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Erschienen in:
Linear Inverse Problems Kapitel lesen Erstes Kapitel lesen

2011 | OriginalPaper | Buchkapitel

Mathematics of Photoacoustic and Thermoacoustic Tomography

verfasst von : Peter Kuchment, Leonid Kunyansky

Erschienen in: Handbook of Mathematical Methods in Imaging

Verlag: Springer New York

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Abstract

The chapter surveys the mathematical models, problems, and algorithms of the thermoacoustic tomography (TAT) and photoacoustic tomography (PAT). TAT and PAT represent probably the most developed of the several novel “hybrid” methods of medical imaging. These new modalities combine different physical types of waves (electromagnetic and acoustic in case of TAT and PAT) in such a way that the resolution and contrast of the resulting method are much higher than those achievable using only acoustic or electromagnetic measurements.

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Vorheriges Kapitel Photoacoustic and Thermoacoustic Tomography: Image Formation Principles
Nächstes Kapitel Wave Phenomena
Literatur
1.
2.
Agranovsky M, Finch D, Kuchment P (2009) Range conditions for a spherical mean transform. Inverse Probl Imaging 3(3):373–38MathSciNetMATHCrossRef
3.
Agranovsky M, Kuchment P (2007) Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Inverse Probl 23:2089–2102MathSciNetMATHCrossRef
4.
Agranovsky M, Kuchment P, Kunyansky L (2009) On reconstruction formulas and algorithms for the thermoacoustic and photoacoustic tomography, Chapter 8. In: Wang LH (ed) Photoacoustic imaging and spectroscopy. CRC Press, Boca Raton, pp 89–101CrossRef
5.
Agranovsky M, Kuchment P, Quinto ET (2007) Range descriptions for the spherical mean Radon transform. J Funct Anal 248: 344–386MathSciNetMATHCrossRef
6.
Agranovsky M, Nguyen L (2009) Range conditions for a spherical mean transform and global extension of solutions of Darboux equation. Preprint arXiv:0904.4225 To appear in J d’Analyse Mathematique
7.
Agranovsky M, Quinto ET (1996) Injectivity sets for the Radon transform over circles and complete systems of radial functions. J Funct Anal 139:383–414MathSciNetMATHCrossRef
8.
9.
Ambartsoumian G, Kuchment P (2006) A range description for the planar circular Radon transform. SIAM J Math Anal 38(2):681–692MathSciNetCrossRef
10.
Ammari H (2008) An Introduction to mathematics of emerging biomedical imaging. Springer, BerlinMATH
11.
Ammari H, Bonnetier E, Capdebosq Y, Tanter M, Fink M (2008) Electrical impedance tomography by elastic deformation. SIAM J Appl Math 68(6):1557–1573MathSciNetMATHCrossRef
12.
Ammari H, Bossy E, Jugnon V, Kang H. Quantitative photo-acoustic imaging of small absorbers. SIAM Review, to appear 
13.
Anastasio MA, Zhang J, Modgil D, Rivière PJ (2007) Application of inverse source concepts to photoacoustic tomography Inverse Probl 23:S21–S35MATH
14.
Anastasio MA, Zhang J, Sidky EY, Zou Z, Dan X, Pan X (2005) Feasibility of half-data image reconstruction in 3-D reflectivity tomography with a spherical aperture. IEEE Trans Med Imaging 24(9):1100–1112CrossRef
15.
Anastasio M, Zhang J, Pan X, Zou Y, Ku G, Wang LV (2005) Half-time image reconstruction in thermoacoustic tomography. IEEE Trans Med Imaging 24:199–210CrossRef
16.
17.
Andreev V, Popov D et al (2002) Image reconstruction in 3D optoacoustic tomography system with hemispherical transducer array. Proc SPIE 4618:137–145CrossRef
18.
Bal G, Jollivet A, Jugnon V (2010) Inverse transport theory of photoacoustics. Inverse Probl 26:025011, doi:10.1088/0266-5611/26/2/025011MathSciNetCrossRef
19.
Bell AG (1880) On the production and reproduction of sound by light. Am J Sci 20: 305–324
