A model of erythropoiesis in adults with sufficient iron availability. (English) Zbl 1303.92023

Summary: 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-\(\alpha\). 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.


92C30 Physiology (general)
92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
Full Text: DOI


[1] Ackleh, AS; Banks, HT; Deng, K, A finite difference approximation for a coupled system of nonlinear size-structured population, Nonlinear Anal, 50, 727-748, (2002) · Zbl 1002.65093
[2] Ackleh, AS; Deng, K; Ito, K; Thibodeaux, J, A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate, Math Biosci, 204, 21-48, (2006) · Zbl 1104.92012
[3] Adimy, M; Crauste, F; Ruan, S, Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases, Bull Math Biol, 68, 2321-2351, (2006) · Zbl 1296.92102
[4] Alfrey, CP; Fishbane, S, Implications of neocytolysis for optimal management of anaemia in chronic kidney disease, Nephron Clin Pract, 106, 149-156, (2007)
[5] Alfrey, CP; Udden, MM; Leach-Huntoon, C; Driscoll, T; Pickett, MH, Control of red blood cell mass in spaceflight, J Appl Physiol, 81, 98-104, (1996)
[6] Banks, HT; Cole, CE; Schlosser, PM; Tran, HT, Modelling and optimal regulation of erythropoiesis subject to benzene intoxication, Math Biosci Eng, 1, 15-48, (2004) · Zbl 1075.34084
[7] Barosi, G; Cazzola, M; Berzuini, C; Quaglini, S; Stefanelli, M, Classification of anemia on the basis of ferrokinetic parameters, Br J Haematol, 61, 357-370, (1985)
[8] Belair, J; Mackey, MC; Mahaffy, JM, Age-structured and two-delay models for erythropoiesis, Math Biosci, 128, 317-346, (1995) · Zbl 0832.92005
[9] Besarab, A; Bolton, WK; Browne, JK; Egrie, JC; Nissenson, AR; Okamoto, DM; Schwab, SJ; Goodkin, DA, 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, 584-590, (1998)
[10] Besarab, A; Reyes, CM; Hornberger, J, Meta-analysis of subcutaneous versus intravenous epoetin in maintenance treatment of anemia in hemodialysis patients, J Kidney Dis, 40, 439-446, (2002)
[11] Chang, CC; Chen, Y; Modi, K; Awar, OG; Alfrey, CP; Rice, L, Changes of red blood cell surface markers in a blood doping model of neocytolysis, J Investig Med, 57, 650-654, (2009)
[12] Cheung, W; Minton, N; Gunawardena, K, Pharmocokinetics and pharmacodynamics of epoetin alfa once weekly and three times weekly, Eur J Clin Pharmacol, 57, 411-418, (2001)
[13] Crauste, F; Pujo-Menjouet, L; Genieys, S; Molina, C; Gandrillon, O, Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis, J Theor Biol, 250, 322-338, (2008) · Zbl 1397.92081
[14] Crichton R (2009) Iron metabolism: from molecular mechanisms to clinical consequences, 3rd edn. Wiley, New York
[15] Feagan, BG; Wong, CJ; Kirkley, A; Johnston, DW; Smith, FC; Whitsitt, P; Wheeler, S; Lau, CY, Erythropoietin with iron supplementation to prevent allogeneic blood transfusion in total hip joint arthroplasty, Ann Intern Med, 133, 845-854, (2000)
[16] Finch, CA, Erythropoiesis, erythropoietin, and iron, Blood The Journal of American Society of Hematology, 60, 1241-1246, (1982)
[17] Finch, S; Haskins, D; Finch, CA, Iron metabolism. hematopoiesis following phlebotomy. iron as a limiting factor, J Clin Investig, 29, 1078-1086, (1950)
[18] Fleming, MD, The regulation of hepcidin and its effects on systemic and cellular iron metabolism, Hematology Journal of American Society of Hematology, 2008, 151-158, (2008)
[19] Fowler, WM; Barner, AP, Rate of hemoglobin regeneration in blood donors, J Am Med Assoc, 118, 421-427, (1942)
[20] Go, AS; Chertow, GM; Fan, D; McCulloch, CE; Hsu, C, Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization, New Engl J Med, 351, 1296-1305, (2004)
