Skip to main content
SpringerLink
Log in

Understanding, Treating and Avoiding Hematological Disease: Better Medicine Through Mathematics?

  • Special Issue Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease—cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It’s also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Alangari AA, Alsultan A, Osman ME, Anazi S, Alkuraya FS (2013) A novel homozygous mutation in G6PC3 presenting as cyclic neutropenia and severe congenital neutropenia in the same family. J Clin Immunol 33:1403–1406

    Article  Google Scholar 

  • Apostu R, Mackey MC (2008) Understanding cyclical thrombocytopenia: a mathematical modeling approach. J Theor Biol 251:297–316

    Article  MathSciNet  Google Scholar 

  • Aprikyan AA, Liles WC, Rodger E, Jonas M, Chi EY, Dale DC (2001) Impaired survival of bone marrow hematopoietic progenitor cells in cyclic neutropenia. Blood 97(1):147–153

    Article  Google Scholar 

  • Aprikyan AA, Kutyavin T, Stein S, Aprikian P, Rodger E, Liles WC, Boxer LA, Dale DC (2003) Cellular and molecular abnormalities in severe congenital neutropenia predisposing to leukemia. Exp Hematol 31(5):372–381

    Article  Google Scholar 

  • Barrachina Barbera L, Perez Martinez A, Leon Garcia S, Pronzato Cuello F, Martin Arenos J, Toornador E (2005) Cyclic neutropenia with anti-NA2 antibodies and treatment with recombinant granulocyte colony-stimulating factor. An Pediatr (Barc) 63:180–182

    Article  Google Scholar 

  • Bernard S, Belair J, Mackey M (2003) Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J Theor Biol 223:283–298

    Article  MathSciNet  Google Scholar 

  • Bonilla MA, Dale D, Zeidler C, Last L, Reiter A, Ruggeiro M, Davis M, Koci B, Hammond W, Gillio A (1994) Long-term safety of treatment with recombinant human granulocyte colony-stimulating factor (r-metHuG-CSF) in patients with severe congenital neutropenias. Br J Haematol 88(4):723–730

    Article  Google Scholar 

  • Brooks G, Provencher G, Lei J, Mackey MC (2012) Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. J Theor Biol 315:97–109

    Article  MathSciNet  Google Scholar 

  • Bunn H (2013) Erythropoietin. Cold Spring Harb Perspect Med 3(a011):619

    Google Scholar 

  • Burns F, Tannock I (1970) On the existence of a G\(_0\) phase in the cell cycle. Cell Tissue Kinet 3:321–334

    Google Scholar 

  • Christopher MJ, Link DC (2007) Regulation of neutrophil homeostasis. Curr Opin Hematol 14(1):3–8

    Article  Google Scholar 

  • Colijn C, Mackey M (2005a) A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. J Theor Biol 237:117–132

    Article  MathSciNet  Google Scholar 

  • Colijn C, Mackey M (2005b) A mathematical model of hematopoiesis: II. Cyclical neutropenia. J Theor Biol 237:133–146

    Article  MathSciNet  Google Scholar 

  • Colijn C, Foley C, Mackey MC (2007) G-CSF treatment of canine cyclical neutropenia: a comprehensive mathematical model. Exper Hematol 35:898–907

    Article  Google Scholar 

  • Craig M, Humphries A, Bélair J, Li J, Mackey M, Nekka F (2014) Mechanistic-based translational model for the optimisation of the concurrent use of rhG-CSF and chemotherapeutic agents. J Theor Biol (submitted)

  • Crawford J, Ozer H, Stoller R, Johnson D, Lyman G, Tabbara I, Kris M, Grous J, Picozzi V, Rausch G (1991) Reduction by granulocyte colony-stimulating factor of fever and neutropenia induced by chemotherapy in patients with small-cell lung cancer. N Engl J Med 325(3):164–170

    Article  Google Scholar 

  • Dale D (2013) Myelosuppression. In: Sonis S, Keefer D (eds) Pathobiology of cancer regimen-related toxicities. Springer-Verlag, New York, pp 187–205

