Skip to main content

Advertisement

SpringerLink
Log in

A mathematical model for reconstitution of granulopoiesis after high dose chemotherapy with autologous stem cell transplantation

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

High dose chemotherapy supported with hematopoietic progenitor cells gives a characteristic neutropenic period (blood neutrophils <0.5⋅109 c/l) ranging from 10 to 16 days. The question of a correlation between the CFU-GM content of the transplanted CD34+ cells and time to neutrophil recovery by patients having been given high-dose chemotherapy (HD-CT) with stem cell support was addressed by means of a mathematical model of granulopoiesis. The model utilizes a convection-reaction partial differential equation (PDE) with feedback from a cytokine compartment on proliferation, maturation, and mobilization of granulocytes from bone marrow to blood. The observed number of CFU-GM cells in the transplanted CD34+ cell autograft was used as input to the model. Using this approach, the observed gross relationship between CFU-GM content in the reinfused blood product and engraftment time could be reproduced. At the same time, the effects of assumed physiological mechanisms, especially some of the effects of G-CSF on proliferation rate, maturation rate, mobilization, and cell death, could be investigated and discussed relative to observed engraftment. The model makes it possible to explain how cytokines interfere with progenitor cell mobilization from bone marrow to blood, and it points out the implications of a regulating mechanism for the granulocyte maturation rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aglietta, M., Piacibello, W., Sanavio, F., Stacchini, A., Aprá, F., Schena, M., Mossetti, C., Carnino, F., Caligaris-Cappio, F., Gavosto, F.: Kinetics of human hemopoietic cells after in vivo administration of granulocyte-macrophage colony-stimulating factor. J. Clin. Invest. 83, 551–557 (1989)

    Google Scholar 

  2. Aurlien, E., Holte, H., Pharo, A., Kvaløy, S., Jakobsen, E., Smeland, E.B., Kvalheim, G.: Combination chemotherapy with mitaguazon, ifosfamide, MTX, etoposide (MIME) and C-CSF can efficiently mobilize PBPC in patients with Hodgkin's and non-Hodgkin's lymphoma. Bone Marrow Transpl. 21, 873–878 (1998)

    Article  Google Scholar 

  3. Avalos, B.: Molecular analysis of the granulocyte colony-stimulating factor receptor. Blood 88(3), 761–777 (1996)

    Google Scholar 

  4. Baiocchi, G., Scambia, G., Benedetti, P., Menichella, G., Testa, U., Pierelli, L., Martucci, R., Foddai, M.L., Bizzi, B., Mancuso, S., Peschle, C.: Autologous stem cell transplantation: Sequential production of hematopoietic cytokines underlying granulocyte recovery. Cancer Research, 53, 1297 (1993)

    Google Scholar 

  5. Benboubker, L., Binet, C., Cartron, C., Bernard, M.C., Clement, N., Delain, M., Degenne, M., Desbois, I., Colombat, P., Domenech, J.: Frequency and differentiation capacity of circulating LTC-IC mobilized by G-CSF or GM-CSF following chemotherapy: a comparison with steady-state bone marrow and peripheral blood. Exp. Hematol. 30(1), 74–81 (2002)

    Article  Google Scholar 

  6. Benestad, H.B., Rytömaa, T.: Regulation of maturation rate of mouse granulocytes. Cell Tissue Kinet. 10, 461–468 (1977)

    Google Scholar 

  7. Bensinger, W.I., Longin, K., Appelbaum, F., Rowley, S., Weaver, C., Lilleby, K., Gooley, T., Lynch, M., Higano, T., Klarnet, J., Chauncey, T., Storb, R., Buckner, C.D.: Peripheral blood stem cells (PBPCs) collected after recombinant granulocyte colony stimulating factor (rhG-CSF): an analysis of factors correlating with the tempo of engraftment after transplantation. Br. J. Haematol. 87, 825–831 (1994)

    Google Scholar 

  8. Bhatia, M., Wang, J.C.Y., Kapp, U., Bonnet, D., Dick, J.: Purification of primitive human hematopoietic cells capable of repopulating immune-deficient mice. Proc. Natl. Acad. Sci. USA 94, 5320–5325 (1997)

