Geometrical modeling of the heart

The heart is a very important human organ, that has a complex structure. Cardiovascular diseases have been the highest cause of death in North America and in Europe for decades. For this reason, a lot of research is made to understand the heart's physiology. One way to better understand the heart is via theoretical modeling of physiological mechanisms, the main ones being • trans-membrane potential wave propagation, • myocardium's contraction and • blood flow in the cardiac chambers. These physiological phenomena can be modeled via systems of partial differential equations (PDEs) that are defined on a domain given by the heart's shape. Numerical methods for solving these equations play a crucial role for validating these models. Numerical simulations also serve to make predictions of the organ's reaction to given stimuli. Thereby medical interventions such as the introduction of a pacemaker can be numerically simulated before attempting the surgical implantation. Such simulations on a complex geometry (the heart muscle or blood chambers) are usually made using the finite element or the finite volume methods. These methods requires a mesh of the computational domain, that is a triangulation of the domain into triangles in 2D or into tetrahedra in a 3D scenario. Thus far, most computations are made on meshes of idealized geometries and there is a lack of accurate 3D geometrical models of the heart. The community is aware of the importance of building accurate 3D models of the heart for understanding its physiology. There is only one realistic heart model that is publicly available. The main achievement of this project is to have built a precise and complete geometrical model of the human heart. The model consists of 1. An accurate and properly refined mesh of the heart muscle and chambers. The model includes fine features such as the pulpillary muscles (pillars) in the left and right ventricles.

[1]  Nahum Kiryati,et al.  Unlevel-Sets: Geometry and Prior-Based Segmentation , 2004, ECCV.

[2]  Alejandro F. Frangi,et al.  Three-dimensional modeling for functional analysis of cardiac images, a review , 2001, IEEE Transactions on Medical Imaging.

[3]  Paul-Louis George,et al.  Delaunay triangulation and meshing : application to finite elements , 1998 .

[4]  Milan Sonka,et al.  3-D active appearance models: segmentation of cardiac MR and ultrasound images , 2002, IEEE Transactions on Medical Imaging.

[5]  Leon Axel.  Tagged MRI-Based Studies of Cardiac Function , 2003, FIMH.

[6]  J. Sethian,et al.  Subjective surfaces: a geometric model for boundary completion , 2000 .

[7]  B. Dacorogna.  Direct methods in the calculus of variations , 1989 .

[8]  Daniel Rueckert,et al.  Atlas-Based Segmentation and Tracking of 3D Cardiac MR Images Using Non-rigid Registration , 2002, MICCAI.

[9]  Daniel Rueckert,et al.  Segmentation of cardiac MR and CT image sequences using model-based registration of a 4D statistical model , 2007, SPIE Medical Imaging.

[10]  Lin He,et al.  Solving the Chan-Vese Model by a Multiphase Level Set Algorithm Based on the Topological Derivative , 2007, SSVM.

[11]  Luigi Landini,et al.  Multimodal cardiac image fusion by geometrical features registration and warping , 2001, Computers in Cardiology 2001. Vol.28 (Cat. No.01CH37287).

[12]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[13]  Pierre Kornprobst,et al.  Mathematical problems in image processing - partial differential equations and the calculus of variations , 2010, Applied mathematical sciences.

[14]  Dimitris N. Metaxas,et al.  Volumetric heart modeling and analysis , 2005, CACM.

[15]  Stefano Alliney,et al.  Recursive median filters of increasing order: a variational approach , 1996, IEEE Trans. Signal Process..

[16]  Olivier Ecabert,et al.  Automatic Whole Heart Segmentation in Static Magnetic Resonance Image Volumes , 2007, MICCAI.

[17]  O. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2002, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[18]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[19]  S. Osher,et al.  A PDE-Based Fast Local Level Set Method 1 , 1998 .

[20]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[21]  Stefano Soatto,et al.  A Pseudo-distance for Shape Priors in Level Set Segmentation , 2003 .

[22]  K. Mikula,et al.  Co-Volume Level Set Method in Subjective Surface Based Medical Image Segmentation , 2005 .

[23]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[24]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[25]  Yves Coudière,et al.  2D/3D Discrete Duality Finite Volume (DDFV) scheme for anisotropic- heterogeneous elliptic equations, application to the electrocardiogram simulation. , 2008 .

