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 1148 products
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02/2024 - 01/13/2024
Parolini, N.; Poiatti, A.; Vene', J.; Verani, M.
Structure-preserving neural networks in data-driven rheological models | Abstract | | In this paper we address the importance and the impact of employing structure preserving neural networks as surrogate of the analytical physics-based models typically employed to describe the rheology of non-Newtonian fluids in Stokes flows. In particular, we propose and test on real-world scenarios a novel strategy to build data-driven rheological models based on the use of Input-Output Convex Neural Networks (ICNNs), a special class of feedforward neural network scalar valued functions that are convex with respect to their inputs. Moreover, we show, through a detailed campaign of numerical experiments, that the use of ICNNs is of paramount importance to guarantee the well-posedness of the associated non-Newtonian Stokes differential problem. Finally, building upon a novel perturbation result for non-Newtonian Stokes problems, we study the impact of our data-driven ICNN based rheological model on the accuracy of the finite element approximation. |
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01/2024 - 01/10/2024
Criseo, M.; Fumagalli, I.; Quarteroni, A.; Marianeschi, S. M.; Vergara, C.
Computational haemodynamics for pulmonary valve replacement by means of a reduced Fluid-Structure Interaction model | Abstract | | Pulmonary Valve Replacement (PVR) consists of substituting a patient’s original valve with a prosthetic one, primarily addressing pulmonary valve insufficiency, which is crucially relevant in Tetralogy of Fallot repairment. While extensive clinical and computational literature on aortic and mitral valve replacements is available, PVR's post-procedural haemodynamics in the pulmonary artery and the impact of prosthetic valve dynamics remain significantly understudied. Addressing this gap, we introduce a reduced Fluid-Structure Interaction (rFSI) model, applied for the first time to the pulmonary valve. This model couples a three-dimensional computational representation of pulmonary artery haemodynamics with a one-degree-of-freedom model to account for valve structural mechanics. Through this approach, we analyse patient-specific haemodynamics pre and post PVR. Patient-specific geometries, reconstructed from CT scans, are virtually equipped with a template valve geometry. Boundary conditions for the model are established using a lumped-parameter model, fine-tuned based on clinical patient data. Our model accurately reproduces patient-specific haemodynamic changes across different scenarios: pre-PVR, six months post-PVR, and a follow up condition after a decade. It effectively demonstrates the impact of valve implantation on sustaining the diastolic pressure gradient across the valve. Preliminary outcomes indicate the reliability of our valve model concerning the robustness of its application across various patients, despite being calibrated initially with data from a single patient. This promising approach provides insights into post-PVR haemodynamics and prosthetic valve effects, shedding light on potential implications for patient-specific outcomes. |
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106/2023 - 12/22/2023
Fontana, N.; Savaré, L.; Ieva, F.
Integrating state-sequence analysis to uncover dynamic drug-utilization patterns to profile heart failure patients | Abstract | | Globally, the incidence of heart failure is increasing, and its principal treatment involves drug therapy. However, widespread non-adherence to therapies is prevalent among heart failure patients and often results in worsening health conditions and an increase in hospital admissions. This study aims to develop an innovative approach, the State-Sequence analysis, to profile heart failure patients based on different drug-utilization patterns. These patterns aim to capture both the multidimensional and dynamic effects of therapies. Subsequently, the study explores how combining clustering algorithms with this technique influences overall patient survival. Findings highlight the importance of continued drug therapy after the first hospitalization in improving heart failure prognosis, irrespective of its severity. The proposed approach can assist healthcare specialists in evaluating the pathways provided to patients, allowing for a change in analysis from a transversal and syntactical approach to a holistic one that leverages statistical tools that are slightly more complex than traditional methods. Moreover, because of the many options available for defining states, temporal granularity, and spacing metrics, SSA is a flexible method applicable to various epidemiological scenarios. |
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109/2023 - 12/22/2023
Clementi, L.; Arnone, E.; Santambrogio, M.D.; Franceschetti, S.; Panzica, F.; Sangalli, L.M.
Anatomically compliant modes of variations: new tools for brain connectivity | Abstract | | Anatomical complexity and data dimensionality present major issues when analysing brain connectivity data. The functional and anatomical aspects of the connections taking place in the brain are in fact equally relevant and strongly intertwined. However, due to theoretical challenges and computational issues, their relationship is often overlooked in neuroscience and clinical research. In this work, we propose to tackle this problem through Smooth Functional Principal Component Analysis, which enables to perform dimensional reduction and exploration of the variability in functional connectivity maps, complying with the formidably complicated anatomy of the grey matter volume. In particular, we analyse a population that includes controls and subjects affected by schizophrenia, starting from fMRI data acquired at rest and during a task-switching paradigm. For both sessions, we first identify the common modes of variation in the entire population. We hence explore whether the subjects’ expressions along these common modes of variation differ between controls and pathological
subjects. In each session, we find principal components that are significantly differently expressed in the healthy vs pathological subjects (with p-values < 0.001), highlighting clearly interpretable differences in the connectivity in the two subpopulations. For instance, the second and third principal components for the rest session capture the imbalance between the Default Mode and Executive Networks characterizing schizophrenia patients. |
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108/2023 - 12/22/2023
Arnone, E.; Negri, L.; Panzica, F.; Sangalli, L.M.
