Isogeometric Approach to Optical Tomography

Optical Tomography is an imaging modality that enhances early diagnosis of disease through use of harmless Near-Infrared rays instead of conventional x-rays. The subsequent images are used to reconstruct the object. However Optical Tomography has not been effectively utilized due to the complicated photon scattering phenomenon and ill-posed nature of the corresponding image reconstruction scheme.

The major method for reconstruction of the object is based on an iterative loop that constantly minimizes the difference between the predicted model of photon scattering with acquired images. Currently the most effective method of predicting the photon scattering pattern is the solution of the Radiative Transfer Equation (RTE) using the Finite Elements Method (FEM). However, the conventional FEM uses classical C0 interpolation functions, which have shortcomings in terms of continuity of the solution over the domain as well as proper representation of geometry. Hence higher discretization is necessary to maintain accuracy of gradient-based results which may significantly increase the computational cost in each iteration.

This research implements the recently developed Isogeometric Approach (IGA) and particularly IGA-based FEM to address the aforementioned issues. The IGA-based FEM has the potential to enhance adaptivity and reduce the computational cost of discretization schemes. The research in this study applies the IGA method to solve the RTE with the diffusion approximation and studies its behavior in comparison to conventional FEM.

The results show comparison of the IGA-based solution with analytical and conventional FEM solutions in terms of accuracy and efficiency. While both methods show high levels of accuracy in reference to the analytical solution, the IGA results clearly excel in accuracy. Furthermore, FE solutions tend to have shorter runtimes in low accuracy results. However, in higher accuracy solutions, where it matters the most, the IGA proves to be considerably faster.