Population balances in case of crossing characteristic curves: Application to T-cells immune response - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Canadian Journal of Chemical Engineering Année : 2016

Population balances in case of crossing characteristic curves: Application to T-cells immune response

Résumé

The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, mass, and protein concentration) is typically modelled by a population balance equation, a first-order linear hyperbolic partial differential equation. The characteristics described by internal variables usually vary monotonically with the passage of time. A particular difficulty appears when the characteristic curves exhibit different slopes from each other and therefore cross each other at certain times. In particular, such a crossing phenomenon occurs during T-cell immune response when the concentrations of protein expressions depend upon each other and also when some global protein (e.g. Interleukin signals) that is shared by all T-cells is involved. At these crossing points, the linear advection equation is not possible by using the hyperbolic conservation laws in a classical way. Therefore, a new transport method is introduced in this article that is able to find the population density function for such processes. A multi-scale mathematical modelling framework is employed. At the first scale, two processes, the activation and reaction terms (assimilated as nucleation and growth in particulate processes), are studied as independent processes. At the second scale, the dynamic variation in the population density of activated T-cells is investigated in the presence of activation and reaction terms. The newly-developed transport method is shown to work in the case of crossing characteristics and to provide a smooth solution at the crossing points in contrast to the classical numerical techniques.
Fichier principal
Vignette du fichier
FG-CJCE-94-6-Orig.pdf (1.25 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01311740 , version 1 (17-06-2016)

Identifiants

Citer

Qasim Ali, Ali Elkamel, Frédéric Gruy, Claude Lambert, Eric Touboul. Population balances in case of crossing characteristic curves: Application to T-cells immune response. Canadian Journal of Chemical Engineering, 2016, 94 (6), pp.1167-1176. ⟨10.1002/cjce.22497⟩. ⟨hal-01311740⟩
320 Consultations
175 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More