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Ma S, Wang R, Qiu S, Li R, Yue Q, Sun Q, Chen L, Yan F, Yang GZ, Feng Y. MR Elastography With Optimization-Based Phase Unwrapping and Traveling Wave Expansion-Based Neural Network (TWENN). IEEE TRANSACTIONS ON MEDICAL IMAGING 2023; 42:2631-2642. [PMID: 37030683 DOI: 10.1109/tmi.2023.3261346] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Magnetic Resonance Elastography (MRE) can characterize biomechanical properties of soft tissue for disease diagnosis and treatment planning. However, complicated wavefields acquired from MRE coupled with noise pose challenges for accurate displacement extraction and modulus estimation. Using optimization-based displacement extraction and Traveling Wave Expansion-based Neural Network (TWENN) modulus estimation, we propose a new pipeline for processing MRE images. An objective function with Dual Data Consistency (Dual-DC) has been used to ensure accurate phase unwrapping and displacement extraction. For the estimation of complex wavenumbers, a complex-valued neural network with displacement covariance as an input has been developed. A model of traveling wave expansion is used to generate training datasets for the network with varying levels of noise. The complex shear modulus map is obtained through fusion of multifrequency and multidirectional data. Validation using brain and liver simulation images demonstrates the practical value of the proposed pipeline, which can estimate the biomechanical properties with minimal root-mean-square errors when compared to state-of-the-art methods. Applications of the proposed method for processing MRE images of phantom, brain, and liver reveal clear anatomical features, robustness to noise, and good generalizability of the pipeline.
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Solamen LM, Gordon-Wylie SW, McGarry MD, Weaver JB, Paulsen KD. Phantom evaluations of low frequency MR elastography. ACTA ACUST UNITED AC 2019; 64:065010. [DOI: 10.1088/1361-6560/ab0290] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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Fovargue D, Nordsletten D, Sinkus R. Stiffness reconstruction methods for MR elastography. NMR IN BIOMEDICINE 2018; 31:e3935. [PMID: 29774974 PMCID: PMC6175248 DOI: 10.1002/nbm.3935] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Revised: 03/27/2018] [Accepted: 03/27/2018] [Indexed: 05/19/2023]
Abstract
Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave-motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.
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Affiliation(s)
- Daniel Fovargue
- Imaging Sciences & Biomedical EngineeringKing's College LondonLondonUK
| | - David Nordsletten
- Imaging Sciences & Biomedical EngineeringKing's College LondonLondonUK
| | - Ralph Sinkus
- Imaging Sciences & Biomedical EngineeringKing's College LondonLondonUK
- Inserm U1148, LVTSUniversity Paris Diderot, University Paris 13Paris75018France
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Testu J, McGarry M, Dittmann F, Weaver J, Paulsen K, Sack I, Van Houten E. Viscoelastic power law parameters of in vivo human brain estimated by MR elastography. J Mech Behav Biomed Mater 2017; 74:333-341. [DOI: 10.1016/j.jmbbm.2017.06.027] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Revised: 06/19/2017] [Accepted: 06/20/2017] [Indexed: 02/06/2023]
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Tan L, McGarry MDJ, Van Houten EEW, Ji M, Solamen L, Weaver JB, Paulsen KD. Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2017; 36:236-250. [PMID: 27608454 PMCID: PMC5256858 DOI: 10.1109/tmi.2016.2604568] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.
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Anderson AT, Van Houten EEW, McGarry MDJ, Paulsen KD, Holtrop JL, Sutton BP, Georgiadis JG, Johnson CL. Observation of direction-dependent mechanical properties in the human brain with multi-excitation MR elastography. J Mech Behav Biomed Mater 2016; 59:538-546. [PMID: 27032311 PMCID: PMC4860072 DOI: 10.1016/j.jmbbm.2016.03.005] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2015] [Revised: 03/01/2016] [Accepted: 03/09/2016] [Indexed: 02/08/2023]
Abstract
Magnetic resonance elastography (MRE) has shown promise in noninvasively capturing changes in mechanical properties of the human brain caused by neurodegenerative conditions. MRE involves vibrating the brain to generate shear waves, imaging those waves with MRI, and solving an inverse problem to determine mechanical properties. Despite the known anisotropic nature of brain tissue, the inverse problem in brain MRE is based on an isotropic mechanical model. In this study, distinct wave patterns are generated in the brain through the use of multiple excitation directions in order to characterize the potential impact of anisotropic tissue mechanics on isotropic inversion methods. Isotropic inversions of two unique displacement fields result in mechanical property maps that vary locally in areas of highly aligned white matter. Investigation of the corpus callosum, corona radiata, and superior longitudinal fasciculus, three highly ordered white matter tracts, revealed differences in estimated properties between excitations of up to 33%. Using diffusion tensor imaging to identify dominant fiber orientation of bundles, relationships between estimated isotropic properties and shear asymmetry are revealed. This study has implications for future isotropic and anisotropic MRE studies of white matter tracts in the human brain.
