Journal of Mathematical Biology

, Volume 66, Issue 6, pp 1209–1240 | Cite as

A model of erythropoiesis in adults with sufficient iron availability

  • Doris H. Fuertinger
  • Franz Kappel
  • Stephan Thijssen
  • Nathan W. Levin
  • Peter Kotanko
Article

Abstract

In this paper we present a model for erythropoiesis under the basic assumption that sufficient iron availability is guaranteed. An extension of the model including a sub-model for the iron dynamics in the body is topic of present research efforts. The model gives excellent results for a number of important situations: recovery of the red blood cell mass after blood donation, adaptation of the number of red blood cells to changes in the altitude of residence and, most important, the reaction of the body to different administration regimens of erythropoiesis stimulating agents, as for instance in the case of pre-surgical administration of Epoetin-α. The simulation results concerning the last item show that choosing an appropriate administration regimen can reduce the total amount of the administered drug considerably. The core of the model consists of structured population equations for the different cell populations which are considered. A key feature of the model is the incorporation of neocytolysis.

Keywords

Erythropoiesis Neocytolysis Structured population models 

Mathematics Subject Classification

92C30 92D25 35Q92 

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References

  1. Ackleh AS, Banks HT, Deng K (2002) A finite difference approximation for a coupled system of nonlinear size-structured population. Nonlinear Anal 50: 727–748MathSciNetMATHCrossRefGoogle Scholar
  2. Ackleh AS, Deng K, Ito K, Thibodeaux J (2006) A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate. Math Biosci 204: 21–48MathSciNetMATHCrossRefGoogle Scholar
  3. Adimy M, Crauste F, Ruan S (2006) Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull Math Biol 68: 2321–2351MathSciNetCrossRefGoogle Scholar
  4. Alfrey CP, Fishbane S (2007) Implications of neocytolysis for optimal management of anaemia in chronic kidney disease. Nephron Clin Pract 106: 149–156CrossRefGoogle Scholar
  5. Alfrey CP, Udden MM, Leach-Huntoon C, Driscoll T, Pickett MH (1996) Control of red blood cell mass in spaceflight. J Appl Physiol 81: 98–104Google Scholar
  6. Banks HT, Cole CE, Schlosser PM, Tran HT (2004) Modelling and optimal regulation of erythropoiesis subject to benzene intoxication. Math Biosci Eng 1: 15–48MathSciNetMATHCrossRefGoogle Scholar
  7. Barosi G, Cazzola M, Berzuini C, Quaglini S, Stefanelli M (1985) Classification of anemia on the basis of ferrokinetic parameters. Br J Haematol 61: 357–370CrossRefGoogle Scholar
  8. Belair J, Mackey MC, Mahaffy JM (1995) Age-structured and two-delay models for erythropoiesis. Math Biosci 128: 317–346MATHCrossRefGoogle Scholar
  9. Besarab A, Bolton WK, Browne JK, Egrie JC, Nissenson AR, Okamoto DM, Schwab SJ, Goodkin DA (1998) The effects of normal as compared with low hematocrit values in patients with cardiac disease who are receiving hemodialysis and epoetin. New Engl J Med 339: 584–590CrossRefGoogle Scholar
  10. Besarab A, Reyes CM, Hornberger J (2002) Meta-analysis of subcutaneous versus intravenous epoetin in maintenance treatment of anemia in hemodialysis patients. J Kidney Dis 40: 439–446CrossRefGoogle Scholar
  11. Chang CC, Chen Y, Modi K, Awar OG, Alfrey CP, Rice L (2009) Changes of red blood cell surface markers in a blood doping model of neocytolysis. J Investig Med 57: 650–654Google Scholar
  12. Cheung W, Minton N, Gunawardena K (2001) Pharmocokinetics and pharmacodynamics of epoetin alfa once weekly and three times weekly. Eur J Clin Pharmacol 57: 411–418CrossRefGoogle Scholar
  13. Crauste F, Pujo-Menjouet L, Genieys S, Molina C, Gandrillon O (2008) Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis. J Theor Biol 250: 322–338MathSciNetCrossRefGoogle Scholar
  14. Crichton R (2009) Iron metabolism: from molecular mechanisms to clinical consequences, 3rd edn. Wiley, New YorkCrossRefGoogle Scholar
  15. Feagan BG, Wong CJ, Kirkley A, Johnston DW, Smith FC, Whitsitt P, Wheeler S, Lau CY (2000) Erythropoietin with iron supplementation to prevent allogeneic blood transfusion in total hip joint arthroplasty. Ann Intern Med 133: 845–854Google Scholar
  16. Finch CA (1982) Erythropoiesis, erythropoietin, and iron. Blood The Journal of American Society of Hematology 60(6): 1241–1246Google Scholar
  17. Finch S, Haskins D, Finch CA (1950) Iron metabolism. Hematopoiesis following phlebotomy. Iron as a limiting factor. J Clin Investig 29: 1078–1086CrossRefGoogle Scholar
  18. Fleming MD (2008) The regulation of hepcidin and its effects on systemic and cellular iron metabolism. Hematology Journal of American Society of Hematology 2008(1): 151–158MathSciNetCrossRefGoogle Scholar
  19. Fowler WM, Barner AP (1942) Rate of hemoglobin regeneration in blood donors. J Am Med Assoc 118(6): 421–427CrossRefGoogle Scholar
