. This new approach has the fundamental advantage of enabling the approximation of the problem using Galerkin projections on Hilbert spaces, which could not be otherwise applied because of regularity issues. This approach, previously applied to second order PDEs, is extended here to the mixed formulation of flow problems with applications to microcirculation. In this way we calculate, in the bulk and on the 1D manifold simultaneously, the approximation of velocity and pressure fields that guarantees good accuracy with respect to mass conservation. |
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43/2016 - 08/11/2016
Ambrosi, D.; Ciarletta, P.; De Falco, C.; Taffetani, M.; Zunino, P.
A multiscale modeling approach to transport of nano-constructs in biological tissues | Abstract | | Nanomedicine is the emerging medical research branch which employs nanotechnological de- vices to improve clinical diagnosis and to design more effective therapeutic methodologies. In particular, functionalized nanoparticles have proved their clinical usefulness for cancer therapy, either as vectors for targeted drug delivery or for hyperthermia treatment. The effectiveness of such novel therapeutic strategies in nanomedicine exploits the capability of the nanoparticles to penetrate into the living tissue through the vascular network and to reach the targeted site. Accordingly, their success is tightly related to the control of the the multi-physics and multi-scale phenomena governing the diffusion and transport properties of the nanoparticles, together with the geometrical and chemo-mechanical factors regulating the nanoparticles- tissue interactions. Indeed, the therapeutic effectiveness of earlier approaches was hindered by a limited ability in penetrating within the tumor tissue essentially due to microfluidic effects. Mathematical modeling is often employed in nanomedicine to analyze in silico the key biophysical mechanisms acting at different scales of investigations, providing useful guidelines to foresee and possibily optimize novel experimental techniques. Since these phenomena involve different characteristic time- and length-scales, a multi-scale modeling approach is mandatory. In this work we outline how a multi-scale analysis starts at the smallest scale, and its results are injected in large-scale models. At the microscale, the transport of nanoparticles is modeled either by the stochastic Langevin equation or by its continuous limit; in both cases short distance interaction forces between particles are considered, such as Coulomb and van der Waals interactions, and small disturbances of the fluid velocity field induced by the presence of nanoparticles are assumed. At the macroscopic scale, the living tissue is typically modeled as a homogeneous (homogenized) porous material of varying permeability, where the fluid flow is modeled by Darcy’s equation and nanoparticle transport is described by a continuum Diffusion-Reaction-Advection equation. One of the most significant features of the model is the ability to incorporate information on the microvascular network based on physiological data. The exploitation of the large aspect ratio between the diameter of a capillary and the intercapillary distance makes it possible to adopt an advanced computational scheme as the embedded multiscale method: with this approach the capillaries are represented as one-dimensional (1D) channels embedded and exchanging mass in a porous medium. Special mathematical operators are used to model the interaction of capillaries with the surrounding tissue. In this general context, we illustrate a bottom-up approach to study the transport and the diffusion of nanoparticles in living materials. We determine the permeability as well as the lumped parameters appearing in the nanoparticle transport equation at the tissue level by means of simulations at the microscale, while the macroscale tissue deposition rate is derived from the results of microscale simulations by means of a suitable upscaling technique.
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42/2016 - 08/11/2016
Iannetti, L.; D'Urso, G.; Conoscenti, G.; Cutri, E.; Tuan, R.S.; Raimondi, M.T.; Gottardi, R.; Zunino, P.
Distributed and lumped parameter models for the characterization of high throughput bioreactors | Abstract | | Next generation bioreactors are being developed to generate multiple human cell-based tissue analogs within the same fluidic system, to better recapitulate the complexity and interconnection of human physiology (1, 2). The effective development of these devices requires a solid understanding of their interconnected fluidics, to predict the transport of nutrients and waste through the constructs and improve the design accordingly. In this work, we focus on a specific model of bioreactor, with multiple input/outputs, aimed at generating osteochondral constructs, i.e., a biphasic construct in which one side is cartilaginous in nature, while the other is osseous. We next develop a general computational approach to model the microfluidics of a multi-chamber, interconnected system that may be applied to human-on-chip devices. This objective requires overcoming several challenges at the level of computational modeling. The main one consists of addressing the multi-physics nature of the problem that combines free flow in channels with hindered flow in porous media. Fluid dynamics is also coupled with advection-diffusion-reaction equations that model the transport of biomolecules throughout the system and their interaction with living tissues and C constructs. Ultimately, we aim at providing a predictive approach useful for the general organ-on- chip community. To this end, we have developed a lumped parameter approach that allows us to analyze the behavior of multi-unit bioreactor systems with modest computational effort, provided that the behavior of a single unit can be fully characterized. |
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41/2016 - 07/11/2016
Giovanardi, B.; Scotti, A.; Formaggia, L.
A hybrid XFEM - Phase Field (Xfield) method for crack propagation in brittle materials | Abstract | | The present work proposes a novel method for the simulation of crack propagation
in brittle elastic materials that combines two of the most popular approaches
in literature. A large scale displacement solution is obtained with the
well known extended finite elements method (XFEM), while propagation is governed
by the solution of a local phase field problem at the tip scale. The method,
which we will refer to as Xfield, is here introduced and tested in 2D under mixed
modes I and II loads. The main features and the capability of the Xfield to efficiently
simulate crack propagation are shown in some numerical tests. |
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