Innovative boundary integral and hybrid methods for diffuse optical imaging

Diffuse Optical Imaging (DOI), the study of the propagation of Near Infra-Red (NIR) light in biological media, is an emerging method in medical imaging. Its state-of-the-art is non-invasive, versatile and reasonably inexpensive. In Diffuse Optical Tomography (DOT), the adaptation of numerical methods such as the Finite Element Method (FEM) and, more recently the Boundary Element Method (BEM), has allowed the treatment of complex problems, even for in vivo functional three-dimensional imaging. This work is the first attempt to combine these two methods in DOT. The BEM-FEM is designed to tackle layered turbid media problems. It focuses on the region of interest by restraining the reconstruction to it. All other regions are treated as piecewiseconstant in a surface-integral approach. We validated the model in concentric spheres and found that it compared well with an analytical result. We then performed functional imaging of the neonate’s motor cortex in vivo, in a reconstruction restricted to the brain, both with FEM and BEM-FEM. Another use of the BEM in DOI is also outlined. NIR Spectroscopy (NIRS) devices are particularly used in brain monitoring and Diffuse Optical Cortical Mapping (DOCM). Unfortunately, they are very often accompanied by rudimentary analysis of the data and the 3D appreciation of the problem is missed. The BEM DOCM developed in the current work represents an improvement, especially since a topographical representation of a motor activation in the cortex is clearly reconstructed in vivo. In the interest of computational speed an acceleration technique for the BEM has been developed. The Fast Multipole Method (FMM), which is based on the decomposition of Green’s function on a basis of Bessel and Hankel functions, eases the evaluation of the BEM matrix, along with a faster calculation of the solutions.