Cardiac Function Estimation from MRI Using a Heart Model and Data Assimilation: Advances and Difficulties

In this paper, we present a framework to estimate local ventricular myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivisions. Then, this model is deformed to fit a clinical MRI, using a semi-automatic fuzzy segmentation, an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart is then presented and simulated. Finally, a data assimilation procedure is described, and applied to this model. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on fitting to patient-specific anatomy and assimilation with simulated data are very promising. Current work on model calibration and estimation of patient parameters opens up possibilities to apply this framework in a clinical environment.

[1]  Jacques-Louis Lions,et al.  Handbook of numerical analysis (volume VIII) , 2002 .

[2]  Carmel Hayes,et al.  Assessment of left ventricular function by breath‐hold cine MR imaging: Comparison of different steady‐state free precession sequences , 2005, Journal of magnetic resonance imaging : JMRI.

[3]  E. McVeigh,et al.  Novel Technique for Cardiac Electromechanical Mapping with Magnetic Resonance Imaging Tagging and an Epicardial Electrode Sock , 2003, Annals of Biomedical Engineering.

[4]  Roy C. P. Kerckhoffs,et al.  Towards Patient Specific Models of Cardiac Mechanics: A Sensitivity Study , 2003, FIMH.

[5]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[6]  Dominique Chapelle,et al.  A Physiologically-Based Model for the Active Cardiac Muscle Contraction , 2001, FIMH.

[7]  Andrew E Arai,et al.  DENSE with SENSE. , 2005, Journal of magnetic resonance.

[8]  A. Hill.  The heat of shortening and the dynamic constants of muscle , 1938 .

[9]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[10]  Peter Boesiger,et al.  k‐t BLAST and k‐t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations , 2003, Magnetic resonance in medicine.

[11]  James S. Duncan,et al.  Medical Image Analysis , 1999, IEEE Pulse.

[12]  J. F. Bradshaw,et al.  The principal axes transformation--a method for image registration. , 1990, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[13]  S. Cowin,et al.  Biomechanics: Mechanical Properties of Living Tissues, 2nd ed. , 1994 .

[14]  D. Chapelle,et al.  MODELING AND ESTIMATION OF THE CARDIAC ELECTROMECHANICAL ACTIVITY , 2006 .

[15]  D. A. Mcdonald.  Blood flow in arteries , 1974 .

[16]  Hervé Delingette,et al.  Simulation of cardiac pathologies using an electromechanical biventricular model and XMR interventional imaging , 2005, Medical Image Anal..

[17]  A. McCulloch,et al.  Modelling cardiac mechanical properties in three dimensions , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  Daniel Rueckert,et al.  Analysis of 3-D myocardial motion in tagged MR images using nonrigid image registration , 2004, IEEE Transactions on Medical Imaging.

[19]  Jerry L Prince,et al.  Cardiac motion tracking using CINE harmonic phase (HARP) magnetic resonance imaging , 1999, Magnetic resonance in medicine.

[20]  A. Rahmouni,et al.  Segmentation of cardiac cine-MR images and myocardial deformation assessment using level set methods. , 2005, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[21]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[22]  R. Aliev,et al.  A simple two-variable model of cardiac excitation , 1996 .

[23]  Johan Montagnat,et al.  4D deformable models with temporal constraints: application to 4D cardiac image segmentation , 2005, Medical Image Anal..

[24]  N. Paragios.  A level set approach for shape-driven segmentation and tracking of the left ventricle , 2003, IEEE Transactions on Medical Imaging.

[25]  Frédérique Clément,et al.  A Biomechanical Model of Muscle Contraction , 2001, MICCAI.

[26]  Guanrong Chen,et al.  Kalman Filtering with Real-time Applications , 1987 .

[27]  Andrew Zisserman,et al.  Estimation of the partial volume effect in MRI , 2002, Medical Image Anal..

[28]  W. Parmley,et al.  Assessment of Passive Elastic Stiffness for Isolated Heart Muscle and the Intact Heart , 1973, Circulation research.

[29]  O. Lutz,et al.  Unveiling extracellular inorganic phosphate signals from blood in human cardiac 31P NMR spectra. , 2001, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

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

[31]  K. Bathe.  Finite Element Procedures , 1995 .

[32]  Kawal S. Rhode,et al.  A system for real-time XMR guided cardiovascular intervention , 2005, IEEE Transactions on Medical Imaging.

[33]  O. Simonetti,et al.  "Black blood" T2-weighted inversion-recovery MR imaging of the heart. , 1996, Radiology.

[34]  J. Humphrey.  Continuum biomechanics of soft biological tissues , 2003 .

[35]  E. Rohan,et al.  Sensitivity analysis and material identification for activated smooth muscle , 2002 .

[36]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. I: Theory , 2007 .

[37]  Bijoy K. Ghosh,et al.  Single camera based motion and shape estimation using extended Kalman filtering , 2001 .

[38]  Dudley J Pennell,et al.  Comparison of interstudy reproducibility of cardiovascular magnetic resonance with two-dimensional echocardiography in normal subjects and in patients with heart failure or left ventricular hypertrophy. , 2002, The American journal of cardiology.

[39]  S. Hiraishi,et al.  Two‐dimensional Echocardiographic Assessment of Left Ventricular Volumes and Ejection Fraction in Children , 1982, Circulation.

[40]  M. Cerqueira,et al.  Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart. A statement for healthcare professionals from the Cardiac Imaging Committee of the Council on Clinical Cardiology of the American Heart Association. , 2002, Circulation.

[41]  Dominique Chapelle,et al.  Data assimilation for an electro-mechanical model of the myocardium , 2003 .

[42]  P. Batchelor,et al.  International Society for Magnetic Resonance in Medicine , 1997 .

