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Model Identification and Parameter Estimation

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System Engineering Approach to Planning Anticancer Therapies

Abstract

Analysis of the models presented in the preceding chapters may be focused on drawing conclusions of either qualitative or quantitative nature. In the first case, parameter values are not needed, as the goal is to determine, for example, stability properties or the form of the optimal control. Such conclusions subsequently provide the basis for quantitative analysis that concerns a particular cancer type and attempts to determine the outcome of a therapy, or, in more advanced studies, the optimal therapy protocol. The latter is of more value from the clinical point of view. However, applicability of modeling results depends on the ability to estimate correct parameter values for the models under consideration. In subsequent sections, estimation of the model parameters is discussed in the context of experimental and numerical procedures, relevant for the models described in previous chapters.

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References

  1. I.A. Adzhubei, S. Schmidt, L. Peshkin, V.E. Ramensky, A. Gerasimova, P. Bork, A.S. Kondrashov, S. Sunyaev, A method and server for predicting damaging missense mutations. Nat. Methods 7, 248–249 (2010)

    Article  Google Scholar 

  2. D.G. Albertson, Gene amplification in cancer. Trends Genet. 22(8), 447–455 (2006)

    Article  MathSciNet  Google Scholar 

  3. M.L. Avent, V.L. Vaska, B.A. Rogers, A.C. Cheng, S.J. van Hal, N.E. Holmes, B.P. Howden, D.L. Paterson, Vancomycin therapeutics and monitoring: a contemporary approach. Int. Med. J. 43(2), 110–119 (2013)

    Article  Google Scholar 

  4. C. Barnes, Importance of pharmacokinetics in the management of hemophilia. Pediatr. Blood Cancer 60(Suppl. 1), S27–S29 (2013)

    Article  Google Scholar 

  5. C.D. Behrsin, C.J. Brandl, D.W. Litchfield, B.H. Shilton, L.M. Wahl, Development of an unbiased statistical method for the analysis of unigenic evolution. BMC Bioinf. 7, 150 (2006)

    Article  Google Scholar 

  6. M. Bentele, I. Lavrik, M. Ulrich, S. Stosser, D.W. Heermann, H. Kalthoff, P.H. Krammer, R. Eils, Mathematical modeling reveals threshold mechanism in cd95-induced apoptosis. J. Cell Biol. 166(6), 839–851 (2004)

    Article  Google Scholar 

  7. R. Bertolusso, B. Tian, Y. Zhao, L. Vergara, A. Sabree, M. Iwanaszko, T. Lipniacki, A.R. Brasier, M. Kimmel, Dynamic cross talk model of the epithelial innate immune response to double-stranded RNA stimulation: coordinated dynamics emerging from cell-level noise PLoS ONE 9(4), e93396 (2014)

    Google Scholar 

  8. S. Bjorkman, E. Berntorp, Pharmacokinetics of coagulation factors: clinical relevance for patients with haemophilia. Clin. Pharmacokinet. 40, 815–832 (2001)

    Article  Google Scholar 

  9. F.Y. Bois, M. Jamei, H.J. Clewell, PBPK modelling of inter-individual variability in the pharmacokinetics of environmental chemicals. Toxicology 278(3), 256–267 (2010)

    Article  Google Scholar 

  10. P.C. Brown, S.M. Beverly, R.T. Schimke, Relationship of amplified Dihydrofolate Reductase genes to double minute chromosomes in unstably resistant mouse fibroblasts cell lines. Mol. Cell. Biol. 1, 1077–1083 (1981)

    Article  Google Scholar 

  11. Y. Bushkin, F. Radford, R. Pine, A. Lardizabat, B.T. Mangura, M.L. Gennaro, S. Tyagi, Profiling T cell activation using single-molecule fluorescence in situ hybridization and flow cytometry. J. Immunol. 194(2), 836–841 (2015)

    Article  Google Scholar 

  12. F. Campolongo, J. Cariboni, A. Saltelli, An effective screening design for sensitivity analysis of large models. Environ. Model Softw. 22, 1509–1518 (2007)