    Article  Google Scholar 

  9. Bogdan, C., Paik, J., Vodovotz, Y., Nathan, C.: Contrasting mechanisms for suppression of macrophage cytokine release by transforming growth factor-beta and interleukin-10. J. Biol. Chem, 267(32), 23301–8 (1992)

    Google Scholar 

  10. Budel, L.M., Touw, I.P., Delwel, R., Löwenberg, B.: Granulocyte colony-stimulating factor receptors in human acute myelocytic leukemia. Blood 74(8), 2668–2673 (1989)

    Google Scholar 

  11. Bødtker, A.: Produksjonen av nøytrofile granulocytter: beregning av kinetiske parametere og simulering av en normalmodell. Cand. Scient. thesis,University of Oslo, 1993

  12. Cavaillon, J.M.: Cytokines and macrophages. Biomed & Pharmacother 48, 445–453 (1994)

    Google Scholar 

  13. Cowling, G.J., Dexter, T.M.: Apoptosis in the haemopoietic system. Phil. Trans. Royal Society London, Series B: Biological Sciences 345(1313), 257–63 (1994)

    Google Scholar 

  14. Dancey, J.T., Deubelbeiss, K.A., Harker, L.A., Finch, C.A.: Neutrophil kinetics in man. J. Clin. Invest. 58, 705–715 (1976)

    Google Scholar 

  15. Denkers, I.A.M., Dragowska, W., Jaggi, B., Palcic, B., Lansdorp, P.M.: Time lapse video recordings of highly purified human hematopoietic progenitor cells in culture. Stem Cells 11, 243–248 (1993)

    Google Scholar 

  16. Dercksen, M.W., Rodenhuis, S., Dirkson, M.K.A., Schaasberg, W.P., Baars, J.W., van der Wall, E., Slaper-Cortenbach, I.C.M., Pinedo, H.M., Von dem Borne, A.E.G.Kr., van der Schoot, C.E., Gerritsen, W.R.: Subsets of CD34+ cells and rapid hematopoietic recovery after peripheral-blood stem-cell transplantation. J. Clin. Oncol. 13, 1922–1932 (1995)

    Google Scholar 

  17. Ericson, S.G., Gao, H., Gericke, G.H., Lewis, L.D.: The role of polymorphonuclear neutrophils (PMNs) in clearance of granulocyte colony-stimulating factor (G-CSF) in vivo and in vitro. Exp. Hematol. 25, 1313–1325 (1997)

    Google Scholar 

  18. Frick, P.: Blut- und Knochenmarksmorphologie: Blutgerinnung, Georg Thieme Verlag 16. Aufl. Stuttgart - New York 1982

  19. Glimm, H., Eaves, C.J.: Direct evidence for multiple self-renewal divisions of human in vivo repopulating hematopoietic cells in short-time culture. Blood 94(7), 2161–2168 (1999)

    Google Scholar 

  20. Gonzalez-Requejo, A., Madero, L., Diaz, M.A., Villa, M., García-Escribano, C., Balas, A., Lillo, R., García-Sanchez, F., Benito, A., Vicario, J.L.: Progenitor cell subsets and engraftment kinetics in children undergoing autologous peripheral blood stem cell transplantation. Br. J. Haematol. 101, 104–110 (1998)

    Article  Google Scholar 

  21. Haas, R., Gericke, G., Witt, B., Cayeux, S., Hunstein, W.: Increased serum levels of granulocyte colony-stimulating factor after autologous bone marrow or blood stem cell transplantation. Exp. Hematol. 21, 109–113 (1993)

    Google Scholar 

  22. Hammond, W.P., Chatta, G.S., Andrews, R., Dale, D.C.: Abnormal responsiveness of granulocyte-committed progenitor cells in cyclic neutropenia. Blood 79(10), 2536–2539 (1992)

    Google Scholar 

  23. Hao, Q.-L., Thiemann, F.T., Petersen, D., Smogorzewska, E.M., Crooks, G.M.: Extended long-term culture reveals a highly quiescent and primitive human hematopoietic progenitor population. Blood 88(9), 3306–3313 (1996)

    Google Scholar 

  24. Hevehan, D.L., Wenning, L.A., Miller, W.M., Papoutsakis, E.T.: Dynamic model of ex vivo granulocytic kinetics to examine the effects of oxygen tension, pH, and interleukin-3. Exp. Hematol. 28, 1016–1028 (2000)

