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Section: New Results
Non conservative transport equations for cell population dynamics
Cell-kinetics based calibration of a multiscale model: application to cell population dynamics in ovarian follicles
Participants : Benjamin Aymard [ICL] , Frédérique Clément, Danielle Monniaux [INRA] , Marie Postel.
In [30] , we present a strategy for tuning the parameters of a multiscale model of structured cell populations in which physiological mechanisms are embedded into the cell scale. This strategy allows one to cope with the technical difficulties raised by such models, that arise from their anchorage in cell biology concepts: localized mitosis, progression within and out of the cell cycle driven by time- and possibly unknown-dependent, and nonsmooth velocity coefficients. We compute different mesoscopic and macroscopic quantities from the microscopic unknowns (cell densities) and relate them to experimental cell kinetic indexes. We study the expression of reaching times corresponding to characteristic cellular transitions in a particle-like reduction of the original model. We make use of this framework to obtain an appropriate initial guess for the parameters and then perform a sequence of optimization steps subject to quantitative specifications. We finally illustrate realistic simulations of the cell populations in cohorts of interacting ovarian follicles.
Dimensional reduction of a multiscale cell population model
Participants : Frédérique Clément, Frédéric Coquel [CMAP] , Marie Postel, Kim Long Tran.
We have designed a dimensional reduction of a multiscale structured cell population model, consisting of a system of 2D transport equations, into a system of twice as many 1D transport equations. The reduced model is obtained by computing the moments of the 2D model with respect to one space variable. The 1D solution is defined from the solution of the 2D model starting from an initial condition that is a Dirac mass in the direction removed by reduction. Long time properties of the 1D model solution are obtained in connection with properties of the support of the 2D solution for general case initial conditions. Finite volume numerical approximations of the 1D reduced model can be used to compute the moments of the 2D solution with satisfying accuracy. The numerical robustness is studied in the scalar case and a full scale vector case is presented.