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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61/2022 - 09/05/2022
Gregorio, C.; Cappelletto, C.; Romani, S.; Stolfo, D.; Merlo, M.; Barbati, G.
Using marginal structural joint models to estimate the effect of a time-varying treatment on recurrent events and survival: An application on arrhythmogenic cardiomyopathy | Abstract | | In many clinical applications to evaluate the effect of a treatment, randomized control trials are difficult to carry out. On the other hand, clinical observational registries are often available and they contain longitudinal data regarding clinical parameters, drug therapies, and outcomes. In the past, much research has addressed causal methods to estimate treatment effects from observational studies. In the context of time-varying treatments, marginal structural models are often used. However, most analyses have focused on binary outcomes or time-to-the-first event analyses. The novelty of our approach is to combine the marginal structural methodology with the case where correlated recurrent events and survival are the outcomes of interest. Our work focuses on solving the nontrivial problem of defining the measures of effect, specifying the model for the time-dependent weights and the model to estimate the outcome, implementing them, and finally estimating the final treatment effects in this life-history setting. Our approach provides a strategy that allows obtaining treatment effect estimates both on the recurrent events and the survival with a clear causal and clinical interpretation. At the same time, the strategy we propose is based on flexible modeling choices such as the use of joint models to capture the correlation within events from the same subject and the specification of time-dependent treatment effects. The clinical problem which motivated our work is the evaluation of the treatment effect of beta-blockers in arrhythmogenic right ventricular cardiomyopathy (ARVC/D), and the dataset comes from the Trieste Heart Muscle Disease Registry. |
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60/2022 - 08/29/2022
Cortellessa, D.; Ferro, N.; Perotto, S.; Micheletti, S.
Enhancing level set-based topology optimization with anisotropic graded meshes | Abstract | | We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to the employment of a strategic computational mesh. We pursue a twofold goal, i.e., to deliver a final layout characterized by a smooth contour and reliable mechanical properties.
The smoothness of the optimized structure is ensured by the employment of an anisotropic adapted mesh, which sharply captures the material/void interface. A robust mechanical performance is guaranteed by a uniform tessellation of the internal part of the optimized configuration. A thorough numerical investigation corroborates the effectiveness of the proposed algorithm as a reliable and computationally affordable design tool, both in two- and three-dimensional contexts. |
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59/2022 - 08/29/2022
Boon, W. M.; Fumagalli, A.
A multipoint vorticity mixed finite element method for incompressible Stokes flow | Abstract | | We propose a mixed finite element method for Stokes flow with one degree of freedom per element and facet of simplicial grids. The method is derived by considering the vorticity-velocity-pressure formulation and eliminating the vorticity locally through the use of a quadrature rule. The discrete solution is pointwise divergence-free and the method is pressure robust. The theoretically derived convergence rates are confirmed by numerical experiments. |
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58/2022 - 08/20/2022
Zingaro, A.; Bucelli, M.; Fumagalli, I.; Dede', L; Quarteroni, A.
Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface Method | Abstract | | A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement.
During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations.}
In this paper, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., 2017) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., 2020) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. |
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57/2022 - 08/15/2022
Ruffino, L.; Santoro, A.; Sparvieri, S.; Regazzoni, F.; Adebo, D.A.; Quarteroni, A.; Vergara, C.; Corno, A.F.
Computational analysis of cardiovascular effects of COVID- 19 infection in children | Abstract | | BACKGROUND. The COVID-19 disease can involve any body part; nevertheless, the most serious consequences affect respiratory and cardiocirculatory systems with variable symptoms. Although the effects of COVID-19 are not fully understood yet, clinical evidence has shown that the virus may cause acute myocardial injury and chronic damages to heart and
blood vessels. There is no or limited experience on pathophysiological effects of COVID-19 infection in children’s cardiovascular system.
OBJECTIVES. The aim of this work is to assess the effects of COVID-19 on the cardiovascular system in children, in terms, e.g., of increased pulmonary resistances, reduced cardiac contraction capacity.
METHODS. We used a computational model based on lumped parameters to describe the whole blood circulation. The model was calibrated to account for data coming from 5 child patients.
RESULTS. Our results highlighted that the effect of COVID-19 on the cardiovascular system in children was characterized by the reduction in cardiac blood pressure and volumes. In particular, we analyzed in detail two patients showing a correlation between myocardial compromise and severity of the infection.
CONCLUSIONS. This study demonstrates that COVID-19 infection causes a complex pathophysiological state to the cardiovascular system, both in asymptomatic and symptomatic pediatric patients. This information is very helpful to prevent long term cardiovascular complications of COVID-19 infection in children. A prospective study with regular cardiology follow-up is recommended. |
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56/2022 - 08/11/2022
Africa, P.C.
lifex: a flexible, high performance library for the numerical solution of complex finite element problems | Abstract | | Numerical simulations are ubiquitous in mathematical and computational modeling, where many industrial and clinical applications are required to deal with multiphysics problems and with complex systems characterized by multiple spatial and temporal scales.
This document introduces the design and the capabilities of lifex, an open source C++ library for high performance finite element simulations of multiphysics, multiscale and multidomain problems. lifex offers a versatile solution to answer the emerging need for efficient computational tools that are also easily approachable by a wide community of users and developers. We showcase illustrative examples of use, benchmarks, advanced application scenarios and demonstrate its parallel performance up to thousands of cores. |
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55/2022 - 08/11/2022
Cavinato, L.; Pegoraro, M.; Ragni, A.; Ieva, F.
Imaging-based representation and stratification of intra-tumor Heterogeneity via tree-edit distance | Abstract | | Personalized medicine is the future of medical practice. In oncology, tumor heterogeneity assessment represents a pivotal step for effective treatment planning and prognosis prediction. Despite new procedures for DNA sequencing and analysis, non-invasive methods for tumor characterization are needed to impact on daily routine. On purpose, imaging texture analysis is rapidly scaling, holding the promise to surrogate histopathological assessment of tumor lesions. In this work, we propose a tree-based representation strategy for describing intra-tumor heterogeneity of patients affected by metastatic cancer. We leverage radiomics information extracted from PET/CT imaging and we provide an exhaustive and easily readable summary of the disease spreading. We exploit this novel patient representation to perform cancer subtyping according to hierarchical clustering technique. To this purpose, a new heterogeneity-based distance between trees is defined and applied to a case study of Prostate Cancer (PCa). Clusters interpretation is explored in terms of concordance with severity status, tumor burden and biological characteristics. Results are promising, as the proposed method outperforms current literature approaches. Ultimately, the pro- posed methods draws a general analysis framework that would allow to extract knowledge from daily acquired imaging data of patients and provide insights for effective treatment planning. |
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54/2022 - 08/11/2022
Bucelli, M.; Zingaro, A.; Africa, P. C.; Fumagalli, I.; Dede', L.; Quarteroni, A.
A mathematical model that integrates cardiac electrophysiology, mechanics and fluid dynamics: application to the human left heart | Abstract | | We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of those partial differential equations that contribute to the model. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images. |
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