    Article  Google Scholar 

  25. Jones, R.J. et al: Nature, 347, 188 (1990)

  26. Kawano, Y., Takaue, Y., Saito, S., Shimizu, T., Suzue, T., Hirao, A., Okamoto, Y., Abe, T., Watanabe, T., Kuroda, Y., Kimura, F., Motoyoshi, K., Asano, S.: Granulocyte colony- stimulating factor (CSF), Macrophage-CSF, granulocyte-macrophage CSF, inter- leukin-3, and interleukin-6 levels in sera from children undergoing blood stem cell autografts. Blood 81, 856–860 (1993)

    Google Scholar 

  27. Kearns, M., Wang, W.C., Stute, N., Ihle, J.N., Evans, W.E.: Disposition of recombinant human granulocyte colony-stimulating factor in children with severe chronic neutropenia. J. of Pediatrics 123, 3 (1993)

    Google Scholar 

  28. Khwaja, A., Carver, J., Jones, H.M., Paterson, D., Linch, D.C.: Expression and dynamic modulation of the human granulocyte colony-stimulating factor receptor in immature and differentiated myeloid cells. Br. J. Haematol. 85, 254–259 (1993)

    Google Scholar 

  29. Kojima, S., Matsuyama, T., Kodera, Y., Nishihira, H., Ueda, K., Shimbo, T., Nakahata, T.: Measurement of endogenous plasma granulocyte colony-stimulating factor in patients with aquired aplastic anemia by a sensitive chemiluminescent immunoassay. Blood 87(4), 1303–1308 (1996)

    Google Scholar 

  30. Koury, M.J.: Programmed cell death (apoptosis) in hematopoiesis. Exp. Hematol. 20, 391–394 (1992)

    Google Scholar 

  31. Kuwabara, T., Kato, Y., Kobayashi, S., Suzuki, H., Sugiyama, Y.: Nonlinear pharmacokinetics of a recombinant human granulocyte colony-stimulating factor derivative (Nartograstim): Species differences among rats, monkeys and humans. J. Pharmacology and Experimental Therapeutics 271, 1535–1543 (1994)

    Google Scholar 

  32. Kuwabara, T., Uchimura, T., Kobayashi, H., Kobayashi, S., Sugiyama, Y.: Receptor-mediated clearance of G-CSF derivative nartograstim in bone marrow of rats. Am. J. Physiol. 269, E1–9 (1995)

  33. Kvalheim, G., Pharo, A., Holte, H., Lenschow, E., Wang, M., Erikstein, B., Kvaløy, S., Nesland, J.M., Smeland, E.: Stem cell isolation with immunomagnetic beads and tumor cell contamination. In: Hematopoietic Stem Cell Transplantation. Editors: Ho AD, Haas R, Champlin RE.,(Marcel Dekker, New York-Basel 2000)

  34. Layton, J.E., Hockman, H., Sheridan, W.P., Morstyn, G.: Evidence for a novel in vivo control mechanism of granulopoiesis: Mature cell-related control of a regulatory growth factor. Blood 74, 1303–1307 (1989)

    Google Scholar 

  35. Leibundgut, K., von Rohr, A., Brülhart, K., Hirt, A., Ischi, E., Jeanneret, C., Muff, J., Ridolfi-Lüthy, A., Wagner, H.P., Tobler, A.: The number of circulating CD34+ blood cells predicts the colony-forming capacity of leukapheresis products in children. Bone Marrow Transpl. 15, 25–31 (1995)

    Google Scholar 

  36. Lenhoff, S., Sallerfors, B., Olofsson, T.: IL-10 as an autocrine regulator of CSF secretion by monocytes: Disparate effects on GM-CSF and G-CSF secretion. Exp Hematol 26, 299–304 (1998)

    Google Scholar 

  37. Lord, B.I., Molineux, G., Pojda, Z., Souza, L.M., Mermod, J.-J., Dexter, T.M.: Myeloid cell kinetics in mice treated with recombinant interleukin-3, granulocyte colony-stimulating factor (CSF), or granulocyte-macrophage CSF in vivo. Blood 77, 2154–2159 (1991)

