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Cell-Kinetics Based Calibration of a Multiscale Model of Structured Cell Populations in Ovarian Follicles

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HAL
Keywords
  • Transport Equations
  • Parameter Calibration
  • Structured Cell Populations
  • Cell Kinetics Ams Subject Classifications 92B05
  • 35Q92
  • [Math] Mathematics [Math]
  • [Sdv] Life Sciences [Q-Bio]
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Abstract

In this paper, 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. Introduction. In this paper, we deal with the question of the numerical calibration of an existing multiscale model of cell-structured populations in the physiological context of ovulation. This model was formulated as a system of weakly coupled, non conservative transport equations with controlled velocities and sink terms, where the unknowns are the cell densities in each follicle [9, 8]. A number of theoretical studies have established the well-posedness of the model [19], examined optimal control problems related to the ovulatory trajectories in the framework of hybrid optimal control theory [6], and studied the reachability of final states corresponding to either ovulatory or atretic cases in the framework of backwards reachable sets [8]. Implementation of the model in an efficient and reliable computing environment has involved the design of a finite-volume scheme dealing with the discontinuous coefficients [3], embedding this scheme within a dedicated adaptive mesh based on a multi-resolution approach [4], and implementing it on parallel architecture [2]. This has left the question of model calibration to biological specifications to be resolved. We have to face a generic, yet unsolved issue in parameter fitting for physiologically-oriented multiscale mathematical models: although mechanistic knowledge in molecular and cell biology is available on the lower scales, quantitative experimental data are rather available on the higher scales. In our case, the question is how to infer the parameters entering the microscopic functions (on the level of the follicular cells) from mesoscopic (on the level of the individual follicles, i.e. the number of follicular cells) or macroscopic (on the level of the populations of follicles) information. In addition, even on the macroscopic level, data remain rather scarce and are rarely obtained directly as

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