A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis
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1.
Department of Pathology and laboratory Medicine, The University of Texas Medical School at Houston, Houston, TX 77030
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Received:
01 March 2004
Accepted:
29 June 2018
Published:
01 July 2004
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MSC :
92C50.
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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.
Citation: Guanyu Wang, Gerhard R. F. Krueger. A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis[J]. Mathematical Biosciences and Engineering, 2004, 1(2): 289-305. doi: 10.3934/mbe.2004.1.289
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Abstract
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.
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