20.
Beylkin G (1984) The inversion problem and applications of the generalized Radon transform. Commun Pur Appl Math 37:579–599MathSciNetMATHCrossRef
21.
Bowen T (1981) Radiation-induced thermoacoustic soft tissue imaging. Proc IEEE Ultrason Symp 2:817–822
22.
Burgholzer P, Grün H, Haltmeier M, Nuster R, Paltauf G (2007) Compensation of acoustic attenuation for high-resolution photoacoustic imaging with line detectors using time reversal. In: Proceedings of the SPIE number 6437–75 Photonics West, BIOS 2007, San Jose
23.
Burgholzer P, Hofer C, Paltauf G, Haltmeier M, Scherzer O (2005) Thermoacoustic tomography with integrating area and line detectors. IEEE Trans Ultrason Ferroelectr Freq Control 52(9):1577–1583CrossRef
24.
Burgholzer P, Hofer C, Matt GJ, Paltauf G, Haltmeier M, Scherzer O (2006) Thermoacoustic tomography using a fiber-based Fabry–Perot interferometer as an integrating line detector. Proc SPIE 6086:434–442
25.
Clason C, Klibanov M (2007) The quasi-reversibility method in thermoacoustic tomography in a heterogeneous medium. SIAM J Sci Comput 30:1–23MathSciNetMATHCrossRef
26.
27.
Courant R, Hilbert D (1962) Methods of mathematical physics. Partial differential equations, vol II. Interscience, New York
28.
Cox BT, Arridge SR, Beard PC (2007) Photoacoustic tomography with a limited aperture planar sensor and a reverberant cavity. Inverse Probl 23:S95–S112MathSciNetMATHCrossRef
29.
Cox BT, Arridge SR, Beard PC (2009) Estimating chromophore distributions from multiwavelength photoacoustic images. J Opt Soc Am A 26:443–455CrossRef
30.
Cox BT, Laufer JG, Beard PC (2009) The challenges for quantitative photoacoustic imaging. Proc SPIE 7177:717713CrossRef
31.
Diebold GJ, Sun T, Khan MI (1991) Photoacoustic monopole radiation in one, two, and three dimensions. Phys Rev Lett 67(24):3384–3387CrossRef
32.
Egorov Yu V, Shubin MA (1992) Partial differential equations I. Encyclopaedia of mathematical sciences, vol 30. Springer, Berlin, pp 1–259
33.
34.
35.
Finch D, Haltmeier M, Rakesh (2007) Inversion of spherical means and the wave equation in even dimensions. SIAM J Appl Math 68(2):392–412MathSciNetMATHCrossRef
36.
Finch D, Patch S, Rakesh (2004) Determining a function from its mean values over a family of spheres. SIAM J Math Anal 35(5):1213–1240MathSciNetMATHCrossRef
37.
Finch D, Rakesh (2006) Range of the spherical mean value operator for functions supported in a ball. Inverse Probl 22:923–938MathSciNetMATHCrossRef
38.
Finch D, Rakesh. Recovering a function from its spherical mean values in two and three dimensions. In [94], pp 77–88
39.
40.
41.
Gelfand I, Gindikin S, Graev M (2003) Selected topics in integral geometry. Transl Math Monogr vol 220, American Mathematical Society, Providence
42.
Grün H, Haltmeier M, Paltauf G, Burgholzer P (2007) Photoacoustic tomography using a fiber based Fabry-Perot interferometer as an integrating line detector and image reconstruction by model-based time reversal method. Proc SPIE 6631:663107CrossRef
43.
Haltmeier M, Burgholzer P, Paltauf G, Scherzer O (2004) Thermoacoustic computed tomography with large planar receivers. Inverse Probl 20:1663–1673MathSciNetMATHCrossRef
44.
Haltmeier M, Scherzer O, Burgholzer P, Nuster R, Paltauf G (2007) Thermoacoustic tomography and the circular radon transform: exact inversion formula. Math Mod Methods Appl Sci 17(4):635–655MathSciNetMATHCrossRef
45.
Helgason S (1980) The Radon transform. Birkh äuser, BaselMATH
46.
Hörmander L (1983) The analysis of linear partial differential operators, vols 1 and 2. Springer, New YorkCrossRef
47.
48.
Hristova Y, Kuchment P, Nguyen L (2008) On reconstruction and time reversal in thermoacoustic tomography in homogeneous and non-homogeneous acoustic media. Inverse Probl 24:055006MathSciNetCrossRef