    Article  Google Scholar 

  13. F.P. Casey, D. Baird, Q. Feng, R.N. Gutenkunst, J.J. Waterfall, C.R. Myers, K.S. Brown, R.A. Cerione, J.P. Sethna, Optimal experimental design in an epidermal growth factor receptor signalling and down-regulation model. IET Syst. Biol. 1(3), 190–202 (2007)

    Article  Google Scholar 

  14. Q. Chang, D. Hedley, Emerging applications of flow cytometry in solid tumor biology. Methods 57, 359–367 (2012)

    Article  Google Scholar 

  15. D. Campbell, O.A. Chkrebtii. Maximum Profile likelihood estimation of differential equation parameters through model based smoothing state estimates bayesian uncertainty. Math. Biosci. 246(2), 283–292 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. J.J. Cruz, Feedback Systems (McGraw-Hill, New York, 1972)

    Google Scholar 

  17. E. da Fidalgo Silva, S. Botsford, L.A. Porter, Derivation of a novel G2 reporter system. Cytotechnology 68(1), 19–24 (2016)

    Article  Google Scholar 

  18. Z. Darzynkiewicz, H. Crissman, J.W. Jacobberger, Cytometry of the cell cycle: cycling through history. Cytometry A 58A, 21–32 (2004)

    Article  Google Scholar 

  19. S.J. Deminoff, J. Tornow, G.M. Santangelo, Unigenic evolution: a novel genetic method localizes a putative leucine zipper that mediates dimerization of the Saccharomyces cerevisiae regulator Gcr1p. Genetics 141, 1263–1274 (1995)

    Google Scholar 

  20. S. Diekmann, C. Hoischen, Biomolecular dynamics and binding studies in the living cell. Phys. Life Rev. 11(1), 1–30 (2014)

    Article  Google Scholar 

  21. M. Dolbniak, M. Kimmel, J. Smieja, Modeling epigenetic regulation of prc1 protein accumulation in the cell cycle. Biol. Direct 10, 62 (2015)

    Article  Google Scholar 

  22. M.J. Downey, D.M. Jeziorska, S. Ott, T.K. Tamai, G. Koentges, et al., Extracting fluorescent reporter time courses of cell lineages from high-throughput microscopy at low temporal resolution. PLoS ONE 6(12), e2788 (2011)

    Google Scholar 

  23. A.D. Fernandes, B.P. Kleinstiver, D.R. Edgell, L.M. Wahl, G.B. Gloor, Estimating the evidence of selection and the reliability of inference in unigenic evolution. Algorithms Mol. Biol. 5, 35 (2010)

    Article  Google Scholar 

  24. L. Ferrante, S. Bompadre, L. Possati, L. Leone, Parameter estimation in a Gompertzian stochastic model for tumor growth. Biometrics 56(4), 1076–1081 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  25. K. Fujarewicz, M. Kimmel, A. Swierniak, On fitting of mathematical models of cell signaling pathways using adjoint systems. Math. Biosci. Eng. 2(3), 527–534 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  26. K. Fujarewicz, M. Kimmel, T. Lipniacki, A. Swierniak, Adjoint systems for models of cell signaling pathways and their application to parameter fitting. IEEE/ACM Trans. Comput. Biol. Bioinform. 4(3), 322–335 (2007)

    Article  Google Scholar 

  27. S.N. Gentry, T.L. Jackson, A mathematical model of cancer stem cell driven tumor initiation: implications of niche size and loss of homeostatic regulatory mechanisms PLoS ONE 8(8), e71128 (2013)

    Google Scholar 

  28. M. Girolami, Bayesian inference for differential equations. Theor. Comput. Sci. 408, 4–16 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  29. R.N. Gutenkunst, F.P. Casey, J.J. Waterfall, C.R. Myers, J.P. Sethna, Extracting falsifiable predictions from sloppy models. Ann. N. Y. Acad. Sci. 1115(1), 203–211 (2007)

    Article  Google Scholar 

  30. R.N. Gutenkunst, J.J. Waterfall, F.P. Casey, K.S. Brown, C.R. Myers, J.P. Sethna, Universally sloppy parameter sensitivities in systems biology models PLoS Comput. Biol. 3(10), e189 (2007)

