{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T07:07:01Z","timestamp":1791270421115,"version":"4.1.0"},"reference-count":78,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.3934\/mbe.2012.9.699","type":"journal-article","created":{"date-parts":[[2012,10,18]],"date-time":"2012-10-18T18:09:32Z","timestamp":1350583772000},"page":"699-736","source":"Crossref","is-referenced-by-count":12,"title":["A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays"],"prefix":"10.3934","volume":"9","member":"2321","reference":[{"key":"1","article-title":"\"A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering,\"","author":"H. T. Banks","year":"2012","journal-title":"CRC Press\/Taylor-Francis"},{"key":"2","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1088\/0266-5611\/17\/1\/308","article-title":"Modelling and estimating uncertainty in parameter estimation<\/em>,","volume":"17","author":"H. T. Banks","year":"2001","journal-title":"Inverse Problems"},{"key":"3","first-page":"05","article-title":"Shrimp biomass and viral infection for production of biological countermeasures<\/em>,","volume":"3","author":"H. T.Banks","year":"2006","journal-title":"CRSC-TR05-45"},{"key":"4","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/S0025-5564(02)00218-3","article-title":"Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics<\/em>,","volume":"183","author":"H. T. Banks","year":"2003","journal-title":"Math. Biosciences"},{"key":"5","first-page":"03","article-title":"Modeling and imaging techniques with potential for application in bioterrorism<\/em>,","volume":"FR28","author":"H. T. Banks","year":"2003","journal-title":"CRSC-TR03-02"},{"key":"6","first-page":"87","article-title":"Modeling and estimation in size structured population models<\/em>,","author":"H. T. Banks","year":"1987","journal-title":"LCDS\/CSS Report 87-13"},{"key":"7","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1016\/j.aml.2010.07.009","article-title":"Label structured cell proliferation models<\/em>,","volume":"23","author":"H. T. Banks","year":"2010","journal-title":"Appl. Math. Letters"},{"key":"8","first-page":"08","article-title":"An inverse problem statistical methodology summary<\/em>,","author":"H. T. Banks","year":"2008","journal-title":"CRSC-TR08-01"},{"key":"9","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1016\/j.apnum.2006.07.016","article-title":"A comparison of approximation methods for the estimation of probability distributions on parameters<\/em>,","volume":"57","author":"H. T. Banks","year":"2007","journal-title":"Appl. Num. Math."},{"key":"10","first-page":"08","article-title":"A comparison of probabilistic and stochastic formulations in modeling growth uncertainty and variability<\/em>,","volume":"3","author":"H. T. Banks","year":"2009","journal-title":"CRSC-TR08-03"},{"key":"11","first-page":"88","article-title":"Inverse problems for distributed systems: statistical tests and ANOVA<\/em>,","volume":"81","author":"H. T. Banks","year":"1989","journal-title":"LCDS\/CSS Report 88-16"},{"key":"12","first-page":"90","article-title":"Estimation of growth rate distributions in size-structured population models<\/em>,","volume":"49","author":"H. T. Banks","year":"1991","journal-title":"CAMS Tech. Rep. 90-2"},{"key":"13","first-page":"04","article-title":"Well-posedness in Maxwell systems with distributions of polarization relaxation parameters<\/em>,","volume":"18","author":"H. T. Banks","year":"2005","journal-title":"CRSC-TR04-01"},{"key":"14","first-page":"05","article-title":"Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters<\/em>,","volume":"64","author":"H. T. Banks","year":"2006","journal-title":"CRSC-TR05-29"},{"key":"15","article-title":"\"Estimation Techniques for Distributed Parameter Systems,\"","author":"H. T. Banks","year":"1989","journal-title":"Birkhauser"},{"key":"16","first-page":"04","article-title":"A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue<\/em>,","volume":"3","author":"H. T. Banks","year":"2005","journal-title":"CRSC-TR04-03"},{"key":"17","first-page":"02","article-title":"Probabilistic methods for addressing uncertainty and variability in biological models: Application to a toxicokinetic model<\/em>,","volume":"192","author":"H. T. Banks","year":"2004","journal-title":"CRSC-TR02-27"},{"key":"18","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/j.jim.2011.08.014","article-title":"A new model for the estimation of cell proliferation dynamics using CFSE data<\/em>,","volume":"373","author":"H. T. Banks","year":"2011","journal-title":"CRSC-TR11-05"},{"key":"19","doi-asserted-by":"publisher","first-page":"09","DOI":"10.1007\/s11538-010-9524-5","article-title":"Estimation of cell proliferation dynamics using CFSE data<\/em>,","volume":"70","author":"H. T. Banks","year":"2011","journal-title":"CRSC-TR09-17"},{"key":"20","first-page":"12","article-title":"A compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays<\/em>,","author":"H. T. Banks","year":"2012","journal-title":"Technical Report CRSC-TR12-03"},{"key":"21","article-title":"\"Mathematical