Investigations On Shape-Based Diffuse Optical Tomography: Theory And Methodology

As a new noninvasive medical imaging technology that can provide functional information of tissues, diffuse optical tomography (DOT) has become one of the focused topics. However, due to the strong scattering nature of most tissue types and relatively limited number of the available measurements, the conventional voxel- based DOT image reconstruction is a severely ill-posed inverse problem, leading to a poor spatial resolution. In this paper we propose a different approach using boundary element method (BEM) based on the diffusion equation (DE) and present a shape-based image reconstruction method. The shape-based DOT can simultaneously reconstruct the boundary-describing parameters and optical properties of the disjoint domains of distinct tissue types, which makes the image reconstruction less ill-posed by providing implicit regularization due to the reduced dimensionality of the problem.The diffusion approximation (DA) to the RTE is commonly used for diffuse optical imaging, which has been validated to give reasonable accuracy in scattering dominated media. The BEM approach is a natural choice for shape-based DOT to recover boundaries, since the boundaries, which are discretized in the boundary integration approach, are just the unknowns of the inverse problem. The result of the forward model is compared with analytical solution and Monte-Carlo simulation to demonstrate its validity. The boundaries of the unknown sub-domains are described by Fourier series representation or spherical harmonics representation. Then the relationship between shape parameters and measurements are established by using BEM approach.Based on the above forward model and the optimization expression of the reconstruction, the More-type Levenberg-Marquardt method and the Gauss-Newton method have been employed to solve the inverse problem. We propose a two-stage image reconstruction strategy to enhance the performance of the image reconstruction. An adjoint scheme based on reciprocity principle has been presented in this paper to avoid the direct calculation of the Jacobian for the corresponding shape derivatives. To eliminate the influence of the instrumental systematic and statistic noise during the reconstruction process, as well as to suppress the amplitude scaling between the experimental and simulated datasets, a difference imaging scheme is employed. The reconstruction results of the numerical simulation under two-dimensional and three-dimensional model with targets of different optical coefficients and topologies illuminate the validity and reliability of the image reconstruction algorithm. The preliminary phantom experiment was implemented by the time-correlated single photon counting system, and the experimental result demonstrates that the proposed methodology is suitable for further application into DOT.