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Mathematical model of radiation effects on thrombopoiesis in rhesus macaques and humans. (English) Zbl 1343.92250
Summary: A mathematical model that describes the effects of acute radiation exposure on thrombopoiesis in primates and humans is presented. Thrombopoiesis is a complex multistage dynamic process with potential differences between species. Due to known differences in cellular radiosensitivities, nadir times, and cytopenia durations, direct extrapolation from rhesus to human platelet dynamics is unrealistic. Developing mathematical models of thrombopoiesis for both humans and primates allows for the comparison of the system’s response across species. Thus, data obtained in primate experiments can be extrapolated to predictions in humans. Parameter values for rhesus macaques and humans were obtained either from direct experimental measurements or through optimization procedures using dynamic data on platelet counts following radiation exposure. Model simulations accurately predict trends observed in platelet dynamics: at low radiation doses platelet counts decline after a time lag, and nadir depth is dose dependent. The models were validated using data that was not used during the parameterization process. In particular, additional experimental data was used for rhesus, and accident and platelet donor data was used for humans. The model aims to simulate the average response in rhesus and humans following irradiation. Variation in platelet dynamics due to individual variability can be modeled using Monte Carlo simulations in which parameter values are sampled from distributions. This model provides insight into the time course of the physiological effects of radiation exposure, information which could be valuable for disaster planning and survivability analysis and help in drug development of radiation medical countermeasures.

92C50 Medical applications (general)
deSolve; diffEq; FME; R
Full Text: DOI
[1] Akca, S., Haji-Michael, P., de Mendona, A., Suter, P., Levi, M., Vincent, J.L., 2002. Time course of platelet counts in critically ill patients. Crit. Care Med. 30 (April (4)), 753-756. ISSN 0090-3493. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/11940740〉.
[2] Andreeff, M., Goodrich, D.W., Pardee, A.B., 2000. Cell proliferation, differentiation, and apoptosis. In: Bast, R.C., Kufe, D.W., Pollock, R.E., Weichselbaum, R.R., Holland, J.F., Frei, E. (Eds.). Holland-Frei Cancer Medicine, 5th ed. BC Decker, Ontario, Canada.
[3] Andrews, G. A.; Sitterson, B. W.; Kretchmar, A. L.; Brucer, M., Criticality accident at the Y-12 plant, Diagn. Treat. Acute Radiat. Inj., 27-48, (1961)
[4] Authier, S. Pouliot, M., Ascah, A., Troncy, E., Forster, R., 2013. Hematopoietic Characterization of a Non-Rodent Model for Acute Radiation Syndrome. URL 〈http://www.citoxlab.com/wp-content/uploads/2014/03/28-2012_SOT_Acute-radiation-syndrome-hematopoietic-characterization-of-a-non-rodent-model.pdf〉.
[5] Baranov, A.E., Selidovkin, G.D., Butturini, A., Gale, R.P., 1994. Hematopoietic recovery after 10-Gy acute total body radiation. Blood 83 (January (2)), 596-599. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/8286754〉.
[6] Basile, L.A. Ellefson, D., Gluzman-Poltorak, Z., Junes-Gill, K., Mar, V., Mendonca, S., Miller, J.D., Tom, J., Trinh, A., Gallaher, T.K., 2012. HemaMax, a recombinant human interleukin-12, is a potent mitigator of acute radiation injury in mice and non-human primates. PloS one 7 (January (2)), e30434. ISSN 1932-6203. http://dx.doi.org/10.1371/journal.pone.0030434, URL 〈http://www.ncbi.nlm.nih.gov/pubmed/22383962〉.
[7] Bond, V. P.; Fliedner, T. M.; Archambeau, J. O., Mammalian radiation lethality: A disturbance in cellular kinetics, (1965), Academic Press New York and London, URL 〈http://www.getcited.org/pub/101214105〉
[8] Broudy, V.C., Lin, N.L., Sabath, D.F., Papayannopoulou, T., Kaushansky, K., 1997. Human platelets display high-affinity receptors for thrombopoietin. Blood 89 (March (6)), 1896-1904. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/9058709〉.
[9] Brun, R., Reichert, P., Knsch, H.R., 2001. Practical identifiability analysis of large environmental simulation models. Water Resour. Res. 37 (April (4)), 1015-1030. ISSN 00431397. http://dx.doi.org/10.1029/2000WR900350. URL 〈http://doi.wiley.com/10.1029/2000WR900350〉.
