Abstract

We obtain vibro-acoustic (VA) spectral signatures of a remotely palpated region in tissue or tissue-like objects through diffusing-wave spectroscopy (DWS) measurements. Remote application of force is through focused ultrasound, and the spectral signatures correspond to vibrational modes of the focal volume (also called the ROI) excited through ultrasound forcing. In DWS, one recovers the time evolution of mean-square displacement (MSD) of Brownian particles from the measured decay of intensity autocorrelation of light, adapted also to local particles pertaining only to the ROI. We observe that the plateau of the MSD-versus-time curve has noisy fluctuations when ultrasound is applied, which disappear when forcing is removed. It is shown that the spectrum of fluctuations contains peaks corresponding to some of the modes of vibration of the ROI. This enables us to measure the vibrational modes carried by VA waves. We also show recovery of components of the orthotropic elastic tensor pertaining to the material of the ROI from the measured vibrational modes. We first recover the elastic constants for agar slabs, which are verified to be isotropic. Thereafter, we repeat the exercise on fat recovered from pork back tissue, which, from these measurements, is seen to be orthotropic. We validate some of our present measurements through independent runs in a rheometer. The present work is the first step taken, to the best of our knowledge, to characterize biological tissue on the basis of the anisotropic elasticity property, which may potentially aid in the diagnosis and tracking of the progress of cancer in soft-tissue organs.

© 2017 Optical Society of America

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References

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  8. F. G. Mitri and R. R. Kinnick, “Vibroacoustography imaging of kidney stones in vitro,” IEEE Trans. Biomed. Eng. 59, 248–254 (2012).
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    [Crossref]
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    [Crossref]
  12. D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  31. R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
    [Crossref]
  32. M. Priestley, “Power spectral analysis of non-stationary random processes,” J. Sound Vibration 6, 86–97 (1967).
    [Crossref]
  33. N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275, 1920–1922 (1997).
    [Crossref]
  34. S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
    [Crossref]
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    [Crossref]
  37. M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
    [Crossref]
  38. D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).
    [Crossref]
  39. M. Venugopal, R. M. Vasu, and D. Roy, “An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems,” IEEE Trans. Autom. Control 61, 823–828 (2016).
    [Crossref]
  40. T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29, 387–398 (2010).
    [Crossref]

2017 (2)

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

D. Mazumder, R. M. Vasu, D. Roy, and R. Kanhirodan, “A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals,” Int. J. Hyperthermia 33, 1–10 (2017).
[Crossref]

2016 (1)

M. Venugopal, R. M. Vasu, and D. Roy, “An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems,” IEEE Trans. Autom. Control 61, 823–828 (2016).
[Crossref]

2015 (1)

S. Sarkar, S. R. Chowdhury, D. Roy, and R. M. Vasu, “Internal noise-driven generalized Langevin equation from a nonlocal continuum model,” Phys. Rev. E 92, 022150 (2015).
[Crossref]

2014 (2)

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

2012 (1)

F. G. Mitri and R. R. Kinnick, “Vibroacoustography imaging of kidney stones in vitro,” IEEE Trans. Biomed. Eng. 59, 248–254 (2012).
[Crossref]

2011 (2)

2010 (2)

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29, 387–398 (2010).
[Crossref]

J. Heikkilä, L. Curiel, and K. Hynynen, “Local harmonic motion monitoring of focused ultrasound surgery—a simulation model,” IEEE Trans. Biomed. Eng. 57, 185–193 (2010).
[Crossref]

2009 (1)

B. Banerjee, D. Roy, and R. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).
[Crossref]

2008 (2)

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).
[Crossref]

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

2007 (1)

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

2005 (2)

X. Zhang, R. R. Kinnick, M. Fatemi, and J. F. Greenleaf, “Noninvasive method for estimation of complex elastic modulus of arterial vessels,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 52, 642–652 (2005).
[Crossref]

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
[Crossref]

2004 (2)