and Experimental Modeling of Physical and Biological Processes,\"","author":"H. T. Banks","year":"2009","journal-title":"CRC Press"},{"key":"22","first-page":"98","article-title":"Estimation of probability distributions for individual parameters using aggregate population observations<\/em>,","author":"H. T. Banks","year":"1998","journal-title":"CRSC-TR98-06"},{"key":"23","first-page":"329","article-title":"Cell growth and division I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures<\/em>,","volume":"7","author":"G. Bell","year":"1967","journal-title":"Biophysical Journal"},{"key":"24","article-title":"\"Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach,\"","author":"K. P. Burnham","year":"2002","journal-title":"(2nd Edition)"},{"key":"25","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1111\/j.1600-065X.2006.00486.x","article-title":"Stochasticity and spatial heterogeneity in T-cell activation<\/em>,","volume":"216","author":"Nigel J. Burroughs","year":"2007","journal-title":"Immunological Reviews"},{"key":"26","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1111\/j.1600-065X.2006.00498.x","article-title":"Modeling T- and B-cell growth and differentiation<\/em>,","volume":"216","author":"R. Callard","year":"2007","journal-title":"Immunological Reviews"},{"key":"27","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1016\/S1471-4906(03)00164-9","article-title":"Fratricide: a mechanism for T memory-cell homeostasis<\/em>,","volume":"24","author":"Robin E. Callard","year":"2003","journal-title":"Trends in Immunology"},{"key":"28","article-title":"\"Transformation and Weighting in Regression,\"","author":"R. J. Carroll","year":"2000","journal-title":"Chapman Hall"},{"key":"29","article-title":"\"Nonlinear Models for Repeated Measurement Data,\"","author":"M. Davidian","year":"2000","journal-title":"Chapman and Hall"},{"key":"30","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1007\/s11538-006-9094-8","article-title":"Estimating lymphocyte division and death rates from CFSE data<\/em>,","volume":"68","author":"R. J. DeBoer","year":"2006","journal-title":"Bull. Math. Biol."},{"key":"31","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.cam.2004.08.020","article-title":"Estimating division and death rates from CFSE data<\/em>,","volume":"184","author":"R. J. DeBoer","year":"2005","journal-title":"J. Comp. and Appl. Mathematics"},{"key":"32","doi-asserted-by":"crossref","first-page":"4963","DOI":"10.4049\/jimmunol.170.10.4963","article-title":"Stochastic model of T cell proliferation: a calculus revealing IL-2 regulation of precursor frequencies, cell cycle time, and survival<\/em>,","volume":"170","author":"E. K. Deenick","year":"2003","journal-title":"J. Immunology"},{"key":"33","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1098\/rsif.2005.0069","article-title":"Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?<\/em>,","volume":"2","author":"Mark R Dowling","year":"2005","journal-title":"J. R. Soc. Interface"},{"key":"34","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s00285-008-0231-x","article-title":"On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics<\/em>,","volume":"59","author":"K. Duffy","year":"2009","journal-title":"J. Math. Biol."},{"key":"35","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1046\/j.1440-1711.1999.00870.x","article-title":"Carboxyfluorescein diacetate succinimidyl ester-based assays for assessment of T cell function in the diagnostic laboratory<\/em>,","volume":"77","author":"D. A. Fulcher","year":"1999","journal-title":"Immunology and Cell Biology"},{"key":"36","doi-asserted-by":"crossref","first-page":"950","DOI":"10.4049\/jimmunol.179.2.950","article-title":"IL-2 regulates expansion of CD4+ T cell populations by affecting cell death: Insights from modeling CFSE data<\/em>,","volume":"179","author":"Vitaly V. Ganusov","year":"2007","journal-title":"J. Immunology"},{"key":"37","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.jim.2005.01.011","article-title":"Quantifying cell turnover using CFSE data<\/em>,","volume":"298","author":"V. V. Ganusov","year":"2005","journal-title":"J. Immunological Methods"},{"key":"38","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1038\/79782","article-title":"A cellular calculus for signal integration by T cells<\/em>,","volume":"1","author":"A. V. Gett","year":"2000","journal-title":"Nature Immunology"},{"key":"39","article-title":"\"Elements of Mathematical Ecology,\"","author":"M. Kot","year":"2001","journal-title":"Cambridge University Press"},{"key":"40","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/BF00160231","article-title":"A nonlinear structured population model of tumor growth with quiescence<\/em>,","volume":"28","author":"M. Gyllenberg","year":"1990","journal-title":"J. Math. Biol."