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2004, 1(2): 289-305. doi: 10.3934/mbe.2004.1.289

A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis

Guanyu Wang 1, and  Gerhard R. F. Krueger 1,

1. 

Department of Pathology and laboratory Medicine, The University of Texas Medical School at Houston, Houston, TX 77030, United States, United States

Received  March 2004 Revised  April 2004 Published  July 2004

T-lymphocyte (T-cell) development constitutes one of the basic and most vital processes in immunology. The process is profoundly affected by the thymic microenvironment, the dysregulation of which may be the pathogenesis or the etiology of some diseases. On the basis of a general conceptual framework, we have designed the first biophysical model to describe thymocyte development. The microclimate within the thymus, which is shaped by various cytokines, is first conceptualized into a growth field $\lambda$ and a differentiation field $\mu$, under the influence of which the thymocytes mature. A partial differential equation is then derived through the analysis of an infinitesimal element of the flow of thymocytes. A general method is presented to estimate the two fields based on experimental data obtained by flow cytometric analysis of the thymus. Numerical examples are given for both normal and pathologic conditions. Our results are quite good, and even the time varying fields can be accurately estimated. Our method has demonstrated its great potential for the study of immunopathogenesis. The plan for implementation of the method is addressed.
Keywords: partial differential equations., immunopathogenesis, T-cell immunology, thymocyte development, mathematical modeling.
Mathematics Subject Classification: 92C5.
Citation: Guanyu Wang, Gerhard R. F. Krueger. A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis. Mathematical Biosciences & Engineering, 2004, 1 (2) : 289-305. doi: 10.3934/mbe.2004.1.289
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