Damien Voyer

COMPARISON OF METHODS FOR MODELING UNCERTAINTIES IN A 2D HYPERTHERMIA PROBLEM

Uncertainties in biological tissue properties are weighed in the case of a hyperthermia problem. Statistic methods, experimental design and kriging technique, and stochastic methods, spectral and collocation approaches, are applied to analyze the impact of these uncertainties on the distribution of the electromagnetic power absorbed inside the body of a patient. The sensitivity and uncertainty analyses made with the different methods show that experimental designs are not suitable in this kind of problem and that the spectral stochastic method is the most efficient method only when using an adaptative algorithm.

A Stochastic Collocation Method Combined With a Reduced Basis Method to Compute Uncertainties in Numerical Dosimetry

A reduced basis method is introduced to deal with a stochastic problem in a numerical dosimetry application in which the field solutions are computed using an iterative solver. More precisely, the computations already performed are used to build an initial guess for the iterative solver. It is shown that this approach significantly reduces the computational cost.

Numerical Dosimetry of Induced Phenomena in the Human Body by a Three-Phase Power Line

We computed by finite element the fields induced in an heterogeneous model of the human body by both the electric and magnetic field generated by a three-phase power line. Results were partially validated and analyzed by comparison with existing data with uniform magnetic field. Induced currents due to both E and B were developed inside the body in an asymmetrical manner.

Probabilistic methods applied to 2D electromagnetic numerical dosimetry

Purpose – The aim is to apply probabilistic approaches to electromagnetic numerical dosimetry problems in order to take into account the variability of the input parameters.Design/methodology/approach – A classic finite element method is coupled with probabilistic methods. These probabilistic methods are based on the expansion of the random parameters in two different ways: a spectral expansion and a nodal expansion.Findings – The computation of the mean and the variance on a simple scattering problem shows that only a few hundreds calculations are required when applying these methods while the Monte Carlo method uses several thousands of samples in order to obtain a comparable accuracy.Originality/value – The number of calculations is reduced using several techniques: a regression technique, sparse grids computed from Smolyak algorithm or a suited coordinate system.

Numerical treatment of rounded and sharp corners in the modeling of 2D electrostatic fields

This work deals with numerical techniques to compute electrostatic fields in devices with rounded corners in 2D situations. The approach leads to the solution of two problems: one on the device where rounded corners are replaced by sharp corners and the other on an unbounded domain representing the shape of the rounded corner after an appropriate rescaling. Both problems are solved using different techniques and numerical results are provided to assess the efficiency and the accuracy of the techniques.

Dynamical modeling of tissue electroporation

In this paper, we propose a new dynamical model of tissue electroporation. The model is based on equivalent circuit approach at the tissue. Considering two current densities from cells and extracellular matrix, we identify the macroscopic homogenised contribution of the cell membranes. Our approach makes it possible to define a macroscopic homogenised electric field and a macroscopic homogenised transmembrane potential. This provides a direct link between the cell scale electroporation models and the tissue models. Finite element method adapted to the new non-linear model of tissue electroporation is used to compare experiments with simulations. Adapting the phenomenological electroporation model of Leguèbe et al. to the tissue scale, we calibrate the tissue model with experimental data. This makes two steps appear in the tissue electroporation process, as for cells. The new insight of the model lies in the well-established equivalent circuit approach to provide a homogenised version of cell scale models. Our approach is tightly linked to numerical homogenisation strategies adapted to bioelectrical tissue modeling.

Numerical Identification of Effective Multipole Moments of Polarizable Particles

In electromechanics of particles, the effective moment method relies on the knowledge of the induced multipole moments. For arbitrary shaped particles, only linear multipole moments are usually considered in the literature. On cylindrically symmetric particles, we show that the neglected multipole moments can be computed, and that they should be taken into consideration.

Eddy Currents and Corner Singularities

Eddy current problems are addressed in a bidimensional setting where the conducting medium is non-magnetic and has a corner singularity. For any fixed parameter δ linked to the skin depth for a plane interface, we show that the flux density |∇Aδ| is bounded near the corner unlike the perfect conducting case. Then as δ goes to zero, the first two terms of a multiscale expansion of the magnetic potential are introduced to tackle the magneto-harmonic problem. The heuristics of the method are given and numerical computations illustrate the obtained accuracy.

Dynamic Modeling of Electroporation for the Computation of the Electric Field Distribution Inside Biological Tissues during the Application of the Pulse Voltage

A dynamic model of electroporation is proposed in order to compute at the tissue scale the distribution of the electric field during the application of the voltage pulse. In this approach, two kinds of density currents are considered: the first one, derived from a model at the cell scale, flows through the cells and the second one flows through the extracellular medium. Simulations have been performed in relation with in vivo experiments made on rabbit livers: they show that the modeling is able to reproduce the chronograms of the current measured through the needles.

PERTURBATION METHOD FOR THE CALCULATION OF LOSSES INSIDE CONDUCTORS IN MICROWAVE STRUCTURES

A perturbation method based on the decoupling of propagation and diffusion phenomenons is proposed in order to calculate losses in microwave structures. Starting from the first problem in which the conducting regions are not described, a perturbation is calculated by solving a second problem restricted to the vicinity of the conductors; iterations between these problems can be performed when the perturbed solution is not sufficiently accurate. The perturbation approach is however more accurate than a method based on a surface impedance model, without introducing the huge calculations that appear when both conducting region and external medium are described in a single problem. 2D examples are presented using the finite element method and the integral equation method.