American Institute of Mathematical Sciences

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November  2010, 4(4): 665-673. doi: 10.3934/ipi.2010.4.665

Synthetic focusing in ultrasound modulated tomography

Peter Kuchment 1, and  Leonid Kunyansky 2,

1. 

Mathematics Department, Texas A&M University, College Station, TX 77843-3368
2. 

Mathematics Department, University of Arizona, Tucson, AZ 85721, United States

Received  January 2009 Revised  May 2009 Published  September 2010

Several hybrid tomographic methods utilizing ultrasound modulation have been introduced lately. Success of these methods hinges on the feasibility of focusing ultrasound waves at an arbitrary point of interest. Such focusing, however, is difficult to achieve in practice. We thus propose a way to avoid the use of focused waves through what we call synthetic focusing, i.e. by reconstructing the would-be response to the focused modulation from the measurements corresponding to realistic unfocused waves. Examples of reconstructions from simulated data are provided. This non-technical paper describes only the general concept, while technical details will appear elsewhere.
Keywords: spherical means, optical tomography, impedance tomography., thermoacoustic tomography, Radon transform.
Mathematics Subject Classification: Primary: 44A12, 92C55; Secondary: 65R3.
Citation: Peter Kuchment, Leonid Kunyansky. Synthetic focusing in ultrasound modulated tomography. Inverse Problems & Imaging, 2010, 4 (4) : 665-673. doi: 10.3934/ipi.2010.4.665
References:
[1]

M. Agranovsky and P. Kuchment, Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,, Inverse Problems, 23 (2007), 2089.  doi: doi:10.1088/0266-5611/23/5/016.  Google Scholar

[2]

M. Agranovsky, P. Kuchment and L. Kunyansky, On reconstruction formulas and algorithms for the thermoacoustic and photoacoustic tomography,, Ch. 8 in Ref 30, (): 89.   Google Scholar

[3]

M. Agranovsky, P. Kuchment and E. T. Quinto, Range descriptions for the spherical mean Radon transform,, J. Funct. Anal., 248 (2007), 344.  doi: doi:10.1016/j.jfa.2007.03.022.  Google Scholar

[4]

M. Agranovsky and E. T. Quinto, Injectivity sets for the Radon transform over circles and complete systems of radial functions,, J. Funct. Anal., 139 (1996), 383.  doi: doi:10.1006/jfan.1996.0090.  Google Scholar

[5]

M. Allmaras and W. Bangerth, Reconstructions in Ultrasound Modulated Optical Tomography,, Preprint, ().   Google Scholar

[6]

H. Ammari, "An Introduction to Mathematics of Emerging Biomedical Imaging,", Springer-Verlag, (2008).   Google Scholar

[7]

H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter and M. Fink, Electrical impedance tomography by elastic deformation,, SIAM J. Appl. Math., 68 (2008), 1557.  doi: doi:10.1137/070686408.  Google Scholar

[8]

D. C. Barber and B. H. Brown, Applied potential tomography,, J. Phys. E.: Sci. Instrum., 17 (1984), 723.  doi: doi:10.1088/0022-3735/17/9/002.  Google Scholar

[9]

L. Borcea, Electrical impedance tomography,, Inverse Problems, 18 (2002).  doi: doi:10.1088/0266-5611/18/6/201.  Google Scholar

[10]

D. Finch, S. Patch and Rakesh, Determining a function from its mean values over a family of spheres,, SIAM J. Math. Anal., 35 (2004), 1213.  doi: doi:10.1137/S0036141002417814.  Google Scholar

[11]

D. Finch and Rakesh, The spherical mean value operator with centers on a sphere,, Inverse Problems, 23 (2007).  doi: doi:10.1088/0266-5611/23/6/S04.  Google Scholar

[12]

D. Finch and Rakesh, Recovering a function from its spherical mean values in two and three dimensions,, In Ref 30, (): 77.   Google Scholar

[13]

B. Gebauer and O. Scherzer, Impedance-acoustic tomography,, SIAM J. Applied Math., 69 (2009), 565.  doi: doi:10.1137/080715123.  Google Scholar

[14]

H. E. Hernandez-Figueroa, M. Zamboni-Rached and E. Recami (Editors), "Localized Waves,", IEEE Press, (2008).   Google Scholar

[15]

M. Kempe, M. Larionov, D. Zaslavsky and A. Z. Genack, Acousto-optic tomography with multiply scattered light,, J. Opt. Soc. Am. A, 14 (1997), 1151.  doi: doi:10.1364/JOSAA.14.001151.  Google Scholar

[16]

P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography,, European J. Appl. Math., 19 (2008), 191.  doi: doi:10.1017/S0956792508007353.  Google Scholar

[17]

P. Kuchment and L. Kunyansky, Ultrasound modulated electric impedance tomography,, in preparation., ().   Google Scholar

[18]