49.
Isakov V (2005) Inverse problems for partial differential equations, 2nd edn. Springer, Berlin
50.
Jin X, Wang LV (2006) Thermoacoustic tomography with correction for acoustic speed variations. Phys Med Biol 51:6437–6448CrossRef
51.
John F (1971) Plane waves and spherical means applied to partial differential equations. Dover, New York
52.
Kowar R, Scherzer O, Bonnefond X. Causality analysis of frequency dependent wave attenuation, preprint arXiv:0906.4678
53.
Kruger RA, Liu P, Fang YR, Appledorn CR (1995) Photoacoustic ultrasound (PAUS)reconstruction tomography. Med Phys 22:1605–1609CrossRef
54.
55.
56.
Kuchment P, Kunyansky L, Synthetic focusing in ultrasound modulated tomography. Inverse Probl Imaging, to appear
57.
Kunyansky L (2007) Explicit inversion formulae for the spherical mean Radon transform. Inverse probl 23:737–783CrossRef
58.
Kunyansky L (2007) A series solution and a fast algorithm for the inversion of the spherical mean Radon transform. Inverse Probl 23:S11–S20MathSciNetMATHCrossRef
59.
Kunyansky L (2008) Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm. Inverse Probl 24(5):055021MathSciNetCrossRef
60.
Lin V, Pinkus A (1994) Approximation of multivariate functions. In: Dikshit HP, Micchelli CA (eds) Advances in computational mathematics. World Scientific, Singapore, pp 1–9
61.
Louis AK, Quinto ET (2000) Local tomographic methods in Sonar. In: Surveys on solution methods for inverse problems. Springer, Vienna, pp 147–154CrossRef
62.
Maslov K, Zhang HF, Wang LV (2007) Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo. Inverse Probl 23:S113–S122MathSciNetMATHCrossRef
63.
Natterer F (1986) The mathematics of computerized tomography. Wiley, New YorkMATH
64.
65.
Nguyen LV. On singularities and instability of reconstruction in thermoacoustic tomography, preprint arXiv:0911.5521v1
66.
Norton SJ (1980) Reconstruction of a two-dimensional reflecting medium over a circular domain: exact solution. J Acoust Soc Am 67:1266–1273MathSciNetMATHCrossRef
67.
Norton SJ, Linzer M (1981) Ultrasonic reflectivity imaging in three dimensions: exact inverse scattering solutions for plane, cylindrical, and spherical apertures. IEEE Trans Biomed Eng 28:200–202CrossRef
68.
Olafsson G, Quinto ET (eds) The radon transform, inverse problems, and tomography. American Mathematical Society Short Course January 3–4, 2005, Atlanta, Georgia, Proc Symp Appl Math, vol 63, AMS, RI, 2006
69.
Oraevsky AA, Jacques SL, Esenaliev RO, Tittel FK (1994) Laser-based ptoacoustic imaging in biological tissues. Proc SPIE 2134A:122–128
70.
71.
Palamodov V (2007) Remarks on the general Funk–Radon transform and thermoacoustic tomography. Preprint arxiv: math.AP/0701204
72.
Paltauf G, Nuster R, Burgholzer P (2009) Weight factors for limited angle photoacoustic tomography. Phys Med Biol 54:3303–3314CrossRef
73.
Paltauf G, Nuster R, Haltmeier M, Burgholzer P (2007) Thermoacoustic computed tomography using a Mach–Zehnder interferometer as acoustic line detector. Appl Opt 46(16):3352–3358CrossRef
74.
Paltauf G, Nuster R, Haltmeier M, Burgholzer P (2007) Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors. Inverse Probl 23:S81–S94MathSciNetMATHCrossRef
75.
Paltauf G, Viator JA, Prahl SA, Jacques SL (2002) Iterative reconstruction algorithm for optoacoustic imaging J. Acoust Soc Am 112(4):1536–1544CrossRef
76.
Paltauf G, Nuster R, Burgholzer P (2009) Characterization of integrating ultrasound detectors for photoacoustic tomography. J Appl Phys 105:102026CrossRef
77.
Passechnik VI, Anosov AA, Bograchev KM (2000) Fundamentals and prospects of passive thermoacoustic tomography. Crit Rev Biomed Eng 28(3–4):603–640
78.
