François Beux

Automatic evaluation of arterial diameter variation from vascular echographic images

An automatic procedure for accurate arterial diameter evaluation from B-mode images obtained by diagnostic ultrasound systems is presented. It is used for measuring brachial artery dilation following reactive hyperemia induced by forearm ischemia, which is an appropriate parameter to study endothelial function in humans. B-mode images obtained from the diagnostic ultrasound system are acquired on a personal computer as grey intensity fields (pixels). A completely automatic algorithm is then applied and the artery walls are identified by two discrete sets of points. Artery diameter is evaluated by parabolic least-square approximation. The accuracy and extensive range of applicability of the diameter evaluation procedure were demonstrated both by preliminary analytic test cases and in vivo analyses. Reproducibility of the diameter estimate was assessed by in vivo measurements. The proposed procedure permits fast and accurate analysis of large amounts of data, because it requires no action by the operator. It thus represents a valuable tool for assessment of endothelium-dependent vasodilation, especially in large, multicentric clinical trials.

Current-density approximation for efficient computation of the electrostatic field in wire-plate precipitators

In this paper, numerical computation of ionic space charge and electric field produced by corona discharge in an electrostatic precipitator is addressed. The problem is defined by a reduced set of the Maxwell equations. The efficiency of numerical iterative computations is significantly improved by deriving an initial field as close as possible to the final solution from an approximation of the current-density field J. Different techniques to approximate J are proposed. A first analytic approximation J/spl tilde/ is derived, which verifies by construction the boundary conditions of the problem and, in particular, gives the correct average value at the plate. A second approximation is also considered, which contains a free parameter that can be computed by an optimization procedure based on the known value of the potential at the wire. Finally, Karhunen-Love (KL) decomposition is used and the current-density field is expressed as the sum of J/spl tilde/ and of a linear combination of few KL basis functions. The coefficients can be determined again by an optimization algorithm. Starting from these approximated J fields, a procedure is proposed to obtain, at negligible computational cost, an estimate of the complete electrostatic field. It is shown that this estimate is in all cases much closer to the exact solution than guesses typically employed in the literature. Hence, when it is used as initialization for standard numerical solvers, this significantly improves the efficiency of the numerical algorithm. In particular, the initialization based on the second approximation gives a significant efficiency gain without any noticeable additional cost.

Original article: Implicit time advancing combined with two finite-volume methods in the simulation of morphodynamic flows

Numerical simulation of morphodynamic problems is considered. The physical model is based on the shallow-water equations coupled with the Exner equation closed by the Grass model to describe the time evolution of the bed profile. The SRNH predictor-corrector scheme and a modified Roe scheme for non-conservative systems of equations are considered for space discretization. Second-order accuracy in space is achieved through variable reconstruction. These schemes were previously used in the simulation of the considered problems together with explicit time advancing. Linearized implicit time-advancing versions are generated here, in which the flux Jacobians are computed through automatic differentiation. Second-order accuracy in time is obtained through a backward differentiation formula associated with a defect-correction approach. For both the considered numerical methods, the explicit and implicit versions are compared in terms of accuracy and efficiency for one-dimensional and two-dimensional morphodynamic problems characterized by different time scales for the evolution of the bed and of the water flow.

Comparison of Explicit and Implicit Time Advancing in the Simulation of a 2D Sediment Transport Problem

The simulation of sediment transport, based on the shallow-water equations coupled with Grass model for the sediment transport equation is considered. The aim of the present paper is to investigate the behavior of implicit linearized schemes in this context. A finite-volume method is considered and second-order accuracy in space is obtained through MUSCL reconstruction. A second-order time accurate explicit version of the scheme is obtained through a two step Runge-Kutta method. Implicit linearized schemes of second-order of accuracy in time are derived thanks to a BDF method associated with a Defect Correction technique. The different time-advancing schemes are compared, using a 2D sediment transport problem, with different types of flow/bed interactions. The implicit one largely outperforms the explicit version for slow flow/bed interactions while in the case of fast flow/bed interactions, the CPU time of both time integration schemes are comparable. Thus, the implicit scheme turns out to be a good candidate to simulate flows with sediment transport in practical applications.