Synthetic focusing in ultrasound modulated tomography

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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

Abstract
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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 and 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), 2089-2102. doi: doi:10.1088/0266-5611/23/5/016.
[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.
[3]	M. Agranovsky, P. Kuchment and E. T. Quinto, Range descriptions for the spherical mean Radon transform, J. Funct. Anal., 248 (2007), 344-386. doi: doi:10.1016/j.jfa.2007.03.022.
[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), 383-414. doi: doi:10.1006/jfan.1996.0090.
[5]	M. Allmaras and W. Bangerth, Reconstructions in Ultrasound Modulated Optical Tomography,, Preprint, ().
[6]	H. Ammari, "An Introduction to Mathematics of Emerging Biomedical Imaging," Springer-Verlag, 2008.
[7]	H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter and M. Fink, Electrical impedance tomography by elastic deformation, SIAM J. Appl. Math., 68 (2008), 1557-1573. doi: doi:10.1137/070686408.
[8]	D. C. Barber and B. H. Brown, Applied potential tomography, J. Phys. E.: Sci. Instrum., 17 (1984), 723-733. doi: doi:10.1088/0022-3735/17/9/002.
[9]	L. Borcea, Electrical impedance tomography, Inverse Problems, 18 (2002), R99-R136. doi: doi:10.1088/0266-5611/18/6/201.
[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), 1213-1240. doi: doi:10.1137/S0036141002417814.
[11]	D. Finch and Rakesh, The spherical mean value operator with centers on a sphere, Inverse Problems, 23 (2007), S37-S50. doi: doi:10.1088/0266-5611/23/6/S04.
[12]	D. Finch and Rakesh, Recovering a function from its spherical mean values in two and three dimensions,, In Ref 30, (): 77.
[13]	B. Gebauer and O. Scherzer, Impedance-acoustic tomography, SIAM J. Applied Math., 69 (2009), 565-576. doi: doi:10.1137/080715123.
[14]	H. E. Hernandez-Figueroa, M. Zamboni-Rached and E. Recami (Editors), "Localized Waves," IEEE Press, J. Wiley & Sons, Inc., Hoboken, NJ 2008.
[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), 1151-1158. doi: doi:10.1364/JOSAA.14.001151.
[16]	P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography, European J. Appl. Math., 19 (2008), 191-224. doi: doi:10.1017/S0956792508007353.
[17]	P. Kuchment and L. Kunyansky, Ultrasound modulated electric impedance tomography,, in preparation., ().
[18]	L. A. Kunyansky, Explicit inversion formulae for the spherical mean Radon transform, Inverse Problems, 23 (2007), 373-383. doi: doi:10.1088/0266-5611/23/1/021.
[19]	B. Lavandier, J. Jossinet and D. Cathignol, Quantitative assessment of ultrasound-induced resistance change in saline solution, Medical & Biological Engineering & Computing, 38 (2000), 150-155. doi: doi:10.1007/BF02344769.
[20]	B. Lavandier, J. Jossinet and D. Cathignol, Experimental measurement of the acousto-electric interaction signal in saline solution, Ultrasonics, 38 (2000), 929-936. doi: doi:10.1016/S0041-624X(00)00029-9.
[21]	J. Li and L.-H. Wang, Methods for parallel-detection-based ultrasound-modulated optical tomography, Applied Optics, 41 (2002), 2079-2084. doi: doi:10.1364/AO.41.002079.
[22]	J. Li and L.-H. Wang, Ultrasound-modulated optical computed tomography of biological tissues, Appl. Phys. Lett., 84 (2004), 1597-1599. doi: doi:10.1063/1.1651330.
[23]	H. Nam, "Ultrasound Modulated Optical Tomography," Ph.D thesis, Texas A&M University, 2002.
[24]	H. Nam and D. Dobson, Ultrasound modulated optical tomography, preprint 2004.
[25]	Linh V. Nguyen, A family of inversion formulas in thermoacoustic tomography, Inverse Probl. Imaging, 3 (2009), 649-675. doi: doi:10.3934/ipi.2009.3.649.
[26]	A. A. Oraevsky and A. A. Karabutov, Optoacoustic tomography, in Ref 29, (2003), 34-1 - 34-34.
[27]	S. K. Patch and O. Scherzer, Photo- and thermo-acoustic imaging (Guest Editors' introduction), Inverse Problems, 23 (2007), S01-S10.
[28]	V. V. Tuchin (Editor), "Handbook of Optical Biomedical Diagonstics," SPIE, Bellingham, WA 2002.
[29]	T. Vo-Dinh (Editor), "Biomedical Photonics Handbook," edited by CRC, Boca Raton, FL, 2003.
[30]	L. H. Wang (Editor), "Photoacoustic imaging and spectroscopy," CRC Press, 2009.
[31]	L. V. Wang and H. Wu, "Biomedical Optics. Principles and Imaging," Wiley-Interscience, 2007.
[32]	M. Xu and L.-H. V. Wang, Universal back-projection algorithm for photoacoustic computed tomography, Phys. Rev. E, 71 (2005), 016706. doi: doi:10.1103/PhysRevE.71.016706.
[33]	M. Xu and L.-H. V. Wang, Photoacoustic imaging in biomedicine, Review of Scientific Instruments, 77 (2006), 041101-01 - 041101-22.
[34]	H. Zhang and L. Wang, Acousto-electric tomography, Proc. SPIE, 5320 (2004), 145-149. doi: doi:10.1117/12.532610.

