255 research outputs found
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
Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description
Developing robust data assimilation methods for hyperbolic conservation laws
is a challenging subject. Those PDEs indeed show no dissipation effects and the
input of additional information in the model equations may introduce errors
that propagate and create shocks. We propose a new approach based on the
kinetic description of the conservation law. A kinetic equation is a first
order partial differential equation in which the advection velocity is a free
variable. In certain cases, it is possible to prove that the nonlinear
conservation law is equivalent to a linear kinetic equation. Hence, data
assimilation is carried out at the kinetic level, using a Luenberger observer
also known as the nudging strategy in data assimilation. Assimilation then
resumes to the handling of a BGK type equation. The advantage of this framework
is that we deal with a single "linear" equation instead of a nonlinear system
and it is easy to recover the macroscopic variables. The study is divided into
several steps and essentially based on functional analysis techniques. First we
prove the convergence of the model towards the data in case of complete
observations in space and time. Second, we analyze the case of partial and
noisy observations. To conclude, we validate our method with numerical results
on Burgers equation and emphasize the advantages of this method with the more
complex Saint-Venant system
Robust filtering for joint state parameter estimation for distributed mechanical systems
International audienceWe present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinite-dimensional mechanical system, the setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment - using a test problem inspired from cardiac biomechanics - demonstrates the effectiveness of our approach
Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging
International audienceWe propose an effective filtering methodology designed to perform estimation in a distributed mechanical system using position measurements. As in a previously introduced method, the filter is inspired from robust control feedback, but here we take full advantage of the estimation specificity to choose a feedback law that can act on displacements instead of velocities and still retain the same kind of dissipativity property which guarantees robustness. This is very valuable in many applications for which positions are more readily available than velocities, as in medical imaging. We provide an in-depth analysis of the proposed procedure, as well as detailed numerical assessments using a test problem inspired from cardiac biomechanics, as medical diagnosis assistance is an important perspective for this approach. The method is formulated first for measurements based on Lagrangian displacements, but we then derive a nonlinear extension allowing to instead consider segmented images, which of course is even more relevant in medical applications
Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart
International audienceWe present the fundamental principles of data assimilation underlying the Verdandi library, and how they are articulated with the modular architecture of the library. This translates -- in particular -- into the definition of standardized interfaces through which the data assimilation library interoperates with the model simulation software and the so-called observation manager. We also survey various examples of data assimilation applied to the personalization of biophysical models, in particular for cardiac modeling applications within the euHeart European project. This illustrates the power of data assimilation concepts in such novel applications, with tremendous potential in clinical diagnosis assistance
Validation of Finite Element Image Registration-based Cardiac Strain Estimation from Magnetic Resonance Images
International audienceAccurate assessment of regional and global function of the heart is an important readout for the diagnosis and routine evaluation of cardiac patients. Indeed, recent clinical and experimental studies suggest that compared to global metrics, regional measures of function could allow for more accurate diagnosis and early intervention for many cardiac diseases. Although global strain measures derived from tagged magnetic resonance (MR) imaging have been shown to be reproducible for the majority of image registration techniques, the measurement of regional heterogeneity of strain is less robust. Moreover, radial strain is underestimated with the current techniques even globally. Finite element (FE)-based techniques offer a mechanistic approach for the regularization of the ill-posed registration problem. This paper presents the validation of a recently proposed FE-based image registration method with mechanical regularization named equilibrated warping. For this purpose, synthetic 3D-tagged MR images are generated from a reference biomechanical model of the left ventricle (LV). The performance of the registration algorithm is consequently tested on the images with different signal-to-noise ratios (SNRs), revealing the robustness of the method
Mortensen Observer for a class of variational inequalities -Lost equivalence with stochastic filtering approaches
We address the problem of deterministic sequential estimation for a nonsmooth
dynamics in R governed by a variational inequality, as illustrated by the
Skorokhod problem with a reflective boundary condition at 0. For smooth
dynamics, Mortensen introduced an energy for the likelihood that the state
variable produces-up to perturbations disturbances-a given observation in a
finite time interval, while reaching a given target state at the final time.
The Mortensen observer is the minimiser of this energy. For dynamics given by a
variational inequality and therefore not reversible in time, we study the
definition of a Mortensen estimator. On the one hand, we address this problem
by relaxing the boundary constraint of the synthetic variable and then
proposing an approximated variant of the Mortensen estimator that uses the
resulting nonlinear smooth dynamics. On the other hand, inspired by the smooth
dynamics approach, we study the vanishing viscosity limit of the
Hamilton-Jacobi equation satisfied by the Hopf-Cole transform of the solution
of the robust Zakai equation. We prove a stability result that allows us to
interpret the limiting solution as the value function associated with a control
problem rather than an estimation problem. In contrast to the case of smooth
dynamics, here the zero-noise limit of the robust form of the Zakai equation
cannot be understood from the Bellman equation of the value function arising in
Mortensen's deterministic estimation. This may unveil a violation of
equivalence for non-reversible dynamics between the Mortensen approach and the
low noise stochastic approach for nonsmooth dynamics
Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems
See also erratum DOI:10.1051/cocv/2011001International audienceWe propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered. The algorithms are derived in discrete time as in the classical UKF formalism - well-adapted to time discretized dynamical equations - and then extended into consistent continuous-time versions. This reduced-order filtering approach can be used in particular for the estimation of parameters in large dynamical systems arising from the discretization of partial differential equations, when state estimation can be handled by an adequate Luenberger observer inspired from feedback control. In this case, we give an analysis of the joint state-parameter estimation procedure based on linearized error, and we illustrate the effectiveness of the approach using a test problem inspired from cardiac biomechanics
Thermodynamical framework for modeling chemo-mechanical coupling in muscle contraction â Formulation and preliminary results
International audienceWe propose a multiscale model of cardiac contraction in which the molecular motors at the origin of the contractile process are considered as multistable mechanical entities endowed with internal degrees of freedom of both mechanical and chemical nature. This model provides a thermodynamical basis for modeling the complex interplay of chemical and mechanical phenomena at the sub-cellular level. Important motivations for this work include the ability to represent the experimentally observed physiological characteristics of the contractile apparatus such as (i) the passive quick force recovery mechanism, (ii) the relation between the contraction velocity and the applied force and (iii) the so called Lymn-Taylor cycle describing the metabolism.Nous proposons un modÚle multi-échelle de la contraction cardiaque dans lequel les moteurs moléculaires à l'origine du processus contractile sont représentés par des élé-ments mécaniques multistables paramétrés à la fois par des degrés de liberté géométriques et par des états chimiques. Ce modÚle permet de poser les fondements thermody-namiques permettant de décrire l'interaction complexe entre les phénomÚnes mécaniques et chimiques a l'échelle sub-cellulaire. Ce travail a pour objet de représenter les car-actéristiques physiologiques du dispositif contractile observées expérimentalement et en particulier (i) le mécanisme passif de récupération rapide de force, (ii) la relation entre la vitesse de contraction et la charge appliquée et (iii) le cycle dit de Lymn-Taylor décrivant l'activité métabolique. Abstract : We propose a multiscale model of cardiac contraction in which the molecular motors at the origin of the contractile process are considered as multistable mechanical entities endowed with internal degrees of freedom of both mechanical and chemical nature. This model provides a thermodynamical basis for modeling the complex interplay of chemical and mechanical phenomena at the sub-cellular level. Important motivations for this work include the ability to represent the experimentally observed physiological characteristics of the contractile apparatus such as (i) the passive quick force recovery mechanism, (ii) the relation between the contraction velocity and the applied force and (iii) the so called Lymn-Taylor cycle describing the metabolism
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