    Google Scholar 

  31. C.V. Harper, B. Finkenstdt, D.J. Woodcock, S. Friedrichsen, S. Semprini, L. Ashall, D.G. Spiller, J.J. Mullins, D.A. Rand, J.R. Davis, M.R. White, Dynamic analysis of stochastic transcription cycles. PLoS Biol. 9(4), e1000607 (2011)

    Google Scholar 

  32. S. Hicks, D.A. Wheeler, S.E. Plon, M. Kimmel, Prediction of missense mutation functionality depends on both the algorithm and sequence alignment employed. Hum. Mutat. 32(6), 661–668 (2011)

    Article  Google Scholar 

  33. H.C. Ishikawa-Ankerhold, R. Ankerhold, G.P. Drummen. Advanced fluorescence microscopy techniques–FRAP, FLIP, FLAP, FRET and FLIM. Molecules 17(4), 4047–4132 (2012)

    Article  Google Scholar 

  34. R.J. Kaufman, P.C. Brown, R.T. Schimke, Loss and stabilization of amplified dihydrofolate reductase genes in mouse sarcoma S-180 cell lines. Mol. Cell. Biol. 1, 1084–1093 (1981)

    Article  Google Scholar 

  35. K.A. Kim, S.L. Spencer, J.G. Albeck, J.M. Burke, P.K. Sorger, S. Gaudet, H. Kim, Systematic calibration of a cell signaling network model. BMC Bioinf. 11, 202 (2010)

    Article  Google Scholar 

  36. M. Kimmel, D.E. Axelrod, Fluctuation test for two-stage mutations: application to gene amplification. Mutat. Res. 306, 45–60 (1994)

    Article  Google Scholar 

  37. J. Leis, M. Kramer, Sensitivity analysis of systems of differential and algebraic equations. Comput. Chem. Eng. 9, 93–96 (1985)

    Article  Google Scholar 

  38. T. Lipniacki, P. Paszek, A.R. Brasier, B. Luxon, M. Kimmel, Mathematical model of NF-kB regulatory module. J. Theor. Biol. 228, 195–215 (2004)

    Article  MathSciNet  Google Scholar 

  39. D. Lu, S. Girish, Y. Gao, B. Wang, J.H. Yi, E. Guardino, M. Samant, M. Cobleigh, M. Rimawi, P. Conte, J.Y. Jin, Population pharmacokinetics of trastuzumab emtansine (T-DM1), a HER2-targeted antibody-drug conjugate, in patients with HER2-positive metastatic breast cancer: clinical implications of the effect of covariates. Cancer Chemother. Pharmacol. 74(2), 399–410 (2014)

    Article  Google Scholar 

  40. A. Marin-Sanguino, S.K. Gupta, E.O. Voit, J. Vera, Biochemical pathway modeling tools for drug target detection in cancer and other complex diseases. Methods Enzymol. 487, 319–369 (2011)

    Article  Google Scholar 

  41. E. Mathe, M. Olivier, S. Kato, C. Ishioka, P. Hainaut, S.V. Tavtigian, Computational approaches for predicting the biological effect of p53 missense mutations: a comparison of three sequence analysis based methods. Nucleic Acids Res. 34, 1317–1325 (2006)

    Article  Google Scholar 

  42. C.A. Miller, B.S. White, N.D. Dees, M. Griffith, J.S. Welch, O.L. Griffith, R. Vij, M.H. Tomasson, T.A. Graubert, M.J. Walter, M.J. Ellis, W. Schierding, J.F. DiPersio, T.J. Ley, E.R. Mardis, R.K. Wilson, L. Ding, SciClone: inferring clonal architecture and tracking the spatial and temporal patterns of tumor evolution PLoS Comput. Biol. 8, e1003665 (2014)

    Google Scholar 

  43. M.D. Morris, Factorial sampling plans for preliminary computational experiments. Technometrics 33(2), 161–174 (1991)

    Article  Google Scholar 

  44. j. Morrow, Genetic analysis of azaguanine resistance in an established mouse cell line. Genetics 65, 279–287 (1970)

    Google Scholar 

  45. J.P. Murnane, M.J. Yezzi, Association of high rate of recombination with amplification of dominant selectable gene in human cells. Somat. Cell Mol. Genet. 14, 273–286 (1988)

