A constrained genetic approach for computing material property of elastic objects

Zhang, Yong; Hall, Lawrence O.; Goldgof, Dmitry B.; Sarkar, Sudeep

doi:10.1109/tevc.2005.860767

Cited by 25 publications

(5 citation statements)

References 62 publications

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“…Stochastic methods, such as with genetic algorithms (GA) have also been proposed for solving the inverse problem (Zhang et al 2006, Khalil et al 2005. Stochastic methods can find the global minimum of the objective function without imposing any additional constraints; therefore, this reconstruction approach strategy may prove useful.…”

Section: Iterative Inversionmentioning

confidence: 99%

Model-based elastography: a survey of approaches to the inverse elasticity problem

2012

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Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This article reviews current approaches to elastography in three areas — quasi-static, harmonic, and transient — and describes inversion schemes for each elastographic imaging approach. Approaches include: first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials; and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper’s objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic, and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the transient behavior of soft tissue; and (3) developing better test procedures to evaluate the performance of modulus elastograms.

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Section: Iterative Inversionmentioning

confidence: 99%

Model-based elastography: a survey of approaches to the inverse elasticity problem

2012

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“…15,16 This problem is not unique to the LM algorithm, as similar concerns exist for genetic algorithms. 15,17,18 An ideal inversion framework would be robust to uncertainty in the initial parameterization, noise in the measured data, misidentified modes, as well as missing or spurious modes, and would consistently converge to the correct solution. Ogi et al 19 demonstrate an optimizer-based inversion framework capable of reliable convergence without the benefit of quality initial guess moduli.…”

Section: A Computational Considerations For Inversionmentioning

confidence: 99%

“…Combining Eqs. (13), (15), (16), and (18) give the necessary expression for log PðXjhÞ=@c 11 . This can be repeated for the other elastic constants as well.…”

Section: Elastic Constantsmentioning

confidence: 99%

Bayesian inference of elastic properties with resonant ultrasound spectroscopy

Bales

Petzold

Goodlet

et al. 2018

The Journal of the Acoustical Society of America

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Bayesian modeling and Hamiltonian Monte Carlo (HMC) are utilized to formulate a robust algorithm capable of simultaneously estimating anisotropic elastic properties and crystallographic orientation of a specimen from a list of measured resonance frequencies collected via Resonance Ultrasound Spectroscopy (RUS). Unlike typical optimization procedures which yield point estimates of the unknown parameters, computing a Bayesian posterior yields probability distributions for the unknown parameters, and HMC is an efficient way to compute this posterior. The algorithms described are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys. First, the elastic constants for a specimen of fine-grain polycrystalline Ti-6Al-4 V with random crystallographic texture and isotropic elastic symmetry are estimated. Second, the elastic constants and crystallographic orientation for a single crystal Ni-based superalloy CMSX-4 specimen are accurately determined, using only measurements of the specimen geometry, mass, and resonance frequencies. The unique contributions of this paper are as follows: the application of HMC for sampling the Bayesian posterior of a probabilistic RUS model, and the procedure for simultaneous estimation of elastic constants and lattice-specimen misorientation. Compared to previous approaches these algorithms demonstrate superior convergence behavior, particularly when the initial parameterization is unknown, and enable substantially simplified experimental procedures.

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“…Alternatively, for iterative methods, the inverse problem is considered as an optimization problem in which the shear modulus is changed iteratively to minimize the error between measured displacement and the simulated displacements (Fu et al 2000, Van Houten et al 2001, Doyley et al 2004, Eskandari et al 2008. This optimization problem may be solved using one of a large number of optimization algorithms such as the Gauss-Newton method (Kallel and Bertrand 1996, Doyley et al 2000, Miga 2003, Khalil et al 2005, gradient-based algorithms (Skovoroda et al 1999, Oberai et al 2003, Oberai et al 2004 or non-gradient approaches (Samani et al 2001, Zhang et al 2006. Some algorithms, such as Gauss-Newton, require the value of the functional, the gradient and the Hessian matrix, but some other algorithms require only the value of the functional and the gradient.…”

Section: Introductionmentioning

confidence: 99%

A comparison of direct and iterative finite element inversion techniques in dynamic elastography

2016

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As part of tissue elasticity imaging or elastography, an inverse problem needs to be solved to find the elasticity distribution from the measured displacements. The finite element method (FEM) is a common method for solving the inverse problem in dynamic elastography. This problem has been solved with both direct and iterative FEM schemes. Each of these methods has its own advantages and disadvantages which are examined in this paper. Choosing the data resolution and the excitation frequency are critical for achieving the best estimation of the tissue elasticity in FEM methods. In this paper we investigate the performance of both direct and iterative FEMs for different ranges of excitation frequency. A new form of iterative method is suggested here which requires a lower mesh density compared to the original form. Also two forms of the direct method are compared in this paper: one using the exact fit for derivatives calculation and the other using the least squares fit. We also perform a study on the spatial resolution of these methods using simulations. The comparison is also validated using a phantom experiment. The results suggest that the direct method with least squares fit is more robust to noise compared to other methods but has slightly lower resolution results. For example, for the homogenous region with 20 dB noise added to the data, the RMS error for the direct method with least squares fit is approximately half of the iterative method. It was observed that the ratio of voxel size to the wavelength should be within a specific range for the results to be reliable. For example for the direct method with least squares fit, for the case of 20 dB noise level, this ratio should be between 0.1 to 0.2. On balance, considering the much higher computational cost of the iterative method, the dependency of the iterative method on the initial guess, and the greater robustness of the direct method to noise, we suggest using the direct method with least squares fit for linear elasticity cases.

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A constrained genetic approach for computing material property of elastic objects

Cited by 25 publications

References 62 publications

Model-based elastography: a survey of approaches to the inverse elasticity problem

Model-based elastography: a survey of approaches to the inverse elasticity problem

Bayesian inference of elastic properties with resonant ultrasound spectroscopy

A comparison of direct and iterative finite element inversion techniques in dynamic elastography

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