Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

Journal of Mathematical Biology

Volumn 59, Issue 5, 2009, Pages 581-603

  Luzyanina, Tatyana ^a   Roose, Dirk ^b   Bocharov, Gennady ^c  

^a INSTITUTE OF MATHEMATICAL PROBLEMS OF BIOLOGY   (Russian Federation)

^b UNIVERSITY OF LEUVEN   (Belgium)

^c INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

Hyperbolic PDE model; Inverse problem; Label structured cell population dynamics; Tikhonov regularization

Indexed keywords

5 (6) CARBOXYFLUORESCEIN DIACETATE SUCCINIMIDYL ESTER; 5-(6)-CARBOXYFLUORESCEIN DIACETATE SUCCINIMIDYL ESTER; FLUORESCEIN DERIVATIVE; SUCCINIMIDE DERIVATIVE;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; CELL DEATH; CELL DIVISION; CELL PROLIFERATION; CHEMISTRY; CONFIDENCE INTERVAL; CYTOLOGY; FLOW CYTOMETRY; HUMAN; KINETICS; METHODOLOGY; STAINING; STATISTICAL MODEL; T LYMPHOCYTE;

ALGORITHMS; CELL DEATH; CELL DIVISION; CELL PROLIFERATION; CONFIDENCE INTERVALS; FLOW CYTOMETRY; FLUORESCEINS; HUMANS; KINETICS; LIKELIHOOD FUNCTIONS; MODELS, BIOLOGICAL; STAINING AND LABELING; SUCCINIMIDES; T-LYMPHOCYTES;

EID: 70349929800     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0244-5     Document Type: Article

References (38)

1. Quah BJ, Warren HS, Parish CR (2007) Monitoring lymphocyte proliferation in vitro and in vivo with the intracellular fluorescent dye carboxyfluorescein diacetate succinimidyl ester. Nat Protocol 2(9): 2049-2056.
2. Hawkins ED, Hommel M, Turner ML, Battye FL, Markham JF, Hodgkin PD (2007) Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data. Nat Protocol 2(9): 2057-2067.
3. Bernard S, Pujo-Menjouet L, Mackey MC (2003) Analysis of cell kinetics using a cell division marker: mathematical modelling of experimental data. Biophys J 84: 3414-3424.
4. De Boer RJ, Perelson AS (2005) Estimating division and death rates from CFSE data. J Comput Appl Math 184: 140-164.
5. Ganusov VV, Pilyugin SS, De Boer RJ, Murali-Krishna K, Ahmed R, Antia R (2005) Quantifying cell turnover using CFSE data. J Immunol Methods 298: 183-200.
6. Leon K, Faro J, Carneiro J (2004) A general mathematical framework to model generation structure in a population of asynchronously dividing cells. J Theor Biol 229: 455-476.
7. Asquith B, Debacq C, Florins A, Gillet N, Sanchez-Alcaraz T, Mosley A, Willems L (2006) Quantifying lymphocyte kinetics in vivo using carboxyfluorescein diacetate succinimidyl ester (CFSE). Proc R Soc B 273: 1165-1171.
8. Luzyanina T, Mrusek S, Edwards JT, Roose D, Ehl S, Bocharov G (2007) Computational analysis of CFSE proliferation assay. J Math Biol 54(1): 57-89.
9. Luzyanina T, Roose D, Schinkel T, Sester M, Ehl S, Meyerhans A, Bocharov G (2007) Numerical modelling of label-structured cell population growth using CFSE distribution data. Theor Biol Math Model 4: 1-26.
10. Sinko JW, Streifer W (1971) A model for populations reproducing by fission. Ecology 52: 330-335.
11. Bell GI, Anderson EC (1967) Cell growth and division I. A mathematical model with application to cell volume distributions in mammalian suspension cultures. Biophys J 7: 330-351.
12. Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations. Lecture notes in biomathematics, vol 68. Springer, Berlin.
13. Kunisch K, White L (1986) Parameter estimation for elliptic equations in multidimensional domains with point and flux observations. Nonlinear Anal TMA 10: 121-146.
14. Banks HT, Daniel Lamm P (1985) Estimation of variable coefficients in parabolic distributed systems. IEEE Trans Automat Control AC-30: 386-398.
15. Banks HT, Murphy KA (1986) Estimation of coefficients and boundary parameters in hyperbolic systems. SIAM J Control Optim 24: 926-950.
16. Wahba G (1987) Three topics in ill-posed problems. In: Engl M, Groetsch G (eds) Inverse and Ill-posed Problems. Academic Press, New York, pp 37-50.
17. Banks HT, Kareiva PM, Lamm PK (1985) Modelling insect dispersal and estimating parameters when mark-release techniques may cause initial disturbances. J Math Biol 22: 259-277.
18. Banks HT, Fitzpatrick BG (1991) Estimation of growth rate distributions in size structured population models. Q Appl Math 49: 215-235.
19. Banks HT, Kunish K (1989) Estimation techniques for distributed parameter systems. Systems and control: foundations and end applications, vol 1. Birkhauser, Basel.
20. Hasanov A, DuChateau P, Pektas B (2006) An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation. J Inverse Ill-Posed Probl 14(5): 435-463.
21. Ackleh AS, Banks HT, Deng K, Hu S (2005) Parameter estimation in a coupled system of nonlinear size-structured populations. Math Biosci Eng 2(2): 289-315.
22. Bitterlich S, Knabner P (2002) An efficient method for solving an inverse problem for the Richards equation. J Comput Appl Math 147: 153-173.
23. Wang G (2007) Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development. J Math Biol 54: 761-786.
24. Hadamard J (1932) Le probléme de Cauchy et les équations aux dérivées partielles linéaires hyperboliques. Hermann, Paris.
25. Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. V. H. Winston & Sons, Washington.
26. Tikhonov AN (1963) Solution of incorrectly formulated problems and the regularization method. Sov Math Dokl 4: 1035-1038.
27. Engl HW, Rundell W, Scherzer O (1994) A regularization scheme for an inverse problem in age-structured populations. J Math Anal Appl 182: 658-679.
28. Grebennikov A (2003) Local regularization algorithms of solving coefficient inverse problems for some differential equations. Inverse Probl Eng 11(3): 201-213.
29. Navon IM (1997) Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dyn Atmos Oceans 27(1): 55-79.
30. DuChateau P, Thelwell R, Butters G (2004) Analysis of an adjoint problem approach to the identification of an unknown diffusion coefficient. Inverse Probl 20: 601-625.
31. Tautenhahn U, Jin Q (2003) Tikhonov regularization and a posteriori rules for solving nonlinear ill posed problems. Inverse Probl 19: 1-21.
32. Perthame B, Zubelli JP (2007) On the inverse problem for a size-structured population model. Inverse Probl 23: 1037-1052.
33. Shampine L (2005) Solving hyperbolic PDEs in MATLAB. Appl Numer Anal Comput Math 2(3): 346-358.
34. Richtmyer RD, Morton KW (1967) Difference methods for initial-value problems. Wiley Interscience, New York.
35. Venzon DJ, Moolgavkar SH (1988) A method for computing profile-likelihood-based confidence intervals. Appl Stat 37(1): 87-94.
36. Burnham KP, Anderson DR (2002) Model selection and multimodel inference-a practical information-theoretic approach. Springer, New York.
37. Morozov VA (1966) On the solution of functional equations by the method of regularization. Sov Math Dokl 7: 414-417.
38. Morozov VA (1984) Methods for solving incorrectly posed problems. Springer, New York.