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Affiliation(s)
- Aaron T Anderson
- Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
| | - Elijah E W Van Houten
- Département de génie mécanique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K2R1; Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA.
| | - Matthew D J McGarry
- Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA.
| | - Keith D Paulsen
- Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA; Dartmouth-Hitchcock Medical Center, Lebanon, New Hampshire 03756, USA.
| | - Joseph L Holtrop
- Bioengineering Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
| | - Bradley P Sutton
- Bioengineering Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
| | - John G Georgiadis
- Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; Biomedical Engineering Department, Illinois Institute of Technology, Chicago, Illinois 60616, USA.
| | - Curtis L Johnson
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA; Department of Biomedical Engineering, University of Delaware, Newark, Delaware 19716, USA.
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Arunachalam SP, Rossman PJ, Arani A, Lake DS, Glaser KJ, Trzasko JD, Manduca A, McGee KP, Ehman RL, Araoz PA. Quantitative 3D magnetic resonance elastography: Comparison with dynamic mechanical analysis. Magn Reson Med 2016; 77:1184-1192. [PMID: 27016276 PMCID: PMC5036985 DOI: 10.1002/mrm.26207] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2015] [Revised: 01/11/2016] [Accepted: 02/17/2016] [Indexed: 01/18/2023]
Abstract
Purpose Magnetic resonance elastography (MRE) is a rapidly growing noninvasive imaging technique for measuring tissue mechanical properties in vivo. Previous studies have compared two‐dimensional MRE measurements with material properties from dynamic mechanical analysis (DMA) devices that were limited in frequency range. Advanced DMA technology now allows broad frequency range testing, and three‐dimensional (3D) MRE is increasingly common. The purpose of this study was to compare 3D MRE stiffness measurements with those of DMA over a wide range of frequencies and shear stiffnesses. Methods 3D MRE and DMA were performed on eight different polyvinyl chloride samples over 20–205 Hz with stiffness between 3 and 23 kPa. Driving frequencies were chosen to create 1.1, 2.2, 3.3, 4.4, 5.5, and 6.6 effective wavelengths across the diameter of the cylindrical phantoms. Wave images were analyzed using direct inversion and local frequency estimation algorithm with the curl operator and compared with DMA measurements at each corresponding frequency. Samples with sufficient spatial resolution and with an octahedral shear strain signal‐to‐noise ratio > 3 were compared. Results Consistency between the two techniques was measured with the intraclass correlation coefficient (ICC) and was excellent with an overall ICC of 0.99. Conclusions 3D MRE and DMA showed excellent consistency over a wide range of frequencies and stiffnesses. Magn Reson Med 77:1184–1192, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.
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Affiliation(s)
| | | | - Arvin Arani
- Department of Radiology, Mayo Clinic, Rochester, Minnesota, USA
| | - David S Lake
- Department of Physiology and Biomedical Engineering, Mayo Clinic, Rochester, Minnesota, USA
| | - Kevin J Glaser
- Department of Radiology, Mayo Clinic, Rochester, Minnesota, USA
| | | | - Armando Manduca
- Department of Physiology and Biomedical Engineering, Mayo Clinic, Rochester, Minnesota, USA
| | - Kiaran P McGee
- Department of Radiology, Mayo Clinic, Rochester, Minnesota, USA
| | - Richard L Ehman
- Department of Radiology, Mayo Clinic, Rochester, Minnesota, USA
| | - Philip A Araoz
- Department of Radiology, Mayo Clinic, Rochester, Minnesota, USA
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Pepin KM, Ehman RL, McGee KP. Magnetic resonance elastography (MRE) in cancer: Technique, analysis, and applications. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2015; 90-91:32-48. [PMID: 26592944 PMCID: PMC4660259 DOI: 10.1016/j.pnmrs.2015.06.001] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Revised: 06/15/2015] [Accepted: 06/16/2015] [Indexed: 05/07/2023]
Abstract
Tissue mechanical properties are significantly altered with the development of cancer. Magnetic resonance elastography (MRE) is a noninvasive technique capable of quantifying tissue mechanical properties in vivo. This review describes the basic principles of MRE and introduces some of the many promising MRE methods that have been developed for the detection and characterization of cancer, evaluation of response to therapy, and investigation of the underlying mechanical mechanisms associated with malignancy.
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Non-identifiability of the Rayleigh damping material model in magnetic resonance elastography. Math Biosci 2013; 246:191-201. [PMID: 24018294 DOI: 10.1016/j.mbs.2013.08.012] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2013] [Revised: 07/24/2013] [Accepted: 08/23/2013] [Indexed: 01/31/2023]
Abstract
Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, μI and ρI. Results show the non-identifiability of the RD model at a single input frequency based on a structural analysis with a series of supporting experimental phantom results. The estimated real shear modulus values (μR) were substantially correct in characterising various material types and correlated well with the expected stiffness contrast of the physical phantoms. However, estimated RD parameters displayed consistent poor reconstruction accuracy leading to unpredictable trends in parameter behaviour. To overcome this issue, two alternative approaches were developed: (1) simultaneous multi-frequency inversion; and (2) parametric-based reconstruction. Overall, the RD model estimates the real shear shear modulus (μR) well, but identifying damping parameters (μI and ρI) is not possible without an alternative approach.
