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13 February 2007 Ultrasound attenuation and thermo/photo/opto-acoustic tomography: theoretical foundation
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Governing equations for ultrasonic propagation in three spatial dimensions with attenuation obeying a frequency power law are derived. Quadratic attenuation corresponds to a partial differential equation of degree four whose operator factors into a product of two parabolic operators, and impulse response is related to the heat kernel. The solutions satisfy primitive causality, but not relativistic causality. For powers that are not even integers, the waves satisfy integral-differential equations.
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S. K. Patch and A. Greenleaf "Ultrasound attenuation and thermo/photo/opto-acoustic tomography: theoretical foundation", Proc. SPIE 6437, Photons Plus Ultrasound: Imaging and Sensing 2007: The Eighth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acousto-optics, 643726 (13 February 2007);

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