Login


Subscription

To subscribe via Internet, visit the following website: isi.cbs.nl/orderform.asp or send an e-mail to Mr. S. Hoesenie shse@cbs.nl.



Please fill in your query. A complete syntax description you will find on the General Help page.
About a generalized model of lymphoma. (English)
J. Math. Anal. Appl. 386, No. 2, 813-829 (2012).
Summary: We introduce and analyze a generalized model of precursor T-lymphoblastic lymphoma as a competition between two clonotypes of naïve T-cells, one “normal" and one tumorous. It is modeled as a continuous-time bivariate Markov process. Using an expansion of the master equation a deterministic approximation and the Fokker-Planck equation are derived. For a deterministic model we show existence and uniqueness of global solutions and positive invariance of the first quadrant of the phase space. Stability analysis of the model is performed, finding conditions guaranteeing the existence of a unique, positive, steady state, which is proved to be globally stable. It is shown that expectations of fluctuations for both clonotypes tend to zero for large time. We also present numerical simulations in which two types of behavior of solutions are observed: either both clonotypes survive in the repertoire or the “normal" clonotypes becomes extinct. Comparing this result with the rules of maintenance of the naïve T-cell repertoire, which say that clonotypes with more specific set of receptors have longer life-span, it seems that “normal" clonotypes follow them, whereas the tumorous one violates them and tends to the maximum possible expansion. The model supports the hypothesis of mutated precursor cells as an origin of cancer.
Classification: 92C37 92C50 60J70 34C60 65C20 37N25
Valid XHTML 1.0 Transitional Valid CSS!