[10] Burdelya, L.G., Krivokrysenko, V.I., Tallant, T.C., Strom, E., Gleiberman, A.S., Gupta, D., Kurnasov, O.V., Fort, F.L., Osterman, A.L., Didonato, J.a., Feinstein, E., Gudkov, A.V., 2008. An agonist of toll-like receptor 5 has radioprotective activity in mouse and primate models. Science 320 (April (5873)), 226-230. ISSN 1095-9203. http://dx.doi.org/10.1126/science.1154986. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/18403709〉.
[11] Deutsch, V.R., Tomer, A., 2013. Advances in megakaryocytopoiesis and thrombopoiesis: from bench to bedside. Br. J. Haematol. 161 (June (6)), 778-793. ISSN 1365-2141. http://dx.doi.org/10.1111/bjh.12328. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/23594368〉.
[12] Dowling, M.R., Josefsson, E.C., Henley, K.J., Hodgkin, P.D., Kile, B.T., 2010. Platelet senescence is regulated by an internal timer, not damage inflicted by hits. Blood, 116 (September (10)), 1776-1778. ISSN 1528-0020. http://dx.doi.org/doi:10.1182/blood-2009-12-259663. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/20530288〉.
[13] Drexel University College of Medicine, 2011. A Compendium of Drugs Used for Laboratory Animal Anesthesia, Analgesia, Tranquilization and Restraint. URL 〈http://www.drexelmed.edu/documents/ULAR/IACUC_drugs.pdf〉.
[14] Ebbe, S., Stohlman, F., Donovan, J., Overcash, J., 1968. Megakaryocyte maturation rate in thrombocytopenic rats. Blood 32 (November (5)), 787-795. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/5687938〉.
[15] Farese, A.M., Williams, D.E., Seiler, F.R., MacVittie, T.J., 1993. Combination protocols of cytokine therapy with interleukin-3 and granulocyte-macrophage colony-stimulating factor in a primate model of radiation-induced marrow aplasia. Blood 82 (November (10)), 3012-3018. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/8219192〉.
[16] Finch, C.A., Harker, L.A., Cook, J.D., 1977. Kinetics of the formed elements of human blood. Blood 50 (October (4)), 699-707. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/332255〉.
[17] Fliedner, T., Friesecke, I., Beyrer, K. (Eds.), 2001. Medical Management of Radiation Accidents: Manual on the Acute Radiation Syndrome. British Institute of Radiology, London, UK. ISBN 0905749464.
[18] Gluzman-Poltorak, Z., Mendonca, S.R., Vainstein, V., Kha, H., Basile, L.A., 2014a. Randomized comparison of single dose of recombinant human IL-12 versus placebo for restoration of hematopoiesis and improved survival in rhesus monkeys exposed to lethal radiation. J. Hematol. Oncol. 7 (January), 31. ISSN 1756-8722. http://dx.doi.org/10.1186/1756-8722-7-31. URL 〈http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=4108131&tool=pmcentrez&rendertype=abstract〉.
[19] Gluzman-Poltorak, Z., Vainstein, V., Basile, L.A., 2014b. Recombinant interleukin-12, but not granulocyte-colony stimulating factor, improves survival in lethally irradiated nonhuman primates in the absence of supportive care: evidence for the development of a frontline radiation medical countermeasure. Am. J. Hematol. 89 (September (9)), 868-873. ISSN 1096-8652. http://dx.doi.org/doi:10.1002/ajh.23770. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/24852354〉.
[20] Goans, R.E., 2012. Radiation Exposure, Illness, and Injury. URL 〈http://www.publichealthontario.ca/en/LearningAndDevelopment/Events/Documents/EMS2-Feb.24,2012.pdf〉.
[21] Graessle, D.H., 2000. Simulation of Radiation Effects Using Biomathematical Models of the Megakaryocytic Cell Renewal System (Ph.D. thesis). Medizinische Fakultt der Universitt Ulm. URL 〈http://www.researchgate.net/publication/29528258_Simulation_of_radiation_effects_using_biomathematical_models_of_the_megakaryocytic_cell_renewal_system/file/79e4150c662224a547.pdf〉.
[22] Greenberg, M.L., Chanana, A.D., Cronkite, E.P., Schiffer, L.M., Stryckmans, P.A., 1968. Extracorporeal irradiation of blood in man: radiation resistance of circulating platelets. Radiat. Res. 35 (July (1)), 147-54. ISSN 0033-7587. http://www.rrjournal.org/doi/abs/10.2307/3572441. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/5241847〉.