B. J. Zadler, J. H. Le Rousseau, J. A. Scales, and M. L. Smith, “Resonant ultrasound spectroscopy: theory and application,” Geophys. J. Int. 156, 154–169 (2004).
[Crossref]

E. Konofagou, M. Ottensmeyer, S. Agabian, S. Dawson, and K. Hynynen, “Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus,” Ultrasonics 42, 951–956 (2004).
[Crossref]

2003 (2)

E. E. Konofagou and K. Hynynen, “Localized harmonic motion imaging: theory, simulations and experiments,” Ultrasound Med. Biol. 29, 1405–1413 (2003).
[Crossref]

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
[Crossref]

2002 (3)

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey, “Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibility,” Ultrasound Med. Biol. 28, 227–235 (2002).
[Crossref]

2001 (1)

F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, “Diffusing-wave spectroscopy of nonergodic media,” Phys. Rev. E 63, 061404 (2001).
[Crossref]

2000 (1)

S. Romer, F. Scheffold, and P. Schurtenberger, “Sol-gel transition of concentrated colloidal suspensions,” Phys. Rev. Lett. 85, 4980–4983 (2000).
[Crossref]

1999 (1)

M. Fatemi and J. F. Greenleaf, “Vibro-acoustography: an imaging modality based on ultrasound-stimulated acoustic emission,” Proc. Natl. Acad. Sci. USA 96, 6603–6608 (1999).
[Crossref]

1998 (1)

M. Fatemi and J. F. Greenleaf, “Ultrasound-stimulated vibro-acoustic spectrography,” Science 280, 82–85 (1998).
[Crossref]

1997 (3)

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

G. Maret, “Diffusing-wave spectroscopy,” Curr. Opin. Colloid Interface Sci. 2, 251–257 (1997).
[Crossref]

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275, 1920–1922 (1997).
[Crossref]

1991 (1)

W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162 (1991).
[Crossref]

1973 (1)

R. Zwanzig, “Nonlinear generalized Langevin equations,” J. Stat. Phys. 9, 215–220 (1973).
[Crossref]

1967 (1)

M. Priestley, “Power spectral analysis of non-stationary random processes,” J. Sound Vibration 6, 86–97 (1967).
[Crossref]

Agabian, S.

E. Konofagou, M. Ottensmeyer, S. Agabian, S. Dawson, and K. Hynynen, “Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus,” Ultrasonics 42, 951–956 (2004).
[Crossref]

Alizad, A.

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

A. Alizad, J. Greenleaf, and M. Fatemi, “Selected applications of dynamic radiation force of ultrasound in biomedicine,” in 11th Mediterranean Conference on Medical and Biomedical Engineering and Computing (Springer, 2007), pp. 1021–1024.

Anderson, J. L.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
[Crossref]

Aquino, W.

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

Asokan, S.

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

Azhari, H.

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29, 387–398 (2010).
[Crossref]

Bandyopadhyay, R.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
[Crossref]

Banerjee, B.

B. Banerjee, D. Roy, and R. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).
[Crossref]

Barannik, E.

E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

Bell, T. M.

W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162 (1991).
[Crossref]

Bishop, C. H.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
[Crossref]

Brigham, J. C.

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

Chandran, R. S.

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

R. S. Chandran, D. Roy, R. Kanhirodan, R. M. Vasu, and C. U. Devi, “Ultrasound modulated optical tomography: Young’s modulus of the insonified region from measurement of natural frequency of vibration,” Opt. Express 19, 22837–22850 (2011).
[Crossref]

Chowdhury, S.

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

Chowdhury, S. R.

S. Sarkar, S. R. Chowdhury, D. Roy, and R. M. Vasu, “Internal noise-driven generalized Langevin equation from a nonlocal continuum model,” Phys. Rev. E 92, 022150 (2015).
[Crossref]

Cubeddu, R.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

Curiel, L.

J. Heikkilä, L. Curiel, and K. Hynynen, “Local harmonic motion monitoring of focused ultrasound surgery—a simulation model,” IEEE Trans. Biomed. Eng. 57, 185–193 (2010).
[Crossref]

Dance, S. L.

