Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter December 2, 2016

Quantitative thermoacoustic tomography with microwaves sources

Hassan Akhouayri , Maïtine Bergounioux EMAIL logo , Anabela Da Silva , Peter Elbau , Amelie Litman and Leonidas Mindrinos

Abstract

We investigate a quantitative thermoacoustic tomography process. We aim to recover the electric susceptibility and the conductivity of a medium when the sources are in the microwaves range. We focus on the case where the source signal has a slow time-varying envelope. We present the direct problem coupling equations for the electric field, the temperature variation and the pressure (to be measured via sensors). Then we give a variational formulation of the inverse problem which takes into account the entire electromagnetic, thermal and acoustic coupled system, and perform the formal computation of the optimality system.

Award Identifier / Grant number: ANR-12-BLAN-BS01-0001-01

Funding source: OeAD-GmbH

Award Identifier / Grant number: WTZ FR14/2013

Funding statement: This work is supported by ANR (AVENTURES – ANR-12-BLAN-BS01-0001-01) and Partenariat Hubert Curien AMADEUS, OEAD WTZ FR14/2013.

References

[1] H. Ammari, E. Bossy, V. Jugnon and H. Kang, Reconstruction of the optical absorption coefficient of a small absorber from the absorbed energy density, SIAM J. Appl. Math. 71 (2011), no. 3, 676–693. 10.1137/09077905XSearch in Google Scholar

[2] H. Ammari, J. Garnier, W. Jing and L. H. Nguyen, Quantitative thermo-acoustic imaging: An exact reconstruction formula, J. Differential Equations 254 (2013), 1375–1395. 10.1016/j.jde.2012.10.019Search in Google Scholar

[3] G. Bal, A. Jollivet and V. Jugnon, Inverse transport theory of photoacoustics, Inverse Problems 26 (2010), no. 2, Article ID 025011. 10.1088/0266-5611/26/2/025011Search in Google Scholar

[4] G. Bal and K. Ren, Multi-source quantitative photoacoustic tomography in a diffusive regime, Inverse Problems 27 (2011), Article ID 075003. 10.1088/0266-5611/27/7/075003Search in Google Scholar

[5] G. Bal, K. Ren, G. Uhlmann and T. Zhou, Quantitative thermo-acoustics and related problems, Inverse Problems 27 (2011), no. 5, Article ID 055007. 10.1088/0266-5611/27/5/055007Search in Google Scholar PubMed

[6] G. Bal and T. Zhou, Hybrid inverse problems for a system of maxwell’s equations, Inverse Problems 30 (2014), no. 5, Article ID 055013. 10.1088/0266-5611/30/5/055013Search in Google Scholar

[7] M. Bergounioux, X. Bonnefond, T. Haberkorn and Y. Privat, An optimal control problem in photoacoustic tomography, Math. Models Methods Appl. Sci. 24 (2014), no. 14, 2943–48. 10.1142/S0218202514500286Search in Google Scholar

[8] M. J. Burfeindt, T. J. Colgan, R. O. Mays, J. D. Shea, N. Behdad, B. D. V. Veen and S. C. Hagness, Mri-derived 3D-printed breast phantom for microwave breast imaging validation, IEEE Antennas and Wireless Propagation Lett. 11 (2012), 1610–1613. 10.1109/LAWP.2012.2236293Search in Google Scholar PubMed PubMed Central

[9] G. Chen, X. Wang and Q. Liu, Microwave-induced thermo-acoustic tomography system using TRM-PSTD technique, PIER-B 48 (2013), 43–59. 10.2528/PIERB12111503Search in Google Scholar

[10] B. Cox and P. Beard, Modeling photoacoustic propagation in tissue using k-space techniques, Photoacoustic Imaging and Spectroscopy, CRC Press, Boca Raton (2009), 25–34. 10.1201/9781420059922-4Search in Google Scholar

[11] F. Duck, Physical Properties of Tissue: A Comprehensive Reference Book, Institution of Physics & Engineering in Medicine & Biology, York, 2012. Search in Google Scholar

[12] P. Elbau, L. Mindrinos and O. Scherzer, Inverse problems of combined photoacoustic and optical coherence tomography, Math. Methods Appl. Sci. (2016), 10.1002/mma.3915. 10.1002/mma.3915Search in Google Scholar PubMed PubMed Central

[13] D. Fallon, L. Yan, G. W. Hanson and S. K. Patch, RF testbed for thermoacoustic tomography, Rev. Sci. Instrument 80 (2009), Article ID 064301. 10.1117/12.809183Search in Google Scholar

[14] S. Gabriel, R. Lau and C. Gabriel, The dielectric properties of biological tissues. II. Measurements in the frequency range 10 Hz to 20 GHz, Phys. Med. Biol. 41 (1996), no. 11, 2251–2269. 10.1088/0031-9155/41/11/002Search in Google Scholar PubMed

[15] H. Gao, H. Zhao and S. Osher, Bregman methods in quantitative photoacoustic tomography, Technical Report 10-42, University of California, Los Angeles, 2010. Search in Google Scholar

[16] M. Haltmeier, L. Neumann and S. Rabanser, Single-stage reconstruction algorithm for quantitative photoacoustic tomography, Inverse Problems 31 (2015), no. 6, Article ID 065005. 10.1088/0266-5611/31/6/065005Search in Google Scholar

[17] L. Huang, L. Yao, L. Liu, J. Rong and H. Jiang, Quantitative thermoacoustic tomography: Recovery of conductivity maps of heterogeneous media, Appl. Phys. Lett. 101 (2012), no. 24, Article ID 244106. 10.1063/1.4772484Search in Google Scholar

[18] J. Jackson, Classical Electrodynamics, Wiley, New York, 1998. Search in Google Scholar

