Biomedical subjects

Guillaume Bal

Publications and source records attributed to Guillaume Bal.

3 recordsLinked to original sources

PubMed2006

Radiative transfer equations with varying refractive index: a mathematical perspective.

Established mathematical techniques to model the energy density of high-frequency waves in random media by radiative transfer equations and to model the small mean-free-path limit of radiative transfer solutions by diffusion equations are reviewed. These techniques are then applied to the derivation of radiative transfer and diffusion equations for the radiance, also known as specific intensity, of electromagnetic waves in situations where the refractive index of the underlying structure varies smoothly in space.

Journal Article↗

PubMed2004

Algorithm for solving the equation of radiative transfer in the frequency domain.

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume methods. Two numerical simulations are presented.

Algorithms↗

PubMed2003

Generalized diffusion model in optical tomography with clear layers.

We introduce a generalized diffusion equation that models the propagation of photons in highly scattering domains with thin nonscattering clear layers. Classical diffusion models break down in the presence of clear layers. The model that we propose accurately accounts for the clear-layer effects and has a computational cost comparable to that of classical diffusion. It is based on modeling the propagation in the clear layer as a local tangential diffusion process. It can be justified mathematically in the limit of small mean free paths and is shown numerically to be very accurate in two- and three-dimensional idealized cases. We believe that this model can be used as an accurate forward model in optical tomography.

Diffusion↗