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Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells.
MedLine Citation:
PMID:  23311362     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
In a previous paper a mathematical model was developed for the dynamics of activation and clonal expansion of T cells during the immune response to a single type of antigen challenge, constructed phenomenologically in the macroscopic framework of a thermodynamic theory of continuum mechanics for reacting and proliferating fluid mixtures. The present contribution deals with approximate smooth solutions, called asymptotic waves, of the system of PDEs describing the introduced model, obtained using a suitable perturbative method. In particular, in the one-dimensional case, after deriving the expression of the velocity along the characteristic rays and the equation of the wave front, the transport equation for the first perturbation term of the asymptotic solution is obtained. Finally, it is shown that this transport equation can be reduced to an equation similar to Burgers equation.
Authors:
D Criaco; M Dolfin; L Restuccia
Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Mathematical biosciences and engineering : MBE     Volume:  10     ISSN:  1551-0018     ISO Abbreviation:  Math Biosci Eng     Publication Date:  2013 Feb 
Date Detail:
Created Date:  2013-01-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101197794     Medline TA:  Math Biosci Eng     Country:  United States    
Other Details:
Languages:  eng     Pagination:  59-73     Citation Subset:  IM    
Affiliation:
Department of Mathematics and Informatics, University of Messina, Viale F. Stagno d'Alcontres n.31, 98166 Messina, Italy. dcriaco@unime.it.
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