Jerome Pousin
@insa-lyon.fr
Institut National des Sciences Appliquees de Lyon
Scopus Publications
Scholar Citations
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Scopus Publications
Jerome Pousin
Elsevier BV
Khadidja Benmansour and Jerome Pousin
Springer Science and Business Media LLC
Imen Mekkaoui, Jérôme Pousin, Jan Hesthaven, and Jing-Rebecca Li
Elsevier BV
The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torrey equation, describing the complex transverse magnetization due to diffusion-encoding magnetic field gradients, was developed to account for the motion and deformation. In that work, the motivation was to cancel the effect of the motion and deformation in the MRI image and the space scale of interest spans multiple voxels. In the present work, we adapt the mathematical equation to study the diffusion MRI signal at the much smaller scale of biological cells. We start with the Bloch-Torrey equation defined on a cell that is moving and deforming and linearize the equation around the magnitude of the diffusion-encoding gradient. The result is a second order signal model in which the linear term gives the imaginary part of the diffusion MRI signal and the quadratic term gives the apparent diffusion coefficient (ADC) attributable to the biological cell. We numerically validate this model for a variety of motions and deformations.
Feng Yang, YueMin Zhu, Lihui Wang, Marc Robini, Jerome Pousin, and Patrick Clarysse
IEEE
We investigate the problem of constructing statistical atlas of human cardiac fiber structure from limited number of datasets. We introduced a Parzen-Gaussian model to construct the probabilistic atlas of human cardiac fiber structure due to the fact that it can generate a general atlas using very small number of samples. Experimental results showed that atlas using Parzen-Gaussian model can avoid FA/MD collapse, which can be introduced by atlas from registered DW images and registered tensor fields.
F. Dabaghi, P. Krejčí, A. Petrov, J. Pousin, and Y. Renard
Elsevier BV
This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes. The convergence as well as an error estimate in time are proved. The analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution. However some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact. To overcome this difficulty, an new unconditionally stable and a very lightly dissipative scheme is proposed.
Franz Chouly, Mathieu Fabre, Patrick Hild, Jérôme Pousin, and Yves Renard
Oxford University Press (OUP)
We introduce a residual-based a posteriori error estimator for contact problems in two and three dimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche's method. Efficiency and reliability of the estimator are proved under a saturation assumption. Numerical experiments illustrate the theoretical properties and the good performance of the estimator.
Elie Bretin, , Imen Mekkaoui, and Jérôme Pousin
American Institute of Mathematical Sciences (AIMS)
We investigate in this paper the diffusion magnetic resonance imaging (MRI) in deformable organs such as the living heart. The difficulty comes from the hight sensitivity of diffusion measurement to tissue motion. Commonly in literature, the diffusion MRI signal is given by the complex magnetization of water molecules described by the Bloch-Torrey equation. When dealing with deformable organs, the Bloch-Torrey equation is no longer valid. Our main contribution is then to introduce a new mathematical description of the Bloch-Torrey equation in deforming media. In particular, some numerical simulations are presented to quantify the influence of cardiac motion on the estimation of diffusion. Moreover, based on a scaling argument and on an asymptotic model for the complex magnetization, we derive a new apparent diffusion coefficient formula. Finally, some numerical experiments illustrate the potential of this new version which gives a better reconstruction of the diffusion than using the classical one.
Franz Chouly, Mathieu Fabre, Patrick Hild, Rabii Mlika, Jérôme Pousin, and Yves Renard
Springer International Publishing
We summarize recent achievements in applying Nitsche's method to some contact and friction problems. We recall the setting of Nitsche's method in the case of unilateral contact with Tresca friction in linear elasticity. Main results of the numerical analysis are detailed: consistency, well-posedness, fully optimal convergence in $H^1(\\Omega)$-norm, residual-based a posteriori error estimation. Some numerics and some recent extensions to multi-body contact, contact in large transformations and contact in elastodynamics are presented as well.
Imen Mekkaoui, Kevin Moulin, Pierre Croisille, Jerome Pousin, and Magalie Viallon
IOP Publishing
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
Farshid Dabaghi, Adrien Petrov, Jérôme Pousin, and Yves Renard
Elsevier BV
Abstract This paper deals with a one-dimensional elastodynamic contact problem and aims to highlight some new numerical results. A new proof of existence and uniqueness results is proposed. More precisely, the problem is reformulated as a differential inclusion problem, the existence result follows from some a priori estimates obtained for the regularized problem while the uniqueness result comes from a monotonicity argument. An approximation of this evolutionary problem combining the finite element method as well as the mass redistribution method which consists on a redistribution of the body mass such that there is no inertia at the contact node, is introduced. Then two benchmark problems, one being new with convenient regularity properties, together with their analytical solutions are presented and some possible discretizations using different time-integration schemes are described. Finally, numerical experiments are reported and analyzed.
Mathieu Fabre, Jérôme Pousin, and Yves Renard
Cellule MathDoc/CEDRAM
In this paper, we develop and analyze a finite element fictitious domain approach based on Nitsche's method for the approximation of frictionless contact problems of two deformable elastic bodies. In the proposed method, the geometry of the bodies and the boundary conditions, including the contact condition between the two bodies, are described independently of the mesh of the fictitious domain. We prove that the optimal convergence is preserved. Numerical experiments are provided which confirm the correct behavior of the proposed method.
Olivier Bernard, Patrick Clarysse, Thomas Dietenbeck, Denis Friboulet, Stéphanie Jehan-Besson, and Jérome Pousin
John Wiley & Sons, Inc.