Analyzing data in complicated 3D domains: smoothing, semiparametric regression and functional principal component analysis | Abstract | | In this work we introduce a family of methods for the analysis of data observed at locations scattered in three-dimensional (3D) domains, with possibly complicated shapes. The proposed family of methods includes smoothing, regression and functional principal component analysis for functional signals defined over (possibly non-convex) 3D domains, appropriately complying with the non-trivial shape of the domain. This constitutes an important advance with respect to the literature, since the available methods to analyse data observed in 3D domains rely on Euclidean distances, that are inappropriate when the shape of the domain influences the phenomenon under study. The common building block of the proposed methods is a nonparametric regression model with differential regularization. We derive the asymptotic properties of the methods and show, through simulation studies, that they are superior to the available alternatives for the analysis of data in 3D domains, even when considering domains with simple shapes. We finally illustrate an application to a neurosciences study, with neuroimaging signals from functional magnetic resonance imaging, measuring neural activity in the grey matter, a non-convex volume with a highly complicated structure. |
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105/2023 - 12/16/2023
Cicci, L.; Fresca, S.; Guo, M.; Manzoni, A.; Zunino, P.
Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression | Abstract | | Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of the need to query expensive numerical solvers repeatedly. Projection-based reduced order models (ROMs), such as the Galerkin-reduced basis (RB) method, have been extensively developed in the last decades to overcome the computational complexity of high fidelity full order models (FOMs), providing remarkable speed-ups when addressing UQ tasks related with parameterized differential problems. Nonetheless, constructing a projection-based ROM that can be efficiently queried usually requires extensive modifications to the original code, a task which is non-trivial for nonlinear problems, or even not possible at all when proprietary software is used. Non-intrusive ROMs – which rely on the FOM as a black box – have been recently developed to overcome this issue. In this work, we consider ROMs exploiting proper orthogonal decomposition to construct a reduced basis from a set of FOM snapshots, and Gaussian process regression (GPR) to approximate the RB projection coefficients. Two different approaches, namely a global GPR and a tensor-decomposition-based GPR, are explored on a set of 3D time-dependent solid mechanics examples. Finally, the non-intrusive ROM is exploited to perform global sensitivity analysis (relying on both screening and variance-based methods) and parameter estimation (through Markov chain Monte Carlo methods), showing remarkable computational speed-ups and very good accuracy compared to high-fidelity FOMs. |
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101/2023 - 12/15/2023
Formaggia, L.; Zunino, P.
Hybrid dimensional models for blood flow and mass transport | Abstract | | Mathematical models accounting of several space scales have proved to be very effective tools in the description and simulation of the cardiovascular system. In this chapter, we review the family of models that are based on partial differential equations defined on domains with hybrid dimension. Referring to the vascular applications, the most prominent example consists of coupling three-dimensional (3D) with one-dimensional (1D) mathematical models for blood flow and mass transport. On the basis of their coupling conditions these models can be subdivided into two main categories: the ones based on sequential coupling and those arising from the embedded coupling. We organize this work in two main sections, reflecting this subdivision. |
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104/2023 - 12/15/2023
Possenti, L.; Gallo, A.; Vitullo, P.; Cicchetti, A.; Rancati, T.; Costantino, M.L.; Zunino, P.
A computational model of the tumor microenvironment applied to fractionated radiotherapy | Abstract | | Radiotherapy consists in delivering a precise radiation dose to a specific tumor target in order to eradicate tumor cells and to achieve local tumor control. The definition of the most suitable radiotherapy treatment schedule is not trivial due to the large tumor heterogeneity reported in clinical practice. The ultimate goal is to prescribe a specific treatment pattern for each patient, considering all the different radiobiological properties of the tumor / normal tissues to achieve the best final result possible. The model presented in this work goes in this direction, analyzing oxygen dependency and the role of the vascular network in the tumor microenvironment, since the efficacy of radiation therapy also depends on local oxygen availability. The main purpose of this work is to develop a mathematical model that describes the interaction between microvascular oxygen transfer and the efficacy of fractionated radiotherapy. |
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