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).
[Crossref]

Davis, B. J.

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

Dawson, S.

E. Konofagou, M. Ottensmeyer, S. Agabian, S. Dawson, and K. Hynynen, “Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus,” Ultrasonics 42, 951–956 (2004).
[Crossref]

Devi, C. U.

Dixon, P.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
[Crossref]

Doyley, M.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Durian, D.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
[Crossref]

Durian, D. J.

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275, 1920–1922 (1997).
[Crossref]

Emelianov, S.

E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

Eringen, A.

A. Eringen, Continuum Physics, Volume 4: Polar and Nonlocal Field Theories (Academic, 1976), p. 288.

Fatemi, M.

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

X. Zhang, R. R. Kinnick, M. Fatemi, and J. F. Greenleaf, “Noninvasive method for estimation of complex elastic modulus of arterial vessels,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 52, 642–652 (2005).
[Crossref]

M. Fatemi and J. F. Greenleaf, “Vibro-acoustography: an imaging modality based on ultrasound-stimulated acoustic emission,” Proc. Natl. Acad. Sci. USA 96, 6603–6608 (1999).
[Crossref]

M. Fatemi and J. F. Greenleaf, “Ultrasound-stimulated vibro-acoustic spectrography,” Science 280, 82–85 (1998).
[Crossref]

A. Alizad, J. Greenleaf, and M. Fatemi, “Selected applications of dynamic radiation force of ultrasound in biomedicine,” in 11th Mediterranean Conference on Medical and Biomedical Engineering and Computing (Springer, 2007), pp. 1021–1024.

Girnyk, A.

E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

Gittings, A.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
[Crossref]

Glozman, T.

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29, 387–398 (2010).
[Crossref]

Greenleaf, J.

A. Alizad, J. Greenleaf, and M. Fatemi, “Selected applications of dynamic radiation force of ultrasound in biomedicine,” in 11th Mediterranean Conference on Medical and Biomedical Engineering and Computing (Springer, 2007), pp. 1021–1024.

Greenleaf, J. F.

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

X. Zhang, R. R. Kinnick, M. Fatemi, and J. F. Greenleaf, “Noninvasive method for estimation of complex elastic modulus of arterial vessels,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 52, 642–652 (2005).
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Hamill, T. M.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
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Heikkilä, J.

J. Heikkilä, L. Curiel, and K. Hynynen, “Local harmonic motion monitoring of focused ultrasound surgery—a simulation model,” IEEE Trans. Biomed. Eng. 57, 185–193 (2010).
[Crossref]

Hood, M.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Huang, Z.

Hynynen, K.

J. Heikkilä, L. Curiel, and K. Hynynen, “Local harmonic motion monitoring of focused ultrasound surgery—a simulation model,” IEEE Trans. Biomed. Eng. 57, 185–193 (2010).
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E. Konofagou, M. Ottensmeyer, S. Agabian, S. Dawson, and K. Hynynen, “Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus,” Ultrasonics 42, 951–956 (2004).
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E. E. Konofagou and K. Hynynen, “Localized harmonic motion imaging: theory, simulations and experiments,” Ultrasound Med. Biol. 29, 1405–1413 (2003).
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D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

D. Mazumder, R. M. Vasu, D. Roy, and R. Kanhirodan, “A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals,” Int. J. Hyperthermia 33, 1–10 (2017).
[Crossref]

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

R. S. Chandran, D. Roy, R. Kanhirodan, R. M. Vasu, and C. U. Devi, “Ultrasound modulated optical tomography: Young’s modulus of the insonified region from measurement of natural frequency of vibration,” Opt. Express 19, 22837–22850 (2011).
[Crossref]

Kennedy, F.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Kinnick, R. R.