    Article  Google Scholar 

  46. G. Neuert, B. Munsky, R.Z. Tan, L. Teytelman, M. Khammash, A. van Oudenaarden, Systematic identification of signal-activated stochastic gene regulation. Science 339(6119), 584–587 (2013)

    Article  Google Scholar 

  47. P.C. Ng, S. Henikoff, Predicting deleterious amino acid substitutions. Genome Res. 11, 863–874 (2001)

    Article  Google Scholar 

  48. H. Nishi, M. Tyagi, S. Teng, B.A. Shoemaker, K. Hashimoto, E. Alexov, S. Wuchty, A.R. Panchenko, Cancer missense mutations alter binding properties of proteins and their interaction networks PLoS ONE 8(6), e66273 (2013)

    Google Scholar 

  49. C.O.T. Oana-Teodora, J.R. Banga, E. Balsa-Canto, Structural identifiability of systems biology models: a critical comparison of methods. PLoS ONE 6, e27755 (2011)

    Article  Google Scholar 

  50. K. Patel, C.M. Kirkpatrick, Pharmacokinetic concepts revisited - basic and applied. Curr. Pharm. Biotechnol. 12(12), 1983–1990 (2011)

    Article  Google Scholar 

  51. T. Peyret, P. Poulin, K. Krishnan, A unified algorithm for predicting partition coefficients for PBPK modeling of drugs and environmental chemicals. Toxicol. Appl. Pharmacol. 249(3), 197–207 (2010)

    Article  Google Scholar 

  52. M. Piazza, X.J. Feng, J.D. Rabinowitz, H. Rabitz, Diverse metabolic model parameters generate similar methionine cycle dynamics. J. Theor. Biol. 251, 628–639 (2008)

    Article  MathSciNet  Google Scholar 

  53. K. Puszynski, P. Lachor, M. Kardynska, J. Smieja, Sensitivity analysis of deterministic signaling pathways models. Bull. Pol. Acad. Sci. Tech. Sci. 60, 471–479 (2012)

    Google Scholar 

  54. A. Raj, P. van den Bogaard, S. Rifkin, A. van Oudenaarden, S. Tyagi, Imaging individual MRNA molecules using multiple singly labeled probes. Nat. Methods 5, 877–887 (2008)

    Article  Google Scholar 

  55. V. Ramensky, P. Bork, S. Sunyaev, Human non-synonymous SNPs: server and survey. Nucleic Acids Res. 30, 3894–3900 (2002)

    Article  Google Scholar 

  56. M. Rathinam, P.W. Sheppard, M. Khammash, Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks. J. Chem. Phys. 132(3), 034103 (2010)

    Google Scholar 

  57. A. Raue, C. Kreutz, T. Maiwald, J. Bachmann, M. Schilling, U. Klingmuller, J. Timmer, Structural and practical identifiability analysis of partially observed dynamical models by exploring the profile likelihood. Bioinformatics 25, 1923–1929 (2009)

    Article  Google Scholar 

  58. B. Reva, Y. Antipin, C. Sander, Predicting the functional impact of protein mutations: application to cancer genomics. Nucleic Acids Res. 39(17), e118 (2011)

    Google Scholar 

  59. M. Roccio, D. Schmitter, M. Knobloch, Y. Okawa, D. Sage, M.P. Lutolf, Predicting stem cell fate changes by differential cell cycle progression patterns. Development 140(2), 459–470 (2013)

    Article  Google Scholar 

  60. A. Rousseau, P. Marquet, Application of pharmacokinetic modelling to the routine therapeutic drug monitoring of anticancer drugs. Fundam. Clin. Pharmacol. 16(4), 253–262 (2002)

    Article  Google Scholar 

  61. A. Saltelli, Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models (Wiley, New York, 2004)

    MATH  Google Scholar 

  62. A. Saltelli, Global Sensitivity Analysis: The Primer (Wiley, New York, 2008)

    MATH  Google Scholar 

  63. J. Smieja, Dynamics, Feedback Loops and Control in Biology - From Physiological to Individual Cell Models (Silesian University of Technology, Gliwice, 2011)