    Chapter  Google Scholar 

  • Dale D, Kelley M, Makaryan V, Rodger E, Otto B, Bolyard A (2013) A feasibility study of home monitoring of blood neutrophil counts in patients with chronic neutropenia. In: European Hematology Association (EHA) Annual Meeting Abstracts, European Hematology Association, p P1027

  • Dale DC, Graw RG (1974) Transplantation of allogenic bone marrow in canine cyclic neutropenia. Science 183:83–84

    Article  Google Scholar 

  • Dale DC, Hammond WP (1988a) Cyclic neutropenia: a clinical review. Blood Rev 2(3):178–185

    Article  Google Scholar 

  • Dale DC, Hammond WP (1988b) Cyclic neutropenia: A clinical review. Blood Rev 2:178–185

    Article  Google Scholar 

  • Dale DC, Ward SB, Kimball JR, Wolff SM (1972) Studies of neutrophil production and turnover in grey collie dogs with cyclic neutropenia. J Clin Invest 51:2190–2196

    Article  Google Scholar 

  • Dale DC, Bonilla MA, Davis MW, Nakanishi AM, Hammond WP, Kurtzberg J, Wang W, Jakubowski A, Winton E, Lalezari P (1993) A randomized controlled phase III trial of recombinant human granulocyte colony-stimulating factor (filgrastim) for treatment of severe chronic neutropenia. Blood 81(10):2496–2502

    Google Scholar 

  • Dale DC, Person RE, Bolyard AA, Aprikyan AG, Bos C, Bonilla MA, Boxer LA, Kannourakis G, Zeidler C, Welte K, Benson KF, Horwitz M (2000) Mutations in the gene encoding neutrophil elastase in congenital and cyclic neutropenia. Blood 96(7):2317–2322

    Google Scholar 

  • Dale DC, Bolyard AA, Schwinzer BG, Pracht G, Bonilla MA, Boxer L, Freedman MH, Donadieu J, Kannourakis G, Alter BP, Cham BP, Winkelstein J, Kinsey SE, Zeidler C, Welte K (2006) The severe chronic neutropenia international registry: 10-year follow-up report. Support Cancer Ther 3(4):220–231

    Article  Google Scholar 

  • Dale DD, Brown C, Carbone P, Wolff S (1971) Cyclic urinary leukopoietic activity in gray collie dogs. Science 173:152–153

    Article  Google Scholar 

  • Erbagci Z (2003) Noma-like gangrenous cheilitis in a child with cyclic neutropenia associated with myeloperoxidase deficiency. Pediatr Dermatol 20(6):519–523

    Article  Google Scholar 

  • Erslev A (1991) Erythropoietin. N Engl J Med 324:1339–1344

    Article  Google Scholar 

  • Foley C, Mackey MC (2009a) Dynamic hematological disease: a review. J Math Biol 58:285–322

    Article  MATH  MathSciNet  Google Scholar 

  • Foley C, Mackey MC (2009b) Mathematical model for G-CSF administration after chemotherapy. J Theor Biol 257(1):27–44

    Article  MathSciNet  Google Scholar 

  • Foley C, Bernard S, Mackey MC (2006) Cost-effectve G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses. J Theor Biol 238(4):754–763

    Article  MathSciNet  Google Scholar 

  • Fortin P, Mackey M (1999) Periodic chronic myelogenous leukemia: spectral analysis of blood cell counts and etiological implications. Brit J Haematol 104:336–345 Please check the page numbers for reference [32].

    Article  Google Scholar 

  • Guerry D, Dale D, Omine DC, Perry S, Wolff SM (1973) Periodic hematopoiesis in human cyclic neutropenia. J Clin Inves 52:3220–3230

    Article  Google Scholar 

  • Hammond WP, Price TH, Souza LM, Dale DC (1989) Treatment of cyclic neutropenia with granulocyte colony-stimulating factor. N Engl J Med 320(20):1306–1311

    Article  Google Scholar 

  • Hammond WP, Csiba E, Canin A, Hockman H, Souza LM, Layton JE, Dale DC (1991) Chronic neutropenia. A new canine model induced by human granulocyte colony-stimulating factor. J Clin Invest 87(2):704–710