F. G. Mitri and R. R. Kinnick, “Vibroacoustography imaging of kidney stones in vitro,” IEEE Trans. Biomed. Eng. 59, 248–254 (2012).
[Crossref]

X. Zhang, R. R. Kinnick, M. Fatemi, and J. F. Greenleaf, “Noninvasive method for estimation of complex elastic modulus of arterial vessels,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 52, 642–652 (2005).
[Crossref]

Konofagou, E.

E. Konofagou, M. Ottensmeyer, S. Agabian, S. Dawson, and K. Hynynen, “Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus,” Ultrasonics 42, 951–956 (2004).
[Crossref]

Konofagou, E. E.

E. E. Konofagou and K. Hynynen, “Localized harmonic motion imaging: theory, simulations and experiments,” Ultrasound Med. Biol. 29, 1405–1413 (2003).
[Crossref]

Le Rousseau, J. H.

B. J. Zadler, J. H. Le Rousseau, J. A. Scales, and M. L. Smith, “Resonant ultrasound spectroscopy: theory and application,” Geophys. J. Int. 156, 154–169 (2004).
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D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).
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G. Maret, “Diffusing-wave spectroscopy,” Curr. Opin. Colloid Interface Sci. 2, 251–257 (1997).
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E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

Mazumder, D.

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

D. Mazumder, R. M. Vasu, D. Roy, and R. Kanhirodan, “A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals,” Int. J. Hyperthermia 33, 1–10 (2017).
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Menon, N.

N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow,” Science 275, 1920–1922 (1997).
[Crossref]

Migliori, A.

W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162 (1991).
[Crossref]

Mitri, F. G.

F. G. Mitri and R. R. Kinnick, “Vibroacoustography imaging of kidney stones in vitro,” IEEE Trans. Biomed. Eng. 59, 248–254 (2012).
[Crossref]

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

Mynderse, L. A.

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

Nichols, N. K.

D. M. Livings, S. L. Dance, and N. K. Nichols, “Unbiased ensemble square root filters,” Physica D 237, 1021–1028 (2008).
[Crossref]

Nightingale, K.

K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey, “Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibility,” Ultrasound Med. Biol. 28, 227–235 (2002).
[Crossref]

Nightingale, R.

K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey, “Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibility,” Ultrasound Med. Biol. 28, 227–235 (2002).
[Crossref]

Ottensmeyer, M.

E. Konofagou, M. Ottensmeyer, S. Agabian, S. Dawson, and K. Hynynen, “Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus,” Ultrasonics 42, 951–956 (2004).
[Crossref]

Paulsen, K.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Pifferi, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

Poplack, S.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Priestley, M.

M. Priestley, “Power spectral analysis of non-stationary random processes,” J. Sound Vibration 6, 86–97 (1967).
[Crossref]

Qin, X.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Rao, G. V.

D. Roy and G. V. Rao, Stochastic Dynamics, Filtering and Optimization (Cambridge University, 2017).

Reinert, R. A.

W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162 (1991).
[Crossref]

Romer, S.

F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, “Diffusing-wave spectroscopy of nonergodic media,” Phys. Rev. E 63, 061404 (2001).
[Crossref]

S. Romer, F. Scheffold, and P. Schurtenberger, “Sol-gel transition of concentrated colloidal suspensions,” Phys. Rev. Lett. 85, 4980–4983 (2000).
[Crossref]

Roy, D.

D. Mazumder, R. M. Vasu, D. Roy, and R. Kanhirodan, “A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals,” Int. J. Hyperthermia 33, 1–10 (2017).
[Crossref]

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

M. Venugopal, R. M. Vasu, and D. Roy, “An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems,” IEEE Trans. Autom. Control 61, 823–828 (2016).
[Crossref]

S. Sarkar, S. R. Chowdhury, D. Roy, and R. M. Vasu, “Internal noise-driven generalized Langevin equation from a nonlocal continuum model,” Phys. Rev. E 92, 022150 (2015).
[Crossref]

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

R. S. Chandran, D. Roy, R. Kanhirodan, R. M. Vasu, and C. U. Devi, “Ultrasound modulated optical tomography: Young’s modulus of the insonified region from measurement of natural frequency of vibration,” Opt. Express 19, 22837–22850 (2011).
[Crossref]

B. Banerjee, D. Roy, and R. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).
[Crossref]

D. Roy and G. V. Rao, Stochastic Dynamics, Filtering and Optimization (Cambridge University, 2017).

Sarkar, S.