[43]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

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

[45]  J. Lions,et al.  Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles , 1968 .

[46]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[47]  Christopher M Kramer,et al.  Black blood gradient echo cine magnetic resonance imaging of the mouse heart , 2005, Magnetic resonance in medicine.

[48]  Jerry L. Prince,et al.  Fast tracking of cardiac motion using 3D-HARP , 2005, IEEE Transactions on Biomedical Engineering.

[49]  Raja Muthupillai,et al.  Quantitative assessment of left ventricular function: steady-state free precession MR imaging with or without sensitivity encoding. , 2005, Radiology.

[50]  Nicholas Ayache.  Computational Models for the Human Body , 2004 .

[51]  B. Philipp Kellerhals,et al.  Financial Pricing Models in Continuous Time and Kalman Filtering , 2001 .

[52]  D N Firmin,et al.  Investigating intrinsic myocardial mechanics: The role of MR tagging, velocity phase mapping, and diffusion imaging , 2000, Journal of magnetic resonance imaging : JMRI.

[53]  Hervé Delingette,et al.  Deformable biomechanical models: Application to 4D cardiac image analysis , 2003, Medical Image Anal..

[54]  J. Goldberger,et al.  Transcutaneous multielectrode basket catheter for endocardial mapping and ablation of ventricular tachycardia in the pig. , 1997, Circulation.

[55]  J. Kennedy,et al.  BLOOD FLOW IN ARTERIES (2nd ed) , 1975 .

[56]  Nicolas P. Smith,et al.  Mathematical modelling of the ischaemic heart , 2001 .

[57]  B. M. Horáček.  The Forward and Inverse Problems of Electrocardiography , 1996 .

[58]  Daniel B Ennis,et al.  3D breath‐held cardiac function with projection reconstruction in steady state free precession validated using 2D cine MRI , 2004, Journal of magnetic resonance imaging : JMRI.

[59]  Daniel Rueckert,et al.  Segmentation of 4D Cardiac MR Images Using a Probabilistic Atlas and the EM Algorithm , 2003, MICCAI.

[60]  L. Glass,et al.  Theory of heart : biomechanics, biophysics, and nonlinear dynamics of cardiac function , 1991 .

[61]  Michael A. E. Schneider,et al.  Clinical experience with a novel multielectrode basket catheter in right atrial tachycardias. , 1999, Circulation.

[62]  F. Yin,et al.  A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. , 1998, Journal of biomechanical engineering.

[63]  Peter J Hunter,et al.  Modeling total heart function. , 2003, Annual review of biomedical engineering.

[64]  Arun V. Holden,et al.  Computational biology of the heart , 1998, The Mathematical Gazette.

[65]  Leon Axel,et al.  Tagged Magnetic Resonance Imaging of the Heart: a Survey , 2004 .

[66]  A V Holden,et al.  Qualitative modeling of mechanoelectrical feedback in a ventricular cell. , 1997, Bulletin of mathematical biology.

[67]  Frank B. Sachse,et al.  Computational Cardiology , 2004, Lecture Notes in Computer Science.

[68]  N. Stergiopulos,et al.  Total arterial inertance as the fourth element of the windkessel model. , 1999, American journal of physiology. Heart and circulatory physiology.

[69]  C S Henriquez,et al.  Myocardial fiber orientation mapping using reduced encoding diffusion tensor imaging. , 2001, Journal of cardiovascular magnetic resonance : official journal of the Society for Cardiovascular Magnetic Resonance.

[70]  Theo Arts,et al.  Towards model-based analysis of cardiac MR tagging data: Relation between left ventricular shear strain and myofiber orientation , 2006, Medical Image Anal..

[71]  M. Cerqueira,et al.  Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart: A statement for healthcare professionals from the Cardiac Imaging Committee of the Council on Clinical Cardiology of the American Heart Association , 2002, The international journal of cardiovascular imaging.

[72]  Gunnar Seemann,et al.  Functional Imaging and Modeling of the Heart , 2003, Lecture Notes in Computer Science.

[73]  Dana H. Brooks,et al.  Direct and inverse methods for cardiac mapping using multielectrode catheter measurernents , 2001 .

[74]  M. Yacoub,et al.  Asymmetric redirection of flow through the heart , 2000, Nature.

[75]  D. R. Veronda,et al.  Mechanical characterization of skin-finite deformations. , 1970, Journal of biomechanics.

[76]  A McCulloch,et al.  Computational biology of the heart: from structure to function. , 1998, Progress in biophysics and molecular biology.

[77]  Frank B. Sachse,et al.  Computational Cardiology , 2004, Lecture Notes in Computer Science.

[78]  A. Huxley.  Muscle structure and theories of contraction. , 1957, Progress in biophysics and biophysical chemistry.

[79]  James S. Duncan,et al.  Estimation of 3D left ventricular deformation from echocardiography , 2001, Medical Image Anal..

[80]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[81]  Eduard Rohan,et al.  Shape optimization of elasto-plastic structures and continua , 2000 .

[82]  Hong Yan,et al.  An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation , 2003, IEEE Transactions on Medical Imaging.

[83]  Peter Boesiger,et al.  Myocardial tagging with 3D‐CSPAMM , 2002, Journal of magnetic resonance imaging : JMRI.

[84]  Nikolas P. Galatsanos,et al.  A spatially constrained mixture model for image segmentation , 2005, IEEE Transactions on Neural Networks.

[85]  Dana H. Brooks,et al.  Direct and inverse methods for cardiac mapping using multielectrode catheter measurements , 2001 .

[86]  Theo Arts,et al.  Modules in Cardiac Modeling: Mechanics, Circulation, and Depolarization Wave , 2001, FIMH.