On Causality of Thermoacoustic Tomography of Dissipative Tissue

  • Richard Kowar
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


Since all attenuation models for dissipative media that come into question for thermoacoustic tomography (TAT) violate causality, a causal attenuation model for TAT is proposed. A goal of this article is to discuss causality in the context of dissipative wave propagation and TAT. In the process we shortly discuss the frequency power law, a causal attenuation model (with a constant wave front speed which can be adjusted via an additional parameter) and the respective wave equation. Afterwards an integral equation model for estimating the unattenuated pressure data of TAT from the attenuated pressure data of TAT is presented and discussed. Our numerical results show a fast decrease of resolution of TAT for increasing distance of the object of interest from the pressure detector.


Green Function Pressure Wave Attenuation Model Dissipative Wave Dissipative Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dautray, R., Lions, J.L.: Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 5. Springer, New York (2000)Google Scholar
  2. 2.
    Kowar, R.: Integral equation models for thermoacoustic imaging of acoustic dissipative tissue. Inverse Problems 26, 095005 (18pp), DOI: 10.1088/0266-5611/26/9/095005 (2010)Google Scholar
  3. 3.
    Kowar, R., Scherzer, O.: Attenuation Models in Photoacoustics. to appear in: Mathematical Modeling in Biomedical Imaging II Lecture Notes in Mathematics, 2012, Volume 2035/2012, 85–130. arXiv:1009.4350
  4. 4.
    Nachman, A.I., Smith, J.F.I., Waag, R.C.: An equation for acoustic propagation in inhomogeneous media with relaxation losses. J. Acoust. Soc. Am. 88(3), 1584–1595 (1990)Google Scholar
  5. 5.
    Waters, K., Mobely, J., Miller, J.G.: Causality-imposed (Kramers-Krönig) relationships between attenuation and dispersion. IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 52(5), 822–833 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut of MathematicsUniversity of InnsbruckInnsbruckAustria

Personalised recommendations