A dynamic elastic model for segmentation and tracking of the heart in MR image sequences Joël Schaerer, Christopher Casta * , Jérôme Pousin, Patrick Clarysse Creatis-LRMN, CNRS UMR #5220, INSERM U630, INSA Bât. Blaise Pascal, F-69621 Villeurbanne Cedex, France article info Article history: Received 28 February 2008 Received in revised form 7 April 2010 Accepted 31 May 2010 Available online xxxx Keywords: Cardiac MRI Dynamic segmentation Deformable elastic template Fourier-based model abstract Strong prior models are a prerequisite for reliable spatio-temporal cardiac image analysis. While several cardiac models have been presented in the past, many of them are either too complex for their parame- ters to be estimated on the sole basis of MR Images, or overly simplified. In this paper, we present a novel dynamic model, based on the equation of dynamics for elastic materials and on Fourier filtering. The explicit use of dynamics allows us to enforce periodicity and temporal smoothness constraints. We pro- pose an algorithm to solve the continuous dynamical problem associated to numerically adapting the model to the image sequence. Using a simple 1D example, we show how temporal filtering can help removing noise while ensuring the periodicity and smoothness of solutions. The proposed dynamic model is quantitatively evaluated on a database of 15 patients which shows its performance and limita- tions. Also, the ability of the model to capture cardiac motion is demonstrated on synthetic cardiac sequences. Moreover, existence, uniqueness of the solution and numerical convergence of the algorithm can be demonstrated. Ó 2010 Elsevier B.V. All rights reserved. 1. 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, mo- tion, 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 se- quences. 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 im- proved by Rouchdy et al. (2007).A Deformable Elastic Template is a combination of:  A topological and geometrical model of the object to be segmented.  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 ap- proach 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 to- wards the desired solution can be established. The paper is organized as follows: after a presentation of previ- ous works in the field, the principle of DET in the static case is re- called before introducing its extension to the dynamic case with the associated assumptions and constraints (Section 3). Implemen- tation 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. 2. 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 pre- sented 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 gray- scale model (Lötjönen et al., 2004). 1361-8415/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.media.2010.05.009 * Corresponding author. Tel.: +33 472438227. E-mail address: christopher.casta@creatis.insa-lyon.fr (C. Casta). Medical Image Analysis xxx (2010) xxx–xxx Contents lists available at ScienceDirect Medical Image Analysis journal homepage: www.elsevier.com/locate/media Please cite this article in press as: Schaerer, J., et al. A dynamic elastic model for segmentation and tracking of the heart in MR image sequences. Med. Image Anal. (2010), doi:10.1016/j.media.2010.05.009