[19] R. Kruger, W. Kiser, K. Miller and H. Reynolds, Thermoacoustic CT: Imaging principles, Proc. SPIE 3916 (2000), 10.1117/12.386316. 10.1117/12.386316Search in Google Scholar

[20] R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger and R. L. Eisenhart, Thermoacoustic computed tomography of the breast at 434 MHz, IEEE MTT-S Internat. Microw. Sympos. Digest 2 (1999), 591–595. 10.1109/MWSYM.1999.779831Search in Google Scholar

[21] P. Kuchment and L. Kunyansky, Mathematics of thermoacoustic tomography, European J. Appl. Math. 19 (2008), 191–224. 10.1017/S0956792508007353Search in Google Scholar

[22] P. Kuchment and L. Kunyansky, Mathematics of photoacoustic and thermoacoustic tomography, Handbook of Mathematical Methods in Imaging, Springer, New York (2015), 1117–1167. 10.1007/978-1-4939-0790-8_51Search in Google Scholar

[23] M. Lazebnik, L. McCartney, D. Popovic, C. Watkins, M. Lindstrom, J. Harter, S. Sewall, A. Magliocco, J. Booske, M. Okoniewski and S. Hagness, A large-scale study of the ultrawideband microwave dielectric properties of normal breast tissue obtained from reduction surgeries, Phys. Med. Biol. 52 (2007), 2637–2656. 10.1088/0031-9155/52/10/001Search in Google Scholar PubMed

[24] C. Li, M. Pramanik, G. Ku and L. Wang, Image distortion in thermoacoustic tomography caused by microwave diffraction, Phys. Rev. E 77 (2008), Article ID 31923. 10.1103/PhysRevE.77.031923Search in Google Scholar PubMed

[25] P. Monk, Finite Element Methods for Maxwell’s Equations, Oxford University Press, Oxford, 2003. 10.1093/acprof:oso/9780198508885.001.0001Search in Google Scholar

[26] W. Naetar and O. Scherzer, Quantitative photoacoustic tomography with piecewise constant material parameters, SIAM J. Imaging Sci. 7 (2014), no. 3, 1755–1774. 10.1137/140959705Search in Google Scholar

[27] L. Nie, D. Xing, D. Yang, L. Zeng and Q. Zhou, Detection of foreign body using fast thermoacoustic tomography with a multielement linear transducer array, Appl. Phys. Lett. 90 (2007), Article ID 174109. 10.1063/1.2732824Search in Google Scholar PubMed PubMed Central

[28] S. K. Patch and O. Scherzer, Photo- and thermo-acoustic imaging introduction, Inverse Problems 23 (2007), no. 6, S1–S10. 10.1088/0266-5611/23/6/S01Search in Google Scholar

[29] M. Pramanik, G. Ku, C. Li and L. V. Wang, Design and evaluation of a novel breast cancer detection system combining both thermoacoustic (ta) and photoacoustic (pa) tomography, Med. Phys. 35 (2008), no. 6, 2218–2223. 10.1118/1.2911157Search in Google Scholar PubMed PubMed Central

[30] T. Saratoon, T. Tarvainen, B. Cox and S. Arridge, A gradient-based method for quantitative photoacoustic tomography using the radiative transfer equation, Inverse Problems 29 (2013), Article ID 075006. 10.1088/0266-5611/29/7/075006Search in Google Scholar

[31] P. Shao, T. Harrison and R. J. Zemp, Iterative algorithm for multiple illumination photoacoustic tomography (mipat) using ultrasound channel data, Biomed. Opt. Express. 3 (2012), 3240–3249. 10.1364/BOE.3.003240Search in Google Scholar PubMed PubMed Central

[32] N. Song, D. C. and A. Da Silva, Considering sources and detectors distributions for quantitative photoacoustic tomography (qpat), Biomed. Opt. Express. 5 (2014), 3960–3974. 10.1364/BOE.5.003960Search in Google Scholar PubMed PubMed Central

[33] K. Wang and M. A. Anastasio, Photoacoustic and thermoacoustic tomography: Image formation principles, Handbook of Mathematical Methods in Imaging, Springer, New York (2015), 1081–1116. 10.1007/978-1-4939-0790-8_50Search in Google Scholar

[34] L. Wang, Photoacoustic Imaging and Spectroscopy, Optical Sci. Eng. 144, CRC Press, Boca Raton, 2009. Search in Google Scholar

[35] L. Wang, X. Zhao, H. Sun and G. Ku, Microwave-induced acoustic imaging of biological tissues, Rev. Sci. Instrum. 70 (1999), no. 9, 3744–3748. 10.1063/1.1149986Search in Google Scholar

[36] X. Wang, D. R. Bauer, R. Witte and H. Xin, Microwave-induced thermoacoustic imaging model for potential breast cancer detection, IEEE Trans. Biomed. Eng. 59 (2012), no. 10, 2782–2791. 10.1109/TBME.2012.2210218Search in Google Scholar PubMed

[37] Z. Yuan and H. Jiang, Quantitative photoacoustic tomography, Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 367 (2009), 3043–54. 10.1098/rsta.2009.0083Search in Google Scholar PubMed PubMed Central

[38] R. J. Zemp, Quantitative photoacoustic tomography with multiple optical sources, Appl. Opt. 49 (2010), no. 18, 3566–3572. 10.1364/AO.49.003566Search in Google Scholar PubMed

Received: 2016-2-5
Revised: 2016-10-10
Accepted: 2016-11-3
Published Online: 2016-12-2
Published in Print: 2017-12-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 3.12.2022 from frontend.live.degruyter.dgbricks.com/document/doi/10.1515/jiip-2016-0012/html
Scroll Up Arrow