American Institute of Mathematical Sciences

Advanced
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

[1]

Victor Palamodov. Remarks on the general Funk transform and thermoacoustic tomography. Inverse Problems & Imaging, 2010, 4 (4) : 693-702. doi: 10.3934/ipi.2010.4.693
[2]

Leonid Kunyansky. Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries. Inverse Problems & Imaging, 2012, 6 (1) : 111-131. doi: 10.3934/ipi.2012.6.111
[3]

Linh V. Nguyen. A family of inversion formulas in thermoacoustic tomography. Inverse Problems & Imaging, 2009, 3 (4) : 649-675. doi: 10.3934/ipi.2009.3.649
[4]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, Jari P. Kaipio, Erkki Somersalo. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part II: Stochastic extension of the boundary map. Inverse Problems & Imaging, 2015, 9 (3) : 767-789. doi: 10.3934/ipi.2015.9.767
[5]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, David Isaacson, Jari P. Kaipio, Debra McGivney, Erkki Somersalo, Joseph Volzer. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part I: Theory and preliminary results. Inverse Problems & Imaging, 2015, 9 (3) : 749-766. doi: 10.3934/ipi.2015.9.749
[6]

Bastian Gebauer. Localized potentials in electrical impedance tomography. Inverse Problems & Imaging, 2008, 2 (2) : 251-269. doi: 10.3934/ipi.2008.2.251
[7]

Ke Zhang, Maokun Li, Fan Yang, Shenheng Xu, Aria Abubakar. Electrical impedance tomography with multiplicative regularization. Inverse Problems & Imaging, 2019, 13 (6) : 1139-1159. doi: 10.3934/ipi.2019051
[8]

Herbert Egger, Manuel Freiberger, Matthias Schlottbom. On forward and inverse models in fluorescence diffuse optical tomography. Inverse Problems & Imaging, 2010, 4 (3) : 411-427. doi: 10.3934/ipi.2010.4.411
[9]

Kari Astala, Jennifer L. Mueller, Lassi Päivärinta, Allan Perämäki, Samuli Siltanen. Direct electrical impedance tomography for nonsmooth conductivities. Inverse Problems & Imaging, 2011, 5 (3) : 531-549. doi: 10.3934/ipi.2011.5.531
[10]

Ville Kolehmainen, Matti Lassas, Petri Ola, Samuli Siltanen. Recovering boundary shape and conductivity in electrical impedance tomography. Inverse Problems & Imaging, 2013, 7 (1) : 217-242. doi: 10.3934/ipi.2013.7.217
[11]

Meghdoot Mozumder, Tanja Tarvainen, Simon Arridge, Jari P. Kaipio, Cosimo D'Andrea, Ville Kolehmainen. Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography. Inverse Problems & Imaging, 2016, 10 (1) : 227-246. doi: 10.3934/ipi.2016.10.227
[12]

Adriana González, Laurent Jacques, Christophe De Vleeschouwer, Philippe Antoine. Compressive optical deflectometric tomography: A constrained total-variation minimization approach. Inverse Problems & Imaging, 2014, 8 (2) : 421-457. doi: 10.3934/ipi.2014.8.421
[13]

Liliana Borcea, Fernando Guevara Vasquez, Alexander V. Mamonov. Study of noise effects in electrical impedance tomography with resistor networks. Inverse Problems & Imaging, 2013, 7 (2) : 417-443. doi: 10.3934/ipi.2013.7.417
[14]

Dong liu, Ville Kolehmainen, Samuli Siltanen, Anne-maria Laukkanen, Aku Seppänen. Estimation of conductivity changes in a region of interest with electrical impedance tomography. Inverse Problems & Imaging, 2015, 9 (1) : 211-229. doi: 10.3934/ipi.2015.9.211
[15]

Gen Nakamura, Päivi Ronkanen, Samuli Siltanen, Kazumi Tanuma. Recovering conductivity at the boundary in three-dimensional electrical impedance tomography. Inverse Problems & Imaging, 2011, 5 (2) : 485-510. doi: 10.3934/ipi.2011.5.485
[16]

Nicolay M. Tanushev, Luminita Vese. A piecewise-constant binary model for electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (2) : 423-435. doi: 10.3934/ipi.2007.1.423
[17]

Nuutti Hyvönen, Lassi Päivärinta, Janne P. Tamminen. Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps. Inverse Problems & Imaging, 2018, 12 (2) : 373-400. doi: 10.3934/ipi.2018017
[18]

Kimmo Karhunen, Aku Seppänen, Jari P. Kaipio. Adaptive meshing approach to identification of cracks with electrical impedance tomography. Inverse Problems & Imaging, 2014, 8 (1) : 127-148. doi: 10.3934/ipi.2014.8.127
[19]

Jérémi Dardé, Harri Hakula, Nuutti Hyvönen, Stratos Staboulis. Fine-tuning electrode information in electrical impedance tomography. Inverse Problems & Imaging, 2012, 6 (3) : 399-421. doi: 10.3934/ipi.2012.6.399
[20]

Erfang Ma. Integral formulation of the complete electrode model of electrical impedance tomography. Inverse Problems & Imaging, 2020, 14 (2) : 385-398. doi: 10.3934/ipi.2020017

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (27)
  • HTML views (0)
  • Cited by (18)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences