Reconstructions in ultrasound modulated optical tomography

Abstract We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused ultrasound signals. Computational results for this model show that the reconstruction of sharp features of the absorption coefficient is possible. A formal linearization of the model leads to an equation with a Fredholm operator, which explains the stability observed in our numerical experiments.

[1]  G. Rybicki.  Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.

[2]  Azriel Z. Genack,et al.  Acousto-optic tomography with multiply scattered light , 1997 .

[3]  G. Maret,et al.  Ultrasonic modulation of multiply scattered light , 1995 .

[4]  P. Kuchment,et al.  Mathematics of thermoacoustic tomography , 2007, European Journal of Applied Mathematics.

[5]  Lihong V. Wang,et al.  Biomedical Optics: Principles and Imaging , 2007 .

[6]  Peter Kuchment,et al.  Synthetic focusing in ultrasound modulated tomography , 2009, 0901.2552.

[7]  W. Bangerth,et al.  deal.II—A general-purpose object-oriented finite element library , 2007, TOMS.

[8]  L V Wang.  Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model. , 2001, Physical review letters.

[9]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[10]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[11]  Anuradha Godavarty,et al.  Near- Infrared Fluorescence Imaging and Spectroscopy in Random Media and Tissues , 2003 .

[12]  M. Kleiber,et al.  Selected Topics from the Mathematical Theory of Finite Elements , 1998 .

[13]  Sandrine Que-Fort.  Three-Dimensional Acousto-Optic Imaging in Biological Tissues with Parallel Signal Processing , 2001 .

[14]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[15]  Ken-iti Sato,et al.  Multi-dimensional diffusion and the Markov process on the boundary , 1965 .

[16]  L. Nirenberg,et al.  On the Hopf Lemma , 2007, 0709.3531.

[17]  H. P. McKean,et al.  Boundary Conditions for the Heat Equation in a Several-Dimensional Region , 1972, Nagoya Mathematical Journal.

[18]  V. Hardman.  Author Information , 2021, Disability and Health Journal.

[19]  S. Lévêque-Fort,et al.  Three-dimensional acousto-optic imaging in biological tissues with parallel signal processing. , 2001, Applied optics.

[20]  Lihong V. Wang.  Ultrasound-Mediated Biophotonic Imaging: A Review of Acousto-Optical Tomography and Photo-Acoustic Tomography , 2004, Disease markers.

[21]  Anuradha Godavarty,et al.  Influence of the refractive index-mismatch at the boundaries measured in fluorescenceenhanced frequency-domain photon migration imaging. , 2002, Optics express.