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), 2089-2102. doi: doi:10.1088/0266-5611/23/5/016.
[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.
[3]	M. Agranovsky, P. Kuchment and E. T. Quinto, Range descriptions for the spherical mean Radon transform, J. Funct. Anal., 248 (2007), 344-386. doi: doi:10.1016/j.jfa.2007.03.022.
[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), 383-414. doi: doi:10.1006/jfan.1996.0090.
[5]	M. Allmaras and W. Bangerth, Reconstructions in Ultrasound Modulated Optical Tomography,, Preprint, ().
[6]	H. Ammari, "An Introduction to Mathematics of Emerging Biomedical Imaging," Springer-Verlag, 2008.
[7]	H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter and M. Fink, Electrical impedance tomography by elastic deformation, SIAM J. Appl. Math., 68 (2008), 1557-1573. doi: doi:10.1137/070686408.
[8]	D. C. Barber and B. H. Brown, Applied potential tomography, J. Phys. E.: Sci. Instrum., 17 (1984), 723-733. doi: doi:10.1088/0022-3735/17/9/002.
[9]	L. Borcea, Electrical impedance tomography, Inverse Problems, 18 (2002), R99-R136. doi: doi:10.1088/0266-5611/18/6/201.
[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), 1213-1240. doi: doi:10.1137/S0036141002417814.
[11]	D. Finch and Rakesh, The spherical mean value operator with centers on a sphere, Inverse Problems, 23 (2007), S37-S50. doi: doi:10.1088/0266-5611/23/6/S04.
[12]	D. Finch and Rakesh, Recovering a function from its spherical mean values in two and three dimensions,, In Ref 30, (): 77.
[13]	B. Gebauer and O. Scherzer, Impedance-acoustic tomography, SIAM J. Applied Math., 69 (2009), 565-576. doi: doi:10.1137/080715123.
[14]	H. E. Hernandez-Figueroa, M. Zamboni-Rached and E. Recami (Editors), "Localized Waves," IEEE Press, J. Wiley & Sons, Inc., Hoboken, NJ 2008.
[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), 1151-1158. doi: doi:10.1364/JOSAA.14.001151.
[16]	P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography, European J. Appl. Math., 19 (2008), 191-224. doi: doi:10.1017/S0956792508007353.
[17]	P. Kuchment and L. Kunyansky, Ultrasound modulated electric impedance tomography,, in preparation., ().
[18]	L. A. Kunyansky, Explicit inversion formulae for the spherical mean Radon transform, Inverse Problems, 23 (2007), 373-383. doi: doi:10.1088/0266-5611/23/1/021.
[19]	B. Lavandier, J. Jossinet and D. Cathignol, Quantitative assessment of ultrasound-induced resistance change in saline solution, Medical & Biological Engineering & Computing, 38 (2000), 150-155. doi: doi:10.1007/BF02344769.
[20]	B. Lavandier, J. Jossinet and D. Cathignol, Experimental measurement of the acousto-electric interaction signal in saline solution, Ultrasonics, 38 (2000), 929-936. doi: doi:10.1016/S0041-624X(00)00029-9.
[21]	J. Li and L.-H. Wang, Methods for parallel-detection-based ultrasound-modulated optical tomography, Applied Optics, 41 (2002), 2079-2084. doi: doi:10.1364/AO.41.002079.
[22]	J. Li and L.-H. Wang, Ultrasound-modulated optical computed tomography of biological tissues, Appl. Phys. Lett., 84 (2004), 1597-1599. doi: doi:10.1063/1.1651330.
[23]	H. Nam, "Ultrasound Modulated Optical Tomography," Ph.D thesis, Texas A&M University, 2002.
[24]	H. Nam and D. Dobson, Ultrasound modulated optical tomography, preprint 2004.
[25]	Linh V. Nguyen, A family of inversion formulas in thermoacoustic tomography, Inverse Probl. Imaging, 3 (2009), 649-675. doi: doi:10.3934/ipi.2009.3.649.
[26]	A. A. Oraevsky and A. A. Karabutov, Optoacoustic tomography, in Ref 29, (2003), 34-1 - 34-34.
[27]	S. K. Patch and O. Scherzer, Photo- and thermo-acoustic imaging (Guest Editors' introduction), Inverse Problems, 23 (2007), S01-S10.
[28]	V. V. Tuchin (Editor), "Handbook of Optical Biomedical Diagonstics," SPIE, Bellingham, WA 2002.
[29]	T. Vo-Dinh (Editor), "Biomedical Photonics Handbook," edited by CRC, Boca Raton, FL, 2003.
[30]	L. H. Wang (Editor), "Photoacoustic imaging and spectroscopy," CRC Press, 2009.
[31]	L. V. Wang and H. Wu, "Biomedical Optics. Principles and Imaging," Wiley-Interscience, 2007.
[32]	M. Xu and L.-H. V. Wang, Universal back-projection algorithm for photoacoustic computed tomography, Phys. Rev. E, 71 (2005), 016706. doi: doi:10.1103/PhysRevE.71.016706.
[33]	M. Xu and L.-H. V. Wang, Photoacoustic imaging in biomedicine, Review of Scientific Instruments, 77 (2006), 041101-01 - 041101-22.
[34]	H. Zhang and L. Wang, Acousto-electric tomography, Proc. SPIE, 5320 (2004), 145-149. doi: doi:10.1117/12.532610.

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