Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging

Seidl, Daniel Thomas; van Bloemen Waanders, Bart G.; Wildey, Timothy Michael

doi:10.1080/17415977.2019.1603222

Title: Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging

Abstract

We present a formulation to simultaneously invert for a heterogeneous shear modulus field and traction boundary conditions in an incompressible linear elastic plane stress model. Our approach utilizes scalable deterministic methods, including adjoint-based sensitivities and quasi-Newton optimization, to reduce the computational requirements for large-scale inversion with partial differential equation (PDE) constraints. Here, we address the use of regularization for such formulations and explore the use of different types of regularization for the shear modulus and boundary traction. We apply this PDE-constrained optimization algorithm to a synthetic dataset to verify the accuracy in the reconstructed parameters, and to experimental data from a tissue-mimicking ultrasound phantom. In all of these examples, we compare inversion results from full-field and sparse data measurements.

Authors:

Seidl, Daniel Thomas ^[1]; van Bloemen Waanders, Bart G. ^[1]; Wildey, Timothy Michael ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Fri Apr 12 00:00:00 EDT 2019

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: ExxonMobil CRADA; USDOE

OSTI Identifier:: 1515211

Report Number(s):: SAND-2019-4125J
Journal ID: ISSN 1741-5977; 674645

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Inverse Problems in Science and Engineering

Additional Journal Information:: Journal Volume: 28; Journal Issue: 2; Journal ID: ISSN 1741-5977

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Inverse elasticity; PDE-constrained optimization; regularization; biomechanical imaging; sparsity

Citation Formats


                    Seidl, Daniel Thomas, van Bloemen Waanders, Bart G., and Wildey, Timothy Michael. Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging.  United States: N. p., 2019. 
Web.  doi:10.1080/17415977.2019.1603222.

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                    Seidl, Daniel Thomas, van Bloemen Waanders, Bart G., & Wildey, Timothy Michael. Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging.  United States.  https://doi.org/10.1080/17415977.2019.1603222

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                    Seidl, Daniel Thomas, van Bloemen Waanders, Bart G., and Wildey, Timothy Michael. Fri .  
"Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging".  United States.  https://doi.org/10.1080/17415977.2019.1603222.  https://www.osti.gov/servlets/purl/1515211.

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@article{osti_1515211,

  title        = {Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging},

  author       = {Seidl, Daniel Thomas and van Bloemen Waanders, Bart G. and Wildey, Timothy Michael},

  abstractNote = {We present a formulation to simultaneously invert for a heterogeneous shear modulus field and traction boundary conditions in an incompressible linear elastic plane stress model. Our approach utilizes scalable deterministic methods, including adjoint-based sensitivities and quasi-Newton optimization, to reduce the computational requirements for large-scale inversion with partial differential equation (PDE) constraints. Here, we address the use of regularization for such formulations and explore the use of different types of regularization for the shear modulus and boundary traction. We apply this PDE-constrained optimization algorithm to a synthetic dataset to verify the accuracy in the reconstructed parameters, and to experimental data from a tissue-mimicking ultrasound phantom. In all of these examples, we compare inversion results from full-field and sparse data measurements.},

  doi          = {10.1080/17415977.2019.1603222},

  journal      = {Inverse Problems in Science and Engineering},

  number       = 2,

  volume       = 28,

  place        = {United States},

  year         = {Fri Apr 12 00:00:00 EDT 2019},

  month        = {Fri Apr 12 00:00:00 EDT 2019}

}

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Works referenced in this record:

On the limited memory BFGS method for large scale optimization
journal, August 1989

Liu, Dong C.; Nocedal, Jorge
Mathematical Programming, Vol. 45, Issue 1-3
DOI: 10.1007/BF01589116

Three-dimensional ultrasound imaging
journal, November 2009

Prager, R. W.; Ijaz, U. Z.; Gee, A. H.
Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, Vol. 224, Issue 2
DOI: 10.1243/09544119JEIM586

Finite Element Analysis of Some Inverse Elasticity Problems
journal, June 1989

Maniatty, Antoinette; Zabaras, Nicholas; Stelson, Kim
Journal of Engineering Mechanics, Vol. 115, Issue 6
DOI: 10.1061/(ASCE)0733-9399(1989)115:6(1303)

Biomechanical imaging of cell stiffness and prestress with subcellular resolution
journal, September 2013

Canović, Elizabeth P.; Seidl, D. Thomas; Polio, Samuel R.
Biomechanics and Modeling in Mechanobiology, Vol. 13, Issue 3
DOI: 10.1007/s10237-013-0526-8

