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.
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.
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.
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.
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.
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.
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
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.
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.
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
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.
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
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
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.
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.
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
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.
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.
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
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.