A high-order finite element method for forward problem in diffuse optical tomography

Diffuse optical tomography (DOT) is a non-invasive imaging modality for visualizing and continuously monitoring tissue and blood oxygenation levels in brain and breast. DOT includes an ill-posed inverse problem. The image reconstruction algorithm in the inverse problem involves generating images by means of forward modeling results and the boundary measurements. A for ward model describes the dependence of the photon intensity data on the distribution of absorbing and scattering coefficients. The ability of the forward model to generate the corresponding data efficiently plays an important issue in DOT image reconstruction. Small measurement or forward modeling errors can lead to unbounded fluctuations in the image reconstruction algorithm. Using a first-order finite element method for forward modeling, the discretization error is reduced by increasing the number of elements. However, increasing the number of elements may cause a critical issue in the ill-posed inverse problem. This paper focuses on applying the high-order finite element method for forward modeling. In this method, the polynomial degree of shape functions is increased and the mesh size is kept fixed. Numerical results are compared with an analytical solution.