Free Access
Math. Model. Nat. Phenom.
Volume 7, Number 5, 2012
Page(s) 24 - 52
Published online 17 October 2012
  1. O. Arino, E. Sanchez, G.F. Webb. Necessary and sufficient conditions for asynchronous exponential growth in age structured cell populations with quiescence. Mathematical Analysis and Applications, 215 (1997), 499–513. [Google Scholar]
  2. B. Asquith, C. Debacq, A. Florins, N. Gillet, T. Sanchez-Alcaraz, A. Mosley, L. Willems. Quantifying lymphocyte kinetics in vivo using carboxyfluorein diacetate succinimidyl ester. Proc. R. Soc. B, 273 (2006), 1165–1171. [CrossRef] [Google Scholar]
  3. H.T. Banks. A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering. CRC Press/Taylor-Francis, Boca Raton London New York, 2012. [Google Scholar]
  4. H.T. Banks, V. A. Bokil, S. Hu, F.C.T. Allnutt, R. Bullis, A.K. Dhar, C.L. Browdy, Shrimp biomass and viral infection for production of biological countermeasures, CRSC-TR05-45. North Carolina State University, December 2005 ; Mathematical Biosciences and Engineering, 3 (2006), 635–660. [CrossRef] [MathSciNet] [Google Scholar]
  5. H.T. Banks, D.M. Bortz, S.E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Math. Biosciences. 183 (2003), 63–91. [CrossRef] [MathSciNet] [Google Scholar]
  6. H.T. Banks, D. M. Bortz, G.A. Pinter, L.K. Potter. Modeling and imaging techniques with potential for application in bioterrorism. CRSC-TR03-02, North Carolina State University, January 2003 ; Chapter 6 in Bioterrorism : Mathematical Modeling Applications in Homeland Security, (H.T. Banks and C. Castillo-Chavez, eds.), Frontiers in Applied Math, FR28, SIAM, Philadelphia, PA, 2003, 129–154. [Google Scholar]
  7. H.T. Banks, L.W. Botsford, F. Kappel, C. Wang, Modeling and estimation in size structured population models. LCDS/CSS Report 87-13, Brown University, March 1987 ; Proc. 2nd Course on Math. Ecology (Trieste, December 8-12, 1986), World Scientific Press, Singapore, 1988, 521–541. [Google Scholar]
  8. H.T. Banks, F. Charles, M. Doumic, K. L. Sutton, W. C. Thompson. Label structured cell proliferation models. CRSC-TR10-10, North Carolina State University, June 2010 ; Appl. Math. Letters, 23 (2010), 1412–1415. [CrossRef] [MathSciNet] [Google Scholar]
  9. H.T. Banks, J.L. Davis, S.L. Ernstberger, S. Hu, E. Artimovich, A.K. Dhar, C.L. Browdy. A comparison of probabilistic and stochastic differential equations in modeling growth uncertainty and variability. CRSC-TR08-03, North Carolina State University, February 2008 ; Journal of Biological Dynamics, 3 (2009), 130–148. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  10. H.T. Banks, J.L. Davis, S. Hu, A computational comparison of alternatives to including uncertainty in structured population models. CRSC-TR09-14, North Carolina State University June 2009 ; in Three Decades of Progress in Systems and Control, X. Hu, U. Jonsson, B. Wahlberg, B. Ghosh (Eds.), Springer, 2010, 19–33. [Google Scholar]
  11. H.T. Banks, B.F. Fitzpatrick. Estimation of growth rate distributions in size-structured population models. CAMS Tech. Rep. 90-2, Univ. of Southern California, January 1990 ; Quart. Appl. Math., 49 (1991), 215–235. [MathSciNet] [Google Scholar]
  12. H.T. Banks, B.G. Fitzpatrick, L.K. Potter, Y. Zhang, Estimation of probability distributions for individual parameters using aggregate population observations. CRSC-TR98-06, North Carolina State University, January 1998 ; Stochastic Analysis, Control, Optimization and Applications (W.McEneaney, G. Yin, and Q. Zhang, eds.), Birkhauser, 1998, 353–371. [Google Scholar]
  13. H.T. Banks, N.L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters. CRSC-TR04-01, North Carolina State University, January 2004 ; Applied Math. Letters, 18 (2005), 423–430. [CrossRef] [MathSciNet] [Google Scholar]