    Google Scholar 

  38. Mary, J.Y.: Normal human granulopoiesis revisited. I. Blood data. Biomedicine & Pharmacotherapy 38, 33–43 (1984)

    Google Scholar 

  39. Mary, J.Y.: Normal human granulopoiesis revisited. II. Bone marrow data. Biomedicine & Pharmacotherapy 38, 66–77 (1984)

    Google Scholar 

  40. Mayani, H., Lansdorp, P.M.: Proliferation of individual hematopoietic progenitors purified from umbilical cord blood. Exp. Hematol. 23, 1453–1462 (1995)

    Google Scholar 

  41. Messner, H.A., Curtis, J.E., Minden, M.D., Tritchler, G., Lockwood, G., Takahashi, T., Lepine, J., Jamal, N., Tweeddale, M., Wandl, U.: Clonogenic hemopoietic precursors in bone marrow transplantation. Blood 70, 1425–1432 (1987)

    Google Scholar 

  42. Miksits, K., Beyer, J., Siegert, W.: Serum concentrations of G-CSF during high-dose chemotherapy with autologous stem cell rescue. Bone Marrow Transpl. 11, 375–377 (1993)

    Google Scholar 

  43. Morrison, S.J., Weissman, I.L.: The long-term repopulating subset of hematopoietic stem cells is deterministic and isolatable by phenotype. Immunity 1, 661–673 (1994)

    Google Scholar 

  44. Morstyn, G., Campbell, L., Souza, L.M., Alton, N.K., Keech, J., Green, M., Sheridan, W., Metcalf, D.: Effect of granulocyte colony stimulating factor on neutropenia induced by cytotoxic chemotherapy. The Lancet 26 (1988)

  45. Nagata, T., Tobitani, W., Kiriike, N., Iketani, T., Yamagami, S.: Capacity to produce cytokines during weight restoration in patients with anorexia nervosa. Psychosomatic Medicine 61, 371–377 (1999)

    Google Scholar 

  46. Nečas, E., Šefc, L., Šulc, K., Barthel, E., Seidel, H.-J.: Estimation of the extent of cell death in different stages of normal murine hematopoiesis. Stem Cells 16, 107–111 (1998)

    Google Scholar 

  47. Nielsen, L.K., Bender, J.G., Miller, W.M., Papoutsakis, E.T.: Population balance model of in vivo neutrophil formation following bone marrow rescue therapy. Cytotechnology 28, 157–162 (1998)

    Article  Google Scholar 

  48. Oostendorp, A.J., Audet, J., Eaves, C.J.: High-resolution tracking of cell division suggests similar cell cycle kinetics of hematopoietic stem cells stimulated in vitro and in vivo. Blood 95, 855–862 (2000)

    Google Scholar 

  49. Price, T.H., Chatta, G.S., Dale, D.C.: Effect of recombinant granulocyte colony-stimulating factor on neutrophil kinetics in normal young and elderly humans. Blood 88, 335–340 (1996)

    CAS  PubMed  Google Scholar 

  50. Ramsfjell, V., Bryder, D., Björgvinsdóttir, H., Kornfält, S., Borge, O.J., Jacobsen, S.E.W.: Distinct requirements for optimal growth and in vitro expansion of human CD34+CD38- bone marrow long-term culture-initiating cells (LTC-IC), extended LTC-IC, and murine in vivo long-term reconstituting stem cells. Blood 94(12), 4093–4102 (1999)

    Google Scholar 

  51. Rubinow, S.I.: A maturity-time representation for cell populations. Biophys. J. 8, 1055–1073 (1968)

    Google Scholar 

  52. Rusten, L.S., Jacobsen, S.E.W., Kaalhus, O., Veiby, O.P., Funderud, S., Smeland, E.B.: Functional differences between CD38- and DR- subfractions of CD34+ bone marrow cells. Blood 84(5), 1473–1481 (1994)

    Google Scholar 

  53. Saito S.-I., Kawano Y., Watanabe T., Okamoto Y., Abe T., Kurada Y., Takaue Y.: Serum granulocyte colony-stimulating factor kinetics in children receiving intense chemotherapy with or without stem cell support. Journ of Hematotherapy 8, 291–297 (1999)

