A dynamic elastic model for segmentation and tracking of the heart in MR image sequences
Introduction
The detailed analysis of cardiac images remains a challenging task. In particular, the automated analysis of cardiac anatomical and functional MR images could yield detailed anatomical and functional cardiac parameters such as 3D shapes and volumes, motion, strain and stresses in the myocardium.
In this paper, we present a new approach for the segmentation and motion tracking of the myocardium in dynamic image sequences. This approach includes strong priors without depending on statistical models. It is based on the Deformable Elastic Template (DET) method introduced by Pham et al. (2001), and later improved by Rouchdy et al. (2007). A Deformable Elastic Template is a combination of:
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A topological and geometrical model of the object to be segmented.
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A constitutive equation (elasticity) defining its behavior under applied external image forces that push the model’s interfaces towards the image edges.
Here, we extend this approach to explicitly take into account the temporal dimension, in order to fully take into account the dynamics of the heart over the cardiac cycle. It is a regularized solution to a data modeling problem, which does not attempt to biophysically simulate the cardiac deformation. The proposed approach adds smoothness and periodicity constraints to the model, thus improving the robustness. It also analyzes all time frames concurrently, contrarily to most other approaches which analyze only one instant at a time. Moreover, existence and uniqueness of a solution, as well as convergence of the numerical algorithm towards the desired solution can be established.
The paper is organized as follows: after a presentation of previous works in the field, the principle of DET in the static case is recalled before introducing its extension to the dynamic case with the associated assumptions and constraints (Section 3). Implementation issues are detailed in Section 4. In a last section, results on synthetic data and real pathological human Magnetic Resonance Imaging sequences (MRI) are presented and discussed.
Section snippets
Previous work
Many methods have been presented to tackle the problem of cardiac cine MRI segmentation. In particular, statistical methods, have encountered a certain success. Mitchell et al. (2001) first presented an Active Appearance Model (AAM) for the segmentation of 2D MR slices of the heart. The method was later extended to a full 3D AAM (Mitchell et al., 2002). Lötjönen et al. presented a method based on a statistical point distribution model and a mean grayscale model (Lötjönen et al., 2004).
Static DET model
Before describing the dynamic model, we briefly introduce the static Deformable Elastic Template (DET), upon which it is based (Pham et al., 2001).
The DET model is a deformable volumetric model submitted to external constraints imposed by the image. The equilibrium of the model is obtained through the minimization of the following global energy functional:where Eelastic represents the elastic deformation energy of the model and Edata is the energy due to the external image
Pseudo-instationary scheme
We now discuss how to solve Eq. (3) when forces depend on the displacement. We propose to solve it by considering a series of linear problems, in a so-called pseudo-instationary process (Ciarlet and Lions, 1990). Roughly speaking, it consists in introducing a parameter τ, and to consider a pseudo-instationary problem with respect to τ derived from the original problem. The original problem will then be recovered as the asymptotic limit of the instationary problem when τ goes to infinity. Doing
Results
The results obtained in the context of a segmentation challenge on a rather large MRI patient database are first presented. Then, we give qualitative results about the estimated motion of the left ventricle from a 2D synthetic sequence.
Conclusion
We have presented a new dynamic elastic model (dynamic DET) for segmentation and motion estimation in cardiac MR sequences, and more generally, for the analysis of images of soft deformable structures in periodic motion. Experiments on a MR database show a good overall ability of the model to track the heart borders and capture the heart motion in 2D image sequences. Its main advantage is that it can process a whole dynamical sequence and provide a temporally consistent segmentation of the LV
Acknowledgements
This work has been supported by the French research project ACI-AGIR (http://www.aci-agir.org) and the Région Rhônes Alpes through the Simed project of cluster ISLE, as well as the CNRS-GDR STIC-Santé through the support of the IMPEIC action (Multicentric Initiative for Evaluation of Cardiac Image segmentation methods). It is also part of the French ANR (http://www.agence-nationale-recherche.fr/) project GWENDIA.
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