  14. H.T. Banks, N.L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters. CRSC-TR05-29, North Carolina State University, August2005 ; Quarterly of Applied Mathematics, 64 (2006), 749–795. [Google Scholar]
  15. H.T. Banks, K. Holm, F. Kappel, Comparison of optimal design methods in inverse problems. CRSC-TR10-11, North Carolina State University, May 2011 ; Inverse Problems, 27 (2011), 075002. [Google Scholar]
  16. H.T. Banks, S. Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations. CRSC-TR11-02, North Carolina State University, January 2011 ; Mathematical Bioscience and Engineering, 9 (2012), 1–25. [Google Scholar]
  17. H.T. Banks, S. Hu. Uncertainty propagation in physiologically structured population models. CRSC-TR12-08, North Carolina State University, Raleigh, NC, March 2012 ; Journal on Mathematical Modelling of Natural Phenomena, submitted. [Google Scholar]
  18. H.T. Banks, K. Kunisch. Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989. [Google Scholar]
  19. H.T. Banks and G.A. Pinter. A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue. CRSC-TR04-03, North Carolina State University, January 2004 ; IAM J. Multiscale Modeling and Simulation, 3 (2005), 395–412. [Google Scholar]
  20. H.T. Banks, L.K. Potter. Probabilistic methods for addressing uncertainty and variability in biological models : Application to a toxicokinetic model. CRSC-TR02-27, North Carolina State University, September 2002 ; Math. Biosci., 192 (2004), 193–225. [Google Scholar]
  21. H.T. Banks, Karyn L. Sutton, W. Clayton Thompson, G. Bocharov, Marie Doumic, Tim Schenkel, Jordi Argilaguet, Sandra Giest, Cristina Peligero, Andreas Meyerhans. A New Model for the Estimation of Cell Proliferation Dynamics Using CFSE Data. CRSC-TR11-05, North Carolina State University, Revised July 2011 ; J. Immunological Methods, 373 (2011), 143–160 ; DOI :10.1016/j.jim.2011.08.014. [Google Scholar]
  22. H.T. Banks, Karyn L. Sutton, W. Clayton Thompson, G. Bocharov, D. Roose, T. Schenkel, A. Meyerhans. Estimation of cell proliferation dynamics using CFSE data. CRSC-TR09-17, North Carolina State University, August 2009 ; Bull. Math. Biol., 70 (2011), 116–150. [Google Scholar]
  23. H.T. Banks, W. Clayton Thompson, Cristina Peligero, Sandra Giest, Jordi Argilaguet, Andreas Meyerhans. A Division-Dependent Compartmental Model for Computing Cell Numbers in CFSE-based Lymphocyte Proliferation Assays. CRSC-TR12-03, North Carolina State University, January 2012 ; Math Biosci. Eng., to appear. [Google Scholar]
  24. H.T. Banks, W. Clayton Thompson. A division-dependent compartmental model with cyton and intracellular label dynamics. CRSC-TR12-12, North Carolina State University, May 2012 ; Intl. J. Pure and Appl. Math 77 (2012), 119–147. [Google Scholar]
  25. H.T. Banks, H.T. Tran, D.E. Woodward. Estimation of variable coefficients in the Fokker-Planck equations using moving node finite elements. SIAM J. Numer. Anal., 30 (1993), 1574–1602. [CrossRef] [MathSciNet] [Google Scholar]
  26. B. Basse, B. Baguley, E. Marshall, G. Wake, D. Wall. Modelling the flow cytometric data obtained from unperturbed human tumour cell lines : Parameter fitting and comparison. Bull. Math. Biol., 67 (2005), 815–830. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. F. Bekkal Brikci, J. Clairambault, B. Ribba, B. Perthame. An age-and-cyclin-structured cell population model for healthy and tumoral tissues. Math. Biol., 57 (2008), 91–110. [Google Scholar]
  28. G. Bell, E. Anderson. Cell Growth and Division I. A Mathematical Model with Applications to Cell Volume Distributions in Mammalian Suspension Cultures, Biophysical Journal, 7 (1967), 329–351. [CrossRef] [PubMed] [Google Scholar]