S. Sarkar, S. R. Chowdhury, D. Roy, and R. M. Vasu, “Internal noise-driven generalized Langevin equation from a nonlocal continuum model,” Phys. Rev. E 92, 022150 (2015).
[Crossref]

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

Sarvazyan, A.

E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

Scales, J. A.

B. J. Zadler, J. H. Le Rousseau, J. A. Scales, and M. L. Smith, “Resonant ultrasound spectroscopy: theory and application,” Geophys. J. Int. 156, 154–169 (2004).
[Crossref]

Scheffold, F.

F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, “Diffusing-wave spectroscopy of nonergodic media,” Phys. Rev. E 63, 061404 (2001).
[Crossref]

S. Romer, F. Scheffold, and P. Schurtenberger, “Sol-gel transition of concentrated colloidal suspensions,” Phys. Rev. Lett. 85, 4980–4983 (2000).
[Crossref]

Schurtenberger, P.

F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, “Diffusing-wave spectroscopy of nonergodic media,” Phys. Rev. E 63, 061404 (2001).
[Crossref]

S. Romer, F. Scheffold, and P. Schurtenberger, “Sol-gel transition of concentrated colloidal suspensions,” Phys. Rev. Lett. 85, 4980–4983 (2000).
[Crossref]

Skipetrov, S.

F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, “Diffusing-wave spectroscopy of nonergodic media,” Phys. Rev. E 63, 061404 (2001).
[Crossref]

Slaughter, W.

W. Slaughter, The Linearized Theory of Elasticity (Springer, 2002).

Smith, M. L.

B. J. Zadler, J. H. Le Rousseau, J. A. Scales, and M. L. Smith, “Resonant ultrasound spectroscopy: theory and application,” Geophys. J. Int. 156, 154–169 (2004).
[Crossref]

Soo, M. S.

K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey, “Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibility,” Ultrasound Med. Biol. 28, 227–235 (2002).
[Crossref]

Suh, S.

R. Bandyopadhyay, A. Gittings, S. Suh, P. Dixon, and D. Durian, “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev. Sci. Instrum. 76, 093110 (2005).
[Crossref]

Taroni, P.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

Tippett, M. K.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
[Crossref]

Torricelli, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

Tovstiak, V.

E. Barannik, A. Girnyk, V. Tovstiak, A. Marusenko, S. Emelianov, and A. Sarvazyan, “Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro,” Ultrasonics 40, 849–852 (2002).
[Crossref]

Trahey, G.

K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey, “Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibility,” Ultrasound Med. Biol. 28, 227–235 (2002).
[Crossref]

Umesh, S.

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

Valentini, G.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

Van Houten, E.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Vasu, R.

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

B. Banerjee, D. Roy, and R. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).
[Crossref]

Vasu, R. M.

D. Mazumder, R. M. Vasu, D. Roy, and R. Kanhirodan, “A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals,” Int. J. Hyperthermia 33, 1–10 (2017).
[Crossref]

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

M. Venugopal, R. M. Vasu, and D. Roy, “An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems,” IEEE Trans. Autom. Control 61, 823–828 (2016).
[Crossref]

S. Sarkar, S. R. Chowdhury, D. Roy, and R. M. Vasu, “Internal noise-driven generalized Langevin equation from a nonlocal continuum model,” Phys. Rev. E 92, 022150 (2015).
[Crossref]

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

R. S. Chandran, D. Roy, R. Kanhirodan, R. M. Vasu, and C. U. Devi, “Ultrasound modulated optical tomography: Young’s modulus of the insonified region from measurement of natural frequency of vibration,” Opt. Express 19, 22837–22850 (2011).
[Crossref]

Venugopal, M.

