TY - JOUR

T1 - Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

AU - Stritzel, J.

AU - Melchert, O.

AU - Wollweber, M.

AU - Roth, B.

N1 - Funding Information: J.S. acknowledges support from the German Federal Ministry of Education and Research (BMBF) in the framework of the project MeDiOO (Grant No. FKZ 03V0826). O.M. acknowledges support from the Volkswagenstiftung within the “Niedersächsisches Vorab” program in the framework of the project “Hybrid Numerical Optics–HYMNOS” (Grant No. ZN 3061). Publisher Copyright: © 2017 American Physical Society. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/9/13

Y1 - 2017/9/13

N2 - The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

AB - The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

UR - http://www.scopus.com/inward/record.url?scp=85029835984&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.033308

DO - 10.1103/PhysRevE.96.033308

M3 - Article

C2 - 29346868

AN - SCOPUS:85029835984

VL - 96

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 3

M1 - 033308

ER -