  29. S. Bernard, L. Pujo-Menjouet, M.C. Mackey. Analysis of cell kinetics using a cell division marker : Mathematical modeling of experimental data. Biophysical Journal, 84 (2003), 3414–3424. [Google Scholar]
  30. S. Bonhoeffer, H. Mohri, D. Ho, A.S. Perelson. Quantification of cell turnover kinetics using 5-Bromo-2’-deoxyuridine. Immunology, 64 (2000), 5049–5054. [CrossRef] [Google Scholar]
  31. Jose A. M. Borghans, R.J. de Boer. Quantification of T-cell dynamics : from telomeres to DNA labeling. Immunological Reviews, 216 (2007), 35–47. [PubMed] [Google Scholar]
  32. K.P. Burnham, D.R. Anderson. Model Selection and Multimodel Inference : A Practical Information-Theoretic Approach (2nd Edition), Springer, New York, 2002. [Google Scholar]
  33. R. Callard, P.D. Hodgkin. Modeling T- and B-cell growth and differentiation. Immunological Reviews, 216 (2007), 119–129. [PubMed] [Google Scholar]
  34. “Cyton Calculator”, Walter and Eliza Ball Institute of Medical Research. Available Online. Accessed 16 March 2012. [Google Scholar]
  35. R.J. DeBoer, V.V. Ganusov, D. Milutinovic, P.D. Hodgkin, A.S. Perelson. Estimating lymphocyte division and death rates from CFSE data. Bull. Math. Biol., 68 (2006), 1011–1031. [CrossRef] [PubMed] [Google Scholar]
  36. R.J. DeBoer, A. S. Perelson. Estimating division and death rates from CFSE data. Comp. and Appl. Mathematics, 184 (2005), 140–164. [CrossRef] [Google Scholar]
  37. E.K. Deenick, A.V. Gett, P.D. Hodgkin. Stochastic model of T cell proliferation : a calculus revealing IL-2 regulation of precursor frequencies, cell cycle time, and survival. Immunology, 170 (2003), 4963–4972. [CrossRef] [Google Scholar]
  38. K. Duffy, V. Subramanian. On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics. Math. Biol., 59 (2009), 255–285. [CrossRef] [MathSciNet] [Google Scholar]
  39. J.Z. Farkas. Stability conditions for the non-linear McKendrick equations. Appl. Math. and Comp., 156 (2004), 771–777. [CrossRef] [Google Scholar]
  40. J.Z. Farkas. Stability conditions for a non-linear size-structured model Nonlinear Analysis : Real World Applications, 6 (2005), 962–969. [CrossRef] [MathSciNet] [Google Scholar]
  41. V. V. Ganusov, D. Milutinovi, R. J. De Boer. IL-2 regulates expansion of CD4+ T cell populations by affecting cell death : insights from modeling CFSE data. Immunology, 179 (2007), 950–957. [CrossRef] [Google Scholar]
  42. V.V. Ganusov, S.S. Pilyugin, R.J. De Boer, K. Murali-Krishna, R. Ahmed, R. Antia. Quantifying cell turnover using CFSE data. Immunological Methods, 298 (2005), 183–200. [Google Scholar]
  43. A.V. Gett, P.D. Hodgkin. A cellular calculus for signal integration by T cells. Nature Immunology, 1 (2000), 239–244. [CrossRef] [PubMed] [Google Scholar]
  44. M. Gyllenberg, G.F. Webb. Age-size structure in populations with quiescence. Mathematical Biosciences, 86 (1987), 67–95. [Google Scholar]
  45. M. Gyllenberg, G.F. Webb. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol., 28 (1990), 671–694. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  46. J. Hasenauer, D. Schittler, F. Allgöwer. A computational model for proliferation dynamics of division- and label-structured populations., arXiv :1202.4923v1,22Feb,2012. [Google Scholar]
  47. E.D. Hawkins, Mirja Hommel, M.L. Turner, F. Battye, J. Markham, P.D. Hodgkin. Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data. Nature Protocols, 2 (2007), 2057–2067. [CrossRef] [PubMed] [Google Scholar]
  48. E.D. Hawkins, M.L. Turner, M.R. Dowling, C. van Gend, P.D. Hodgkin. A model of immune regulation as a consequence of randomized lymphocyte division and death times. Proc. Natl. Acad. Sci., 104 (2007), 5032–5037. [CrossRef] [Google Scholar]