M. Venugopal, R. M. Vasu, and D. Roy, “An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems,” IEEE Trans. Autom. Control 61, 823–828 (2016).
[Crossref]

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

Visscher, W. M.

W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162 (1991).
[Crossref]

Wang, R. K.

Weaver, J.

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Whitaker, J. S.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
[Crossref]

Wilson, T. M.

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

Zadler, B. J.

B. J. Zadler, J. H. Le Rousseau, J. A. Scales, and M. L. Smith, “Resonant ultrasound spectroscopy: theory and application,” Geophys. J. Int. 156, 154–169 (2004).
[Crossref]

Zhang, X.

X. Zhang, R. R. Kinnick, M. Fatemi, and J. F. Greenleaf, “Noninvasive method for estimation of complex elastic modulus of arterial vessels,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 52, 642–652 (2005).
[Crossref]

Zwanzig, R.

R. Zwanzig, “Nonlinear generalized Langevin equations,” J. Stat. Phys. 9, 215–220 (1973).
[Crossref]

Curr. Opin. Colloid Interface Sci. (1)

G. Maret, “Diffusing-wave spectroscopy,” Curr. Opin. Colloid Interface Sci. 2, 251–257 (1997).
[Crossref]

Geophys. J. Int. (1)

B. J. Zadler, J. H. Le Rousseau, J. A. Scales, and M. L. Smith, “Resonant ultrasound spectroscopy: theory and application,” Geophys. J. Int. 156, 154–169 (2004).
[Crossref]

IEEE Trans. Autom. Control (1)

M. Venugopal, R. M. Vasu, and D. Roy, “An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems,” IEEE Trans. Autom. Control 61, 823–828 (2016).
[Crossref]

IEEE Trans. Biomed. Eng. (3)

J. Heikkilä, L. Curiel, and K. Hynynen, “Local harmonic motion monitoring of focused ultrasound surgery—a simulation model,” IEEE Trans. Biomed. Eng. 57, 185–193 (2010).
[Crossref]

F. G. Mitri and R. R. Kinnick, “Vibroacoustography imaging of kidney stones in vitro,” IEEE Trans. Biomed. Eng. 59, 248–254 (2012).
[Crossref]

F. G. Mitri, B. J. Davis, A. Alizad, J. F. Greenleaf, T. M. Wilson, L. A. Mynderse, and M. Fatemi, “Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility,” IEEE Trans. Biomed. Eng. 55, 2584–2592 (2008).
[Crossref]

IEEE Trans. Ultrason. Ferroelect. Freq. Control (1)

X. Zhang, R. R. Kinnick, M. Fatemi, and J. F. Greenleaf, “Noninvasive method for estimation of complex elastic modulus of arterial vessels,” IEEE Trans. Ultrason. Ferroelect. Freq. Control 52, 642–652 (2005).
[Crossref]

Int. J. Hyperthermia (1)

D. Mazumder, R. M. Vasu, D. Roy, and R. Kanhirodan, “A remote temperature sensor for an ultrasound hyperthermia system using the acoustic signal derived from the heating signals,” Int. J. Hyperthermia 33, 1–10 (2017).
[Crossref]

J. Acoust. Soc. Am. (1)

W. M. Visscher, A. Migliori, T. M. Bell, and R. A. Reinert, “On the normal modes of free vibration of inhomogeneous and anisotropic elastic objects,” J. Acoust. Soc. Am. 90, 2154–2162 (1991).
[Crossref]

J. Appl. Phys. (1)

J. C. Brigham, W. Aquino, F. G. Mitri, J. F. Greenleaf, and M. Fatemi, “Inverse estimation of visco-elastic material properties for solids immersed in fluidsusing vibro-acoustic techniques,” J. Appl. Phys. 101, 023509 (2007).
[Crossref]

J. Sound Vibration (1)

M. Priestley, “Power spectral analysis of non-stationary random processes,” J. Sound Vibration 6, 86–97 (1967).
[Crossref]

