5,338 research outputs found
Using parametric model order reduction for inverse analysis of large nonlinear cardiac simulations
Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization. We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting
Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
This work addresses the inverse problem of electrocardiography from a new
perspective, by combining electrical and mechanical measurements. Our strategy
relies on the defini-tion of a model of the electromechanical contraction which
is registered on ECG data but also on measured mechanical displacements of the
heart tissue typically extracted from medical images. In this respect, we
establish in this work the convergence of a sequential estimator which combines
for such coupled problems various state of the art sequential data assimilation
methods in a unified consistent and efficient framework. Indeed we ag-gregate a
Luenberger observer for the mechanical state and a Reduced Order Unscented
Kalman Filter applied on the parameters to be identified and a POD projection
of the electrical state. Then using synthetic data we show the benefits of our
approach for the estimation of the electrical state of the ventricles along the
heart beat compared with more classical strategies which only consider an
electrophysiological model with ECG measurements. Our numerical results
actually show that the mechanical measurements improve the identifiability of
the electrical problem allowing to reconstruct the electrical state of the
coupled system more precisely. Therefore, this work is intended to be a first
proof of concept, with theoretical justifications and numerical investigations,
of the ad-vantage of using available multi-modal observations for the
estimation and identification of an electromechanical model of the heart
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Fast and Reliable Reduced-Order Models for Cardiac Electrophysiology
Mathematical models of the human heart are increasingly playing a vital role
in understanding the working mechanisms of the heart, both under healthy
functioning and during disease. The aim is to aid medical practitioners
diagnose and treat the many ailments affecting the heart. Towards this,
modelling cardiac electrophysiology is crucial as the heart's electrical
activity underlies the contraction mechanism and the resulting pumping action.
The governing equations and the constitutive laws describing the electrical
activity in the heart are coupled, nonlinear, and involve a fast moving wave
front, which is generally solved by the finite element method. The simulation
of this complex system as part of a virtual heart model is challenging due to
the necessity of fine spatial and temporal resolution of the domain. Therefore,
efficient surrogate models are needed to predict the dynamics under varying
parameters and inputs. In this work, we develop an adaptive, projection-based
surrogate model for cardiac electrophysiology. We introduce an a posteriori
error estimator that can accurately and efficiently quantify the accuracy of
the surrogate model. Using the error estimator, we systematically update our
surrogate model through a greedy search of the parameter space. Furthermore,
using the error estimator, the parameter search space is dynamically updated
such that the most relevant samples get chosen at every iteration. The proposed
adaptive surrogate modelling technique is tested on three benchmark models to
illustrate its efficiency, accuracy, and ability of generalization.Comment: 28 pages, 17 figures, 1 tabl
Modelling mitral valvular dynamicsâcurrent trend and future directions
Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed
Overcoming slowly decaying Kolmogorov n-width by transport maps: application to model order reduction of fluid dynamics and fluid--structure interaction problems
In this work we focus on reduced order modelling for problems for which the
resulting reduced basis spaces show a slow decay of the Kolmogorov -width,
or, in practical calculations, its computational surrogate given by the
magnitude of the eigenvalues returned by a proper orthogonal decomposition on
the solution manifold. In particular, we employ an additional preprocessing
during the offline phase of the reduced basis method, in order to obtain
smaller reduced basis spaces. Such preprocessing is based on the composition of
the snapshots with a transport map, that is a family of smooth and invertible
mappings that map the physical domain of the problem into itself. Two test
cases are considered: a fluid moving in a domain with deforming walls, and a
fluid past a rotating cylinder. Comparison between the results of the novel
offline stage and the standard one is presented.Comment: 26 pages, 11 figure
Asymptotics of conduction velocity restitution in models of electrical excitation in the heart
We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest non-trivial spatially extended problem in excitable media, and in the case of cardiac tissue it is an important tool for prediction of cardiac arrhythmias and fibrillation. An idealized conduction velocity restitution curve requires solving a non-linear eigenvalue problem with periodic boundary conditions, which in the cardiac case is very stiff and calls for the use of asymptotic methods. We compare asymptotics of restitution curves in four examples, two generic excitable media models, and two ionic cardiac models. The generic models include the classical FitzHughâNagumo model and its variation by Barkley. They are treated with standard singular perturbation techniques. The ionic models include a simplified âcaricatureâ of Noble (J. Physiol. Lond. 160:317â352, 1962) model and Beeler and Reuter (J. Physiol. Lond. 268:177â210, 1977) model, which lead to non-Tikhonov problems where known asymptotic results do not apply. The Caricature Noble model is considered with particular care to demonstrate the well-posedness of the corresponding boundary-value problem. The developed method for calculation of conduction velocity restitution is then applied to the BeelerâReuter model. We discuss new mathematical features appearing in cardiac ionic models and possible applications of the developed method
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