    Article  Google Scholar 

  54. Scheding, S., Franke, H., Diehl, V., Wichmann, H.E., Brugger, W., Kanz, L., Schmitz, S.: How many myeloid post-progenitor cells have to be transplanted to completely abrogate neutropenia after peripheral blood progenitor cell transplantation? Results of a computer simulation. Exp. Hematol. 27, 956–965 (1999)

    Article  Google Scholar 

  55. Schmitz, S., Franke, H., Loeffler, M., Wichmann, H.E., Diehl, V.: Reduced variance of bone marrow transit time of granulopoiesis: a possible pathomechanism of human cyclic neutropenia. Cell Prolif. 27, 655–667 (1994)

    Google Scholar 

  56. Schmitz, S., Franke, H., Wichmann, H.E., Diehl, V.: The effect of continuous G-CSF application in human cyclic neutropenia: a model analysis. Br. J. Haematol. 90, 41–47 (1995)

    Google Scholar 

  57. Schmitz, S., Franke, H., Loeffler, M., Wichmann, H.E., Diehl, V.: Model analysis of the contrasting effects of GM-CSF and G-CSF treatment on peripheral blood neutrophils observed in three patients with childhood-onset cyclic neutropenia. Br. J. Haematol. 95, 616–625 (1996)

    Google Scholar 

  58. Serke, S., Arseniev, L., Watts, M., Fritsch, G., Ingles-Esteve, J., Johnsen, H.E., Linch, D., Cancelas, J.A., Meyer, O., Kadar, J.G., Huhn, D., Matcham, J.: Imprecision of counting CFU-GM colonies and CD34-expressing cells. Bone Marrow Transpl. 20, 57–61 (1997)

    Article  Google Scholar 

  59. Shimazaki, C., Uchiyama, H., Fujita, N., Araki, S., Sudo, Y., Yamagata, N., Ashihara, E., Goto, H., Inaba, T., Haruyama, H., Nakagawa, M.: Serum levels of endogenous and exogenous granulocyte colony-stimulating factor after autologous blood stem cell transplantation. Exp. Hematol. 23, 1497–1502 (1995)

    Google Scholar 

  60. Spitzer, G., Verma, D.S., Fisher, R., Zander, A., Vellekoop, L., Litam, J., McCredie, K.B., Dicke, K.A.: The myeloid progenitor cell: its value in predicting haemapoietic recovery after autologous transplantation. Blood 55, 317–323 (1980)

    Google Scholar 

  61. Steen, R., Tjønnfjord, G.E., Grøseth, L.A.G., Heldal, D., Egeland, T.: Efflux of CD34+ cells from bone marrow to peripheral blood is selective in steady-state hematopoiesis and during G-CSF administration. J. Hematoth. 6, 563–573 (1997)

    Google Scholar 

  62. Steinbach, K.H., Raffler, H., Pabst, G., Fliedner, T.M.: A mathematical model of canine granulocytopoiesis. J. Math. Biol. 10(1), 1–12 (1980)

    MATH  Google Scholar 

  63. Steinman, R.A., Tweardy, D.J.: Granulocyte colony-stimulating factor receptor mRNA upregulation is an immediate early marker of myeloid differentiation and exhibits dysfunctional regulation in leukemic cells. Blood 83(1), 119–127 (1994)

    Google Scholar 

  64. Sturgill, M.G., Huhn, R.D., Drachtman, R.A., Ettinger, A.G., Ettinger, L.J.: Pharmacokinetics of intravenous recombinant human granulocyte colony-stimulating factor (rhG-CSF) in children receiving myelosuppressive cancer chemotherapy: Clearance increases in relation to absolute neutrophil count with repeated dosing. Am. J. Hematol. 54, 124–130 (1997)

    Article  Google Scholar 

  65. Stute, N., Santana, V.M., Rodman, J.H., Schell, M.J., Ihle, J.N., Evans, W.E.: Pharma- cokinetics of subcutaneous recombinant human granulocyte colony-stimulating factor in children. Blood 11, 2849–2854 (1992)

    Google Scholar 

  66. Sutherland, H.-J., Eaves, C.-J., Landsdorp, P.-M., Phillips, G.-L., Hogge, D-.E.: Kine- tics of committed and primitive blood progenitor mobilization after chemotherapy and growth factor treatment and their use in autotransplants. Blood 83, 3008–3014 (1995)

