Section: New Results

Application of shape and topology design to biology and medecine

Participants : Abderrahmane Habbal, Nicholas Ayache [ Asclepios Project ] , Grégoire Malandain [ Asclepios Project ] , H. Barelli [ IPMC ] , B. Mari [ IPMC ] .

In the framework of a research collaborative action COLOR 2005, involving three research teams specialized in cell biology (IPMC), image processing and mathematical modeling (Asclepios and Opale project-teams), two test-cases have been defined : angiogenesis and wound healing. The latter application has been given particular emphasis, since experimental results from biology can be obtained more easily.

Thus, several images and movies are quickly collected from experimental results in biology, concerning mono-layer MDCK cell healing. The analysis of these images allows us to observe that the cell migration velocity is constant during the healing.

In order to numerically model the migration, Fisher's model (non-linear parabolic equations) seems relevant to us. Indeed, it is characterized by a constant front velocity. The first results obtained (see Figure 6 ). are very promising and confirm the adequacy of Fisher's model. As a consequence of this work, new data are provided to biologists (diffusive coefficients) to describe the behavior of MDCK cells in presence of HGF and inhibitors.

Figure 6. Mathematical modeling of the dorsal closure of Drosophila (DC). Understanding wound dynamics is a keystone in designing healing processes and computational modeling is expected to help specialists with qualitative and quantitative information, as soon as the model is validated. The picture shows a PDE-based theoretical wound (in red) which perfectly fits the biological videoscopy during all the closure duration. (From Almeida-Bagnerini-Habbal-Serman-Noselli .)