Linear and nonlinear elasticity imaging of soft tissue in vivo : demonstration of feasibility
journal, January 2009

Oberai, Assad A.; Gokhale, Nachiket H.; Goenezen, Sevan
Physics in Medicine and Biology, Vol. 54, Issue 5
DOI: 10.1088/0031-9155/54/5/006

Force traction microscopy: An inverse problem with pointwise observations
journal, November 2012

Vitale, G.; Preziosi, L.; Ambrosi, D.
Journal of Mathematical Analysis and Applications, Vol. 395, Issue 2
DOI: 10.1016/j.jmaa.2012.05.074

Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study
journal, January 2009

Richards, Michael S.; Barbone, Paul E.; Oberai, Assad A.
Physics in Medicine and Biology, Vol. 54, Issue 3
DOI: 10.1088/0031-9155/54/3/019

Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional
journal, January 2013

Banerjee, Biswanath; Walsh, Timothy F.; Aquino, Wilkins
Computer Methods in Applied Mechanics and Engineering, Vol. 253
DOI: 10.1016/j.cma.2012.08.023

Iterative Methods for Total Variation Denoising
journal, January 1996

Vogel, C. R.; Oman, M. E.
SIAM Journal on Scientific Computing, Vol. 17, Issue 1
DOI: 10.1137/0917016

Cell traction force and measurement methods
journal, January 2007

Wang, James H-C.; Lin, Jeen-Shang
Biomechanics and Modeling in Mechanobiology, Vol. 6, Issue 6
DOI: 10.1007/s10237-006-0068-4

A numerical method for the inverse problem of cell traction in 3D
journal, August 2012

Vitale, G.; Preziosi, L.; Ambrosi, D.
Inverse Problems, Vol. 28, Issue 9
DOI: 10.1088/0266-5611/28/9/095013

Three-dimensional Ultrasound Elasticity Imaging on an Automated Breast Volume Scanning System
journal, May 2017

Wang, Yuqi; Nasief, Haidy G.; Kohn, Sarah
Ultrasonic Imaging, Vol. 39, Issue 6
DOI: 10.1177/0161734617712238

Solution of inverse problems in elasticity imaging using the adjoint method
journal, February 2003

Oberai, Assad A.; Gokhale, Nachiket H.; Feij o., Gonzalo R.
Inverse Problems, Vol. 19, Issue 2
DOI: 10.1088/0266-5611/19/2/304

Updating quasi-Newton matrices with limited storage
journal, September 1980

Nocedal, Jorge
Mathematics of Computation, Vol. 35, Issue 151
DOI: 10.1090/S0025-5718-1980-0572855-7

Algorithms for quantitative quasi-static elasticity imaging using force data: ALGORITHMS FOR QUANTITATIVE QUASI-STATIC ELASTICITY IMAGING
journal, August 2014

Tyagi, Mohit; Goenezen, Sevan; Barbone, Paul E.
International Journal for Numerical Methods in Biomedical Engineering, Vol. 30, Issue 12
DOI: 10.1002/cnm.2665

Traction patterns of tumor cells
journal, April 2008

Ambrosi, D.; Duperray, A.; Peschetola, V.
Journal of Mathematical Biology, Vol. 58, Issue 1-2
DOI: 10.1007/s00285-008-0167-1

Investigation of regularization parameters and error estimating in inverse elasticity problems
journal, March 1994

Maniatty, Antoinette M.; Zabaras, Nicholas J.
International Journal for Numerical Methods in Engineering, Vol. 37, Issue 6
DOI: 10.1002/nme.1620370610

Model-based elastography: a survey of approaches to the inverse elasticity problem
journal, January 2012

Doyley, M. M.
Physics in Medicine and Biology, Vol. 57, Issue 3
DOI: 10.1088/0031-9155/57/3/R35

High Resolution Traction Force Microscopy Based on Experimental and Computational Advances
journal, January 2008

Sabass, Benedikt; Gardel, Margaret L.; Waterman, Clare M.
Biophysical Journal, Vol. 94, Issue 1
DOI: 10.1529/biophysj.107.113670

Simultaneous identification of unknown groundwater pollution sources and estimation of aquifer parameters
journal, September 2009

Datta, Bithin; Chakrabarty, Dibakar; Dhar, Anirban
Journal of Hydrology, Vol. 376, Issue 1-2
DOI: 10.1016/j.jhydrol.2009.07.014

Bayesian estimation of heat flux and thermal diffusivity using liquid crystal thermography
journal, January 2015

Konda Reddy, B.; Balaji, C.
International Journal of Thermal Sciences, Vol. 87
DOI: 10.1016/j.ijthermalsci.2014.07.012

