1,721,314 research outputs found
An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics
Full text linkIn this paper we address an unresolved problem in the numerical modeling of cardiac electromechanics, that is the onset of numerical oscillations due to the dependence of force generation models on the fibers shortening velocity. A way to avoid numerical oscillations is to use monolithic schemes for the solution of the coupled problem of active-passive mechanics. However, staggered strategies, which foresee the sequential solution of the models of force generation and of tissue mechanics, are preferable, due to their reduced computational cost and low implementation effort. In this paper we propose a cure for this issue, by introducing, with respect to the standard staggered scheme, a numerically consistent stabilization term. This term is derived in virtue of the identification of the cause of instability in the mismatch between macroscopic and microscopic strains, inconsistently expressed in Lagrangian and Eulerian coordinates, respectively. By considering a model problem of active mechanics we prove that the proposed scheme is unconditionally absolutely stable (i.e. it is stable for any time step size), yet within a fully staggered framework. As such, the new scheme removes the non-physical oscillations, as we prove by applying it to three force generation models, namely the Niederer-Hunter-Smith model, the model by Land and coworkers, and the mean-field force generation model that we have recently proposed. (C) 2020 The Author(s). Published by Elsevier B.V.CMC
The role of statistics in the era of big data: A computational scientist' perspective
No full textCMC
Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator
Full text linkThe results of numerical simulations of cardiac electromechanics are typically characterized by a long transient before reaching a periodic solution known as limit cycle. This yields a serious computational overhead, as the only clinically relevant output is associated with such limit cycle. 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, built through an automated data-driven algorithm on the basis of pressurevolume transients of as few as three heartbeats simulated with the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, can provide the 3D model with an initial guess, such that in just two heartbeats a solution is reached that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the 3D model. 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. Indeed, the construction of the emulator does not have to be repeated when the parameters of the circulation model it is coupled with 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. This paper is accompanied by a Python library implementing the proposed algorithm, open to integration with existing cardiac solvers.CMC
Taking Mathematics to Heart
No full textOneday, a virtual version of your own heart may helpdoctors diagnose heart disease and determine the besttreatment for you, without the need for unnecessary inva-sive clinical practices. The five-year ERC Advanced GrantiHEART (an integrated heart model for the simulation ofthe cardiac function) of the European Research Council has precisely the ambition to make a significant stepforward in the direction of constructing a mathematicalvirtual heart. Its ultimate goal is to simulate heart functionwith increasing accuracy and to be personalized to yourheart based on medical imaging (CT scans, MRI, etc.). Thiswould hopefully help to prevent or treat cardiovasculardisease by providing a personalized virtual heart to pa-tients, essentially a detailed mathematical description ofa patient’s heart and how it functions—or malfunctions.has precisely the ambition to make a significant stepforward in the direction of constructing a mathematicalvirtual heart. Its ultimate goal is to simulate heart functionwith increasing accuracy and to be personalized to yourheart based on medical imaging (CT scans, MRI, etc.). Thiswould hopefully help to prevent or treat cardiovasculardisease by providing a personalized virtual heart to pa-tients, essentially a detailed mathematical description ofa patient’s heart and how it functions—or malfunctions
A Primer on Mathematical Modelling
No full textIn this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers.
A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites.
This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio
This book is addressed to any student interested in learning how to construct and apply mathematical models
I delfini delle Eolie, i battiti del cuore, i motori di ricerca
No full textChe cos'hanno in comune la dinamica tra prede e predatori, la circolazione del sangue e l'ordinamento delle pagine web svolto da un motore di ricerca? La risposta è la matematica, o meglio, i modelli matematici, che consentono di descrivere i fenomeni della realtà.
Con questo volume per le scuole superiori (corredato da una piattaforma online) viene presentata la matematica che sta sotto la realtà. I modelli matematici sono infatti come scatole magiche: partendo dal mondo reale si formulano equazioni e si calcolano soluzioni al computer.
Se i congegni dentro la scatola sono ben costruiti, si può prevedere come cambia il numero dei delfini delle Eolie al variare della disponibilità di cibo e dell'attività umana, si può descrivere il flusso del sangue in una rete di capillari o calcolare il PageRank delle pagine del web
Free Form Deformation Techniques Applied to 3D Shape Optimization Problems
Full text linkThe purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation
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