Oscillations in a maturation model of blood cell production

SIAM Journal on Applied Mathematics

Volumn 66, Issue 6, 2006, Pages 2027-2048

  Drobnjak, Ivana ^a   Fowler, A C ^a   Mackey, Michael C ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Blood cell production; Chronic myelogenous leukemia; Cyclical neutropenia; Delay equation; Mathematical model; Maturation

Indexed keywords

BLOOD; CELL CULTURE; OSCILLATIONS;

BLOOD CELL PRODUCTION; CHRONIC MYELOGENOUS LEUKEMIA; CYCLICAL NEUTROPENIA; DELAY EQUATION; MATURATION;

MATHEMATICAL MODELS;

EID: 33845543482     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050648055     Document Type: Article

References (16)

1. S. BERNARD. J. BÉLAIR, AND M. C. MACKEY, Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, J. Theoret. Biol., 223 (2003), pp. 283-298.
2. G. CHIKKAPPA, G. BORNER, H. BURLINGTON, A.D. CHANANA, E.P. CRONKITE, S. ÖHL, M. PAVELEC, AND J. S. ROBERTSON, Periodic oscillation of blood leukocytes, platelets, and reticulocytes in a patient with chronic myelocytic leukemia, Blood, 47 (1976), pp. 1023-1030.
3. R. CRABB, M. C. MACKEY, AND A. D. REY, Propagating fronts, chaos, and multistability in a cell replication model, Chaos, 6 (1996), pp. 477-492.
4. D. C. DALE AND W. P. HAMMOND IV. Cyclical neutropenia: A clinical review, Blood Rev., 2 (1988), pp. 178-185.
5. J. DYSON, R. VILLELLA-BRESSON, AND G. F. WEBB, A singular transport equation modelling a proliferating maturity structured cell population, Can. Appl. Math. Q., 4 (1996), pp. 65-95.
6. A. S. FOKAS, J.B. KELLER, AND B.D. CLARKSON, Mathematical model of granulocytopoiesis and chronic myelogenous leukemia, Cancer Res., 51 (1991), pp. 2084-2091.
7. P. FORTIN AND M. C. MACKEY, Periodic chronic myelogenous leukemia: Spectral analysis of blood cell counts and etiological implications, Br. J. Haematol., 104 (1999), pp. 336-345.
8. A. C. FOWLER AND M.C. MACKEY, Relaxation oscillations in a class of delay differential equations. SIAM J. Appl. Math., 63 (2002), pp. 299-323.
9. D. GUERRY IV. D. C. DALE, M. OMINE, S. PERRY, AND S. M. WOLFF, Periodic hematopoiesis in human cyclic neutropenia, J. Clin. Invest., 52 (1973), pp. 3220-3230.
10. C. HAURIE, D. C. DALE. AND M. C. MACKEY, Cyclical neutropenia and other periodic hematological disorders: A review of mechanisms and mathematical models, Blood, 92 (1998), pp. 2629-2640.
11. M. C. MAOKEY, A unified hypothesis for the origin of aplastic anaemia and periodic haematopoesis, Blood, 51 (1978), pp. 941-956.
12. M. C. MACKEY, Cell kinetic status of haematopoietic stem cells, Cell. Prolif., 34 (2001), pp. 71-83.
13. M. C. MACKEY AND R. RUDNICKI, Global stability in a delayed partial differential equation describing cellular replication, J. Math. Biol., 33 (1994), pp. 89-109.
14. M. C. MACKEY AND R. RUDNICKI, A new criterion for the global stability of simultaneous cell replication and maturation processes, J. Math. Biol., 38 (1999), pp. 195-219.
15. J. D. MURRAY, Mathematical Biology, I. An Introduction, Springer-Verlag, New York, 2002.
16. A. D. REY AND M.C. MACKEY, Multistability and boundary layer development in a transport equation with delayed arguments, Can. Appl. Math. Q., 1 (1993), pp. 61-81.