  49. E.D. Hawkins, J.F. Markham, L.P. McGuinness, P.D. Hodgkin. A single-cell pedigree analysis of alternative stochastic lymphocyte fates. Proc. Natl. Acad. Sci., 106 (2009), 13457–13462. [CrossRef] [Google Scholar]
  50. O. Hyrien, M.S. Zand. A mixture model with dependent observations for the analysis of CFSE-labeling experiments. American Statistical Association, 103 (2008), 222–239. [CrossRef] [MathSciNet] [Google Scholar]
  51. O. Hyrien, R. Chen, M.S. Zand. An age-dependent branching process model for the analysis of CFSE-labeling experiments. Biology Direct, 5 (2010), Published Online. [Google Scholar]
  52. H.Y. Lee, E.D. Hawkins, M.S. Zand, T. Mosmann, H. Wu, P.D. Hodgkin, A.S. Perelson. Interpreting CFSE obtained division histories of B cells in vitro with Smith-Martin and Cyton type models. Bull. Math. Biol., 71 (2009), 1649–1670. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  53. H.Y. Lee, A.S. Perelson. Modeling T cell proliferation and death in vitro based on labeling data : generalizations of the Smith-Martin cell cycle model. Bull. Math. Biol., 70 (2008), 21–44. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  54. K. Leon, J. Faro, J. Carneiro. A general mathematical framework to model generation structure in a population of asynchronously dividing cells. Theoretical Biology, 229 (2004), 455–476. [CrossRef] [MathSciNet] [Google Scholar]
  55. T. Luzyanina, D. Roose, G. Bocharov. Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data. Math. Biol., 59 (2009), 581–603. [CrossRef] [MathSciNet] [Google Scholar]
  56. T. Luzyanina, D. Roose, T. Schenkel, M. Sester, S. Ehl, A. Meyerhans, G. Bocharov. Numerical modelling of label-structured cell population growth using CFSE distribution data. Theoretical Biology and Medical Modelling, 4 (2007), Published Online. [Google Scholar]
  57. A.B. Lyons. Divided we stand : tracking cell proliferation with carboxyfluorescein diacetate succinimidyl ester. Immunology and Cell Biology, 77 (1999), 509–515. [CrossRef] [PubMed] [Google Scholar]
  58. A.B. Lyons, J. Hasbold, P.D. Hodgkin. Flow cytometric analysis of cell division history using diluation of carboxyfluorescein diacetate succinimidyl ester, a stably integrated fluorescent probe. Methods in Cell Biology, 63 (2001), 375–398. [CrossRef] [PubMed] [Google Scholar]
  59. A.B. Lyons, K.V. Doherty. Flow cytometric analysis of cell division by dye dilution. Current Protocols in Cytometry, (2004), 9.11.1-9.11.10. [Google Scholar]
  60. A.B. Lyons, C.R. Parish. Determination of lymphocyte division by flow cytometry. Immunol. Methods, 171 (1994), 131–137. [CrossRef] [Google Scholar]
  61. G. Matera, M. Lupi, P. Ubezio. Heterogeneous cell response to topotecan in a CFSE-based proliferative test. Cytometry A, 62 (2004), 118–128. [CrossRef] [PubMed] [Google Scholar]
  62. J.A. Metz, O. Diekmann. The Dynamics of Physiologically Structured Populations. Springer Lecture Notes in Biomathematics 68, Heidelberg, 1986. [Google Scholar]
  63. H. Miao, X. Jin, A. Perelson, H. Wu. Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data. Bull. Math. Biol., 74 (2012), 300–326 ; DOI 10.1007/s11538-011-9668-y. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  64. K. Murphy, aneway’s Immunobiology, 8th[entity !#x20 !]Edition. Garland Science, London New York, 2012. [Google Scholar]
  65. R.E. Nordon, Kap-Hyoun Ko, R. Odell, T. Schroeder. Multi-type branching models to describe cell differentiation programs. Theoretical Biology, 277 (2011), 7–18. [CrossRef] [Google Scholar]
  66. R.E. Nordon, M. Nakamura, C. Ramirez, R. Odell. Analysis of growth kinetics by division tracking. Immunology and Cell Biology, 77 (1999), 523–529. [CrossRef] [PubMed] [Google Scholar]