    Google Scholar 

  67. Sutherland, H.-J., Eaves C.-J., Eaves, A.C., Dragowska, W., Lansdorp, P.M.: Characterization and partial purification of human marrow cells capable of initiating long-term hematopoiesis in vitro. Blood 74(5), 1563–1570 (1989)

    Google Scholar 

  68. Takamatsu, Y., Akashi, K., Harada, M., Teshima, T., Inaba, S., Shimoda, K., Eto, T., Shibuya, T., Okamura, S., Niho, Y.: Cytokine production by peripheral blood monocytes and T cells during haematopoietic recovery after intensive chemotherapy. Brit. J. Haematol. 83, 21–27 (1993)

    Google Scholar 

  69. Tanaka, R., Katayama, N., Ohishi, K., Mahmud, N., Itoh, R., Tanaka, Y., Komada, Y., Minami, N., Sakurai, M., Shirakawa, S., Shiku, H.: Accelerated cell-cycling of hematopoietic progenitor cells by growth factors. Blood 86(1), 73–79 (1995)

    Google Scholar 

  70. Terashi, K., Oka, M., Ohdo, S., Furukubo, T., Ikeda, C., Fukuda, M., Soda, H., Higuchi, S., Kohno, S.: Close association between clearance of recombinant human granulocyte colony-stimulating factor (G-CSF) and G-CSF receptor on neutrophils in cancer patients. Antimicrobial Agents and Chemotherapy Jan., 21–24 (1999)

  71. To, L.B., Dyson, P.G., Juttner, C.A.: Cell dose effect in circulating stem cell autografting. Lancet, ii, 404 (1986)

  72. Uchiyama H., Shimazaki C., Fujita N., Tatsumi T., Yamagata N., Hirata T., Ashihara E., Oku N., Goto H., Inaba T.: Kinetics in serum cytokines in adults undergoing peripheral blood progenitor cell transplantation. Br J Haemat 88(3), 639 (1994)

    Google Scholar 

  73. Wang, X., Fjerdingstad, H., Strøm-Gundersen, I., Benestad, H.B.: Maturation rate of mouse neutrophilic granulocytes: Acceleration by retardation of proliferation, but no detectable influence from G-CSF or stromal cells. Stem Cells 17, 253–264 (1999)

    MATH  Google Scholar 

  74. de Waal Malefyt, R., Abrams, J., Bennett, B., Figdor, C.G., de Vries, J.E.: Interleukin 10(IL-10) inhibits cytokine synthesis by human monocytes: an autoregulatory role of IL-10 produced by monocytes. J Exp Med 174(5), 1209–20 (1991)

    Google Scholar 

  75. Watari, K., Ozawa, K., Takahashi, S., Tojo, A., Tani, K., Kamachi, S., Asano, S.: Pharmacokinetic studies of intravenous glycosylated recombinant human granulocyte colony-stimulating factor in various hematological disorders: inverse correlation between the half-life and bone marrow myeloid cell pool. Int. J. Hematol. 66, 57–67 (1997)

    Article  Google Scholar 

  76. Weaver, C.-H., Hazelton, B., Birch, R., Palmer, P., Allen, C., Schwartzberg, L., West, W.: An analysis of engraftment kinetics as a function of the CD34 content of peripheral blood progenitor cell collections in 692 patients after the administration of myeloablative chemotherapy. Blood 14, 3961–3969 (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, University of Oslo, 0316 Oslo, Norway

    Ivar Østby & Per Grøttum

  2. Stem Cell Laboratory, The Norwegian Radium Hospital, 0310 Oslo, Norway

    Leiv S. Rusten & Gunnar Kvalheim

Authors
  1. Ivar Østby
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leiv S. Rusten
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gunnar Kvalheim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Per Grøttum
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivar Østby.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Østby, I., Rusten, L., Kvalheim, G. et al. A mathematical model for reconstitution of granulopoiesis after high dose chemotherapy with autologous stem cell transplantation. J. Math. Biol. 47, 101–136 (2003). https://doi.org/10.1007/s00285-003-0198-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-003-0198-6

Keywords

Search

Navigation