Mathematical analysis of the photo-acoustic imaging modality using resonating dielectric nano-particles: the \(2D\) TM-model. (English) Zbl 1478.92101

In this paper, the focus is on the photoacoustic imaging modality using dielectric nano-particles as contrast agents.
A heterogeneous tissue is considered, and represented by a bounded domain \(\Omega\). By means of an electromagnetic wave, heat is generated, and consequently an acoustic pressure wave, that can be detected and measured on the accessible boundary \(\partial\Omega\). This allows to extract information about optical properties of the tissue.
Two different studies are carried out, according as single nano-particles, or couples of closely spaced nano-particles (i.e. dimers), are injected.
From the measure of the acoustic pressure before and after the injection process, the authors are able to localize the center points of the nano-particles previously injected.
This leads to transform the photoacoustic problem into the inversion of phaseless internal electric fields in the first case, while, in the second case, the permittivity and the conductivity of the tissue on the centers is obtained.
A comparison is provided with authors’ knowledge about the photo-acoustic imaging modality using contrast agents


92C55 Biomedical imaging and signal processing
78A70 Biological applications of optics and electromagnetic theory
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35R30 Inverse problems for PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
Full Text: DOI arXiv


[1] Agranovsky, M.; Kuchment, P., Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography, Inverse Probl., 23, 5, 2089-2102 (2007) · Zbl 1126.35087
[2] Ammari, H.; Challa, D.; Choudhury, P. A.; Sini, M., The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies, J. Differ. Equ., 267, 4, 2104-2191 (2019) · Zbl 1447.35371
[3] Ammari, H.; Dabrowski, A.; Fitzpatrick, B.; Millien, P.; Sini, M., Subwavelength resonant dielectric nanoparticles with high refractive indices, Math. Methods Appl. Sci., 42, 18, 6567-6579 (2019) · Zbl 1434.35203
[4] Ammari, H.; Garnier, J.; Kang, H.; Nguyen, L. H.; Seppecher, L., Mathematics of super-resolution biomedical imaging (2016), Seminar for Applied Mathematics, ETH: Seminar for Applied Mathematics, ETH Zürich, Switzerland, Technical Report 2016-31
[5] Anderson, J. M.; Khavinson, D.; Lomonosov, V., Spectral properties of some integral operators arising in potential theory, Q. J. Math., 43, 387-407 (1992) · Zbl 0764.31001
[6] Belizzi, G.; Bucci, O. M., Microwave cancer imaging exploiting magnetic nanaparticles as contrast agent, IEEE Trans. Biomed. Eng., 58, 9 (September 2011)
[7] Chen, Y.; Craddock, I. J.; Kosmas, P., Feasibility study of lesion classification via contrast-agent-aided UWB breast imaging, IEEE Trans. Biomed. Eng., 57, 5 (May 2010)
[8] Colton, D.; Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory (2013), Springer: Springer Berlin · Zbl 1266.35121
[9] Arridge, S. R.; Beard, P. C.; Cox, B. T., Photoacoustic tomography with a limited-aperture planar sensor and a reverberant cavity, Inverse Probl., 23, S95-S112 (2007) · Zbl 1125.92036
[10] Fear, E. C.; Meaney, P. M.; Stuchly, M. A., Microwaves for breast cancer, IEEE Potentials, 22, 1, 12-18 (2003)
[11] Finch, D.; Haltmeier, M.; Rakesh, Inversion of spherical means and the wave equation in even dimensions, SIAM J. Appl. Math., 68, 2, 392-412 (2007) · Zbl 1159.35073
[12] Kalmenov, T.; Suragan, D., A boundary condition and spectral problems for the Newtonian potential, (Modern Aspects of the Theory of Partial Differential Equations. Modern Aspects of the Theory of Partial Differential Equations, Oper. Theory Adv. Appl., vol. 216 (2011), Birkhäuser/Springer Basel AG: Birkhäuser/Springer Basel AG Basel), 187-210
[13] Kuchment, P.; Kunyansky, L., Mathematics of thermoacoustic and photoacoustic tomography, (Scherzer, O., Handbook of Mathematical Methods in Imaging (2010), Springer-Verlag), 817-866 · Zbl 1259.92065
[14] Kuchment, P.; Kunyansky, L., Mathematics of thermoacoustic tomography, Eur. J. Appl. Math., 19, 02 (2008) · Zbl 1185.35327
[15] Landau, L. J., Ratios of Bessel functions and roots of \(\alpha J_\nu(x) + x J_\nu^\prime(x) = 0\), J. Math. Anal. Appl., 240, 174-204 (1999) · Zbl 0938.33002
[16] Chen, X.; Li, W., Gold nanoparticles for photoacoustic imaging, Nanomedicine (Lond.), 10, 2, 299-320 (2015)
[17] Naetar, W.; Scherzer, O., Quantitative photoacoustic tomography with piecewise constant material parameters, SIAM J. Imaging Sci., 7, 1755-1774 (2014) · Zbl 1361.94018
[18] Natterer, F., The Mathematics of Computerized Tomography (2001), Society for Industrial and Applied Mathematics · Zbl 0973.92020
[19] Bossy, E.; Poisson, F.; Prost, A., Photoacoustic generation by gold nanosphere: from linear to nonlinear thermoelastic in the long-pulse illumination regime
[20] Caskey, C. F.; Ferrara, K. W.; Qin, S., Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering, Phys. Med. Biol., 54, 6, R27 (2009, March 21)
[21] Pinchover, Y.; Rubinstein, J., An Introduction to Partial Differential Equations (2005), Cambridge University Press: Cambridge University Press USA · Zbl 1065.35001
[22] Ruzhansky, M.; Suragan, D., Isoperimetric inequalities for the logarithmic potential operator, J. Math. Anal. Appl., 434, 1676-1689 (2016) · Zbl 1330.47063
[23] Scherzer, O., Handbook of Mathematical Methods in Imaging (2010), Springer-Verlag
[24] Hagness, S. C.; Kosmas, P.; Shea, J. D.; Van Veen, B. D., Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms, Inverse Probl., 26, 7, 1-22 (2010) · Zbl 1194.92051
[25] Stefanov, P.; Uhlmann, G., Thermoacoustic tomography with variable sound speed, Inverse Probl., 25, Article 075011 pp. (2009) · Zbl 1177.35256
[26] Triki, F.; Vauthrin, M., Mathematical modelization of the photoacoustic effect generated by the heating of metallic nanoparticles, Q. Appl. Math., 76, 673-698 (2018) · Zbl 1403.35296
[27] Watson, G. N., A Treatise on the Theory of Bessel Functions (1995), Cambridge University Press · Zbl 0849.33001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.