Patch SK (2004) Thermoacoustic tomography – consistency conditions and the partial scan problem. Phys Med Biol 49:1–11CrossRef
79.
Patch S (2009) Photoacoustic or thermoacoustic tomography: consistency conditions and the partial scan problem, in [94], 103–116
80.
Patch SK, Haltmeier M (2006) Thermoacoustic tomography – ultrasound attenuation artifacts. IEEE Nucl Sci Sym Conf 4:2604–2606
81.
Popov DA, Sushko DV (2002) A parametrix for the problem of optical-acoustic tomography. Dokl Math 65(1):19–21MATH
82.
83.
La Rivière PJ, Zhang J, Anastasio MA (2006) Image reconstruction in optoacoustic tomography for dispersive acoustic media. Opt Lett 31(6):781–783CrossRef
84.
85.
Stefanov P, Uhlmann G (2008) Integral geometry of tensor fields on a class of non-simple Riemannian manifolds. Am J Math 130(1):239–268MathSciNetMATHCrossRef
86.
87.
Steinhauer D. A uniqueness theorem for thermoacoustic tomography in the case of limited boundary data, preprint arXiv:0902.2838
88.
Tam AC (1986) Applications of photoacoustic sensing techniques. Rev Mod Phys 58(2):381–431CrossRef
89.
Tuchin VV (ed) (2002) Handbook of optical biomedical diagnostics. SPIE, Bellingham
90.
Vainberg B (1975) The short-wave asymptotic behavior of the solutions of stationary problems, and the asymptotic behavior as t → ∞ of the solutions of nonstationary problems. Russ Math Surv 30(2):1–58MathSciNetMATHCrossRef
91.
Vainberg B (1982) Asymptotics methods in the equations of mathematical physics. Gordon & Breach, New York
92.
Vo-Dinh T (ed) (2003) Biomedical photonics handbook. CRC Press, Boca Raton
93.
Wang K, Anastasio MA. Photoacoustic and thermoacoustic tomography: image formation principles, Chapter 28 in this volume
94.
Wang L (ed) (2009) Photoacoustic imaging and spectroscopy. CRC Press, Boca Raton
95.
Wang LV, Wu H (2007) Biomedical optics. Principles and imaging. Wiley, New York
96.
Xu M, Wang L-HV (2002) Time-domain reconstruction for thermoacoustic tomography in a spherical geometry. IEEE Trans Med Imaging 21:814–822CrossRef
97.
Xu M, Wang L-HV (2005) Universal back-projection algorithm for photoacoustic computed tomography. Phys Rev E71:016706CrossRef
98.
Xu Y, Feng D, Wang L-HV (2002) Exact frequency-domain reconstruction for thermoacoustic tomography: I Planar geometry. IEEE Trans Med Imag 21:823–828CrossRef
99.
Xu Y, Xu M, Wang L-HV (2002) Exact frequency-domain reconstruction for thermoacoustic tomography: II Cylindrical geometry. IEEE Trans Med Imaging 21:829–833CrossRef
100.
Xu Y, Wang L, Ambartsoumian G, Kuchment P (2004) Reconstructions in limited view thermoacoustic tomography. Med Phys 31(4):724–733CrossRef
101.
Xu Y, Wang L, Ambartsoumian G, Kuchment P (2009) Limited view thermoacoustic tomography, Ch. 6. In: Wang LH (ed) Photoacoustic imaging and spectroscopy. CRC Press, Boca Raton, pp 61–73
102.
Zangerl G, Scherzer O, Haltmeier M (2009) Circular integrating detectors in photo and thermoacoustic tomography. Inverse Probl Sci Eng 17(1):133–142MathSciNetMATHCrossRef
103.
Yuan Z, Zhang Q, Jiang H (2006) Simultaneous reconstruction of acoustic and optical properties of heterogeneous media by quantitative photoacoustic tomography. Opt Express 14(15):6749CrossRef
104.
Zhang J, Anastasio MA (2006) Reconstruction of speed-of-sound and electromagnetic absorption distributions in photoacoustic tomography. Proc SPIE 6086:608619CrossRef
Metadaten
Titel
Mathematics of Photoacoustic and Thermoacoustic Tomography
verfasst von
Peter Kuchment
Leonid Kunyansky
Copyright-Jahr
2011
Verlag
Springer New York
Buch
Handbook of Mathematical Methods in Imaging

Print ISBN: 978-0-387-92919-4

Electronic ISBN: 978-0-387-92920-0

Copyright-Jahr: 2011

DOI
https://doi.org/10.1007/978-0-387-92920-0_19