A homogenized cerebrospinal fluid model for diffuse optical tomography in the neonatal head.

Diffuse optical tomography is a non-invasive and non-irradiating medical imaging technique that is particularly suitable for cerebral monitoring of newborns since it can be used at the bedside of the patient. Here, a new model for optical tomography in the neonatal brain is presented that takes into account the presence of arachnoid trabeculae in the cerebrospinal fluid (CSF). It is known that the classical diffusion approximation (DA) for light propagation is at the limit of validity in the CSF layer due to the low values of the absorption and scattering coefficients. The new model is obtained by the DA of the homogenized radiative transfer equation and is rigorously justified. Numerical results in two and three dimensions attest for the improved sensitivity of the new model to the presence of perturbations in the brain layer.

EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity.

The paper is devoted to the analysis of electroencephalography (EEG) in neonates. The goal is to investigate the impact of fontanels on EEG measurements, i.e. on the values of the electric potential on the scalp. In order to answer this clinical issue, a complete mathematical study (modeling, existence and uniqueness result, realistic simulations) is carried out. A model for the forward problem in EEG source localization is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. From a mathematical point of view, the model consists in solving an elliptic problem with a singular source term in an inhomogeneous medium. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy norm (H¹-norm). Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model including or not the fontanels have been obtained and corroborate the theoretical results. A mathematical tool related to the concept of Gâteau derivatives is introduced which is able to measure the sensitivity of the electric potential with respect to small variations in the fontanel conductivity. This study attests that the presence of fontanels in neonates does have an impact on EEG measurements.