Cellular Traction as an Inverse Problem
journal, January 2006

Ambrosi, D.
SIAM Journal on Applied Mathematics, Vol. 66, Issue 6
DOI: 10.1137/060657121

A nonlinear elasticity phantom containing spherical inclusions
journal, July 2012

Pavan, Theo Z.; Madsen, Ernest L.; Frank, Gary R.
Physics in Medicine and Biology, Vol. 57, Issue 15
DOI: 10.1088/0031-9155/57/15/4787

Direct error in constitutive equation formulation for plane stress inverse elasticity problem
journal, February 2017

Babaniyi, Olalekan A.; Oberai, Assad A.; Barbone, Paul E.
Computer Methods in Applied Mechanics and Engineering, Vol. 314
DOI: 10.1016/j.cma.2016.10.026

Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem
journal, July 2004

Rodrigues, F. A.; Orlande, H. R. B.; Dulikravich, G. S.
Mathematics and Computers in Simulation, Vol. 66, Issue 4-5
DOI: 10.1016/j.matcom.2004.02.005

Simultaneous Inverse Identification of Transient Thermal Properties and Heat Sources Using Sparse Sensor Information
journal, December 2007

Phillips, Sanford W.; Aquino, Wilkins; Chirdon, William M.
Journal of Engineering Mechanics, Vol. 133, Issue 12
DOI: 10.1061/(ASCE)0733-9399(2007)133:12(1341)

Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling
journal, July 1992

Wagner, Brian J.
Journal of Hydrology, Vol. 135, Issue 1-4
DOI: 10.1016/0022-1694(92)90092-A

Efficient determination of multiple regularization parameters in a generalized L-curve framework
journal, July 2002

Belge, Murat; Kilmer, Misha E.; Miller, Eric L.
Inverse Problems, Vol. 18, Issue 4
DOI: 10.1088/0266-5611/18/4/314

Inferring spatial variations of microstructural properties from macroscopic mechanical response
journal, September 2016

Liu, Tengxiao; Hall, Timothy J.; Barbone, Paul E.
Biomechanics and Modeling in Mechanobiology, Vol. 16, Issue 2
DOI: 10.1007/s10237-016-0831-0

Modified error in constitutive equations (MECE) approach for ultrasound elastography
journal, October 2017

Ghosh, Susanta; Zou, Zilong; Babaniyi, Olalekan
The Journal of the Acoustical Society of America, Vol. 142, Issue 4
DOI: 10.1121/1.5006911

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods
journal, August 2012

Ramani, S.; Rosen, J.
IEEE Transactions on Image Processing, Vol. 21, Issue 8
DOI: 10.1109/TIP.2012.2195015

Recovery of cellular traction in three-dimensional nonlinear hyperelastic matrices
journal, February 2017

Dong, Li; Oberai, Assad A.
Computer Methods in Applied Mechanics and Engineering, Vol. 314
DOI: 10.1016/j.cma.2016.05.020

Quantitative Compression Optical Coherence Elastography as an Inverse Elasticity Problem
journal, May 2016

Dong, Li; Wijesinghe, Philip; Dantuono, James T.
IEEE Journal of Selected Topics in Quantum Electronics, Vol. 22, Issue 3
DOI: 10.1109/JSTQE.2015.2512597

An overview of the Trilinos project
journal, September 2005

Heroux, Michael A.; Phipps, Eric T.; Salinger, Andrew G.
ACM Transactions on Mathematical Software, Vol. 31, Issue 3
DOI: 10.1145/1089014.1089021

Inverse problems in elasticity
journal, February 2005

Bonnet, Marc; Constantinescu, Andrei
Inverse Problems, Vol. 21, Issue 2
DOI: 10.1088/0266-5611/21/2/R01

A fast hybrid algorithm combining regularized motion tracking and predictive search for reducing the occurrence of large displacement errors
journal, April 2011

Jingfeng Jiang, ; Hall, T. J.; Jiang, Jingfeng
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 58, Issue 4
DOI: 10.1109/TUFFC.2011.1865

Computational Methods for Inverse Problems
book, January 2002

Vogel, Curtis R.
Frontiers in Applied Mathematics
DOI: 10.1137/1.9780898717570

A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion
journal, May 2008

Epanomeritakis, I.; Akçelik, V.; Ghattas, O.
Inverse Problems, Vol. 24, Issue 3
DOI: 10.1088/0266-5611/24/3/034015

Towards the mechanical characterization of abdominal wall by inverse analysis
journal, February 2017

