Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

Abstract

Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/ two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

Simultaneous reconstruction of absorption, scattering and anisotropy factor distributions in quantitative photoacoustic tomography

“…To overcome the limitations of the DE, the Radiative Transfer Equation (RTE) has been addressed as a rigorous model for light transport in biological tissues and has become a focus of investigations in QPAT [15][16][17][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

“…Consequently, the anisotropy factor can provide an additional intrinsic contrast for optical imaging. To overcome the limitations of the DE, the Radiative Transfer equation (RTE) has been addressed as a rigorous model for light transport in biological tissues and has become a focus of investigations in QPAT [15][16][17][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In the optical inverse problem of QPAT, it has been shown that the absorption coefficient μ a can be reconstruct if one light source is used whereas the simultaneous reconstruction of (μ a , μ s ) needs multiple optical illuminations, so-called multisource QPAT [16,25,36,37].…”