},{"key":"41","article-title":"A computational model for proliferation dynamics of division- and label-structured populations<\/em>,","author":"J. Hasenauer","year":"2012","journal-title":"Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data<\/em>,","volume":"2","author":"E. D. Hawkins","year":"2007","journal-title":"Nature Protocols"},{"key":"43","doi-asserted-by":"publisher","first-page":"13457","DOI":"10.1073\/pnas.0905629106","article-title":"A single-cell pedigree analysis of alternative stochastic lymphocyte fates<\/em>,","volume":"106","author":"E. D. Hawkins","year":"2009","journal-title":"Proc. Natl. Acad. Sci."},{"key":"44","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.4049\/jimmunol.179.4.2250","article-title":"TCR affinity promotes CD8+ T-cell expansion by regulating survival<\/em>,","volume":"179","author":"Mirja Hommel","year":"2007","journal-title":"J. Immunology"},{"key":"45","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1198\/016214507000000194","article-title":"A mixture model with dependent observations for the analysis of CFSE-labeling experiments<\/em>,","volume":"103","author":"O. Hyrien","year":"2008","journal-title":"J. American Statistical Association"},{"key":"46","doi-asserted-by":"crossref","DOI":"10.1186\/1745-6150-5-41","article-title":"An age-dependent branching process model for the analysis of CFSE-labeling experiments<\/em>,","volume":"5","author":"O. Hyrien","year":"2010","journal-title":"Biology Direct"},{"key":"47","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1600-065X.2007.00490.x","article-title":"Toward a multiscale model of antigen presentation in immunity<\/em>,","volume":"216","author":"D. E. Kirschner","year":"2007","journal-title":"Immunological Reviews"},{"key":"48","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1007\/s11538-009-9418-6","article-title":"Interpreting CFSE obtained division histories of B cells in vitro with Smith-Martin and Cyton type models<\/em>,","volume":"71","author":"H. Y. Lee","year":"2009","journal-title":"Bull. Math. Biol."},{"key":"49","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s11538-007-9239-4","article-title":"Modeling T cell proliferation and death in vitro based on labeling data: Generalizations of the Smith-Martin cell cycle model<\/em>,","volume":"70","author":"H. Y. Lee","year":"2008","journal-title":"Bull. Math. Biol."},{"key":"50","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.jtbi.2004.04.011","article-title":"A general mathematical framework to model generation structure in a population of asynchronously dividing cells<\/em>,","volume":"229","author":"K. Leon","year":"2004","journal-title":"J. Theoretical Biology"},{"key":"51","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1111\/j.1600-065X.2006.00495.x","article-title":"The evolution of mathematical immunology<\/em>,","volume":"216","author":"Y. Louzoun","year":"2007","journal-title":"Immunological Reviews"},{"key":"52","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/s00285-008-0244-5","article-title":"Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data<\/em>,","volume":"59","author":"T. Luzyanina","year":"2009","journal-title":"J. Math. Biol."},{"key":"53","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s00285-006-0046-6","article-title":"Computational analysis of CFSE proliferation assay<\/em>,","volume":"54","author":"T. Luzyanina","year":"2007","journal-title":"J. Math. Biol."},{"key":"54","doi-asserted-by":"crossref","DOI":"10.1186\/1742-4682-4-26","article-title":"Numerical modelling of label-structured cell population growth using CFSE distribution data<\/em>,","volume":"4","author":"T. Luzyanina","year":"2007","journal-title":"Theoretical Biology and Medical Modelling"},{"key":"55","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0022-1759(94)90236-4","article-title":"Determination of lymphocyte division by flow cytometry<\/em>,","volume":"171","author":"A. B. Lyons","year":"1994","journal-title":"J. Immunol. Methods"},{"key":"56","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/S0091-679X(01)63021-8","article-title":"Flow cytometric analysis of cell division history using diluation of carboxyfluorescein diacetate succinimidyl ester, a stably integrated fluorescent probe<\/em>,","volume":"63","author":"A. B. Lyons","year":"2001","journal-title":"Methods in Cell Biology"},{"key":"57","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1002\/cyto.a.20097","article-title":"Heterogeneous cell response to topotecan in a CFSE-based proliferative test<\/em>,","volume":"62","author":"G. Matera","year":"2004","journal-title":"Cytometry A"},{"key":"58","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-13159-6","article-title":"\"The Dynamics of Physiologically Structured Populations,\"","volume":"68","author":"J. A. Metz","year":"1986","journal-title":"Springer Lecture Notes in Biomathematics"},{"key":"59","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1007\/s11538-011-9668-y","article-title":"Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data<\/em>,","volume":"74","author":"H. Miao","year":"2012","journal-title":"Bull. Math. Biol."