Simón-Allué, R.; Calvo, B.; Oberai, A. A.
Journal of the Mechanical Behavior of Biomedical Materials, Vol. 66
DOI: 10.1016/j.jmbbm.2016.11.007

Simultaneous optical flow and source estimation: Space–time discretization and preconditioning
journal, October 2015

Andreev, R.; Scherzer, O.; Zulehner, W.
Applied Numerical Mathematics, Vol. 96
DOI: 10.1016/j.apnum.2015.04.007

Visualizing the Stress Distribution Within Vascular Tissues Using Intravascular Ultrasound Elastography: A Preliminary Investigation
journal, June 2015

Richards, Michael S.; Perucchio, Renato; Doyley, Marvin M.
Ultrasound in Medicine & Biology, Vol. 41, Issue 6
DOI: 10.1016/j.ultrasmedbio.2015.01.022

High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
conference, January 2003

Akcelik, Vokan; Tu, Tiankai; Urbanic, John
Proceedings of the 2003 ACM/IEEE conference on Supercomputing - SC '03
DOI: 10.1145/1048935.1050202

Simultaneous full‐waveform inversion for source wavelet and earth model
conference, October 2009

Wang, Ke; Krebs, Jerry R.; Hinkley, Dave
SEG Technical Program Expanded Abstracts 2009
DOI: 10.1190/1.3255372

Multiparameter material model and source signature full waveform inversion
conference, May 2011

Akçelik, Volkan; Denli, Huseyin; Kanevsky, Alex
SEG Technical Program Expanded Abstracts 2011
DOI: 10.1190/1.3627692

Three-dimensional ultrasound imaging
journal, January 2005

Huang, Changhe; Auner, Gregory W.; Caulfield, H. John
Acoustics Research Letters Online, Vol. 6, Issue 1
DOI: 10.1121/1.1815074

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Similar Records

Title: Simultaneous inversion of shear modulus and traction boundary conditions in biomechanical imaging

Abstract

Citation Formats

On the limited memory BFGS method for large scale optimization journal, August 1989

Three-dimensional ultrasound imaging journal, November 2009

Finite Element Analysis of Some Inverse Elasticity Problems journal, June 1989

Biomechanical imaging of cell stiffness and prestress with subcellular resolution journal, September 2013

Linear and nonlinear elasticity imaging of soft tissue in vivo : demonstration of feasibility journal, January 2009

Force traction microscopy: An inverse problem with pointwise observations journal, November 2012

Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study journal, January 2009

Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional journal, January 2013

Iterative Methods for Total Variation Denoising journal, January 1996

Cell traction force and measurement methods journal, January 2007

A numerical method for the inverse problem of cell traction in 3D journal, August 2012

Three-dimensional Ultrasound Elasticity Imaging on an Automated Breast Volume Scanning System journal, May 2017

Solution of inverse problems in elasticity imaging using the adjoint method journal, February 2003

Updating quasi-Newton matrices with limited storage journal, September 1980

Algorithms for quantitative quasi-static elasticity imaging using force data: ALGORITHMS FOR QUANTITATIVE QUASI-STATIC ELASTICITY IMAGING journal, August 2014

Traction patterns of tumor cells journal, April 2008

Investigation of regularization parameters and error estimating in inverse elasticity problems journal, March 1994

Model-based elastography: a survey of approaches to the inverse elasticity problem journal, January 2012

High Resolution Traction Force Microscopy Based on Experimental and Computational Advances journal, January 2008

Simultaneous identification of unknown groundwater pollution sources and estimation of aquifer parameters journal, September 2009

Bayesian estimation of heat flux and thermal diffusivity using liquid crystal thermography journal, January 2015

Cellular Traction as an Inverse Problem journal, January 2006

A nonlinear elasticity phantom containing spherical inclusions journal, July 2012

Direct error in constitutive equation formulation for plane stress inverse elasticity problem journal, February 2017

Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem journal, July 2004

Simultaneous Inverse Identification of Transient Thermal Properties and Heat Sources Using Sparse Sensor Information journal, December 2007

Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling journal, July 1992

Efficient determination of multiple regularization parameters in a generalized L-curve framework journal, July 2002

Inferring spatial variations of microstructural properties from macroscopic mechanical response journal, September 2016

Modified error in constitutive equations (MECE) approach for ultrasound elastography journal, October 2017

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods journal, August 2012

Recovery of cellular traction in three-dimensional nonlinear hyperelastic matrices journal, February 2017

Quantitative Compression Optical Coherence Elastography as an Inverse Elasticity Problem journal, May 2016

