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A new reconstruction algorithm for fluorescence diffuse optical tomography of biological tissues is proposed. The radiative transport equation in the frequency domain is used to model light propagation. The adjoint method studied in this work provides an efficient way for solving the inverse problem. The methodology is applied to a 2D tissue-like phantom subjected to a collimated laser beam. Indocyanine Green is used as fluorophore. Reconstructed images of the spatial fluorophore absorption distribution is assessed taking into account the residual fluorescence in the medium. We show that illuminating the tissue surface from a collimated centered direction near the inclusion gaves a better reconstruction quality. Two closely positioned inclusions can be accurately localized. Additionally, their fluorophore absorption coefficients can be quantified. However, the algorithm failes to reconstruct smaller or deeper inclusions. This is due to light attenuation in the medium. Reconstructions with noisy data are also achieved with a reasonable accuracy. Keywords fluorescence molecular imaging, radiative transport equation, modified finite volume method, frequency domain, inverse fluorescent source problem, Lagrangian formulation, adjoint method, biological tissue. Nomenclature c speed of light in vacuum (= 2.99793 10 8), m s −1 C concentration, M = mol cm −3 d measured fluorescent light intensity g anisotropy factor of the Henyey-Greenstein phase function * adjoint operator em emission field ex excitation field

Purpose Near‐infrared optical imaging aims to reconstruct the absorption μa and scattering μs coefficients in order to detect tumors at early stage. However, the reconstructions have only been limited to μa and μs due to theoretical and computational limitations. The authors propose an efficient method of the reconstruction, in three‐dimensional geometries, of the anisotropy factor g of the Henyey–Greenstein phase function as a new optical imaging biomarker. Methods The light propagation in biological tissues is accurately modeled by the radiative transfer equation (RTE) in the frequency‐domain. The reconstruction algorithm is based on a gradient‐based updating scheme. The adjoint method is used to efficiently compute the gradient of the objective function which represents the discrepancy between simulated and measured boundary data. A parallel implementation is carried out to reduce the computational time. Results We show that by illuminating only one surface of a tissue‐like phantom, the algorithm is able to accurately reconstruct optical values and different shapes (spherical and cylindrical) that characterize small tumor‐like inclusions. Numerical simulations show the robustness of the algorithm to reconstruct the anisotropy factor with different contrast levels, inclusion depths, initial guesses, heterogeneous background, noise levels, and two‐layered medium. The crosstalk problem when reconstructing simultaneously μs and g has been reported and achieved with a reasonable quality. Conclusions The proposed RTE‐based reconstruction algorithm is robust to spatially retrieve and localize small tumoral inclusions. Heterogeneities in g‐factor have been accurately reconstructed which makes the new algorithm a candidate of choice to image this factor as new intrinsic contrast biomarker for optical imaging.

We present for the first time the simultaneous reconstruction of three optical parameters distributions of biological tissues namely, the absorption µ a and scattering µ s coefficients, as well as the anisotropy factor g of the Henyey-Greenstein phase function as a new optical contrast. The 2D images are obtained from the simulation experiments and multi-source quantitative photoacoustic tomography with the radiative transfer equation (RTE) as light transport model. The image reconstruction method is based on a gradient-based optimization scheme. The adjoint method applied to the RTE is used to efficiently compute the gradient of the objective function. The results show simultaneous reconstructions of the three optical properties even with noisy data. The crosstalk problem between the three parameters is highlighted. Superior quality images are obtained for µ a compared to those of µ s and g. Moreover, our algorithm allows reconstructing inserts-like heterogeneities with very good spatial resolution and qualitative accuracy.

In optical tomography, the reconstructions have only been limited to the absorption µ a and scattering µ s coefficients of biological tissues due to theoretical and computational limitations. In this study, The authors propose an efficient method to reconstruct, in 3D geometries, the anisotropy factor g of the Henyey-Greenstein phase function as a new optical contrast for cancer diagnosis. The light propagation in biological tissues is accurately modeled by the Radiative Transfer Equation (RTE) in the frequency domain. The adjoint method is used to efficiently compute the gradient of the objective function. A parallel implementation is carried out to reduce the computational times. The results show the robustness of the algorithm to reconstruct the g-factor for different contrast levels and for different initial guesses. The crosstalk problem between µ s and g has been achieved with a reasonable quality which makes the new algorithm a candidate of choice to image this factor as new intrinsic contrast for optical imaging.

A new reconstruction algorithm for fluorescence optical tomography of biological tissues is proposed. The radiative transport equation in the frequency domain is used to model light propagation. The adjoint method studied in this work provides an efficient way for solving the inverse problem. The methodology is applied to a 2D tissue-like phantom subjected to a collimated laser beam. Indocyanine Green is used as fluorophore. Reconstructed images of the spatial fluorophore absorption distribution is assessed taking into account the residual fluorescence in the medium. We show that illuminating the tissue surface from a collimated centered direction near the inclusion gaves a better reconstruction quality. Two closely positioned inclusions can be accurately localized and quantified. However, the algorithm fails to reconstruct smaller or deeper inclusions due to light attenuation in the medium. Reconstructions with noisy data are also achieved with a reasonable accuracy.