# American Institute of Mathematical Sciences

• Previous Article
An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells
• MBE Home
• This Issue
• Next Article
Complex Behavior in a Discrete Coupled Logistic Model for the Symbiotic Interaction of Two Species
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

 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.
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
 [1] Lisette dePillis, Trevor Caldwell, Elizabeth Sarapata, Heather Williams. Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 915-943. doi: 10.3934/dcdsb.2013.18.915 [2] Guanyu Wang. The Effects of Affinity Mediated Clonal Expansion of Premigrant Thymocytes on the Periphery T-Cell Repertoire. Mathematical Biosciences & Engineering, 2005, 2 (1) : 153-168. doi: 10.3934/mbe.2005.2.153 [3] Hongjing Shi, Wanbiao Ma. An improved model of t cell development in the thymus and its stability analysis. Mathematical Biosciences & Engineering, 2006, 3 (1) : 237-248. doi: 10.3934/mbe.2006.3.237 [4] Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973-986. doi: 10.3934/mbe.2011.8.973 [5] Yueping Dong, Rinko Miyazaki, Yasuhiro Takeuchi. Mathematical modeling on helper T cells in a tumor immune system. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 55-72. doi: 10.3934/dcdsb.2014.19.55 [6] Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda Teboh-Ewungkem, Lisette dePillis. A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 323-336. doi: 10.3934/dcdsb.2009.12.323 [7] Reihaneh Mostolizadeh, Zahra Afsharnezhad, Anna Marciniak-Czochra. Mathematical model of Chimeric Anti-gene Receptor (CAR) T cell therapy with presence of cytokine. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 63-80. doi: 10.3934/naco.2018004 [8] Gennadi M. Henkin, Victor M. Polterovich. A difference-differential analogue of the Burgers equations and some models of economic development. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 697-728. doi: 10.3934/dcds.1999.5.697 [9] Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907 [10] Herbert Koch. Partial differential equations with non-Euclidean geometries. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 481-504. doi: 10.3934/dcdss.2008.1.481 [11] Wilhelm Schlag. Spectral theory and nonlinear partial differential equations: A survey. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 703-723. doi: 10.3934/dcds.2006.15.703 [12] Eugenia N. Petropoulou, Panayiotis D. Siafarikas. Polynomial solutions of linear partial differential equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1053-1065. doi: 10.3934/cpaa.2009.8.1053 [13] Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515 [14] Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167 [15] Barbara Abraham-Shrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 577-582. doi: 10.3934/dcdss.2018032 [16] Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1345-1360. doi: 10.3934/cpaa.2011.10.1345 [17] Houssein Ayoub, Bedreddine Ainseba, Michel Langlais, Rodolphe Thiébaut. Parameters identification for a model of T cell homeostasis. Mathematical Biosciences & Engineering, 2015, 12 (5) : 917-936. doi: 10.3934/mbe.2015.12.917 [18] Cliburn Chan, Andrew J.T. George, Jaroslav Stark. T cell sensitivity and specificity - kinetic proofreading revisited. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 343-360. doi: 10.3934/dcdsb.2003.3.343 [19] Heiko Enderling, Alexander R.A. Anderson, Mark A.J. Chaplain, Glenn W.A. Rowe. Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Mathematical Biosciences & Engineering, 2006, 3 (4) : 571-582. doi: 10.3934/mbe.2006.3.571 [20] Rafael Potrie. Partial hyperbolicity and foliations in $\mathbb{T}^3$. Journal of Modern Dynamics, 2015, 9: 81-121. doi: 10.3934/jmd.2015.9.81

2018 Impact Factor: 1.313