[26]  John K. Tsotsos,et al.  A Novel Algorithm for Fitting 3-D Active Appearance Models: Applications to Cardiac MRI Segmentation , 2005, SCIA.

[27]  Luminita A. Vese,et al.  Image Decomposition Using Total Variation and div(BMO) , 2005, Multiscale Model. Simul..

[28]  F. Gibou.  A fast hybrid k-means level set algorithm for segmentation , 2005 .

[29]  M. Burger,et al.  Projected Gradient Flows for BV/Level Set Relaxation , 2005 .

[30]  Bernhard N Flury.  Multivariate Statistics: A Practical Approach , 1988 .

[31]  R. Winslow,et al.  Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. , 1998, The American journal of physiology.

[32]  Ron Kimmel,et al.  Fast Edge Integration , 2003 .

[33]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[34]  Stanley Osher,et al.  Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal , 2000, SIAM J. Sci. Comput..

[35]  Luis Ibáñez,et al.  The ITK Software Guide , 2005 .

[36]  Alessandro Sarti,et al.  Left ventricular volume estimation for real-time three-dimensional echocardiography , 2002, IEEE Transactions on Medical Imaging.

[37]  Karol Mikula,et al.  Parallel Co-Volume Subjective Surface Method For 3d Medical Image Segmentation , 2007 .

[38]  Olivier Ecabert,et al.  Discriminative boundary detection for model-based heart segmentation in CT images , 2007, SPIE Medical Imaging.

[39]  Jérôme Darbon,et al.  A Note on the Discrete Binary Mumford-Shah Model , 2007, MIRAGE.

[40]  Dimitris N. Metaxas,et al.  LV-RV Shape Modeling Based on a Blended Parameterized Model , 2002, MICCAI.

[41]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[42]  Peter Smereka,et al.  Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion , 2003, J. Sci. Comput..

[43]  Luminita A. Vese,et al.  Energy Minimization Based Segmentation and Denoising Using a Multilayer Level Set Approach , 2005, EMMCVPR.

[44]  W. Rudin.  Principles of mathematical analysis , 1964 .

[45]  Simon Baker,et al.  Equivalence and efficiency of image alignment algorithms , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[46]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[47]  Luigi Ambrosio,et al.  ON THE APPROXIMATION OF FREE DISCONTINUITY PROBLEMS , 1992 .

[48]  M J Ackerman,et al.  The Visible Human Project , 1998, Proc. IEEE.

[49]  Tien D. Bui,et al.  Image segmentation and selective smoothing by using Mumford-Shah model , 2005, IEEE Transactions on Image Processing.

[50]  E. Giusti.  Minimal surfaces and functions of bounded variation , 1977 .

[51]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[52]  Olivier Ecabert,et al.  Automatic Intra-operative Generation of Geometric Left Atrium/Pulmonary Vein Models from Rotational X-Ray Angiography , 2008, MICCAI.

[53]  D. Mumford,et al.  Riemannian Geometries on Spaces of Plane Curves , 2003, math/0312384.

[54]  R Malladi,et al.  Subjective surfaces: a method for completing missing boundaries. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[55]  Stefano Alliney,et al.  Digital filters as absolute norm regularizers , 1992, IEEE Trans. Signal Process..

[56]  Stefano Alliney,et al.  A property of the minimum vectors of a regularizing functional defined by means of the absolute norm , 1997, IEEE Trans. Signal Process..

[57]  Edmund J. Crampin,et al.  Multiscale computational modelling of the heart , 2004, Acta Numerica.

[58]  T. Chan,et al.  A fast algorithm for level set based optimization , 2002 .

[59]  Alessandro Sarti,et al.  Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation , 2006 .

[60]  Olivier Ecabert,et al.  A multi-modality segmentation framework: application to fully automatic heart segmentation , 2009, Medical Imaging.

[61]  Hervé Delingette,et al.  A Computational Framework for the Statistical Analysis of Cardiac Diffusion Tensors: Application to a Small Database of Canine Hearts , 2007, IEEE Transactions on Medical Imaging.

[62]  Mila Nikolova,et al.  Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers , 2002, SIAM J. Numer. Anal..

[63]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[64]  Tony F. Chan,et al.  Aspects of Total Variation Regularized L[sup 1] Function Approximation , 2005, SIAM J. Appl. Math..