J. Stat. Phys. (1)

R. Zwanzig, “Nonlinear generalized Langevin equations,” J. Stat. Phys. 9, 215–220 (1973).
[Crossref]

J. Ultrasound Med. (1)

T. Glozman and H. Azhari, “A method for characterization of tissue elastic properties combining ultrasonic computed tomography with elastography,” J. Ultrasound Med. 29, 387–398 (2010).
[Crossref]

Med. Phys. (1)

J. Weaver, M. Doyley, E. Van Houten, M. Hood, X. Qin, F. Kennedy, S. Poplack, and K. Paulsen, “Evidence of the anisotropic nature of the mechanical properties of breast tissue,” Med. Phys. 29, 1291 (2002).

Mon. Weather Rev. (1)

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. S. Whitaker, “Ensemble square root filters,” Mon. Weather Rev. 131, 1485–1490 (2003).
[Crossref]

Opt. Express (2)

Phys. Med. Biol. (3)

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[Crossref]

D. Mazumder, S. Umesh, R. M. Vasu, D. Roy, R. Kanhirodan, and S. Asokan, “Quantitative vibro-acoustography of tissue-like objects by measurement of resonant modes,” Phys. Med. Biol. 62, 107–126 (2017).
[Crossref]

B. Banerjee, D. Roy, and R. Vasu, “A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements,” Phys. Med. Biol. 54, 285–305 (2009).
[Crossref]

Phys. Rev. E (3)

R. S. Chandran, S. Sarkar, R. Kanhirodan, D. Roy, and R. M. Vasu, “Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume,” Phys. Rev. E 90, 012303 (2014).
[Crossref]

S. Sarkar, S. R. Chowdhury, D. Roy, and R. M. Vasu, “Internal noise-driven generalized Langevin equation from a nonlocal continuum model,” Phys. Rev. E 92, 022150 (2015).
[Crossref]

F. Scheffold, S. Skipetrov, S. Romer, and P. Schurtenberger, “Diffusing-wave spectroscopy of nonergodic media,” Phys. Rev. E 63, 061404 (2001).
[Crossref]

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[Crossref]

Physica D (2)

S. Sarkar, S. Chowdhury, M. Venugopal, R. Vasu, and D. Roy, “A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification,” Physica D 270, 46–59 (2014).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (10)

Fig. 1.
Fig. 1.

Schematic representation of the object (slab) as an orthotropic material showing axes of symmetry.

Fig. 2.
Fig. 2.

(a) Variation of the storage moduli versus frequency of the agar slabs as measured by rheometer. (b) Same as (a) but showing loss moduli.

Fig. 3.
Fig. 3.

Schematics of the experimental setup. The ergodic medium-object slab composite object, immersed in a water bath (maintained at 27 ± 0.5 °C) is insonified by the intersecting focal volume (ROI) of two ultrasound transducers. The ROI is illuminated by a coherent beam from a He–Ne laser. The scattered light is detected by a single-mode fiber and given to a PMT. The output from the PMT after signal conditioning is input to the correlator and then to the personal computer. PA, power amplifier; US, ultrasound; ROI, region of interest; DCFG, dual channel function generator; CORR, correlator; COM, personal computer.

Fig. 4.
Fig. 4.

Variation of MSD with τ from the measured g 1 ( τ ) from the pork slab. The thin curve corresponds to when the ultrasound is on, and the thick curve to when it is off.

Fig. 5.
Fig. 5.

Comparison of MSD versus τ plot from a pork slab, obtained experimentally (thick curve) with the corresponding one obtained through solving the GLE [Eq. (3)] (thin curve).

Fig. 6.
Fig. 6.

