An ℋ ∞ approach for elasticity properties reconstruction

• Published in: Medical physics (Lancaster) Vol. 39; no. 1; pp. 475 - 481
• Main Authors: Liu, Huafeng, Hu, Hongjie, Sinusas, Albert J., Shi, Pengcheng
• Format: Journal Article
• Language: English
• Published: United States American Association of Physicists in Medicine 01.01.2012
• Subjects: Algorithms; biomechanics; biomedical MRI; cardiology; Computer Simulation; Digital computing or data processing equipment or methods, specially adapted for specific applications; Elastic moduli; Elastic Modulus - physiology; elasticity; Elasticity Imaging Techniques - methods; Electrical, thermal, and mechanical properties of biological matter; extended Kaman filter; filter; Finite element methods; Heart - physiology; Humans; Image analysis; Image data processing or generation, in general; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; image reconstruction; Involving electronic [emr] or nuclear [nmr] magnetic resonance, e.g. magnetic resonance imaging; Kinematics; least-square; Magnetic resonance imaging; material characterization; Medical image contrast; Medical image noise; medical image processing; Medical imaging; Models, Cardiovascular; Numerical optimization; Poisson's equation; Reconstruction; Reproducibility of Results; robust estimation; Sensitivity and Specificity; state space representation; Tissues; Young's modulus; ℋ∞ filter; state space representation; least-square; material characterization; ℋ∞ filter; robust estimation; extended Kaman filter
• ISSN: 0094-2405; 2473-4209
• DOI: 10.1118/1.3673066

Purpose: Quantification of object elasticity properties has significant technical implications as well as important practical applications, such as medical disease diagnosis. In general, given noisy measurements on the kinematic states of the objects from imaging data, the aim is to recover the elasticity parameters for assumed material constitutive models of the objects. The implementation is complicated caused by the large dimensionality of the parameters. Methods: Various versions of the least-square (LS) methods have been widely used, which, however, do not perform well under reasonably realistic levels of disturbances. Another popular strategy, based on the extended Kalman filter (EKF), is also far from optimal and subject to divergence if either the initializations are poor or the noises are not Gaussian. In this paper, the authors propose a robust system identification paradigm for the quantitative analysis of object elasticity. It is derived and extended from the ℋ ∞ filtering principles and is particularly powerful for real-world situations where the types and levels of the disturbances are unknown. Results: Using synthetic data, the authors investigate the sensitivity of the strategies toward different types (Gaussian and Poisson) and levels of noises, as well as various initializations. The experimental results show consistently superior performance of the proposed method over the LS and EKF algorithms in reliably identifying object elastic modulus distributions. Conclusions: Results from phase contrast imaging data of canine hearts and human MRI data are also presented, which demonstrate the power of the framework.