A 2D strain estimator with numerical optimization method for soft-tissue elastography

Liu, Ke; Zhang, Pengfei; Shao, Jinhua; Zhu, Xun; Zhang, Yun; Bai, Jing

doi:10.1016/j.ultras.2009.05.004

Cited by 24 publications

(11 citation statements)

References 31 publications

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“…A mathematical model for the displacement and strain estimation of the tissue‐mimicking material sample is considered in this section. As shown in Fig.…”

Section: Mathematic Modelmentioning

confidence: 99%

“…We can derive the displacements and strains from Fig. , that is to say, the displacements and strains of point

Q^{'} true(x_{Q^{'}}, y_{Q^{'}} true)

are represented by

true{\begin{matrix} u_{Q^{'}} = u + u_{x} true(x_{Q} - x_{P} true) + u_{y} true(y_{Q} - y_{P} true) \\ v_{Q^{'}} = v + v_{x} true(x_{Q} - x_{P} true) + v_{y} true(y_{Q} - y_{P} true) \end{matrix}

where

u

and

v

are the lateral and axial displacements of point

P^{'} true(x_{P^{'}}, y_{P^{'}} true)

u_{x} = {\partial u / \partial x}_{Q}

u_{y} = {\partial u / \partial y}_{Q}

v_{x} = {\partial v / \partial x}_{Q}

and

v_{y} = {\partial v / \partial y}_{Q}

are the first‐order partial differentials, standing for lateral strain, lateral shear strain, axial shear strain and axial strain , respectively.…”

Section: Mathematic Modelmentioning

confidence: 99%

“…Equation is often discussed as the tissue motion model in ultrasound‐based strain estimation , and it is also an affine transformation. Coefficients in the affine transformation have been estimated using optical flow method , least square method , and numerical optimization method . However, Pan proposed direct a cost function which minimizes the sum of squared differences between pre‐ and post‐deformation sub‐images, and this method has higher time cost.…”

Section: Mathematic Modelmentioning

confidence: 99%

“…Pan proposed a two‐step optical flow method to calculate the strain distribution in tissue, and the prior strain information was an essential part. Liu presented a numerical optimization method with Powell's algorithm to compute simultaneously 2D displacements and strains, but this method needed higher time cost.…”

Section: Introductionmentioning

confidence: 99%

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An efficient optimal method for a 2D strain estimation of ultrasound tissue‐mimicking material phantom

Zhu

Zhou

et al. 2015

Polymer Engineering & Sci

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Elastography is a relatively new technique in ultrasound or magnetic resonance imaging (MRI). This fact has motivated many investigators to investigate the preparation of tissue‐mimicking material and the imaging of the tissue‐mimicking phantom. In this article, an efficient numerical optimization method based on Quasi‐Newton algorithm is presented for calculating a 2D strain image of tissue‐mimicking material (TMM) sample. The first step in the proposed method is that the initial values for the displacement fields are estimated using the cross‐correlation method. Then, the numerical optimization method based on the Quasi‐Newton algorithm is adopted to improve the displacement and strain through selecting one moving subfield. The basic idea of the proposed method is to construct an object function based on a homogeneous affine transformation between pre‐ and post‐compression data and optimize the displacement and strain image for the initial displacement data. For a validation, the results of the proposed method compare with those of other numerical optimization methods. The simulated and experimental results demonstrate the potential of our two‐step strategy for the strain imaging of tissue‐mimicking phantom with high efficiency and accuracy. POLYM. ENG. SCI., 55:2751–2760, 2015. © 2015 Society of Plastics Engineers

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“…A mathematical model for the displacement and strain estimation of the tissue‐mimicking material sample is considered in this section. As shown in Fig.…”

Section: Mathematic Modelmentioning

confidence: 99%

“…We can derive the displacements and strains from Fig. , that is to say, the displacements and strains of point

Q^{'} true(x_{Q^{'}}, y_{Q^{'}} true)

are represented by

true{\begin{matrix} u_{Q^{'}} = u + u_{x} true(x_{Q} - x_{P} true) + u_{y} true(y_{Q} - y_{P} true) \\ v_{Q^{'}} = v + v_{x} true(x_{Q} - x_{P} true) + v_{y} true(y_{Q} - y_{P} true) \end{matrix}

where

u

and

v

are the lateral and axial displacements of point

P^{'} true(x_{P^{'}}, y_{P^{'}} true)

u_{x} = {\partial u / \partial x}_{Q}

u_{y} = {\partial u / \partial y}_{Q}

v_{x} = {\partial v / \partial x}_{Q}

and

v_{y} = {\partial v / \partial y}_{Q}

are the first‐order partial differentials, standing for lateral strain, lateral shear strain, axial shear strain and axial strain , respectively.…”

Section: Mathematic Modelmentioning

confidence: 99%

Section: Mathematic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An efficient optimal method for a 2D strain estimation of ultrasound tissue‐mimicking material phantom

Zhu

Zhou

et al. 2015

Polymer Engineering & Sci

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“…The first stage can be considered to be an instance of the general deformable image registration problem [1], [2]. Approaches to the registration problem include differential methods of estimating optical flow [3], [4], optimization of a global deformation model’s parameters [5]–[7], and block-matching methods [8]–[12] While global deformational models are popular for registration in other imaging modalities, the pixel dimensions and high frequency speckle content of ultrasonic signals lead to a significant computational burden, along with a difficult to navigate optimization parameter space with abundant local extrema [7], [13]. Block-matching methods are not as computationally expensive, but only local information determines displacement estimated from a matching-block.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Regularization Applied to Ultrasound Strain Imaging

McCormick

Rubert

Varghese

2011

IEEE Trans. Biomed. Eng.

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Noise artifacts due to signal decorrelation and reverberation are a considerable problem in ultrasound strain imaging. For block-matching methods, information from neighboring matchingblocks has been utilized to regularize the estimated displacements. We apply a recursive Bayesian regularization algorithm developed by Hayton et al. (1999) to phase-sensitive ultrasound radiofrequency signals to improve displacement estimation. The parameter of regularization is reformulated, and its meaning examined in the context of strain imaging. Tissue-mimicking experimental phantoms and radiofrequency data incorporating finite element models for the tissue deformation and frequency-domain ultrasound simulations are used to compute the optimal parameter with respect to nominal strain and algorithmic iterations. The optimal strain regularization parameter was found to be twice the nominal strain and did not vary significantly with algorithmic iterations. The technique demonstrates superior performance over median filtering in noise reduction at strains 5% and higher for all quantitative experiments performed. For example, the strain signal-to-noise ratio was 11 dB higher than that obtained using a median filter at 7% strain. It has to be noted that for applied deformations lower than 1%, since signal decorrelation errors are minimal, using this approach may degrade the displacement image.

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