Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases...
This study presents a numerical investigation of basic interactions between respiratory
mucus motion, air circulation and epithelium ciliated cells vibration. One focuses on
identification of meaningful rheological parameters, physiological and numerical
simulation dimensioning. These preliminary results are crucial before the study of more
general configurations of respiratory mucus motion. The numerical study presented in this
work aims at providing...
In this work, we investigate the influence of a spray evolving in the air, in the
respiration framework. We consider two kinds of situations: a moving spray in a motionless
fluid, and motionless particles in a Poiseuille flow. We observe that the spray
retroaction may not be neglected in some situations which can really happen, for instance,
when one considers rather big particles, as it is possible for polluting particles and
even for some therapeutic...
This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time
dependent case. Whereas in the second part some preliminary numerical simulations aim to
give orders of magnitudes in terms of numerical costs of direct 3D simulations.
We consider, in the first part, the time dependent rough problem for a simplified heat
equation in a straight channel that...
This work is devoted to the study of migraine with aura in the human brain. Following
[6], we class migraine as a propagation of a wave of depolarization through
the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly
presented. The equation is considered in a duct containing a bend, in order to model one
of the numerous circumvolutions of the brain. For a wide set of parameters, one can
establish the existence...
Polymerization of proteins is a biochemical process involved in different diseases.
Mathematically, it is generally modeled by aggregation-fragmentation-type equations. In
this paper we consider a general polymerization model and propose a high-order numerical
scheme to investigate the behavior of the solution. An important property of the equation
is the mass conservation. The WENO scheme is built to preserve the total mass of proteins
along time....
We consider the radiative transfer equation (RTE) with reflection in a three-dimensional
domain, infinite in two dimensions, and prove an existence result. Then, we study the
inverse problem of retrieving the optical parameters from boundary measurements, with help
of existing results by Choulli and Stefanov. This theoretical analysis is the framework of
an attempt to model the color of the skin. For this purpose, a code has been developed to
solve...
In this work, we are interested in two different diffusion models for multicomponent
mixtures. We numerically recover experimental results underlining the inadequacy of the
usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in
various situations. This model nonlinearly couples the mole fractions and the fluxes of
each component of the mixture. We then consider a subregion of the lower part of the lung,
in which we compare...
We prescrit a method to simulate the motion of self-propelled rigid particles in a
twodimensional Stokesian fluid, taking into account chemotactic behaviour. Self-propulsion
is modelled as a point force associated to each particle, placed at a certain distance
from its gravity centre. The method for solving the fluid flow and the motion of the
bacteria is based on a variational formulation on the whole domain, including fluid and
particles: rigid...
Electroporation consists in increasing the permeability of a tissue by applying high
voltage pulses. In this paper we discuss the question of optimal placement and optimal
loading of electrodes such that electroporation holds only in a given open set of the
domain. The electroporated set of the domain is where the norm of the electric field is
above a given threshold value. We use a standard gradient algorithm to optimize the
loading of the electrodes...
This article is devoted to the construction of a mathematical model describing the early
formation of atherosclerotic lesions. The early stage of atherosclerosis is an
inflammatory process that starts with the penetration of low density lipoproteins in the
intima and with their oxidation. This phenomenon is closely linked to the local blood flow
dynamics. Extending a previous work [5] that was mainly restricted to a
one-dimensional setting, we couple...
In this article we propose a model to describe the inflammatory process which occurs
during ischemic stroke. First, an introduction to some basic concepts about the biological
phenomenon is given. Then, a detailed derivation of the model and the numerical scheme
used are presented. Finally, the studies of the model robustness and sensitivity are
showed and some numerical results on the time and space evolution of the process are
presented and discussed....
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