# Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 3, page 15-27
- ISSN: 0973-5348

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topAfenya, E., and Mundle, S.. "Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics." Mathematical Modelling of Natural Phenomena 5.3 (2010): 15-27. <http://eudml.org/doc/197677>.

@article{Afenya2010,

abstract = {Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. The
lingering controversies related to various diseases are highlighted. A simple
biomathematical model of bone marrow - peripheral blood dynamics in the normal state is
proposed and used to investigate cell behavior in normal hematopoiesis from a mathematical
viewpoint. Analysis of the steady state and properties of the model are used to make
postulations about the phenomenon of massive apoptosis in MDS. Simulations of the model
show situations in which homeostatic equilibrium can be achieved and maintained.
Consequently, it is postulated that hematopoietic growth factors may possess the
capabilities of preventing oscillatory dynamics and enhancing faster evolution towards
homeostatic equilibrium.},

author = {Afenya, E., Mundle, S.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {hematologic disorders; mathematical model; normal hematopoiesis},

language = {eng},

month = {4},

number = {3},

pages = {15-27},

publisher = {EDP Sciences},

title = {Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics},

url = {http://eudml.org/doc/197677},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Afenya, E.

AU - Mundle, S.

TI - Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/4//

PB - EDP Sciences

VL - 5

IS - 3

SP - 15

EP - 27

AB - Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. The
lingering controversies related to various diseases are highlighted. A simple
biomathematical model of bone marrow - peripheral blood dynamics in the normal state is
proposed and used to investigate cell behavior in normal hematopoiesis from a mathematical
viewpoint. Analysis of the steady state and properties of the model are used to make
postulations about the phenomenon of massive apoptosis in MDS. Simulations of the model
show situations in which homeostatic equilibrium can be achieved and maintained.
Consequently, it is postulated that hematopoietic growth factors may possess the
capabilities of preventing oscillatory dynamics and enhancing faster evolution towards
homeostatic equilibrium.

