Section: New Results

Other new results

Superconvergent Cartesian Methods for Poisson type Equations in 2D–domains [21]

Team participants: Olivier Gallinato, Clair Poignard

In this work, we present three superconvergent Finite Difference methods on Cartesian grids for Poisson type equations with Dirichlet, Neumann or Robin conditions. Our methods are based on finite differences and high-order discretizations of the Laplace operator, to reach the superconvergence properties, in the sense that the first-order (and possibly the second-order) derivatives of the numerical solution are computed at the same order as the solution itself. We exhibit the numerical conditions that have to be fulfilled by the schemes to get such superconvergences and extensively illustrate our purpose by numerical simulations. We conclude by applying our method to a free boundary problem for cell protrusion formation recently proposed by the authors and colleagues. Note that quasistatic Stefan-like problem can be accurately solved by our methods.

Adaptive radiotherapy in routine: The radiation oncologist's point of view [14]

Team participant: Olivier Saut

Other participants: Bénédicte Henriques de Figueiredo, Adeline Petit, Paul Sargos, Guy Kantor, Claudia Pouypoudat, Christina Zacharatou, Mikael Antoine (Institut Bergonié, radiology department)

Adaptive radiotherapy is defined as all processes leading to the modification of a treatment plan on the basis of patient-specific variations observed during the course of a treatment. This concept is currently of particular relevance due to the development of onboard volumetric imaging systems, which allow for daily viewing of variations in both tumour and organs at risk in terms of position, shape or volume. However, its application in routine clinical practice is limited due to the demanding nature of the processes involved (re-delineation and replanning) and increased dependence on available human resources. Even if "online" strategies, based on deformable image registration (DIR) algorithms, could lead to a reduction in both work and calculation time, for the moment their use is limited to the research field due to uncertainties surrounding the validity of results gathered. Other strategies without DIR can be used as "offline" or "hybrid offline-online" strategies that seem to offer a compromise between time consumption and therapeutic gain for the patient.