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Local mechanical properties of white matter structures in the human brain. Neuroimage 2013; 79:145-52. [PMID: 23644001 DOI: 10.1016/j.neuroimage.2013.04.089] [Citation(s) in RCA: 131] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2013] [Revised: 04/22/2013] [Accepted: 04/25/2013] [Indexed: 12/12/2022] Open
Abstract
The noninvasive measurement of the mechanical properties of brain tissue using magnetic resonance elastography (MRE) has emerged as a promising method for investigating neurological disorders. To date, brain MRE investigations have been limited to reporting global mechanical properties, though quantification of the stiffness of specific structures in the white matter architecture may be valuable in assessing the localized effects of disease. This paper reports the mechanical properties of the corpus callosum and corona radiata measured in healthy volunteers using MRE and atlas-based segmentation. Both structures were found to be significantly stiffer than overall white matter, with the corpus callosum exhibiting greater stiffness and less viscous damping than the corona radiata. Reliability of both local and global measures was assessed through repeated experiments, and the coefficient of variation for each measure was less than 10%. Mechanical properties within the corpus callosum and corona radiata demonstrated correlations with measures from diffusion tensor imaging pertaining to axonal microstructure.
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Bayly PV, Clayton EH, Genin GM. Quantitative imaging methods for the development and validation of brain biomechanics models. Annu Rev Biomed Eng 2012; 14:369-96. [PMID: 22655600 PMCID: PMC3711121 DOI: 10.1146/annurev-bioeng-071811-150032] [Citation(s) in RCA: 67] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Rapid deformation of brain tissue in response to head impact or acceleration can lead to numerous pathological changes, both immediate and delayed. Modeling and simulation hold promise for illuminating the mechanisms of traumatic brain injury (TBI) and for developing preventive devices and strategies. However, mathematical models have predictive value only if they satisfy two conditions. First, they must capture the biomechanics of the brain as both a material and a structure, including the mechanics of brain tissue and its interactions with the skull. Second, they must be validated by direct comparison with experimental data. Emerging imaging technologies and recent imaging studies provide important data for these purposes. This review describes these techniques and data, with an emphasis on magnetic resonance imaging approaches. In combination, these imaging tools promise to extend our understanding of brain biomechanics and improve our ability to study TBI in silico.
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Affiliation(s)
- Philip V. Bayly
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130
| | - Erik H. Clayton
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130
| | - Guy M. Genin
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130
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Abstract
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper 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 complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.
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Affiliation(s)
- M M Doyley
- University of Rochester, Department of Electrical and Computer Engineering, Hopeman Engineering Building 413, Box 270126, Rochester, NY 14627, USA.
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Abstract
Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper 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 complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.
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Affiliation(s)
- M M Doyley
- University of Rochester, Department of Electrical and Computer Engineering, Hopeman Engineering Building 413, Box 270126, Rochester, NY 14627, USA.
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Okamoto RJ, Clayton EH, Bayly PV. Viscoelastic properties of soft gels: comparison of magnetic resonance elastography and dynamic shear testing in the shear wave regime. Phys Med Biol 2011; 56:6379-400. [PMID: 21908903 DOI: 10.1088/0031-9155/56/19/014] [Citation(s) in RCA: 72] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Magnetic resonance elastography (MRE) is used to quantify the viscoelastic shear modulus, G*, of human and animal tissues. Previously, values of G* determined by MRE have been compared to values from mechanical tests performed at lower frequencies. In this study, a novel dynamic shear test (DST) was used to measure G* of a tissue-mimicking material at higher frequencies for direct comparison to MRE. A closed-form solution, including inertial effects, was used to extract G* values from DST data obtained between 20 and 200 Hz. MRE was performed using cylindrical 'phantoms' of the same material in an overlapping frequency range of 100-400 Hz. Axial vibrations of a central rod caused radially propagating shear waves in the phantom. Displacement fields were fit to a viscoelastic form of Navier's equation using a total least-squares approach to obtain local estimates of G*. DST estimates of the storage G' (Re[G*]) and loss modulus G″ (Im[G*]) for the tissue-mimicking material increased with frequency from 0.86 to 0.97 kPa (20-200 Hz, n = 16), while MRE estimates of G' increased from 1.06 to 1.15 kPa (100-400 Hz, n = 6). The loss factor (Im[G*]/Re[G*]) also increased with frequency for both test methods: 0.06-0.14 (20-200 Hz, DST) and 0.11-0.23 (100-400 Hz, MRE). Close agreement between MRE and DST results at overlapping frequencies indicates that G* can be locally estimated with MRE over a wide frequency range. Low signal-to-noise ratio, long shear wavelengths and boundary effects were found to increase residual fitting error, reinforcing the use of an error metric to assess confidence in local parameter estimates obtained by MRE.
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Affiliation(s)
- R J Okamoto
- Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, 1 Brookings Drive, Campus Box 1185, St Louis, MO 63130, USA.
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