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.
In optical tomography, the reconstructions have only been limited to the absorption μa and scattering μs 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 μs 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.
An important issue in tissue optics and Optical Tomography is to have an efficient forward solver. In this work, a new numerical algorithm was developed for solving light propagation with the radiative transport equation within a three-dimensional absorbing and a highly forward-scattering medium such as a biological tissue subjected to an incident beam. Both elastically scattered light and fluorescence light were studied. Two steady state problems used to assess the performance and accuracy of the proposed algorithm are presented. We show that it is possible to obtain a good level of accuracy with a deterministic numerical method: relative differences less than 1.7% and 4.5% were obtained when compared against Monte Carlo solutions for problems of elastically scattered light and fluorescence light, respectively.
We examine the accuracy of a modified finite volume method compared to analytical and Monte Carlo solutions for solving the radiative transfer equation. The model is used for predicting light propagation within a two-dimensional absorbing and highly forward-scattering medium such as biological tissue subjected to a collimated light beam. Numerical simulations for the spatially resolved reflectance and transmittance are presented considering refractive index mismatch with Fresnel reflection at the interface, homogeneous and two-layered media. Time-dependent as well as steady-state cases are considered. In the steady state, it is found that the modified finite volume method is in good agreement with the other two methods. The relative differences between the solutions are found to decrease with spatial mesh refinement applied for the modified finite volume method obtaining <2.4% . In the time domain, the fourth-order Runge-Kutta method is used for the time semi-discretization of the radiative transfer equation. An agreement among the modified finite volume method, Runge-Kutta method, and Monte Carlo solutions are shown, but with relative differences higher than in the steady state.
Optical tomography is a medical imaging technique based on light propagation in the near infrared (NIR) part of the spectrum. We present a new way of predicting the short-pulsed NIR light propagation using a time-dependent two-dimensional-global radiative transfer equation in an absorbing and strongly anisotropically scattering medium. A cell-vertex finite-volume method is proposed for the discretization of the spatial domain. The closure relation based on the exponential scheme and linear interpolations was applied for the first time in the context of time-dependent radiative heat transfer problems. Details are given about the application of the original method on unstructured triangular meshes. The angular space (4πSr) is uniformly subdivided into discrete directions and a finite-differences discretization of the time domain is used. Numerical simulations for media with physical properties analogous to healthy and metastatic human liver subjected to a collimated short-pulsed NIR light are presented and discussed. As expected, discrepancies between the two kinds of tissues were found. In particular, the level of light flux was found to be weaker (inside the medium and at boundaries) in the healthy medium than in the metastatic one.
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