An overview of the Trilinos project journal, September 2005

Inverse problems in elasticity journal, February 2005

A fast hybrid algorithm combining regularized motion tracking and predictive search for reducing the occurrence of large displacement errors journal, April 2011

Computational Methods for Inverse Problems book, January 2002

A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion journal, May 2008

Towards the mechanical characterization of abdominal wall by inverse analysis journal, February 2017

Simultaneous optical flow and source estimation: Space–time discretization and preconditioning journal, October 2015

Visualizing the Stress Distribution Within Vascular Tissues Using Intravascular Ultrasound Elastography: A Preliminary Investigation journal, June 2015

High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers conference, January 2003

Simultaneous full‐waveform inversion for source wavelet and earth model conference, October 2009

Multiparameter material model and source signature full waveform inversion conference, May 2011

Three-dimensional ultrasound imaging journal, January 2005

On the limited memory BFGS method for large scale optimization
journal, August 1989

Three-dimensional ultrasound imaging
journal, November 2009

Finite Element Analysis of Some Inverse Elasticity Problems
journal, June 1989

Biomechanical imaging of cell stiffness and prestress with subcellular resolution
journal, September 2013

Linear and nonlinear elasticity imaging of soft tissue in vivo : demonstration of feasibility
journal, January 2009

Force traction microscopy: An inverse problem with pointwise observations
journal, November 2012

Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study
journal, January 2009

Large scale parameter estimation problems in frequency-domain elastodynamics using an error in constitutive equation functional
journal, January 2013

Iterative Methods for Total Variation Denoising
journal, January 1996

Cell traction force and measurement methods
journal, January 2007

A numerical method for the inverse problem of cell traction in 3D
journal, August 2012

Three-dimensional Ultrasound Elasticity Imaging on an Automated Breast Volume Scanning System
journal, May 2017

Solution of inverse problems in elasticity imaging using the adjoint method
journal, February 2003

Updating quasi-Newton matrices with limited storage
journal, September 1980

Algorithms for quantitative quasi-static elasticity imaging using force data: ALGORITHMS FOR QUANTITATIVE QUASI-STATIC ELASTICITY IMAGING
journal, August 2014

Traction patterns of tumor cells
journal, April 2008

Investigation of regularization parameters and error estimating in inverse elasticity problems
journal, March 1994

Model-based elastography: a survey of approaches to the inverse elasticity problem
journal, January 2012

High Resolution Traction Force Microscopy Based on Experimental and Computational Advances
journal, January 2008

Simultaneous identification of unknown groundwater pollution sources and estimation of aquifer parameters
journal, September 2009

Bayesian estimation of heat flux and thermal diffusivity using liquid crystal thermography
journal, January 2015

Cellular Traction as an Inverse Problem
journal, January 2006

A nonlinear elasticity phantom containing spherical inclusions
journal, July 2012

Direct error in constitutive equation formulation for plane stress inverse elasticity problem
journal, February 2017

Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem
journal, July 2004

Simultaneous Inverse Identification of Transient Thermal Properties and Heat Sources Using Sparse Sensor Information
journal, December 2007

Simultaneous parameter estimation and contaminant source characterization for coupled groundwater flow and contaminant transport modelling
journal, July 1992

Efficient determination of multiple regularization parameters in a generalized L-curve framework
journal, July 2002

Inferring spatial variations of microstructural properties from macroscopic mechanical response
journal, September 2016

Modified error in constitutive equations (MECE) approach for ultrasound elastography
journal, October 2017

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods
journal, August 2012

Recovery of cellular traction in three-dimensional nonlinear hyperelastic matrices
journal, February 2017

Quantitative Compression Optical Coherence Elastography as an Inverse Elasticity Problem
journal, May 2016

An overview of the Trilinos project
journal, September 2005

Inverse problems in elasticity
journal, February 2005

A fast hybrid algorithm combining regularized motion tracking and predictive search for reducing the occurrence of large displacement errors
journal, April 2011

Computational Methods for Inverse Problems
book, January 2002

A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion
journal, May 2008

Towards the mechanical characterization of abdominal wall by inverse analysis
journal, February 2017

Simultaneous optical flow and source estimation: Space–time discretization and preconditioning
journal, October 2015

Visualizing the Stress Distribution Within Vascular Tissues Using Intravascular Ultrasound Elastography: A Preliminary Investigation
journal, June 2015

High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
conference, January 2003

Simultaneous full‐waveform inversion for source wavelet and earth model
conference, October 2009

Multiparameter material model and source signature full waveform inversion
conference, May 2011

Three-dimensional ultrasound imaging
journal, January 2005