  67. C. Parish. Fluorescent dyes for lymphocyte migration and proliferation studies. Immunology and Cell Biol., 77 (1999), 499–508. [CrossRef] [Google Scholar]
  68. B. Perthame. Transport Equations in Biology. Birkhauser Frontiers in Mathematics, Basel, 2007. [Google Scholar]
  69. S. S. Pilyugin, V. V. Ganusov, K. Murali-Krishnac, R. Ahmed, R. Antia. The rescaling method for quantifying the turnover of cell populations. Theoretical Biology, 225 (2003), 275–283. [CrossRef] [MathSciNet] [Google Scholar]
  70. B.J.C. Quah, C.R. Parish. New and improved methods for measuring lymphocyte proliferation in vitro and in vivo using CFSE-like fluorescent dyes. Immunological Methods, (2012), to appear. [Google Scholar]
  71. B. Quah, H. Warren, C. Parish. Monitoring lymphocyte proliferation in vitro and in vivo with the intracellular fluorescent dye carboxyfluorescein diacetate succinimidyl ester. Nature Protocols, 2 (2007), 2049–2056. [CrossRef] [PubMed] [Google Scholar]
  72. P. Revy, M. Sospedra, B. Barbour, A. Trautmann. Functional antigen-independent synapses formed between T cells and dendritic cells. Nature Immunology, 2 (2001), 925–931. [CrossRef] [PubMed] [Google Scholar]
  73. M. Roederer. Interpretation of cellular proliferation data : Avoid the panglossian, Cytometry A, 79 (2011), 95–101. [PubMed] [Google Scholar]
  74. D. Schittler, J. Hasenauer, F. Allgöwer. A generalized model for cell proliferation : Integrating division numbers and label dynamics. Proc. Eighth International Workshop on Computational Systems Biology (WCSB 2011), June 2001, Zurich, Switzerland, p. 165–168. [Google Scholar]
  75. J. Sinko, W. Streifer. A New Model for Age-Size Structure of a Population. Ecology, 48 (1967), 910–918. [CrossRef] [Google Scholar]
  76. J.A. Smith, L. Martin. Do Cells Cycle ? Proc. Natl. Acad. Sci., 70 (1973), 1263–1267. [Google Scholar]
  77. V.G. Subramanian, K.R. Duffy, M.L. Turner, P.D. Hodgkin. Determining the expected variability of immune responses using the cyton model. Math. Biol., 56 (2008), 861–892. [CrossRef] [MathSciNet] [Google Scholar]
  78. H. Veiga-Fernandez, U. Walter, C. Bourgeois, A. McLean, B. Rocha. Response of naive and memory CD8+ T cells to antigen stimulation in vivo, Nature Immunology. 1 (2000), 47–53. [CrossRef] [PubMed] [Google Scholar]
  79. W. C. Thompson. Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays. Ph.D. Dissertation, Dept. of Mathematics, North Carolina State University, Raleigh, December, 2011. [Google Scholar]
  80. P.K. Wallace, J.D. Tario, Jr., J.L. Fisher, S.S. Wallace, M.S. Ernstoff, K.A. Muirhead. Tracking antigen-driven responses by flow cytometry : monitoring proliferation by dye dilution. Cytometry A, 73 (2008), 1019–1034. [PubMed] [Google Scholar]
  81. H. S. Warren. Using carboxyfluorescein diacetate succinimidyl ester to monitor human NK cell division : Analysis of the effect of activating and inhibitory class I MHC receptors. Immunology and Cell Biology, 77 (1999), 544–551. [CrossRef] [PubMed] [Google Scholar]
  82. C. Wellard, J. Markham, E.D. Hawkins, P.D. Hodgkin. The effect of correlations on the population dynamics of lymphocytes. Theoretical Biology, 264 (2010), 443–449. [CrossRef] [MathSciNet] [Google Scholar]
  83. J.M. Witkowski. Advanced application of CFSE for cellular tracking. Current Protocols in Cytometry, 44 (2008), 9.25.1–9.25.8. [Google Scholar]
  84. A. Yates, C. Chan, J. Strid, S. Moon, R. Callard, A.J.T. George, J. Stark. Reconstruction of cell population dynamics using CFSE. BMC Bioinformatics, 8 (2007), Published Online. [Google Scholar]

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