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Section: New Results

Validation of time dependent diffusion approaches for activated and inhibited cell sheet closure

Participants : Abderrahmane Habbal, Hélène Barelli [Univ. Nice Sophia Antipolis, CNRS, IPMC] , Grégoire Malandain [Inria, EPI Morpheme] , Boutheina Yahyaoui [PhD, LAMSIN, Univ. Tunis Al Manar] , Mekki Ayadi [LAMSIN, Univ. Tunis Al Manar] .

We have studied in [21] five MDCK cell monolayer assays in a reference, activated and inhibited migration conditions. Modulo the inherent variability of biological assays, we have shown that in the assay where migration was not exogeneously activated or inhibited, the wound velocity was constant and the Fisher-KPP equation was able to accurately predict, until the final closure of the wound, the evolution of the wound area, the mean velocity of the cell front, and the time at which the closure occurred. When activated or inhibited, the F-KPP equation with constant parameters was unable to reproduce the observed biological cell sheet behavior. We modify the original equation, making the diffusion and proliferation parameters time dependent, following a sigmoid profile. We then set up an optimization loop to identify the sigmoids parameters, by computing a classical error indicator (difference between a computed density and the observed one, obtained through image processing) as done in the cited reference. We then obtain results which convincingly show that our approach is efficient : in both cases, inhibited and activated, the time varying identified parameters allow us to accurately predict until the final closure the evolution of the wound area.