A Parameter Estimation Model of G-CSF: Mathematical Model of Cyclical Neutropenia


We investigate the FFT (Fast Fourier Transform) model and G-CSF (granulocyte colony-stimulating factor) treatment of CN (Cyclical Neutropenia). We collect grey collies and normal dog’s data from CN and analyze the G-CSF treatment. The model develops the dynamics of circulating blood cells before and after the G-CSF treatment. This is quite natural and useful for the collection of laboratory data for investigation. The proposed interventions are practical. This reduces the quantity of G-CSF required for potential maintenance. This model gives us good result in treatment. The changes would be practical and reduce the risk side as well as the cost of treatment in G-CSF.

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S. Balamuralitharan and S. Rajasekaran, "A Parameter Estimation Model of G-CSF: Mathematical Model of Cyclical Neutropenia," American Journal of Computational Mathematics, Vol. 2 No. 1, 2012, pp. 12-20. doi: 10.4236/ajcm.2012.21002.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Adimy and F. Crauste, “Global Stability of a Partial Differential Equation with Distributed Delay Due to Cellular Replication,” Nonlinear Analysis: Theory, Methods & Applications, Vol. 54, No. 8, 2003, pp. 1469-1491. doi:10.1016/S0362-546X(03)00197-4
[2] S. Balamuralitharan and S. Rajasekaran, “A Mathematical Age-Structured Model on Aiha Using Delay Partial Differential Equations,” Australian Journal of Basic and Applied Sciences, Vol. 5, No. 4, 2011, pp. 9-15.
[3] S. Balamuralitharan and S. Rajasekaran, “A Mathematical Age-structured Model on CN Using Delay Partial Differential Equations,” Proceedings of the Interna-tional Conference on Emerging Trends in Mathematics and Computer Applications. MEPCO Schlenk Engineering College, Sivakasi, 16-18 December 2010, pp. 183-187.
[4] J. Bélair, M. C. Mackey and J. M. Mahaffy, “Age-Structured and Two-Delay Models for Erythropoiesis,” Mathematical Biosci-ences, Vol. 128, No. 1-2, 1995, pp. 317-346. doi:10.1016/0025-5564(94)00078-E
[5] S. Bernard, J. Belair and M. Mackey, “Oscillations in Cyclical Neutropenia: New Evidence Based on Mathematical Modeling,” Journal of Theoretical Biology, Vol. 223, No. 3, 2003, pp. 283-298. doi:10.1016/S0022-5193(03)00090-0
[6] A. Beuter, L. Glass, M. C. Mackey and M. S. Titcombe, “Nonlinear Dynamics in Physiology and Medicine,” Springer-Verlag, New York, 2003.
[7] S. P. Blythe, R. M. Nisbet and W. S. C. Gurney, “The Dynamics of Population Models with Distributed Matura-tion Periods,” Theoretical Population Biology, Vol. 25, No. 3, 1984, pp. 289-311. doi:10.1016/0040-5809(84)90011-X
[8] T. Cohen and D. P. Cooney, “Cyclical Thrombocytopenia: Case Report and Review of Literature,” Scandinavian Journal of Haematology, Vol. 16, 1974, pp. 133-138.
[9] C. Colijn and M. Mackey, “A Mathematical Model of Hematopoiesis: II. Cyclical Neutro-penia,” Journal of Theoretical Biology, Vol. 237, No. 2, 2005, pp. 133-146. doi:10.1016/j.jtbi.2005.03.034
[10] C. Colijn, A. C. Fowler and M. C. Mackey, “High Frequency Spikes in Long Period Blood Cell Oscillations,” Journal of Mathematical Biology, Vol. 53, No. 4, 2006, pp. 499-519. doi:10.1007/s00285-006-0027-9
[11] D. C. Dale and W. P. Hammond, “Cyclic Neutropenia: A Clinical Review,” Blood Reviews, Vol. 2, No. 3, 1988, pp. 178-185. doi:10.1016/0268-960X(88)90023-9
[12] D. Fargue, “Re-ductibilite des systemes hereditaires,” International Journal of Non-Linear Mechanics, Vol. 9, No. 5, 1974, pp. 331-338. doi:10.1016/0020-7462(74)90018-3
[13] C. Foley and M. Mackey, “Dynamic Hematological Disease: A Review,” Journal of Mathematical Biology, Vol. 58, No. 1-2, 2008, pp. 285-322.
[14] C. Foley, S. Bernard and M. Mackey, “Cost-Effective G-CSF Therapy Strategies for Cyclical Neu-tropenia: Mathematical Modelling Based Hypotheses,” Journal of Theoretical Biology, Vol. 238, No. 4, 2006, pp. 754-763. doi:10.1016/j.jtbi.2005.06.021
[15] P. Fortin and M. C. Mackey, “Periodic Chronic Myelogenous Leukemia: Spectral Analysis of Blood Cell Counts and Etiological Implications,” British Journal of Haematology, Vol. 104, No. 2, 1999, pp. 336-245. doi:10.1046/j.1365-2141.1999.01168.x