[65]  Dimitris N. Metaxas,et al.  A Finite Element Model for Functional Analysis of 4D Cardiac-Tagged MR Images , 2003, MICCAI.

[66]  Guy Marchal,et al.  Automated multi-moda lity image registration based on information theory , 1995 .

[67]  Francisco Torrent-Guasp,et al.  The helical ventricular myocardial band: global, three-dimensional, functional architecture of the ventricular myocardium. , 2006, European journal of cardio-thoracic surgery : official journal of the European Association for Cardio-thoracic Surgery.

[68]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[69]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[70]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[71]  Alejandro F. Frangi,et al.  Three-dimensional cardiovascular image analysis , 2002, IEEE Transactions on Medical Imaging.

[72]  O. Gérard,et al.  Efficient model-based quantification of left ventricular function in 3-D echocardiography , 2002, IEEE Transactions on Medical Imaging.

[73]  Alejandro F Frangi,et al.  Computational Anatomy Atlas of the Heart , 2007, 2007 5th International Symposium on Image and Signal Processing and Analysis.

[74]  Olivier Faugeras,et al.  Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics , 2006, Statistics and Analysis of Shapes.

[75]  J. Alison Noble,et al.  Automated 3-D echocardiography analysis compared with manual delineations and SPECT MUGA , 2002, IEEE Transactions on Medical Imaging.

[76]  Marie-Pierre Jolly,et al.  Automatic Segmentation of the Left Ventricle in Cardiac MR and CT Images , 2006, International Journal of Computer Vision.

[77]  Rachid Deriche,et al.  Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[78]  Demetri Terzopoulos,et al.  A dynamic finite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis. , 1995, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[79]  Anuj Srivastava,et al.  Elastic-string models for representation and analysis of planar shapes , 2004, CVPR 2004.

[80]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[81]  Anthony J. Yezzi,et al.  Gradient flows and geometric active contour models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[82]  P. Hunter,et al.  Ventricular mechanics in diastole: material parameter sensitivity. , 2003, Journal of biomechanics.

[83]  Olivier Ecabert,et al.  Segmentation of the heart and major vascular structures in cardiovascular CT images , 2008, SPIE Medical Imaging.

[84]  Tony F. Chan,et al.  Level set based shape prior segmentation , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[85]  P. Hunter,et al.  Laminar structure of the heart: a mathematical model. , 1997, The American journal of physiology.

[86]  Timothy F. Cootes,et al.  Active Appearance Models , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[87]  Tony F. Chan,et al.  Image processing and analysis - variational, PDE, wavelet, and stochastic methods , 2005 .

[88]  Charles Pierre,et al.  Segmented medical images based simulations of Cardiac electrical activity and electrocardiogram: a model comparison , 2009 .

[89]  Alejandro F. Frangi,et al.  Automatic construction of multiple-object three-dimensional statistical shape models: application to cardiac modeling , 2002, IEEE Transactions on Medical Imaging.

[90]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[91]  Mila Nikolova,et al.  Regularizing Flows for Constrained Matrix-Valued Images , 2004, Journal of Mathematical Imaging and Vision.

[92]  Jonathan Richard Shewchuk,et al.  Improving tetrahedral meshes , 2008 .

[93]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[94]  Timothy F. Cootes,et al.  Statistical models of appearance for computer vision , 1999 .

[95]  Luigi Landini,et al.  A new algorithm for 3D automatic detection and tracking of cardiac wall motion , 1999, Computers in Cardiology 1999. Vol.26 (Cat. No.99CH37004).

[96]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[97]  P. Smereka.  The numerical approximation of a delta function with application to level set methods , 2006 .

[98]  Karl D. Fritscher,et al.  3D image segmentation by using statistical deformation models and level sets , 2006, International Journal of Computer Assisted Radiology and Surgery.

[99]  Mila Nikolova,et al.  Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models , 2006, SIAM J. Appl. Math..

[100]  L. Ambrosio,et al.  Approximation of functional depending on jumps by elliptic functional via t-convergence , 1990 .

[101]  Olivier Ecabert,et al.  Modeling shape variability for full heart segmentation in cardiac computed-tomography images , 2006, SPIE Medical Imaging.