[23] Haario, H.; Saksman, E.; Tamminen, J., An adaptive metropolis algorithm, Bernoulli, 7, 2, 223-242, (2001) · Zbl 0989.65004
[24] Haigh, M.V., Paterson, E., 1956. Effects of a single session of whole body irradiation in the rhesus monkey. Br. J. Radiol. 29 (March (339)), 148-157. ISSN 0007-1285. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/13304287〉.
[25] Harker, L.A., Marzec, U.M., Kelly, A.B., Cheung, E., Tomer, A., Nichol, J.L., Hanson, S.R., Stead, R.B., 1997. Prevention of thrombocytopenia and neutropenia in a nonhuman primate model of marrow suppressive chemotherapy by combining pegylated recombinant human megakaryocyte growth and development factor and recombinant human granulocyte colony-stimulating factor. Blood 89 (January (1)) 155-165. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/8978288〉.
[26] Harker, L.A., Roskos, L.K., Marzec, U.M., Carter, R.A., Cherry, J.K., Sundell, B., Cheung, E.N., Terry, D., Sheridan, W., 2000. Effects of megakaryocyte growth and development factor on platelet production, platelet life span, and platelet function in healthy human volunteers. Blood 95 (8), 2514-2522. URL 〈http://bloodjournal.hematologylibrary.org/content/95/8/2514.short〉.
[27] Hempelmann, L.H., Lisco, H., Hoffman, J.G., 1952. The acute radiation syndrome: a study of nine cases and a review of the problem. Ann. Intern. Med. 36 (February (2:1)), 279-510. ISSN 0003-4819. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/14895043〉.
[28] Heylmann, D., Rdel, F., Kindler, T., Kaina, B., 2014. Radiation sensitivity of human and murine peripheral blood lymphocytes, stem and progenitor cells. Biochim. Biophys. Acta 1846 (August (1)), 121-129. ISSN 0006-3002. http://dx.doi.org/10.1016/j.bbcan.2014.04.009. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/24797212〉.
[29] Hirama, T., Tanosaki, S., Kandatsu, S., Kuroiwa, N., Kamada, T., Tsuji, H., Yamada, S., Katoh, H., Yamamoto, N., Tsujii, H., Suzuki, G., Akashi, M., 2003. Initial medical management of patients severely irradiated in the Tokai-mura criticality accident. Br. J. Radiol. 76 (April (904)), 246-253. ISSN 0007-1285. http://dx.doi.org/10.1259/bjr/82373369, URL 〈http://bjr.birjournals.org/cgi/doi/10.1259/bjr/82373369, http://www.birpublications.org/doi/abs/10.1259/bjr/82373369〉.
[30] Housinger, T.A., Brinkerhoff, C., Warden, G.D., 1993. The relationship between platelet count, sepsis, and survival in pediatric burn patients. Arch. Surg. 128 (January (1)), 65-67. ISSN 0004-0010. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/8418782〉.
[31] Hrodin, F., Roy, L., Grenier, N., Delaunay, C., Baug, S., Vaurijoux, A., Grgoire, E., Martin, C., Alonso, A., Mayol, J.-F., Drouet, M., 2007. Antiapoptotic cytokines in combination with pegfilgrastim soon after irradiation mitigates myelosuppression in nonhuman primates exposed to high irradiation dose. Exp. Hematol. 35 (August (8)), 1172-1181. ISSN 0301-472X. http://dx.doi.org/doi:10.1016/j.exphem.2007.04.017. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/17560010〉.
[32] Jammet, H., Mathe, G., Pendic, B., Duplan, J.F., Maupin, B., Latarjet, R., Kalic, D., Schwarzenberg, L., Djukic, Z., Vigna, J., 1959. Study of six cases of accidental acute total irradiation. Rev. franaise d׳tudes Clin. Biol. 4 (March (3)), 210-225. ISSN 0370-4793. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/13646286〉.
[33] Joiner, M. C., Quantifying cell kill and cell survival, (Joiner, M. C.; vander Kogel, A., Basic Clinical Radiobiology, (2009), CRC Press Boca Raton, FL), 42-55
[34] Kashiwakura, I., Kuwabara, M., Inanami, O., Murakami, M., Hayase, Y., Takahashi, T.A., Takagi, Y., 2000. Radiation sensitivity of megakaryocyte colony-forming cells in human placental and umbilical cord blood. Radiat. Res. 153 (February (2)), 144-152. ISSN 0033-7587. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/10629613〉.