[16] D. Guerry, D. Dale, D. C. Omine, S. Perry and S. M. Wolff, “Periodic Hema-topoiesis in Human Cyclic Neutropenia,” Journal of Clinical Investigation, Vol. 52, No. 12, 1973, pp. 3220-3230. doi:10.1172/JCI107522
[17] W. P. Hammond, T. H. Price, L. M. Souza and D. C. Dale, “Treatment of Cyclic Neutropenia with Granulocyte Colony Stimulating Factor,” The New Eng-land Journal of Medicine, Vol. 320, 1989, pp. 1306-1311. doi:10.1056/NEJM198905183202003
[18] C. Haurie, M. C. Mackey and D. C. Dale, “Cyclical Neutropenia and Other Pe-riodic Hematological Diseases: A Review of Mechanisms and Mathematical Models,” Blood, Vol. 92, 1998, pp. 2629-2640.
[19] C. Haurie, D. C. Dale, R. Rudnicki, and M. C. Mackey, “Modeling Complex Neutrophil Dynamics in the Grey Collie,” Journal of Theoretical Biology, Vol. 204, No. 4, 2000, pp. 504-519. doi:10.1006/jtbi.2000.2034
[20] T. Hearn, C. Haurie and M. C. Mackey, “Cyclical Neutropenia and the Peripherial Control of White Blood Cell Production,” Journal of Theoretical Biology, Vol. 192, No. 2, 1998, pp. 167-181. doi:10.1006/jtbi.1997.0589
[21] M. Horwitz, K. F. Benson, Z. Duan, F.-Q. Li and R. E. Person, “Hereditary Neutropenia: Dogs Explain Human Neutrophil Elastase Mutations,” Trends in Molecular Medicine, Vol. 10, No. 4, 2004, pp. 163-170. doi:10.1016/j.molmed.2004.02.002
[22] E. A. King-Smith and A. Morley, “Computer Simulation of Granulopoiesis: Normal and Impaired Granulopoiesis,” Blood, Vol. 36, 1970, pp. 254-262.
[23] M. J. Koury, “Programmed Cell Death (Apop-tosis) in Hematopoiesis,” Experimental Hematology, Vol. 20, 1992, pp. 391-394.
[24] M. Loeffler and K. Pantel, “A Mathematical Model of Erythropoiesis Suggests an Altered Plasma Volume Control as Cause for Anemia in Aged Mice,” Experimental Gerontology, Vol. 25, No. 5, 1990, pp. 483-495. doi:10.1016/0531-5565(90)90036-2
[25] N. MacDonald, “Time Lags in Biological Models,” Spr- inger-Verlag, New York, 1978. doi:10.1007/978-3-642-93107-9
[26] M. C. Mackey, “Periodic Auto-Immune Hemolytic Anemia: An Induced Dynamical Disease,” Bulletin of Mathe- matical Biology, Vol. 41, 1979, pp. 829-834.
[27] M. C. Mackey and A. Rudnicki, “Global Stability in a Delayed Partial Differential Equation Describing Cellu-lar Replication,” Journal of Mathematical Biology, Vol. 33, No. 1, 1994, pp. 89-109. doi:10.1007/BF00160175
[28] J. Mahaffy, J. Belair and M. Mackey, “Hematopoietic Model with Moving Boundary Condition and State Dependent Delay: Applications in Erythropoiesis,” Journal of Theoretical Biology Vol. 190, No. 2, 1998, pp. 135-146. doi:10.1006/jtbi.1997.0537
[29] I. Ostby, G. Kvalheim, L. S. Rusten and P. Grottum, “Mathematical Modeling of Granulo-cyte Reconstitution after High-Dose Chemotherapy with Stem Cell Support: Effect of Posttransplant G-CSF Treatment,” Journal of Theoretical Biology, Vol. 231, No. 1, 2004, pp. 69-83. doi:10.1016/j.jtbi.2004.05.010
[30] T. H. Price, G. S. Chatta and D. C. Dale, “Effect of Recombinant Granulocyte Colony Stimulating Factor on Neutrophil Kinetics in Normal Young and Elderly Humans,” Blood, Vol. 88, 1996, pp. 335-340.
[31] I. Roeder, “Quantitative Stem Cell Biology: Computa-tional Studies in the Hematopoietic System,” Current Opinion in Hematology, Vol. 13, No. 4, 2006, pp. 222- 228. doi:10.1097/01.moh.0000231418.08031.48
[32] S. I. Rubinow and J. L. Lebowitz, “A Mathematical Model of Neutrophil Production and Control in Normal Man,” Journal of Mathe-matical Biology, Vol. 1, No. 3, 1975, pp. 187-225. doi:10.1007/BF01273744
[33] M. Santillan, J. Mahaffy, J. Belair and M. Mackey, “Regulation of Platelet Production: The Normal Response to Perturbation and Cyclical Platelet Dis-ease,” Journal of Theoretical Biology, Vol. 206, No. 4, 2000, pp. 585-603. doi:10.1006/jtbi.2000.2149
[34] S. Balamuralitharan and S. Rajasekaran, “Analysis of G-CSF Treatment of CN Using Fast Fourier Transform,” Salt Lake, Kolkata, 2011. http://www.imbic.org/forthcoming.html

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