[21] Goodnough, LT, The role of iron in erythropoiesis in the absence and presence of erythropoietin therapy, Nephrol Dial Transplant, 17, 14-18, (2002)
[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, Philadelphia
[23] Ito K, Kappel F (2002) Evolution equations and approximations. World Scientific, Singapore · Zbl 1014.34045
[24] Jandl JH (1987) Blood. Textbook of Hematology. Little, Brown and Company, Boston
[25] Jaspan, D, Erythropoietic therapy: cost efficiency and reimbursement, Am J Health-System Pharm,, 64, 19-29, (2007)
[26] Kappel, F; Zhang, K, Approximation of linear age-structured population models using Legendre polynomials, J Math Anal Appl, 180, 518-549, (1993) · Zbl 0819.65123
[27] Kotanko, P; Kuhlmann, MK; Levin, NW; Feehally, J (ed.); Floege, J (ed.); Johnson, JR (ed.), Hemodialysis: technology, adequacy, and outcomes, 953-966, (2007), Philadelphia
[28] Lichtman, MA, Beutler, E, Kipps, TJ, Seligsohn, U, Kaushansky, K, Prchal, JT (eds) (2005) Williams hematology, 7th edn. McGraw-Hill, New York
[29] Loeffler, M; Pantel, K; Wulff, H; Wichmann, HE, A mathematical model of erythropoiesis in mice and rats. part 1. structure of the model, Cell Tissue Kinetics, 22, 13-30, (1989)
[30] Mahaffy, JM; Belair, J; Mackey, MC, Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis, J Theor Biol, 190, 135-146, (1998)
[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 92182-0314
[32] Pottgiesser, T; Specker, W; Umhau, M; Dickhuth, HH; Roecker, K; Schumacher, YO, Recovery of hemoglobin mass after blood donation, Transfusion, 48, 1390-1397, (2008)
[33] Rice, L; Alfrey, CP, The negative regulation of red cell mass by neocytolysis: physiologic and pathophysiologic manifestations, Cell Physiol Biochem, 15, 245-250, (2005)
[34] Rice, L; Alfrey, CP; Driscoll, T; Whitley, CE; Hachey, DL; Suki, W, Neocytolysis contributes to the anemia of renal disease, Am J Kidney Dis, 33, 59-62, (1999)
[35] Rice, L; Ruiz, W; Driscoll, T; Whitley, CE; Tapia, R; Hachey, DL; Conzales, GF; Alfrey, CP, Neocytolysis on descent from altitude: a newly recognized mechanism for the control of red cell mass, Ann Intern Med, 134, 652-656, (2001)
[36] Roeder, I, Quantitative stem cell biology: computational studies in the hematopoietic system, Curr Opin Hematol, 13, 222-228, (2006)
[37] Roeder, I; Loeffler, M, A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity, Exp Hematol, 30, 853-861, (2002)
[38] Schaefer, RM; Schaefer, L, Iron monitoring and supplementation: how do we achieve the best results, Nephrol Dial Transplant, 13, 9-12, (1998)
[39] Stefanelli, M; Bentley, DP; Cavill, I; Roeser, HP, Quantitation of reticuloendothelial iron kinetics in humans, Am J Physiol, 247, 842-849, (1984)
[40] Strippoli, GF; Craig, JC; Manno, C; Schena, FP, Hemoglobin targets for the anemia of chronic kidney disease: a meta-analysis of randomized, controlled trials, J Am Soc Nephrol, 15, 3154-3165, (2004)
[41] Udden, MM; Driscoll, TB; Pickett, MH; Leach-Huntoon, CS; Alfrey, CP, Decreased production of red blood cells in human subjects exposed to microgravity, J Lab Clin Med, 125, 442-449, (1995)
[42] Wichmann, HE; Loeffler, M; Pantel, K; Wulff, HH, A mathematical model of erythropoiesis in mice and rats. part 2. stimulated erythropoiesis, Cell Tissue Kinetics, 22, 31-49, (1989)
[43] Wu, H; Liu, X; Jaenisch, R; Lodish, HF, Generation of committed erythroid BFU-E and CFU-E progenitors does not require erythropoietin or the erythropoietin receptor, Cell, 83, 59-67, (1995)
[44] Wulff, H; Wichmann, HE; Pantel, K; Loeffler, M, A mathematical model of erythropoiesis in mice and rats. part 3: suppressed erythropoiesis, Cell Tissue Kinetics, 22, 51-61, (1989)
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