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 1268 products
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06/2022 - 02/02/2022
Pozzi, G.; Grammatica, B.; Chaabane, L.; Catucci, M.; Mondino, A.; Zunino, P.; Ciarletta, P.
T cell therapy against cancer: a predictive diffuse-interface mathematical model informed by pre-clinical studies | Abstract | | T cell therapy has become a new therapeutic opportunity against solid cancers. Predicting T cell behaviour and efficacy would help therapy optimization and clinical implementation. In this work, we model responsiveness of mouse prostate adenocarcinoma to T cell-based therapies. The mathematical model is based on a Cahn-Hilliard diffuse interface description of the tumour, coupled with Keller-Segel type equations describing immune components dynamics. The model is fed by pre-clinical magnetic resonance imaging data describing anatomical features of prostate adenocarcinoma developed in the context of the Transgenic Adenocarcinoma of the Mouse Prostate model. We perform computational simulations based on the finite element method to describe tumor growth dynamics in relation to local T cells concentrations. We report that when we include in the model the possibility to activate tumor-associated vessels and by that increase the number of T cells within the tumor mass, the model predicts higher therapeutic effects (tumor regression) shortly after therapy administration. The simulated results are found in agreement with reported experimental data. Thus, this diffuse-interface mathematical model well predicts T cell behavior in vivo and represents a proof-of-concept for the role such predictive strategies may play in optimization of immunotherapy against cancer. |
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05/2022 - 01/14/2022
Aspri, A; Beretta, E.; Cavaterra, C.; Rocca, E.; Verani, M.
Identification of cavities and inclusions in linear elasticity with a phase-field approach | Abstract | | In this paper we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For this goal, we consider a constrained minimization problem involving a boundary quadratic misfit functional with a regularization term that penalizes the perimeter of the cavity or inclusion to be identified.
Then using a phase field approach we derive a robust algorithm for the reconstruction of elastic inclusions and of cavities modelled as inclusions with a very small elasticity tensor. |
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04/2022 - 01/11/2022
Africa, P.C.; Piersanti, R.; Fedele, M.; Dede', L.; Quarteroni, A.
lifex - heart module: a high-performance simulator for the cardiac function | Abstract | | Modeling the whole cardiac function involves several complex multi-
physics and multi-scale phenomena that are highly computationally
demanding, which makes calling for simpler yet accurate, high-performance computational tools still a paramount challenge to be addressed. Despite all the efforts made by several research groups worldwide, no software has progressed as a standard reference tool for whole-heart fully-coupled cardiac simulations in the scientific community yet.
In this work we present the first publicly released package of the
heart module of lifex, a high-performance solver for multi-physics
and multi-scale problems, aimed at cardiac applications.
The goal of lifex is twofold. On the one side, it aims at making
in silico experiments easily reproducible and accessible to the wider
public, targeting also users with a background in medicine or bioengineering, thanks to an extensive documentation and user guide.
On the other hand, being conceived as an academic research library,
lifex can be exploited by scientific computing experts to explore new
modeling and numerical methodologies within a robust development
framework.
lifex has been developed with a modular structure and will be
released bundled in different modules/packages. This initial release
includes a generator for myocardial fibers based on Laplace-Dirichlet-
Rule-Based-Methods (LDRBMs). This report comes with an extensive technical and mathematical documentation to welcome new users to
the core structure of a prototypical lifex application and to provide
them with a possible approach to include the generated cardiac fibers
into more sophisticated computational pipelines. |
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03/2022 - 01/09/2022
Giacomini, M.; Perotto, S.
Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information | Abstract | | A finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a region-based energy functional and on an anisotropic recovery-based error estimate to drive mesh adaptation. More precisely, a Bayesian energy functional is considered to account for image spatial information, ensuring that the methodology is able to identify inhomogeneous spatial patterns in complex images.
In addition, the anisotropic mesh adaptation guarantees a sharp detection of the interface between background and foreground of the image, with a reduced number of degrees of freedom.
The resulting split-adapt Bregman algorithm is tested on a set of real images showing the accuracy and robustness of the method, even in the presence of Gaussian, salt and pepper and speckle noise. |
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02/2022 - 01/09/2022
Antonietti, P.F.; Scacchi, S.; Vacca, G.; Verani, M.
$C^1$-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration | Abstract | | We consider the $C^1$-Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard problem and the Cahn-Hilliard inpainting problem. We present the numerical approximation and several numerical results to assess the efficacy of the proposed methodology.
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01/2022 - 01/09/2022
Gavazzoni, M.; Ferro, N.; Perotto, S.; Foletti, S.
Multi-physics inverse homogenization for the design of innovative cellular materials: application to thermo-mechanical problems | Abstract | | We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-mechanical setting, by promoting the design of unit cells characterized both by an isotropic and an anisotropic behaviour with respect to mechanical and thermal requirements. The proposed procedure generalizes microSIMPATY algorithm to a multi-physics framework, by preserving all the good properties of the reference design methodology. The resulting layouts exhibit non-standard topologies and are characterized by very sharp contours, thus limiting the post-processing before manufacturing. The new cellular materials are compared with the state-of-art in engineering practice in terms of thermo-mechanical properties, thus highlighting the good performance of the new layouts which, in some cases, outperform the consolidated choices. |
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95/2021 - 12/28/2021
Di Gregorio, S.; Vergara, C.; Montino Pelagi, G.; Baggiano, A.; Zunino, P.; Guglielmo, M.; Fusini, L.; Muscogiuri, G.; Rossi, A.; Rabbat, M.G.; Quarteroni, A.; Pontone, G.
Prediction of myocardial blood flow under stress conditions by means of a computational model | Abstract | | Purpose. Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This complex protocol has limited reproducibility and non-negligible side effects for the patient. We aim to mitigate these drawbacks by proposing a computational model able to reproduce MBF maps.
Methods. A computational perfusion model was used to reproduce MBF maps. The model parameters were estimated by using information from cCTA and MBF measured from stress-CTP (MBFCTP) maps. The relative error between the computational MBF under stress conditions (MBFCOMP) and MBFCTP was evaluated to assess the accuracy of the proposed computational model.
Results. Applying our method to 9 patients (4 control subjects without ischemica vs 5 patients with myocardial ischemia), we found an excellent agreement between the values of MBFCOMP and MBFCTP. In all patients, the relative error was below 8% over all the myocardium, with an average-in-space value below 4%.
Conclusion. The results of this pilot work demonstrate the accuracy and reliability of the proposed computational model in reproducing MBF under stress conditions. This consistency test is a preliminary step in the framework of a more ambitious project which is currently under investigation, i.e. the construction of a computational tool able to predict MBF avoiding the stress protocol and potential side effects while reducing radiation exposure.
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94/2021 - 12/27/2021
Antonietti, P.F.; Berrone, S.; Busetto, M.; Verani, M.
Agglomeration-based geometric multigrid schemes for the Virtual Element Method | Abstract | | In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order C0-conforming Virtual Element discretization of two-dimensional second-order elliptic partial differential equations. The sequence of agglomerated tessellations are nested, but the corresponding multilevel virtual discrete spaces are generally non-nested thus resulting into non-nested multigrid algorithms. We prove the uniform convergence of the two-level method with respect to the mesh size and the uniform convergence of the W-cycle and the V-cycle multigrid algorithms with respect to the mesh size and the number of levels. Numerical experiments confirm the theoretical findings. |
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