Investigations On Radiative Transfer Equation-Based Diffuse Optical Tomography

Diffuse optical tomography(DOT) is a new noninvasive optical imaging technology. In DOT, images of optical properties which are relative to the physiological and pathological information of tissues are derived based on the measurements of radiance on the surface of the object which is irradiate by visible light or near-infrared light. The model-based iterative image reconstruction scheme is extensively adopted in DOT. It is very important to establish a forward model which can accurately describe the migration of photon in tissue. At the present time, the Diffusion Equation(DE) is the widely accepted forward model in DOT. But, DE is restricted in some region due to it is a diffusion approximation to Radiative Transfer Equation(RTE). As a result, developing a DOT scheme based on RTE is necessary.According to the three-dimensional RTE, the two-dimensional time independent RTE which rigorously satisfies the migration of photon in tissue is derived. The discrete solid angle method and finite difference method is advanced to numerically solve the 2D time independent RTE. The numerical result is compared with the golden rule-Monte Carlo simulation. In allusion to the accuracy of numerical result, the RTE is solved under different number of discrete solid angle and different step-size of spatial mesh grid. The computation time and average relative error are recorded to evaluate the performance of the numerical results. The 120 and 0.25mm is decided to be the best strategy of number of discrete solid angle and step-size of mesh grid in solving the RTE. Compared the outgoing photon densities which are acquired by numerical solving the RTE with natural boundary condition and inflow zero boundary condition, the difference-data is proposed to decrease the error which caused by mismatch of boundary condition. The numerical method is extend to solve three dimensional time independent RTE.Based on the RTE and the algebraic reconstruction technique (ART), an advanced algorithm of diffusion optical tomography is developed within the framework of Newton- -Jacobi matrix is derived using perturbation and Green function which avoid massive calculation in directly solving Jacobi matrix. The standard ART is improved to achieve simultaneous reconstruction of both the absorption and the scattering images for small-animal-sized geometry. The numerical simulations validated the feasibility of the proposed scheme and demonstrated the superiority of the modified ART over the standard one in separation of both the coefficients.The origin of cross-talk in reconstruction of both optical coefficients is analyzed, and the generalized pulse spectrum technique(GPST) is advanced in time-domain DOT to erase the cross-talk in reconstructed image. The reconstructed images of several typical simulated tissues using GPST proved that the scheme is effectively restrain the cross-talk in reconstruction of both optical coefficients.Finally, the forward model and image reconstruction algorithm advanced in this article is tested using previously established time-correlated single photon counting system in our laboratory.