LA - eng

KW - hematologic disorders; mathematical model; normal hematopoiesis

UR - http://eudml.org/doc/197677

ER -

## References

top- A. Raza, S. Gezer, S. Mundle, X. Gao, S. Alvi, R. Borok, S. Rifkin, A. Iftikhar, V. Shetty, A. Parcharidou, J. Loew, B. Marcus, Z. Khan, C. Chaney, J. Showel, S. Gregory, H. Preisler. Apoptosis in bone marrow biopsy samples involving stromal and hematopoietic cells in 50 patients with myelodysplastic syndromes. Blood, 86 (1995), No. 1, 268–276.
- A. Fokas, J. Keller, B. Clarkson. Mathematical model of granulocytopoiesis and chronic myelogenous leukemia. Can. Res., 51 (1991), 2084.
- A. Parcharidou, A. Raza, T. Economopoulos, E. Papageorgiou, D. Anagnostou, T. Papadaki, S. Raptis. Extensive apoptosis of bone marrow cells as evaluated by the in situ end-labelling (ISEL) technique may be the basis for ineffective hematopoiesis in patients with myelodysplastic syndromes. Eur. J. Haemat., 62 (1999), 19–26.
- A. Raza, S. Mundle, A. Iftikhar, S. Gregory, B. Marcus, Z. Khan, S. Alvi, V. Shetty, S. Dameron, V. Wright, S. Adler, J. Loew, S. Shott, S. Ali, H. Preisler. Simultaneous assessment of cell kinetics and programmed cell death in bone marrow biopsies of myelodysplastics reveals extensive apoptosis as the probable basis for ineffective hematopoiesis. Amer. J. Hematol., 48 (1995), 143–154.
- B. Djulbegovic, S. Svetina. Mathematical model of acute myeloblastic leukaemia: an investigation of relevant kinetic parameters. Cell Tissue Kinet., 18 (1985), 307–319.
- B. Lord, H. Gurney, J. Chang, N. Thatcher, D. Crowther, T. Dexter. Haemopoietic cell kinetics in humans treated with RGM-CSF. Int. J. Cancer, 50 (1992), 26–31.
- B. Lord, N. Testa, S. Bretti, J. Chang, H. Demuynck, L. Coutinho, E. Campos, L. Fitzsimmons, H. Scarffe. Haemopoietic progenitor and myeloid cell kinetics in humans treated with interleukin-3 and granulocyte/macrophage colony-stimulating factor in combination. Int. J. Cancer, 59 (1994), 483–490.
- B. Lowenberg, J. Griffin, M. Tallman. Acute myeloid leukemia and acute promyelocytic leukemia. Amer. Soc. Hematol., 2003
- D. Bouscary, J. Vos, M. Guesnu, K. Jondeau, F. Viguier, J. Melle, F. Picard, F. Dreyfus, M. Fontenay-Roupie. Fas/Apo-1 (cd95) expression and apoptosis in patients with myelodysplastic syndromes. Leuk., 11 (1997), 839–845.
- D. Dale, W. Liles, C. Llewellyn, T. Price. Effects of granulocyte-macrophage colony-stimulating factor (GM-CSF) on neutrophil kinetics and function in normal human volunteers. Amer. J. Hematol., 57 (1998), 7–15.
- D. Steensma, A. Tefferi. The myelodysplastic syndrome(s): a perspective and review highlighting current controversies. Leuk. Res., 27 (2003), 95–120.
- E. Afenya, C. Calderon. Normal cell decline and inhibition in acute leukemia: a biomathematical modeling approach. J. Can. Det. Prev., 20 (1996), No. 3, 171–179.
- E. Afenya. Acute leukemia and chemotherapy: a modeling viewpoint. Math. Biosci., 138 (1996), 79–100.
- E. Hellstrom-Lindberg, L. Kanter-Lewensohn, A. Ost. Morphological changes and apoptosis in bone marrow from patients with myelodysplastic syndromes treated with granulocyte-CSF and erythropoietin. Leuk. Res., 21(1997), No. 5, 415–425.
- E. Hofer, S. Brucher, K. Mehr, B. Tibken. An approach to a biomathematical model lymphocytopoiesis. Stem Cells, 13 (1995), No. 1, 290–300.
- H. Foerster. Some remarks on changing populations. In: The Kinetics of Cellular Proliferation (F. Stohlman, Jr., ed.), Grune and Stratton, p. 382, New York, 1959.
- H. Wichmann, M. Loeffler, S. schmitz. A concept of hemopoeitic regulation and its biomathematical realization. Blood Cells, 14 (1988), 411.
- I. Roeder, M. Herberg, M. Horn. An "age"-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bull. Math. Biol., 71 (2009), 602–626.
- J. Anderson, F. Appelbaum, L. Fisher, G. Stoch, H. Shulman, C. Anasetti, W. Bensinger, E. Bryant, C. Buckner, K. Doney, P. Martin, J. Sanders, K. Sullivan, E. Thomas, R. Witherspoon, J. Hansen, R. Storb. Allogeneic bone marrow transplantation for 93 patients with myelodysplastic syndromes. Blood, 82 (1993), 677.
- J. Parker, G. Mufti, F. Rasool, A. Mijovic, S. Devereux, A. Pagliuca. the role of apoptosis, proliferation, and bcl-2 related proteins in myelodysplastic syndromes and acute myeloid leukemia secondary to MDS. Blood, 96 (2000), No. 12, 3932–3938.
