TY - JOUR
T1 - A robust method to estimate the time constant of elastographic parameters
AU - Islam, Md Tauhidul
AU - Chaudhry, Anuj
AU - Righetti, Raffaella
N1 - Funding Information:
Manuscript received August 20, 2018; revised January 7, 2019 and January 9, 2019; accepted January 10, 2019. Date of publication January 24, 2019; date of current version May 31, 2019. This work was supported in part by the U.S. Department of Defense under Grant W81XWH-18-1-0544 (BC171600). (Corresponding author: Raffaella Righetti.) The authors are with the Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843 USA (e-mail: righetti@ece.tamu.edu).
Publisher Copyright:
© 2019 IEEE.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/6
Y1 - 2019/6
N2 - Novel viscoelastic and poroelastic elastography techniques rely on the accurate estimation of the temporal behavior of the axial or lateral strains and related parameters. From the temporal curve of the elastographic parameter of interest, the time constant (TC) is estimated using analytical models and curve-fitting techniques such as Levenberg-Marquardt (LM), Nelder-Mead (NM), and trust-region reflective (TR). In this paper, we propose a new technique named variable projection (VP) to estimate accurately and robustly the TC and steady-state value of the elastographic parameter of interest from its temporal curve. As a testing platform, the method is used with a novel analytical model, which can be used for both poroelastic and viscoelastic tissues and in most practical experimental conditions of clinical interest. Finite element and ultrasound simulations and experimental results demonstrate that VP is robust to noise and capable of estimating the TC of the elastographic parameter with accuracy higher than that of typically employed curve-fitting techniques. The results also demonstrate that the performance of VP is not affected by an incorrect initial TC guess. For example, in simulations, VP can estimate the TC of axial strain and effective Poisson's ratio accurately for initial guesses ranging from 0.001 to infinite times of the true TC value even in fairly noisy conditions (30-dB signal to noise ratio). In experiments, VP always estimates the axial strain TC reliably, whereas the LM, NM, and TR methods fail to converge or converge to wrong solutions in most of the cases.
AB - Novel viscoelastic and poroelastic elastography techniques rely on the accurate estimation of the temporal behavior of the axial or lateral strains and related parameters. From the temporal curve of the elastographic parameter of interest, the time constant (TC) is estimated using analytical models and curve-fitting techniques such as Levenberg-Marquardt (LM), Nelder-Mead (NM), and trust-region reflective (TR). In this paper, we propose a new technique named variable projection (VP) to estimate accurately and robustly the TC and steady-state value of the elastographic parameter of interest from its temporal curve. As a testing platform, the method is used with a novel analytical model, which can be used for both poroelastic and viscoelastic tissues and in most practical experimental conditions of clinical interest. Finite element and ultrasound simulations and experimental results demonstrate that VP is robust to noise and capable of estimating the TC of the elastographic parameter with accuracy higher than that of typically employed curve-fitting techniques. The results also demonstrate that the performance of VP is not affected by an incorrect initial TC guess. For example, in simulations, VP can estimate the TC of axial strain and effective Poisson's ratio accurately for initial guesses ranging from 0.001 to infinite times of the true TC value even in fairly noisy conditions (30-dB signal to noise ratio). In experiments, VP always estimates the axial strain TC reliably, whereas the LM, NM, and TR methods fail to converge or converge to wrong solutions in most of the cases.
KW - Cancer imaging
KW - Levenberg-Marquardt
KW - Time constant estimation
KW - Ultrasound poroelastography
KW - Variable projection
KW - Viscoelastic imaging
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U2 - 10.1109/TMI.2019.2894782
DO - 10.1109/TMI.2019.2894782
M3 - Article
C2 - 30703014
AN - SCOPUS:85066982772
VL - 38
SP - 1358
EP - 1370
JO - IEEE Transactions on Medical Imaging
JF - IEEE Transactions on Medical Imaging
SN - 0278-0062
IS - 6
M1 - 8625607
ER -