Abstract
A stochastic finite element method (SFEM) based framework is proposed for the simultaneous estimation of cardiac kinematics functions and material model parameters. While existing biomechanics studies of myocardial material constitutive laws have assumed known kinematics, and image analyses of cardiac kinematics have relied on chosen constraining models (mathematical or mechanical), we believe that a probabilistic strategy is needed to achieve robust and optimal estimates of kinematics functions and material parameters at the same time. For a particular a priori patient-dependent constraining material model with uncertain parameters and a posteriori noisy observations, stochastic differential equations are combined with the finite element method. The material parameters and the imaging/image-derived data are treated as random variables with known prior statistics in the dynamic system equations of the heart. In our current implementation, extended Kalman filter (EKF) procedures are adopted to linearize the equations and to provide the joint estimates. Because of the periodic nature of the cardiac dynamics, we conclude experimentally that it is possible to adopt this physical-model based optimal estimation approach to achieve converged estimates. Results from canine MR phase contrast images with linear elastic model are presented.
Chapter PDF
Similar content being viewed by others
Keywords
- Extend Kalman Filter
- Linear Elastic Model
- Stochastic Finite Element Method
- Kinematic Function
- Extend Kalman Filter Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Contreras, H.: The stochastic finite element method. Computer and Structure 12 (1980) 341–348
Frangi, A.J., Niessen, W.J., Viergever, M.A.: Three-dimensional modeling for functional analysis of cardiac images. IEEE Trans. Med. Imag. 20(1) (2001) 2–25
Glad T, T., Ljung, L.: Control Theory. Tylor & Francis (2000) London
Hunter, P.J., Smaill, B.H.: The analysis of cardiac function: a continuum approach. Progress in Biophysics and Molecular Biology 52 (1989) 101–164
Ljung, L.: Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear system. IEEE Trans. on Auto. Control AC24(1) (1979) 36–50
Moulton, M.J., Creswell, L.L., Actis, R.L., Myers, K.W., Vannier, M.W., Szabo, B.A., Pasque, M.K.: An inverse approach to determining myocardial material properties. Journal of Biomechanics 28(8) (1995) 935–948
Park, J., Metaxas, D.N., Axel, L.: Analysis of left ventricular wall motion based on volumetric deformable models and MRI-SPAMM. Medical Image Analysis 1(1) (1996) 53–71
Rao, S.K.: Comments on “Optimal guidance of proportional navigation”. IEEE Transactions on Aerospace and Electronic systems 34(3) (1998) 981–982
Shi, P., Sinusas, A.J., Constable, R.T., Duncan, J.S.: Volumetric deformation analysis using mechanics-based data fusion: application in cardiac motion recovery. International Journal of Computer Vision 35(1) (1999) 87–107
Shi, P., Sinusas, A.J., Constable, R.T., Duncan, J.S.: Point-tracked quantitative analysis of left ventricular motion from 3D image sequences. IEEE Transactions on Medical Imaging 19(1) (2000) 36–50
Wong, L.N., Shi, P.: Velocity field constrained front propagation for segmentation of cardiac images. submitted to IEEE Workshop on Application of Computer Vision
Yamada, H.: Strength of Biological Material. Williams and Wilkins (1970)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shi, P., Liu, H. (2002). Stochastic Finite Element Framework for Cardiac Kinematics Function and Material Property Analysis. In: Dohi, T., Kikinis, R. (eds) Medical Image Computing and Computer-Assisted Intervention — MICCAI 2002. MICCAI 2002. Lecture Notes in Computer Science, vol 2488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45786-0_78
Download citation
DOI: https://doi.org/10.1007/3-540-45786-0_78
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44224-0
Online ISBN: 978-3-540-45786-2
eBook Packages: Springer Book Archive