L. A. Kunyansky, Explicit inversion formulae for the spherical mean Radon transform,, Inverse Problems, 23 (2007), 373.  doi: doi:10.1088/0266-5611/23/1/021.  Google Scholar

[19]

B. Lavandier, J. Jossinet and D. Cathignol, Quantitative assessment of ultrasound-induced resistance change in saline solution,, Medical & Biological Engineering & Computing, 38 (2000), 150.  doi: doi:10.1007/BF02344769.  Google Scholar

[20]

B. Lavandier, J. Jossinet and D. Cathignol, Experimental measurement of the acousto-electric interaction signal in saline solution,, Ultrasonics, 38 (2000), 929.  doi: doi:10.1016/S0041-624X(00)00029-9.  Google Scholar

[21]

J. Li and L.-H. Wang, Methods for parallel-detection-based ultrasound-modulated optical tomography,, Applied Optics, 41 (2002), 2079.  doi: doi:10.1364/AO.41.002079.  Google Scholar

[22]

J. Li and L.-H. Wang, Ultrasound-modulated optical computed tomography of biological tissues,, Appl. Phys. Lett., 84 (2004), 1597.  doi: doi:10.1063/1.1651330.  Google Scholar

[23]

H. Nam, "Ultrasound Modulated Optical Tomography,", Ph.D thesis, (2002).   Google Scholar

[24]

H. Nam and D. Dobson, Ultrasound modulated optical tomography,, preprint 2004., (2004).   Google Scholar

[25]

Linh V. Nguyen, A family of inversion formulas in thermoacoustic tomography,, Inverse Probl. Imaging, 3 (2009), 649.  doi: doi:10.3934/ipi.2009.3.649.  Google Scholar

[26]

A. A. Oraevsky and A. A. Karabutov, Optoacoustic tomography,, edited by CRC, (2003), 34.   Google Scholar

[27]

S. K. Patch and O. Scherzer, Photo- and thermo-acoustic imaging (Guest Editors' introduction),, Inverse Problems, 23 (2007).   Google Scholar

[28]

V. V. Tuchin (Editor), "Handbook of Optical Biomedical Diagonstics,", SPIE, (2002).   Google Scholar

[29]

T. Vo-Dinh (Editor), "Biomedical Photonics Handbook,", edited by CRC, (2003).   Google Scholar

[30]

L. H. Wang (Editor), "Photoacoustic imaging and spectroscopy,", CRC Press, (2009).   Google Scholar

[31]

L. V. Wang and H. Wu, "Biomedical Optics. Principles and Imaging,", Wiley-Interscience, (2007).   Google Scholar

[32]

M. Xu and L.-H. V. Wang, Universal back-projection algorithm for photoacoustic computed tomography,, Phys. Rev. E, 71 (2005).  doi: doi:10.1103/PhysRevE.71.016706.  Google Scholar

[33]

M. Xu and L.-H. V. Wang, Photoacoustic imaging in biomedicine,, Review of Scientific Instruments, 77 (2006), 041101.   Google Scholar

[34]

H. Zhang and L. Wang, Acousto-electric tomography,, Proc. SPIE, 5320 (2004), 145.  doi: doi:10.1117/12.532610.  Google Scholar

show all references

References:
[1]

M. Agranovsky and P. Kuchment, Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed,, Inverse Problems, 23 (2007), 2089.  doi: doi:10.1088/0266-5611/23/5/016.  Google Scholar

[2]

M. Agranovsky, P. Kuchment and L. Kunyansky, On reconstruction formulas and algorithms for the thermoacoustic and photoacoustic tomography,, Ch. 8 in Ref 30, (): 89.   Google Scholar

[3]

M. Agranovsky, P. Kuchment and E. T. Quinto, Range descriptions for the spherical mean Radon transform,, J. Funct. Anal., 248 (2007), 344.  doi: doi:10.1016/j.jfa.2007.03.022.  Google Scholar

[4]

M. Agranovsky and E. T. Quinto, Injectivity sets for the Radon transform over circles and complete systems of radial functions,, J. Funct. Anal., 139 (1996), 383.  doi: doi:10.1006/jfan.1996.0090.  Google Scholar

[5]

M. Allmaras and W. Bangerth, Reconstructions in Ultrasound Modulated Optical Tomography,, Preprint, ().   Google Scholar

[6]

H. Ammari, "An Introduction to Mathematics of Emerging Biomedical Imaging,", Springer-Verlag, (2008).   Google Scholar

[7]

H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter and M. Fink, Electrical impedance tomography by elastic deformation,, SIAM J. Appl. Math., 68 (2008), 1557.  doi: doi:10.1137/070686408.  Google Scholar

[8]

D. C. Barber and B. H. Brown, Applied potential tomography,, J. Phys. E.: Sci. Instrum., 17 (1984), 723.  doi: doi:10.1088/0022-3735/17/9/002.  Google Scholar

[9]