    Article  Google Scholar 

  • Haurie C, Mackey MC, Dale DC (1998) Cyclical neutropenia and other periodic hematological diseases: a review of mechanisms and mathematical models. Blood 92:2629–2640

    Google Scholar 

  • Haurie C, Dale DC, Mackey MC (1999a) Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic, and cyclical neutropenic patients before and during treatment with G-CSF. Exp Hematol 27:401–409

    Article  Google Scholar 

  • Haurie C, Person R, Dale DC, Mackey M (1999) Haematopoietic dynamics in grey collies. Exper Hematol 27:1139–1148

    Article  Google Scholar 

  • Haurie C, Dale DC, Rudnicki R, Mackey MC (2000) Modeling complex neutrophil dynamics in the grey collie. J Theor Biol 204:504–519

    Article  Google Scholar 

  • Hearn T, Haurie C, Mackey M (1998) Cyclical neutropenia and the peripherial control of white blood cell production. J Theor Biol 192:167–181

    Article  Google Scholar 

  • Hitchcock I, Kaushansky K (2014) Thrombopoietin from beginning to end. Br J Haematol 165:259–268

    Article  Google Scholar 

  • Horwitz M, Benson KF, Person RE, Aprikyan AG, Dale DC (1999) Mutations in ELA2, encoding neutrophil elastase, define a 21-day biological clock in cyclic haematopoiesis. Nat Genet 23(4):433–436

    Article  Google Scholar 

  • Kaushansky K (2006) Lineage-specific hematopoietic growth factors. N Engl J Med 354(19):2034–2045

    Article  Google Scholar 

  • Kazarinoff ND, van den Driessche P (1979) Control of oscillations in hematopoiesis. Science 203:1348–1350

    Article  MATH  MathSciNet  Google Scholar 

  • King-Smith EA, Morley A (1970) Computer simulation of granulopoiesis: normal and impaired granulopoiesis. Blood 36:254–262

    Google Scholar 

  • Kollner I, Sodeik B, Schreek S, Heyn H, von Neuhoff N, Germeshausen M, Zeidler C, Kruger M, Schlegelberger B, Welte K, Beger C (2006) Mutations in neutrophil elastase causing congenital neutropenia lead to cytoplasmic protein accumulation and induction of the unfolded protein response. Blood 108(2):493–500

    Article  Google Scholar 

  • Lei J, Mackey M (2007) Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system. SIAM J Appl Math 67:387–407

    Article  MATH  MathSciNet  Google Scholar 

  • Lei J, Mackey MC (2011) Multistability in an age-structured model of hematopoiesis: cyclical neutropenia. J Theor Biol 270:143–153

    Article  MathSciNet  Google Scholar 

  • Lei J, Levin S, Nie Q (2014) Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation. Proc Natl Acad Sci USA 111:880–887

    Article  MathSciNet  Google Scholar 

  • Lomb NR (1976) Least-squares frequency analysis of unequally spaced data. Astrophys Space Sci 39:447–462

    Article  Google Scholar 

  • Lund JE, Padgett GA, Ott RL (1967) Cyclic neutropenia in grey collie dogs. Blood 29(4):452–461

    Google Scholar 

  • MacDonald N (1978) Cyclical neutropenia: models with two cell types and two time lags. In: Valleron A, Macdonald P (eds) Biomathematics and cell kinetics. Elsevier/North-Holland, Amsterdam, pp 287–295

    Google Scholar 

  • Mackey MC (1978a) A unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis. Blood 51:941–956

    Google Scholar 

  • Mackey MC (1978b) A unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis. Blood 51:941–956

    Google Scholar 

  • Mackey MC (1979) Dynamic haematological disorders of stem cell origin. In: Vassileva-Popova JG, Jensen EV (eds) Biophysical and biochemical information transfer in recognition. Plenum Publishing Corp, New York, pp 373–409

    Chapter  Google Scholar 

  • Mackey MC (1996) Mathematical models of hematopoietic cell replication and control. In: Othmer H, Adler F, Lewis M, Dallon J (eds) The art of mathematical modeling: case studies in ecology, physiology and biofluids. Prentice Hall, New York, pp 149–178