- K. Hara, A. Yasunobu, N. Hirase, M. Shiratsuchi, T. Kihara, J. Nishimura, H. Nawata, K. Muta. Apoptosis resistance of mature neutrophils in a case of chronic neutrophilic leukaemia. Eur. J. Haematol., 66 (2001), 70–71.
- K. Shimazaki, K. Oshima, J. Suzumiya, C. Kawasaki, M. Kikuchi. Evaluation of apoptosis as a prognostic factor in myelodysplastic syndromes. Br. J. Haemat., 110 (2000), 584–590.
- L. Glass, M. Mackey. From clocks to chaos. Princeton University Press, Princeton, 1988.
- M. Aljurf, S. Zaidi. Chemotherapy and hematopoietic stem cell transplantation for adult T-cell lymphoblastic lymphoma: current status and controversies. Biol. Blood Marrow Transplant.11 (2005), No. 10, 739–754.
- M. Mackey, L. Glass. Oscillation and chaos in physiological control systems. Science, 197 (1977), 287–289.
- M. Mackey. Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood, 51 (1978), No. 5, 941–956.
- N. Kazarinoff, P. denDriessche. Control of oscillations in hematopoiesis. Science, 203 (1979), 1348–1349.
- N. Marer, P. Skacel. Up-regulation of 2,6 sialylation during myeloid maturation: a potential role in myeloid cell release from the bone marrow. J. Cell. Phy., 179 (1999), 315–324.
- O. Scherbaum, G. Rasch. cell size distribution and single cell growth in Tetrahymena Pyriformis GL. Acta Pathol. Microbiol. Scand., 41 (1957), 161.
- P. Lepelley, L. Campergue, N. Grardel , C. Preudhomme, A. Cosson, P. Fenaux. Is apoptosis a massive process in myelodysplastic syndromes? Brit.J. Haematol., 95 (1996), 368–371.
- R. Stone, M. Sekeres, G. Garcia-Maneros, R. Lyons. Recent advances in low- and intermediate-1-risk myelodysplastic syndrome: developing a consensus for optimal therapy. Clin. Adv. Hematol. Oncol., 6 (2008), No. 12, 1–15.
- S. Khan, A. Raza, M. Barcos, N. Yousuf, T. Saikia, M. Masterson, J. Bennett, G. Browman, J. Goldberg, H. Grunwald, R. Larson, A. Sandberg, R. Vogler, H. Preisler. Cell cycle and clinical characteristics of patients with acute myeloid leukemia and myelodysplasia whose biopsies are reactive with anti-factor VIII antibody. Leuk. Res., 15 (1991), No. 1, 51–57.
- S. Mundle, P. Venugopal, J. Cartlidge, D. Pandav, L. Broady-Robinson, S. Gezer, E. Robin, S. Rifkin, M. Klein, D. Alston, B. Hernandez, D. Rosi, S. Alvi, V. Shetty, S. Gregory, A. Raza. Indication of an involvement of interleukin-1 converting enzyme-like protease in intramedullary apoptotic cell death in the bone marrow of patients with myelodysplastic syndromes. Blood, 88 (1996), No. 7, 2640–2647.
- S. Mundle, V. Shetty, A. Raza. Caspases and apoptosis in myelodysplastic syndromes. Letters to the Editor/Exp. Hematol., (2000), 1–2.
- S. Mundle. Lingering dilemmas about the status of progenitor cells in myelodysplasia. Arch. Med. Res., 34 (2003), 515–519.
- S. Rubinow, J. Lebowitz. A mathematical model of neutrophil production and control in normal man. J. Math. Biol., 1 (1975), 187–225.
- S. Rubinow, J. Lebowitz. A mathematical model of the acute myeloblastic leukemic state in man. Biophys. J., 16 (1976), 897–910.
- S. Schmitz, H. Franke, J. Brusis, H. Wichmann. 1993 Quantification of the cell kinetic effects of G-CSF using a model of human granulopoiesis. Exp. Hematol., 21 (1993), 755–760.
- S. Schrier. Hematopoiesis and red blood cell function. Sci. Am. Med., I (1988), 2–8.
- T. Price, G. Chatta, D. Dale. Effect of recombinant granulocyte colony-stimulating factor on neutrophil kinetics in normal young and elderly humans. Blood, 88 (1996), No. 1, 335–340.
- U. Creutzig, D. Reinhardt, M. Zimmermann, T. Klingebiel, H. Gadner. Intensive chemotherapy versus bone marrow transplantation in pediatric acute myeloid leukemia: a matter of controversies. Blood, 97 (2001), No. 11, 3671–3672.
- V. Shetty, S. Hussaini, L. Broady-Robinson, K. Allampallam, S. Mundle, R. Borok, E. Broderick, L. Mazzoran, F. Zorat, A. Raza. Intramedullary apoptosis of hematopoietic cells in myelodysplastic syndrome patients can be massive: apoptotic cells recovered from high-density fraction of bone marrow aspirates. Blood, 96 (2000), No. 4, 1388–1392.
- W. Stock. Controversies in the treatment of AML: case-based discussion. Amer. Soc. Hematol., 2006

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