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 1249 products
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42/2021 - 06/23/2021
Calissano, A.; Fontana, M.; Zeni, G.; Vantini, S.
Conformal Prediction Sets for Populations of Graphs | Abstract | | In the latest years, scholars started focusing on how to develop statistical tool for the analysis of population of complex data, such as sets of labelled or unlabelled graphs graphs. The present works adds to this literature by focusing on a strangely overlooked area, namely the formulation of prediction sets.
By exploiting cutting edge techniques in the realm of machine learning, we propose a forecasting method for populations of both labelled and unlabelled graphs based on Conformal Prediction, able to identify prediction regions. Our method is model-free, achieves finite-sample validity, is computationally efficient and it identifies interpretable prediction sets, in the shape of a parallelotope. To explore the features of this novel forecasting technique, a simulation study and and a real-world example are presented. |
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41/2021 - 06/21/2021
Costa, G., Cavinato, L., Maschi, C., Fiz, F., Sollini, M., Politi, L. S., Chiti, A., Balzarini, L., Aghemo, A., di Tommaso, L., Ieva, F., Torzilli, G., Viganò, L.
Virtual Biopsy for Diagnosis of Chemotherapy-Associated Liver Injuries and Steatohepatitis: A Combined Radiomic and Clinical Model in Patients with Colorectal Liver Metastases | Abstract | | Non-invasive diagnosis of chemotherapy-associated liver injuries (CALI) is still an unmet need. The present study aims to elucidate the contribution of radiomics to the diagnosis of sinusoidal dilatation (SinDil), nodular regenerative hyperplasia (NRH), and non-alcoholic steatohepatitis (NASH). Patients undergoing hepatectomy for colorectal metastases after chemotherapy (January 2018-February 2020) were retrospectively analyzed. Radiomic features were extracted from a standardized volume of non-tumoral liver parenchyma outlined in the portal phase of preoper- ative post-chemotherapy computed tomography. Seventy-eight patients were analyzed: 25 had grade 2–3 SinDil, 27 NRH, and 14 NASH. Three radiomic fingerprints independently predicted SinDil: GLRLM_f3 (OR = 12.25), NGLDM_f1 (OR = 7.77), and GLZLM_f2 (OR = 0.53). Combining clinical, laboratory, and radiomic data, the predictive model had accuracy = 82%, sensitivity = 64%, and specificity = 91% (AUC = 0.87 vs. AUC = 0.77 of the model without radiomics). Three radiomic parameters predicted NRH: conventional_HUQ2 (OR = 0.76), GLZLM_f2 (OR = 0.05), and GLZLM_f3 (OR = 7.97). The combined clinical/laboratory/radiomic model had accuracy = 85%, sensitivity = 81%, and specificity = 86% (AUC = 0.91 vs. AUC = 0.85 without radiomics). NASH was predicted by conventional_HUQ2 (OR = 0.79) with accuracy = 91%, sensitivity = 86%, and specificity = 92% (AUC = 0.93 vs. AUC = 0.83 without radiomics). In the validation set, accuracy was 72%, 71%, and 91% for SinDil, NRH, and NASH. Radiomic analysis of liver parenchyma may provide a signature that, in combination with clinical and laboratory data, improves the diagnosis of CALI. |
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39/2021 - 06/15/2021
Barnafi, N.; Di Gregorio, S.; Dede', L.; Zunino, P.; Vergara, C.; Quarteroni, A.
A multiscale poromechanics model integratingmyocardial perfusion and systemic circulation | Abstract | | The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multi-compartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential.
To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with pre-computed cardiac displacements, obtained form other models or medical imaging data.
We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon,
which is particularly challenging to capture as it arises from the interaction of several parts of the model. |
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40/2021 - 06/15/2021
Martinolli, M.; Cornat, F.; Vergara, C.
Computational Fluid-Structure Interaction Study of a new Wave Membrane Blood Pump | Abstract | | Purpose: Wave Membrane Blood Pumps (WMBP) are novel pump designs in which blood is propelled by means of wave propagation by an undulating membrane. In this paper, we computationally studied the performance of a new WMBP design (J-shaped) for different working conditions, in view of potential applications in human patients.
Methods: Fluid-Structure Interaction (FSI) simulations were conducted in 3D pump geometries and numerically discretized by means of the Extended Finite Element Method (XFEM). A contact model was introduced to capture membrane-wall collisions in the pump head. Mean flow rate and membrane envelope were determined to evaluate hydraulic performance. A preliminary hemocompatibility analysis was performed via calculation of fluid shear stress.