},{"key":"60","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/j.jtbi.2011.02.006","article-title":"Multi-type branching models to describe cell differentiation programs<\/em>,","volume":"277","author":"Robert E. Nordon","year":"2011","journal-title":"J. Theoretical Biology"},{"key":"61","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1046\/j.1440-1711.1999.00869.x","article-title":"Analysis of growth kinetics by division tracking<\/em>,","volume":"77","author":"R. E. Nordon","year":"1999","journal-title":"Immunology and Cell Biology"},{"key":"62","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1046\/j.1440-1711.1999.00877.x","article-title":"Fluorescent dyes for lymphocyte migration and proliferation studies<\/em>,","volume":"77","author":"C. Parish","year":"1999","journal-title":"Immunology and Cell Biol."},{"key":"63","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/S0022-5193(03)00245-5","article-title":"The rescaling method for quantifying the turnover of cell populations<\/em>,","volume":"225","author":"Sergei S. Pilyugin","year":"2003","journal-title":"J. Theoretical Biology"},{"key":"64","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1038\/nprot.2007.296","article-title":"Monitoring lymphocyte proliferation in vitro and in vivo with the intracellular fluorescent dye carboxyfluorescein diacetate succinimidyl ester<\/em>,","volume":"2","author":"B. Quah","year":"2007","journal-title":"Nature Protocols"},{"key":"65","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1038\/ni713","article-title":"Functional antigen-independent synapses formed between T cells and dendritic cells<\/em>,","volume":"2","author":"P. Revy","year":"2001","journal-title":"Nature Immunology"},{"key":"66","article-title":"\"Nonlinear Regression,\"","author":"G. A. Sever","year":"2003","journal-title":"Wiley"},{"key":"67","first-page":"165","article-title":"A generalized model for cell proliferation: Integrating division numbers and label dynamics<\/em>,","author":"D. Schittler","year":"2011","journal-title":"Proc. Eighth International Workshop on Computational Systems Biology (WCSB 2011)"},{"key":"68","doi-asserted-by":"publisher","first-page":"910","DOI":"10.2307\/1934533","article-title":"A new model for age-size structure of a population<\/em>,","volume":"48","author":"J. Sinko","year":"1967","journal-title":"Ecology"},{"key":"69","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1007\/s00285-007-0142-2","article-title":"Determining the expected variability of immune responses using the cyton model<\/em>,","volume":"56","author":"V. G. Subramanian","year":"2008","journal-title":"J. Math. Biol."},{"key":"70","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1128\/MCB.00882-09","article-title":"Cyclin-dependent kinase 1-mediated $Bcl-x_L$\/Bcl-2 phosphorylation acts as a functional link coupling mitotic arrest and apoptosis<\/em>,","volume":"30","author":"David T. Terrano","year":"2010","journal-title":"Mol. Cell. Biol."},{"key":"71","article-title":"\"Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays,\"","author":"W. Clayton Thompson","year":"2011","journal-title":"Ph.D. Dissertation"},{"key":"72","article-title":"DataThief III.","author":"B. Tummers","journal-title":"2006. (Quantitative regulation of B cell division destiny by signal strength<\/em>,","volume":"181","author":"M. L. Turner","year":"2008","journal-title":"J. Immunology"},{"key":"74","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1038\/76907","article-title":"Response of naive and memory CD8+ T cells to antigen stimulation in vivo<\/em>,","volume":"1","author":"H. Veiga-Fernandez","year":"2000","journal-title":"Nature Immunology"},{"key":"75","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1002\/cyto.a.20619","article-title":"Tracking antigen-driven responses by flow cytometry: monitoring proliferation by dye dilution<\/em>,","volume":"73","author":"P. K. Wallace","year":"2008","journal-title":"Cytometry A"},{"key":"76","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1016\/j.jtbi.2010.02.019","article-title":"The effect of correlations on the population dynamics of lymphocytes<\/em>,","volume":"264","author":"C. Wellard","year":"2010","journal-title":"J. Theoretical Biology"},{"key":"77","first-page":"1","article-title":"Advanced application of CFSE for cellular tracking<\/em>,","author":"J. M. Witkowski","year":"2008","journal-title":"Current Protocols in Cytometry"},{"key":"78","doi-asserted-by":"crossref","DOI":"10.1186\/1471-2105-8-196","article-title":"Reconstruction of cell population dynamics using CFSE<\/em>,","volume":"8","author":"A. Yates","year":"2007","journal-title":"BMC Bioinformatics"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.aimspress.com\/article\/10.3934\/mbe.2012.9.699\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,1]],"date-time":"2020-02-01T09:01:47Z","timestamp":1580547707000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/10.3934\/mbe.2012.9.699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":78,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2012.9.699","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2012]]}}}