    Google Scholar 

  64. J. Smieja, M. Jamalludin, A.R. Brasier, M. Kimmel, Model-based analysis of interferon-b induced signaling pathway. Bioinformatics 24(20), 2363–2369 (2008)

    Article  Google Scholar 

  65. J. Smieja, M. Kardynska, A. Jamroz, The meaning of sensitivity functions in signaling pathways analysis. Discrete Contin. Dyn. Syst. Ser. B 10(8), 2697–2707 (2014)

    MATH  MathSciNet  Google Scholar 

  66. I. Sobol, Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Math. Comput. Simul. 55, 271–280 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  67. R.G. Staudte, R.M. Huggins, J. Zhang, D.E. Axelrod, M. Kimmel, Estimating clonal heterogeneity and interexperiment variability with the bifurcating autoregressive model for cell lineage data. Math. Biosci. 143(2), 103–121 (1997)

    Article  MATH  Google Scholar 

  68. E.D. Strome, X. Wu, M. Kimmel, S.E. Plon, Heterozygous screen in Saccharomyces cerevisiae identifies dosage-sensitive genes that affect chromosome stability. Genetics 178(3), 1193–1207 (2008). doi:10.1534/genetics.107.084103

    Article  Google Scholar 

  69. M. Sugiyama, A. Sakaue-Sawano, T. Iimura, K. Fukami, T. Kitaguchi, et al., Illuminating cell cycle progression in the developing zebrafish embryo. Proc. Natl. Acad. Sci. 106, 20812–20817 (2009)

    Article  Google Scholar 

  70. D.M. Suter, N. Molina, D. Gatfield, K. Schneider, U. Schibler, F. Naef, Mammalian genes are transcribed with widely different bursting kinetics. Science 332(6028), 472–474 (2011)

    Article  Google Scholar 

  71. S.V. Tavtigian, M.S. Greenblatt, F. Lesueur, G.B. Byrnes, IARC Unclassified Genetic Variants Working Group, In silico analysis of missense substitutions using sequence-alignment based methods. Hum. Mutat. 29, 1327–1336 (2008)

    Google Scholar 

  72. M. Thattai, A. van Oudenaarden, Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. 98, 8614–8619 (2001)

    Article  Google Scholar 

  73. M.A. Thomas, B. Weston, M. Joseph, W. Wu, A. Nekrutenko, P.J. Tonellato, Evolutionary dynamics of oncogenes and tumor suppressor genes: higher intensities of purifying selection than other genes. Mol. Biol. Evol. 20(6), 964–968 (2003)

    Article  Google Scholar 

  74. T. Tlsty, B.H. Margolin, K. Lum, Differences in the rates of gene amplification in nontumorigenic and tumorigenic cell lines as measured by Luria-Delbruck fluctuation analysis. Proc. Natl. Acad. Sci. 86, 9441–9445 (1989)

    Article  Google Scholar 

  75. A. Tourovskaia, M. Fauver, G. Kramer, S. Simonson, T. Neumann, Tissue-engineered microenvironment systems for modeling human vasculature. Exp. Biol. Med. (Maywood) 239(9), 1264–1271 (2014)

    Google Scholar 

  76. R.D. Travasso, E. Corvera Poir, M. Castro, J.C. Rodrguez-Manzaneque, A. Hernndez-Machado, Tumor angiogenesis and vascular patterning: a mathematical model. PLoS ONE 6(5), e19989 (2011)

    Google Scholar 

  77. A.F. van der Meer, M.A. Marcus, D.J. Touw, J.H. Proost, C. Neef, Optimal sampling strategy development methodology using maximum a posteriori Bayesian estimation. Ther. Drug Monit. 33(2), 133–146 (2011)

    Google Scholar 

  78. A.D. van der Meer, V.V. Orlova, P. ten Dijke, A. van den Berg, C.L. Mummery, Three-dimensional co-cultures of human endothelial cells and embryonic stem cell-derived pericytes inside a microfluidic device. Lab Chip 13(18), 3562–3568 (2013)

