Two-dimensional complex shear modulus imaging of soft tissues by integration of Algebraic Helmoltz Inversion and LMS filter into dealing with noisy data: a simulation study

Thu-Ha Pham-Thi; Quang-Hai luong; Van-Dung Nguyen; Duc-Tan Tran; Huu-Tue Huynh; Thu-Ha Pham-Thi; Quang-Hai luong; Van-Dung Nguyen; Duc-Tan Tran; Huu-Tue Huynh

doi:10.3934/mbe.2020022

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 1: 404-417. doi: 10.3934/mbe.2020022

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Research article

Two-dimensional complex shear modulus imaging of soft tissues by integration of Algebraic Helmoltz Inversion and LMS filter into dealing with noisy data: a simulation study

1.
Hanoi National University of Education, Vietnam
2.
Faculty of Control Engineering, Le Quy Don technical University, 236 Hoang Quoc Viet, Bac Tu Liem, Hanoi 11313, Vietnam
3.
Nguyen Tat Thanh University, Vietnam
4.
Faculty of Electrical and Electronic Engineering, Phenikaa University, Hanoi 12116, Vietnam
5.
Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group JSC, No.167 Hoang Ngan, Trung Hoa, Cau Giay, Hanoi 11313, Vietnam
6.
International University, HCM Vietnam National University, Vietnam

Received: 17 June 2019 Accepted: 26 September 2019 Published: 11 October 2019

Elasticity and viscosity of soft tissues can be obtained from the complex shear modulus imaging (CSMI). CSMI is often used not only to investigate the structure of tissues but also to detect tumors in tissues. One of the most popular ways to categorize the methods used in CSMI is into quasi-static and dynamic methods. In the dynamic method, a force excitation is used to create the shear wave propagation, and the particle velocities are measured to extract their amplitude and phase at spatial locations. These parameters are then employed to directly or indirectly estimate the Complex Shear Modulus (CSM) represented by elasticity and viscosity. Algebraic Helmholtz Inversion (AHI) algorithm provides the direct estimation of CSM using the Finite Difference Time Domain (FDTD) technique. The limitation of this method, however, is that the noise generated from measuring the particle velocity strongly degrades the accuracy of the estimation. To overcome this problem, we proposed in this paper an adaptive AHI (AAHI) algorithm that offers a good performance in CSMI with a mean error of 2.06%.
- shear wave,
- elasticity,
- viscosity,
- CSM estimation,
- least mean square,
- Algebraic Helmholtz Inversion
Citation: Thu-Ha Pham-Thi, Quang-Hai luong, Van-Dung Nguyen, Duc-Tan Tran, Huu-Tue Huynh. Two-dimensional complex shear modulus imaging of soft tissues by integration of Algebraic Helmoltz Inversion and LMS filter into dealing with noisy data: a simulation study[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 404-417. doi: 10.3934/mbe.2020022

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Abstract

Elasticity and viscosity of soft tissues can be obtained from the complex shear modulus imaging (CSMI). CSMI is often used not only to investigate the structure of tissues but also to detect tumors in tissues. One of the most popular ways to categorize the methods used in CSMI is into quasi-static and dynamic methods. In the dynamic method, a force excitation is used to create the shear wave propagation, and the particle velocities are measured to extract their amplitude and phase at spatial locations. These parameters are then employed to directly or indirectly estimate the Complex Shear Modulus (CSM) represented by elasticity and viscosity. Algebraic Helmholtz Inversion (AHI) algorithm provides the direct estimation of CSM using the Finite Difference Time Domain (FDTD) technique. The limitation of this method, however, is that the noise generated from measuring the particle velocity strongly degrades the accuracy of the estimation. To overcome this problem, we proposed in this paper an adaptive AHI (AAHI) algorithm that offers a good performance in CSMI with a mean error of 2.06%.

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