  20. Go AS, Chertow GM, Fan D, McCulloch CE, Hsu C (2004) Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization. New Engl J Med 351: 1296–1305CrossRefGoogle Scholar
  21. Goodnough LT (2002) The role of iron in erythropoiesis in the absence and presence of erythropoietin therapy. Nephrol Dial Transplant 17: 14–18CrossRefGoogle Scholar
  22. Greer JP, Foerster J, Rodgers GM, Paraskevas F, Glader B, Arber DA, Means RTJ (2009) Wintrobe’s clinical hematology, vol 1, 12th edn. Lippincott Williams and Wilkins, PhiladelphiaGoogle Scholar
  23. Ito K, Kappel F (2002) Evolution equations and approximations. World Scientific, SingaporeMATHGoogle Scholar
  24. Jandl JH (1987) Blood. Textbook of Hematology. Little, Brown and Company, BostonGoogle Scholar
  25. Jaspan D (2007) Erythropoietic therapy: cost efficiency and reimbursement. Am J Health-System Pharm, 64(16 Suppl 11): 19–29. doi: 10.2146/ajhp070246 CrossRefGoogle Scholar
  26. Kappel F, Zhang K (1993) Approximation of linear age-structured population models using Legendre polynomials. J Math Anal Appl 180: 518–549MathSciNetMATHCrossRefGoogle Scholar
  27. Kotanko P, Kuhlmann MK, Levin NW (2007) Hemodialysis: technology, adequacy, and outcomes. In: Feehally J, Floege J, Johnson JR (eds) Comprehensive clinical nephrology, chap 83. Mosby Elsevier, Philadelphia, pp 953–966Google Scholar
  28. Lichtman, MA, Beutler, E, Kipps, TJ, Seligsohn, U, Kaushansky, K, Prchal, JT (eds) (2005) Williams hematology, 7th edn. McGraw-Hill, New YorkGoogle Scholar
  29. Loeffler M, Pantel K, Wulff H, Wichmann HE (1989) A mathematical model of erythropoiesis in mice and rats. Part 1. Structure of the model. Cell Tissue Kinetics 22: 13–30Google Scholar
  30. Mahaffy JM, Belair J, Mackey MC (1998) Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. J Theor Biol 190: 135–146CrossRefGoogle Scholar
  31. Mahaffy JM, Polk SW, Roeder RK (1999) An age-structured model for erythropoiesis following a phlebotomy. Tech. Rep. CRM-2598, Department of Mathematical Sciences, San Diego State University, San Diego, CA 92182-0314Google Scholar
  32. Pottgiesser T, Specker W, Umhau M, Dickhuth HH, Roecker K, Schumacher YO (2008) Recovery of hemoglobin mass after blood donation. Transfusion 48: 1390–1397CrossRefGoogle Scholar
  33. Rice L, Alfrey CP (2005) The negative regulation of red cell mass by neocytolysis: physiologic and pathophysiologic manifestations. Cell Physiol Biochem 15: 245–250CrossRefGoogle Scholar
  34. Rice L, Alfrey CP, Driscoll T, Whitley CE, Hachey DL, Suki W (1999) Neocytolysis contributes to the anemia of renal disease. Am J Kidney Dis 33: 59–62CrossRefGoogle Scholar
  35. Rice L, Ruiz W, Driscoll T, Whitley CE, Tapia R, Hachey DL, Conzales GF, Alfrey CP (2001) Neocytolysis on descent from altitude: a newly recognized mechanism for the control of red cell mass. Ann Intern Med 134: 652–656Google Scholar
  36. Roeder I (2006) Quantitative stem cell biology: computational studies in the hematopoietic system. Curr Opin Hematol 13: 222–228CrossRefGoogle Scholar
  37. Roeder I, Loeffler M (2002) A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp Hematol 30: 853–861CrossRefGoogle Scholar
  38. Schaefer RM, Schaefer L (1998) Iron monitoring and supplementation: how do we achieve the best results. Nephrol Dial Transplant 13: 9–12CrossRefGoogle Scholar
  39. Stefanelli M, Bentley DP, Cavill I, Roeser HP (1984) Quantitation of reticuloendothelial iron kinetics in humans. Am J Physiol 247: 842–849Google Scholar
  40. Strippoli GF, Craig JC, Manno C, Schena FP (2004) Hemoglobin targets for the anemia of chronic kidney disease: a meta-analysis of randomized, controlled trials. J Am Soc Nephrol 15: 3154–3165CrossRefGoogle Scholar
  41. Udden MM, Driscoll TB, Pickett MH, Leach-Huntoon CS, Alfrey CP (1995) Decreased production of red blood cells in human subjects exposed to microgravity. J Lab Clin Med 125: 442–449Google Scholar
  42. Wichmann HE, Loeffler M, Pantel K, Wulff HH (1989) A mathematical model of erythropoiesis in mice and rats. Part 2. Stimulated erythropoiesis. Cell Tissue Kinetics 22: 31–49Google Scholar
  43. Wu H, Liu X, Jaenisch R, Lodish HF (1995) Generation of committed erythroid BFU-E and CFU-E progenitors does not require erythropoietin or the erythropoietin receptor. Cell 83(1): 59–67CrossRefGoogle Scholar
  44. Wulff H, Wichmann HE, Pantel K, Loeffler M (1989) A mathematical model of erythropoiesis in mice and rats. Part 3: suppressed erythropoiesis. Cell Tissue Kinetics 22: 51–61Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Doris H. Fuertinger
    • 1
  • Franz Kappel
    • 1
  • Stephan Thijssen
    • 2
  • Nathan W. Levin
    • 2
  • Peter Kotanko
    • 2
  1. 1.Institute for Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  2. 2.Renal Research Institute New YorkNew YorkUSA

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