    Article  Google Scholar 

  79. N.A.W. Van Riel, Dynamic modelling and analysis of biochemical networks: mechanism based models and model-based experiments. Brief. Bioinform. 7(4), 364–374 (2006)

    Article  Google Scholar 

  80. N.B. Varshaver, M.I. Marshak, N.I. Shapiro, The mutational origin of serum independence in Chinese hamster cells in vitro. Int. J. Cancer 31, 471–475 (1983)

    Article  Google Scholar 

  81. D. Wang, F. Liu, L. Wang, S. Huang, J. Yu, Nonsynonymous substitution rate (Ka) is a relatively consistent parameter for defining fast-evolving and slow-evolving protein-coding genes Biol. Direct 6, 13 (2011)

    Article  Google Scholar 

  82. N. Watanabe, S. Yamashiro, D. Vavylonis, T. Kiuchi, Molecular viewing of actin polymerizing actions and beyond: combination analysis of single-molecule speckle microscopy with modeling, FRAP and s-FDAP (sequential fluorescence decay after photoactivation). Dev. Growth Differ. 55(4), 508–514 (2013)

    Article  Google Scholar 

  83. J.J. Waterfall, F.P. Casey, R.N. Gutenkunst, K.S. Brown, C.R. Myers, P.W. Brouwer, V. Elser, J.P. Sethna, Sloppy-model universality class and the Vandermonde matrix. Phys. Rev. Lett. 97(15), 150601 (2006)

    Google Scholar 

  84. D.J. Woodcock, K.W. Vance, M. Komorowski, G. Koentges, B. Finkenstaedt, D.A. Rand, A hierarchical model of transcriptional dynamics allows robust estimation of transcription rates in populations of single cells with variable gene copy number. Bioinformatics 29(12), 1519–1525 (2013)

    Article  Google Scholar 

  85. X. Wu, E.D. Strome, Q. Meng, P.J. Hastings, S.E. Plon, M. Kimmel, A robust estimator of mutation rates. Mutat. Res. 661(1–2), 101–109 (2009). doi:10.1016/j.mrfmmm.2008.11.015

    Article  Google Scholar 

  86. T.R. Xu, V. Vyshemirsky, A. Gormand, A. von Kriegsheim, M. Girolami, G.S. Baillie, D. Ketley, A.J. Dunlop, G. Milligan, M.D. Houslay, W. Kolch, Inferring signaling pathway topologies from multiple perturbation measurements of specific biochemical species. Sci. Signal. 3(113), ra20 (2010)

    Google Scholar 

  87. T. Yamada, J. Ou, C. Furusawa, T. Hirasawa, T. Yomo, H. Shimizu, Relationship between noise characteristics in protein expressions and regulatory structures of amino acid biosynthesis pathways. IET Syst. Biol. 4(1), 82–89 (2010)

    Article  Google Scholar 

  88. H. Yue, M. Brown, J. Knowles, H. Wang, D.S. Broomhead, D.B. Kell, Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an nf-kappab signalling pathway. Mol. BioSyst. 2(12), 640–649 (2006)

    Article  Google Scholar 

  89. D.E. Zak, R.K. Pearson, R. Vadigepalli, G.E. Gonye, J.S. Schwaber, F.J. Doyle 3rd., Continuous time identification of gene expression models. OMICS: J. Integr. Biol. 7(4), 373–386 (2003)

    Article  Google Scholar 

  90. Y. Zhao, A.R. Brasier, Applications of selected reaction monitoring (SRM)-mass spectrometry (MS) for quantitative measurement of signaling pathways. Methods 61(3), 313–322 (2013)

    Article  Google Scholar 

  91. Z. Zi, K.H. Chob, M.H. Sung, X. Xia, J. Zheng, Z. Sun, In silico identification of the key components and steps in IFN-g induced JAK-STAT signaling pathway. FEBS Lett. 579, 1101–1108 (2005)

    Article  Google Scholar 

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Świerniak, A., Kimmel, M., Smieja, J., Puszynski, K., Psiuk-Maksymowicz, K. (2016). Model Identification and Parameter Estimation. In: System Engineering Approach to Planning Anticancer Therapies. Springer, Cham. https://doi.org/10.1007/978-3-319-28095-0_6

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