Results: Numerical results, validated against in-vitro experimental data, showed that the hydraulic output increases when either the frequency or the amplitude of membrane oscillations were higher, with limited increase in the fluid stresses, suggesting good hemocompatility properties.
Also, we showed better performance in terms of hydraulic power with respect to a previous design of the pump. We finally studied an operating point which achieves physiologic flow rate target at diastolic head pressure of $80$ mmHg.
Conclusions: A new design of WMBP was computationally studied.
The proposed FSI model with contact was employed to predict the new pump hydraulic performance and it could help to properly select an operating point for the upcoming first-in-human trials. |
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37/2021 - 06/11/2021
Dassi, F.; Fumagalli, A.; Mazzieri, I.; Scotti, A.; Vacca, G.
A Virtual Element Method for the wave equation on curved edges in two dimensions | Abstract | | In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as well as internal interfaces corresponding to the change of some mechanical parameters. As opposite to the classic and isoparametric Finite Element approaches, where the geometry of the domain is approximated respectively by piecewise straight lines and by higher order polynomial maps, in the proposed method the geometry is exactly represented, thus ensuring a highly accurate numerical solution. Indeed, if in the former approach the geometrical error might deteriorate the quality of the numerical solution, in the latter approach the curved interfaces/boundaries are approximated exactly guaranteeing the expected order of convergence for the numerical scheme. Theoretical results and numerical findings confirm the validity of the proposed approach. |
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36/2021 - 06/11/2021
Parolini, N.; Dede', L; Antonietti, P. F.; Ardenghi, G.; Manzoni, A.; Miglio, E.; Pugliese, A.; Verani, M.; Quarteroni, A.
SUIHTER: A new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy | Abstract | | The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated infected (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of reproducing the past history of the epidemic in Italy, surfaced in late February and still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are daily made available from the Italian Civil Protection. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak emerged in Fall 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at national level. |
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38/2021 - 06/11/2021
Giusteri, G. G.; Miglio, E.; Parolini, N.; Penati, M.; Zambetti, R.
Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands | Abstract | | We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables and elements of the special Euclidean algebra. This perspective emerges naturally from the evolution equations for strands, that are one-dimensional submanifolds, of the special Euclidean group. The discretization of the corresponding equations for the three-dimensional motion of a Cosserat rod is performed, in space, by using a staggered grid. The time evolution is then approximated with a semi-implicit method. Within this approach we can easily include dissipative effects due to both the action of external forces and the presence of internal mechanical dissipation. The comparison with results obtained with different schemes shows the effectiveness of the proposed method, which is able to provide very good predictions of nonlinear dynamical effects and shows competitive computation times also as an energy-minimizing method to treat static problems. |
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35/2021 - 06/04/2021
Regazzoni, F.; Quarteroni, A.
Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator | Abstract | | The results of numerical simulations of 3D cardiac electromechanical models are typically characterized by a long transient before reaching a periodic solution known as limit cycle. Since the only clinically relevant output is the one associated with such limit cycle, a long transient translates into a serious computational overhead. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator. This emulator is built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated through the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, allows to accurately detect the location of the limit cycle in less than one minute on a standard laptop. Then, using as an initial guess for the 3D model the solution obtained with its 0D surrogate, it is possible to reach in just two heartbeats a solution that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the full-order 3D model. In this manner, the proposed approach achieves an overall speedup in the simulation of about an order of magnitude.
In practical applications, an electromechanical model needs to be coupled with a model for the external circulation. The latter is typically represented by either a Windkessel-type preload-afterload model, emulating the boundary conditions, or by a closed-loop model of the entire circulatory network. The closed-loop model provides higher quality results in terms of physiological soundness; however, reaching a limit cycle is more challenging in this setting. It is in this context that our 0D emulator turns out to be particularly effective.
The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. As a matter of fact, the emulator does not depend on the circulation model to which it is coupled, hence its construction does not have to be repeated when the parameters of the circulation model vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. In all these cases, our numerical results show that the emulator is able to provide the 3D model with an initial guess such that, after only two heartbeats, the solution is very close to the limit cycle. This paper is accompanied by a Python library implementing the proposed algorithm, open to the integration with existing cardiac solvers. |
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