    Google Scholar 

  • Mackey MC (2000) Cell kinetic status of haematopoietic stem cells. Cell Prolif 34:71–83

    Article  Google Scholar 

  • Mackey MC, Tyran-Kamińska M, Yvinec R (2013) Dynamic behavior of stochastic gene expression models in the presence of bursting. SIAM J Appl Math 73:1830–1852

    Article  MATH  MathSciNet  Google Scholar 

  • Mahaffy J, Belair J, Mackey M (1998) Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. J Theor Biol 190:135–146

    Article  Google Scholar 

  • Makaryan V, Zeidler C, Bolyard A, Skokowa J, Kelley M, Boxer L, Bonilla M, Newburger P, Shimamura A, Welte K, Dale D (2012) Clinical outcomes for patients with severe chronic neutropenia due to mutations in the gene for neutrophil elastase, elane. Blood 120:3275

    Google Scholar 

  • Marziliano N, Mannarino S, Nespoli L, Diegoli M, Pasotti M, Malattia C, Grasso M, Pilotto A, Porcu E, Raisaro A, Raineri C, Dore R, Maggio PP, Brega A, Arbustini E (2007) Barth syndrome associated with compound hemizygosity and heterozygosity of the TAZ and LDB3 genes. Am J Med Genet A 143A(9):907–915

    Article  Google Scholar 

  • Morley A (1970) Periodic diseases, physiological rhythms and feedback control-a hypothesis. Aust Ann Med 3:244–249

    Google Scholar 

  • Morley A, Stohlman F (1970) Cyclophosphamide induced cyclical neutropenia. N Engl J Med 282:643–646

    Article  Google Scholar 

  • Morley A, King-Smith EA, Stohlman F (1969) The oscillatory nature of hemopoiesis. In: Stohlman F (ed) Hemopoietic cellular proliferation. Grune & Stratton, New York, pp 3–14

    Google Scholar 

  • Morley AA, Carew JP, Baikie AG (1967) Familial cyclical neutropenia. Br J Haematol 13(5):719–738

    Article  Google Scholar 

  • Nanua S, Murakami M, Xia J, Grenda DS, Woloszynek J, Strand M, Link DC (2011) Activation of the unfolded protein response is associated with impaired granulopoiesis in transgenic mice expressing mutant Elane. Blood 117(13):3539–3547

    Article  Google Scholar 

  • Page AR, Good RA (1957) Studies on cyclic neutropenia: a clinical and experimental investigation. AMA J Dis Child 94(6):623–661

    Article  Google Scholar 

  • Palmer SE, Dale DC, Livingston RJ, Wijsman EM, Stephens K (1994) Autosomal dominant cyclic hematopoiesis: exclusion of linkage to the major hematopoietic regulatory gene cluster on chromosome 5. Hum Genet 93(2):195–197

    Article  Google Scholar 

  • Price TH, Chatta GS, Dale DC (1996) Effect of recombinant granulocyte colony-stimulating factor on neutrophil kinetics in normal young and elderly humans. Blood 88(1):335–340

    Google Scholar 

  • Reeve J (1973) An analogue model of granulopoiesis for the analysis of isotopic and other data obtained in the non-steady state. Br J Haematol 25:15–32

    Article  Google Scholar 

  • Reimann H, DeBerardinis CT (1949) Periodic (cyclic) neutropenia, an entity: a collection of 16 cases. Blood 4(10):1109–1116

    Google Scholar 

  • Rosenberg PS, Alter BP, Bolyard AA, Bonilla MA, Boxer LA, Cham B, Fier C, Freedman M, Kannourakis G, Kinsey S, Schwinzer B, Zeidler C, Welte K, Dale DC (2006) The incidence of leukemia and mortality from sepsis in patients with severe congenital neutropenia receiving long-term G-CSF therapy. Blood 107(12):4628–4635

    Article  Google Scholar 

  • Rosenberg PS, Zeidler C, Bolyard AA, Alter BP, Bonilla MA, Boxer LA, Dror Y, Kinsey S, Link DC, Newburger PE, Shimamura A, Welte K, Dale DC (2010) Stable long-term risk of leukaemia in patients with severe congenital neutropenia maintained on G-CSF therapy. Br J Haematol 150(2):196–199