L. Borcea, Electrical impedance tomography,, Inverse Problems, 18 (2002).  doi: doi:10.1088/0266-5611/18/6/201.  Google Scholar

[10]

D. Finch, S. Patch and Rakesh, Determining a function from its mean values over a family of spheres,, SIAM J. Math. Anal., 35 (2004), 1213.  doi: doi:10.1137/S0036141002417814.  Google Scholar

[11]

D. Finch and Rakesh, The spherical mean value operator with centers on a sphere,, Inverse Problems, 23 (2007).  doi: doi:10.1088/0266-5611/23/6/S04.  Google Scholar

[12]

D. Finch and Rakesh, Recovering a function from its spherical mean values in two and three dimensions,, In Ref 30, (): 77.   Google Scholar

[13]

B. Gebauer and O. Scherzer, Impedance-acoustic tomography,, SIAM J. Applied Math., 69 (2009), 565.  doi: doi:10.1137/080715123.  Google Scholar

[14]

H. E. Hernandez-Figueroa, M. Zamboni-Rached and E. Recami (Editors), "Localized Waves,", IEEE Press, (2008).   Google Scholar

[15]

M. Kempe, M. Larionov, D. Zaslavsky and A. Z. Genack, Acousto-optic tomography with multiply scattered light,, J. Opt. Soc. Am. A, 14 (1997), 1151.  doi: doi:10.1364/JOSAA.14.001151.  Google Scholar

[16]

P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography,, European J. Appl. Math., 19 (2008), 191.  doi: doi:10.1017/S0956792508007353.  Google Scholar

[17]

P. Kuchment and L. Kunyansky, Ultrasound modulated electric impedance tomography,, in preparation., ().   Google Scholar

[18]

L. A. Kunyansky, Explicit inversion formulae for the spherical mean Radon transform,, Inverse Problems, 23 (2007), 373.  doi: doi:10.1088/0266-5611/23/1/021.  Google Scholar

[19]

B. Lavandier, J. Jossinet and D. Cathignol, Quantitative assessment of ultrasound-induced resistance change in saline solution,, Medical & Biological Engineering & Computing, 38 (2000), 150.  doi: doi:10.1007/BF02344769.  Google Scholar

[20]

B. Lavandier, J. Jossinet and D. Cathignol, Experimental measurement of the acousto-electric interaction signal in saline solution,, Ultrasonics, 38 (2000), 929.  doi: doi:10.1016/S0041-624X(00)00029-9.  Google Scholar

[21]

J. Li and L.-H. Wang, Methods for parallel-detection-based ultrasound-modulated optical tomography,, Applied Optics, 41 (2002), 2079.  doi: doi:10.1364/AO.41.002079.  Google Scholar

[22]

J. Li and L.-H. Wang, Ultrasound-modulated optical computed tomography of biological tissues,, Appl. Phys. Lett., 84 (2004), 1597.  doi: doi:10.1063/1.1651330.  Google Scholar

[23]

H. Nam, "Ultrasound Modulated Optical Tomography,", Ph.D thesis, (2002).   Google Scholar

[24]

H. Nam and D. Dobson, Ultrasound modulated optical tomography,, preprint 2004., (2004).   Google Scholar

[25]

Linh V. Nguyen, A family of inversion formulas in thermoacoustic tomography,, Inverse Probl. Imaging, 3 (2009), 649.  doi: doi:10.3934/ipi.2009.3.649.  Google Scholar

[26]

A. A. Oraevsky and A. A. Karabutov, Optoacoustic tomography,, edited by CRC, (2003), 34.   Google Scholar

[27]

S. K. Patch and O. Scherzer, Photo- and thermo-acoustic imaging (Guest Editors' introduction),, Inverse Problems, 23 (2007).   Google Scholar

[28]

V. V. Tuchin (Editor), "Handbook of Optical Biomedical Diagonstics,", SPIE, (2002).   Google Scholar

[29]

T. Vo-Dinh (Editor), "Biomedical Photonics Handbook,", edited by CRC, (2003).   Google Scholar

[30]

L. H. Wang (Editor), "Photoacoustic imaging and spectroscopy,", CRC Press, (2009).   Google Scholar

[31]

L. V. Wang and H. Wu, "Biomedical Optics. Principles and Imaging,", Wiley-Interscience, (2007).   Google Scholar

[32]

M. Xu and L.-H. V. Wang, Universal back-projection algorithm for photoacoustic computed tomography,, Phys. Rev. E, 71 (2005).  doi: doi:10.1103/PhysRevE.71.016706.  Google Scholar

[33]

M. Xu and L.-H. V. Wang, Photoacoustic imaging in biomedicine,, Review of Scientific Instruments, 77 (2006), 041101.   Google Scholar

[34]

H. Zhang and L. Wang, Acousto-electric tomography,, Proc. SPIE, 5320 (2004), 145.  doi: doi:10.1117/12.532610.  Google Scholar

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