PhD program started in July 2008
Diffuse Optical Imaging (DOI), the study of the propagation of Near Infra-Red (NIR) light in biological
media, is an emerging method answering the current concerns in medical imaging. Its state-of-the-art is
non-invasive, versatile and reasonably expensive, allowing new investigations to be carried out.
The DOI physical problem is here treated with the Diffusion Approximation (DA) scheme and
various reconstruction techniques. In the particular framework of Diffuse Optical Tomography (DOT),
the development 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 in vivo
functional three-dimensional imaging. However, these two methods have always been separated and
this work is the first attempt to combine them. Though not new in numerical simulations and problem
solving, this combination of the Boundary Elements Method (BEM) and the Finite Elements Method
(FEM) needed a theoretical study in our domain.
The BEM-FEM is designed to tackle layered turbid media problems. It focuses on the region of
interest by creating a volume mesh and reconstructing in this region only. All other regions are treated
as piecewise-constant in a surface-integral approach. We validate the model in concentric spheres, with
different positions of the volume-integral treated area and found 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. These results show the effectiveness of the BEM-
FEM in situations where the organ of interest is surrounded by superficial layers.
In the interest of computational speed, we are developing an acceleration technique for the BEM
part of the code. Such a method could ease the evaluation of the BEM matrix, along with a faster
obtention of the solutions.
Another use of the BEM in Diffuse Optical Imaging (DOI) is also outlined. NIR Spectroscopy
(NIRS) is nowadays a common sight in any research group equipment which deals with blood-related is-
sues. It is particularly used in brain monitoring. Unfortunately, this technique is very often accompanied
by rudimentary analysis of the data and the three-dimensional appreciation of the problem is missed.
The innovative method we are developing represents a great leap forward.