    Google Scholar 

  • Roskos LK, Lum P, Lockbaum P, Schwab G, Yang BB (2006) Pharmacokinetic/pharmacodynamic modeling of pegfilgrastim in healthy subjects. J Clin Pharmacol 46(7):747–757

    Article  Google Scholar 

  • Santillan M, Mahaffy J, Belair J, Mackey M (2000) Regulation of platelet production: The normal response to perturbation and cyclical platelet disease. J Theor Biol 206:585–603

    Article  Google Scholar 

  • Scargle JD (1982) Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Astrophys J 263:835–853

    Article  Google Scholar 

  • Schmitz S, Loeffler M, Jones JB, Lange RD, Wichmann HE (1990) Synchrony of bone marrow proliferation and maturation as the origin of cyclic haemopoiesis. Cell Tissue Kinet 23:425–441

    Google Scholar 

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

    Article  Google Scholar 

  • von Schulthess GK, Fehr J, Dahinde C (1983) Cyclic neutropenia: amplification of granulocyte oscillations by lithium and long-term suppression of cycling by plasmapheresis. Blood 62:320–332

    Google Scholar 

  • Shvitra D, Laugalys R, Kolesov YS (1983) Mathematical modeling of the production of white blood cells. In: Marchuk G, Belykh L (eds) Mathematical modeling in immunology and medicine. North-Holland, Amsterdam, pp 211–223

    Google Scholar 

  • Swinburne J, Mackey M (2000) Cyclical thrombocytopenia: Characterization by spectral analysis and a review. J Theor Med 2:81–91

    Article  MATH  Google Scholar 

  • von Schulthess GK, Mazer NA (1982) Cyclic neutropenia (CN): a clue to the control of granulopoiesis. Blood 59:27–37

    Google Scholar 

  • Wang B, Ludden TM, Cheung EN, Schwab GG, Roskos LK (2001) Population pharmacokinetic-pharmacodynamic modeling of filgrastim (r-metHuG-CSF) in healthy volunteers. J Pharmacokinet Pharmacodyn 28(4):321–342

    Article  Google Scholar 

  • Welte K, Platzer E, Lu L, Gabrilove JL, Levi E, Mertelsmann R, Moore MA (1985) Purification and biochemical characterization of human pluripotent hematopoietic colony-stimulating factor. Proc Natl Acad Sci USA 82(5):1526–1530

    Article  Google Scholar 

  • Wichmann HE, Loeffler M, Schmitz S (1988) A concept of hemopoietic regulation and its biomathematical realization. Blood Cells 14:411–429

    Google Scholar 

  • Winfree AT (1980) The geometry of biological time. Biomathematics, vol 8. Springer-Verlag, Berlin

    Google Scholar 

  • Wright DG, Dale DC, Fauci AS, Wolff SM (1981) Human cyclic neutropenia: clinical review and long-term follow-up of patients. Medicine (Baltimore) 60(1):1–13

    Article  Google Scholar 

  • Xia J, Link DC (2008) Severe congenital neutropenia and the unfolded protein response. Curr Opin Hematol 15(1):1–7

    Article  Google Scholar 

  • Zhuge C, Lei J, Mackey MC (2012) Neutrophil dynamics in response to chemotherapy and G-CSF. J Theor Biol 293:111–120

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Medicine, University of Washington, Seattle, WA, 98195, USA

    David C. Dale

  2. Departments of Mathematics, Physics, Physiology and Centre for Applied Mathematics in Bioscience and Medicine, Mcgill University, 3655 Promenade Sir William Osler, Montreal, QC, H3G 1Y6, Canada

    Michael C. Mackey

Authors
  1. David C. Dale
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael C. Mackey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael C. Mackey.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dale, D.C., Mackey, M.C. Understanding, Treating and Avoiding Hematological Disease: Better Medicine Through Mathematics?. Bull Math Biol 77, 739–757 (2015). https://doi.org/10.1007/s11538-014-9995-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-014-9995-x

Keywords

Search

Navigation