The analysis of imaged anatomical or biological structures and of their dynamics is an important task in terms of application and therefore of diagnostics. Such an analysis involves in the first place the extraction of these structures from the acquired images according to a given modality, which corresponds, in image processing terminology, to a segmentation phase. Segmentation methods are conventionally qualified as “region-based approaches” or “contour-based approaches”. The two types of information – image properties and a priori constraints – must be integrated into a common formalism, itself numerically implemented as an algorithm. This chapter details more particularly two deformable model approaches: deformable templates (DTs) and variational active contours. It presents the implementation of variational active contour methods in cardiac imaging, describing the choices carried out. The chapter focuses on two examples of active contours, applied to the segmentation of cardiac ultrasound images in 2D and 3D ultrasound echography
Patrick Clarysse and Jérome Pousin
John Wiley & Sons, Inc.
C. Beitone, K. Bianchi, P. Bouges, R. Stoica, V. Tuyisenge, L. Cassagnes, F. Chausse, P. Clarysse, G. Clerfond, P. Croisille,et al.
Elsevier BV
The aim of this project is to design a generic formalism for parietal and regional tracking of the left ventricle (LV) and to adapt it to 3D+t3D+t cardiac imaging modalities used in clinical routine (echocardiography, gated-SPECT, cine-MRI). The estimated displacement field must be reliable enough and insensitive to various artifacts to assess regional myocardial function in 3D from the accurate and precise computation of strain. The strain has recently proved to be of great interest for diagnosis and prognostic in cardiology, but its interpretation remains difficult because of the relative nature of the indices. The clinical objective of the 3DStrain project is to bring answers about the knowledge of normality.
Khadidja Benmansour and Jérôme Pousin
IOS Press
The result presented in this article is an adaptation of the gradient flow technique applied to a periodic problem combined with a singular perturbation method. The motivation for considering such a question originates from problems of cardiac images segmentation and of tracking cardiac images in medical image analysis. The 'elastic deformable template' model introduced previously for image segmentation is improved and adapted to the image tracking problem. A result of convergence is proved, for a periodic linear elastic model, the elastic tensor of which vanishes, when the parameter associated to the quasi-static technique goes to infinity.
Farshid Dabaghi, Adrien Petrov, Jérôme Pousin, and Yves Renard
EDP Sciences
This paper focuses on a one-dimensional wave equation being subjected to a unilateral boundary condition. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. The mass redistribution method, which is based on a redistribution of the body mass such that there is no inertia at the contact node, is introduced and its convergence is proved. Finally, some numerical experiments are reported.
S. Boujena, A. Chiboub, and J. Pousin
Springer Science and Business Media LLC
Classical numerical methods exhibit numerical discrepancies, when we are dealing with the transport equation in domain of heterogeneous sizes. In this work, a numerical scheme, based on a domain decomposition strategy is built to avoid numerical discrepancies. Let us mention that this work is inspired from the results given in Picq and Pousin (Variational reduction for the transport equation and plants growth, 2007).
Răzvan Stoica, Jérôme Pousin, Christopher Casta, Pierre Croisille, Yue-Min Zhu, and Patrick Clarysse
Springer Berlin Heidelberg
The dynamic deformable elastic template (DET) model has been previously introduced for the retrieval of personalized anatomical and functional models of the heart from dynamic cardiac image sequences. The dynamic DET model is a finite element deformable model, for which the minimum of the energy must satisfy a simplified equation of Dynamics. In this paper, we extend the model by integrating fiber constraints in order to improve the retrieval of cardiac deformations from cinetic magnetic resonance imaging (cineMRI). Evaluation conducted until now on cine MRI sequences shows an improvement of the recovery of the motion in images that present a low level of obvious rotation.
Gustavo C. Buscaglia, Jérôme Pousin, and Kamel Slimani
Informa UK Limited
The method of asymptotic partial decomposition of a domain aims at replacing a 3D or 2D problem by a hybrid problem 3D − 1D; or 2D − 1D, where the dimension of the problem decreases in part of the domain. The location of the junction between the heterogeneous problems is asymptotically estimated in certain circumstances, but for numerical simulations it is important to be able to determine the location of the junction accurately. In this article, by reformulating the problem in a mixed formulation context and by using an a posteriori error estimate, we propose an indicator of the error due to a wrong position of the junction. Minimizing this indicator allows us to determine accurately the location of the junction. Some numerical results are presented for a toy problem.
Patrick Clarysse, Martine Picq, and Jérôme Pousin
Elsevier BV
This work was motivated by the necessity of defining and computing a solution @r of a transport equation (1)@?"t@r+v@?@?"x@r=f(t,x,@r). subject to a non-convex pointwise constraint @r@?C. For when the velocity v is a regular function and when f is a Lipschitz function, in [9] sufficient conditions are given for the solution to the transport equation (15) to satisfy such a constraint. In this paper an algorithm for computing a relaxed solution is investigated.
Olivier Besson and Jérôme Pousin
IOP Publishing
An existence and uniqueness result for a linear conservation law subject to the initial and final conditions by using a spacetime least-squares formulation is proved. Some numerical simulations of a linear conservation law with a non-well-known velocity field are shown. An application to cardiac image reconstruction is presented.
S. Boujena, A. Chiboub, and J. Pousin
EDP Sciences
In this article a variational reduction method, how to handle the case of heterogenous domains for the Transport equation, is presented. This method allows to get rid of the restrictions on the size of time steps due to the thin parts of the domain. In the thin part of the domain, only a differential problem, with respect to the space variable, is to be approximated numerically. Numerical results are presented with a simple example. The variational reduction method can be extended to thin domains multi-branching in 3 dimensions, which is a work in progress.