Mathematical modeling for the activation of t-lymphocytes: population balance modeling with non conventional growth law

Qasim Ali (1, 2, 3) , Eric Touboul (4, 5) , Frédéric Gruy (1, 2, 3) , Claude Lambert (1, 6, 7, 8)

1 LPMG-EMSE - Laboratoire des Procédés en Milieux Granulaires
2 SPIN-ENSMSE - Centre Sciences des Processus Industriels et Naturels
3 PROPICE-ENSMSE - Département PROcédés Poudres, Interfaces, Cristallisation et Ecoulements
4 3MI-ENSMSE - Département Méthodes et Modèles Mathématiques pour l'Industrie
5 FAYOL-ENSMSE - Institut Henri Fayol
6 Laboratoire d'Immunologie
7 CIS-ENSMSE - Centre Ingénierie et Santé
8 IFRESIS - Institut Fédératif de Recherche en Sciences et Ingénierie de la Santé

This article focuses on the mathematical modeling techniques applied to the particulate processes in biological sciences particularly Immunology. T-cell activation is studied with respect to their surface protein (CD3) concentration that is described in-terms of two particulate processes, growth and birth processes. The production of new proteins and change in their concentrations (on cells) has created the idea of balance law in the form of hyperbolic problems. In order to add a new dimension to the problem, CPBM (Cell Population Balance Model) is used with respect to multi-proteins concentrations. A mathematical model is used to find analytical solution while Finite volume scheme is used to approximate numerically the solution of PBE (Population Balance Equation) in order to anticipate and analyze the density of activated T-cells according to the given initial protein concentration.

Mots clés: Hyperbolic problems; T-lymphocytes; Cell population balances; Activation kinetics; Hyperbolic problems.

Domaines: Génie des procédés

Qasim Ali, Eric Touboul, Frédéric Gruy, Claude Lambert. Mathematical modeling for the activation of t-lymphocytes: population balance modeling with non conventional growth law. 5th Asian Particle Technology Symposium, Jul 2012, Singapour, Singapore. pp.ISBN = 978-981-07-2518-1, ⟨10.3850/978-981-07-2518-1_195⟩. ⟨hal-00721905⟩