(a) Power spectrum obtained from the plateau of the experimentally obtained MSD versus τ curve from 0.5% agar slab, displaying the peaks (resonant modes) at 75.5, 78.7, 84.2, and 90.4 Hz. (b) Same as (a), but for 1% agar slab. The peaks are at 108.0, 110.0, 135.0, and 142.0 Hz. (c) Same as (a), but for 1.5% agar slab. The peaks are at 135.8, 151.0, 165.0, and 191.4 Hz. (d) Same as (a), but for the pork slab. The peaks are at 214.8, 228.9, 253.9, and 269.5 Hz.

Fig. 7.
Fig. 7.

Estimated Young’s moduli, E 1 , E 2 , and E 3 from the measured resonant modes for slabs (a) with 0.5% agar, (b) with 1% agar, (c) with 1.5% agar, and (d) pork fat. Notice that for pork, being orthotropic, E 1 , E 2 , and E 3 are different at convergence. For all four cases, the object was modeled to be linear, orthotropic material. Inset shows the initial convergence with assumption of isotropy.

Fig. 8.
Fig. 8.

Same as Fig. 7, but showing shear moduli (a) with 0.5% agar, (b) with 1% agar, (c) with 1.5% agar, and (d) for pork fat. Notice that for pork, being orthotropic, G 23 , G 13 , and G 12 are different at convergence. For all four cases, the object was modeled to be linear, orthotropic material. Inset shows the initial convergence with assumption of isotropy.

Fig. 9.
Fig. 9.

Pork back fat used during the experiment with the coordinate axis (inset), representing the material directions. The surface visible in this figure was just below the skin, as can be confirmed from its grainy appearance.

Fig. 10.
Fig. 10.

Behavior of root-mean-square error with iteration number during the recovery of the orthotropic elastic parameters of pork fat. During the first 20 iterations, the sample was modeled isotropic, and in the next 100, orthotropic.

Tables (3)

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Table 1. Verification of the Experimentally Measured Resonant Modes of the Objects through Those Computed Using a Modal Analysis [23] a

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Table 2. Comparison of Elastic Parameters Estimated by the Present Method with Measurements from Rheometer or Published Results, as the Case May Be

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Table 3. Error in Recovered Young’s and Shear Moduli of Pork Fat Owing to Error in the Measured Modal Frequencies

Equations (13)

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1 c 2 p ¨ a 0 . p a 0 = S 0 ( r ) cos ( 2 π Δ ϖ t ) , r Ω Ω ROI .
ρ u ¨ = · σ + f 0 ( r ) cos ( 2 π Δ ϖ t ) .
m u ¨ p + k u p + 0 t η ( t s ) u ˙ p ( s ) d s = f ( t ) + ξ ( t ) + 0 t W s t ( t s ) u p ( s ) d s .
ω 2 M · α = Γ · α ,
( σ 11 σ 22 σ 33 σ 23 σ 13 σ 12 ) = [ E 1 ( 1 ν 23 ν 32 ) ϒ E 1 ( ν 21 + ν 31 ν 23 ) ϒ E 1 ( ν 31 + ν 21 ν 32 ) ϒ 0 0 0 E 2 ( 1 ν 13 ν 31 ) ϒ E 2 ( ν 32 + ν 12 ν 31 ) ϒ 0 0 0 E 3 ( 1 ν 12 ν 21 ) ϒ 0 0 0 Symmetric G 23 0 0 G 13 0 G 12 ] ( ϵ 11 ϵ 22 ϵ 33 ϵ 23 ϵ 13 ϵ 12 ) ,
M ( r , τ ) = exp [ ( L l * ) k 0 2 Δ r 2 ( r , τ ) ] .
( ω 2 M Γ ) α = 0 .
det ( ω 2 M Γ ) = 0 .
X ˙ t = η t ,
m t = Θ ( X t ) + γ t ,
E 1 , E 2 , E 3 , G 23 , G 31 , G 12 > 0 ,
ν i j E i = ν j i E j i , j = 1 , 2 , 3 ,
ν 21 ν 32 ν 13 < 1 ν 21 2 E 1 E 2 ν 32 2 E 2 E 3 ν 13 2 E 3 E 1 2 < 1 2 .

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