Ultrasound Modulated Bioluminescence Tomography and Controllability of the Radiative Transport Equation

Abstract

Abstract. We propose a method to reconstruct the density of an optical source in a highly scattering medium from ultrasound-modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the radiative transport equation (RTE). A controllability result for the RTE plays an essential role in the analysis.

Acousto-optic effect in random media

“…Fourth, when the medium is not known to consist of isolated inhomogeneities, it is of interest to recover the spatial dependence of the absorption. This inverse problem has so far only been studied for the case of the incoherent acoustooptic effect [20,[29][30][31][32][33][34][35]. This paper provides the necessary radiative transport and diffusion equations to study the coherent problem.…”

“…The image is created by scanning the focus of the beam and recording the intensity of the scattered light at a fixed detector. Tomographic imaging utilizes an inverse scattering method to reconstruct images of the optical properties of the medium [20,22,[29][30][31][32][33][34][35].…”

Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements

“…Note that the time variable t in ε is the time on the acoustic time scale, which is approximately constant during the much faster optical process. According to [6] the quantum efficiency η(x) is not modulated by the acoustic field. Combining this with the stationary RTE (3), we obtain the governing equation for fUMOT in the transport regime,…”

A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation

“…The radiative transport model plays an important role in quantitative modeling and analysis of particle transport processes in many physical and biological applications such as astrophysics [5,19], nuclear engineering [23,30], biomedical optics [1,2,25,33,41], radiation therapy [20,37]. In this paper, we consider the numerical solution to the timedependent radiative transport equation (RTE) with isotropic scattering kernel:…”