[35] Kato, K., Omori, A., Kashiwakura, I., 2013. Radiosensitivity of human haematopoietic stem/progenitor cells. J. Radiol. Prot.: Off. J. Soc. Radiol. Prot. 33 (March (1)), 71-80. ISSN 1361-6498. http://dx.doi.org/doi:10.1088/0952-4746/33/1/71. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/23295782〉.
[36] Kaushansky, K., 2005. The molecular mechanisms that control thrombopoiesis. J. Clin. Investig. 115 (December (12)), 3339-3347. ISSN 0021-9738. http://dx.doi.org/doi:10.1172/JCI26674. URL 〈http://www.jci.org/cgi/content/abstract/115/12/3339http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1297257&tool=pmcentrez&rendertype=abstract〉.
[37] Kuwaki, T., Hagiwara, T., Yuki, C., Kodama, I., Kato, T., Miyazaki, H., 1998. Quantitative analysis of thrombopoietin receptors on human megakaryocytes. FEBS Lett. 427 (May (1)), 46-50. ISSN 0014-5793. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/9613597〉.
[38] Laine, M., Adaptive MCMC Methods with Applications in Environmental and Geophysical Models (Dissertation), (2008), Finish Meteorological Institute Lappeenranta, Finland
[39] Lasky, L.C., Lin, A., Kahn, R.A., McCullough, J., 1981. Donor platelet response and product quality assurance in plateletpheresis. Transfusion 21 (3), 247-260. ISSN 0041-1132. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/7233509〉.
[40] Levine, R.F., 1980. Isolation and characterization of normal human megakaryocytes. Br. J. Haematol. 45 (July (3)), 487-497. ISSN 0007-1048. URL 〈http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2141.1980.tb07168.x/abstract, http://www.ncbi.nlm.nih.gov/pubmed/7000150〉.
[41] MacDonald, N., Time lags in biological models. lecture notes in biomathematics, (1978), Springer-Verlag Berlin
[42] Math, G.; Amiel, J. L.; Schwarzenberg, L., Treatment of acute total-body irradiation injury in man, Ann. N.Y. Acad. Sci., 114, 1, 368-392, (1964), URL 〈http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.1964.tb53591.x/full〉
[43] Mettler, F. A., Accidents in industrial radiation facilities, (Gusev, I. A.; Guskova, A. K.; Mettler, F. A., Medical Management of Radiation Accidents, (2001), CRC Press Boca Raton), 211-222
[44] Mettler, F.A., Voelz, B.L., Nnot, J.C., Gusev, I.A., 2001. Criticality accidents. In: Gusev, I.A., Guskova, A.K., Mettler, F.A. (Eds.), Medical Management of Radiation Accidents, 2nd ed. CRC Press, Boca Raton, pp. 173-194.
[45] Mezzano, D., Hwang, K., Aster, R.H., 1982. Characteristics of total platelet populations and of platelets isolated in platelet-rich plasma. Transfusion 22 (3), 197-202. ISSN 0041-1132. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/7090031〉.
[46] Miller, L.S., Fletcher, G.H., Gerstner, H.B., 1958. Radiobiologic observations on cancer patients treated with whole-body x-irradiation. Radiat. Res. 8 (February (2)), 150-165. ISSN 0033-7587. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/13506043〉.
[47] Monzen, S., Osuda, K., Miyazaki, Y., Hayashi, N., Takahashi, K., Kashiwakura, I., 2009. Radiation sensitivities in the terminal stages of megakaryocytic maturation and platelet production. Radiat. Res. 172 (September (3)), 314-320. ISSN 0033-7587. http://dx.doi.org/10.1667/RR1519.1. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/19708780〉.
[48] Mor, J. J., The Levenberg-Marquardt algorithm: implementation and theory, In Numerical Analysis, 105-116, (1978), Springer Berlin, Heidelberg
[49] Murphy, E.A., Francis, M.E., 1971. The estimation of blood platelet survival. II. The multiple hit model. Thromb. diath. Haemorrh. 25 (January (1)), 53-80. ISSN 0340-5338. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/5577974〉.
[50] Pegg, D. E., Bone marrow transplantation, (1966), Year Book Medical Publishers Chicago
[51] Pe, M., 2012. Estimation of doses received by operators in the 1958 RB reactor accident using the MCNP5 computer code simulation. Nucl. Technol. Radiat. Protect. 27 (3), 199-221. ISSN 1451-3994. http://dx.doi.org/10.2298/NTRP1203199P. URL 〈http://www.doiserbia.nb.rs/Article.aspx?ID=1451-39941203199P〉.
[52] R Core Team, 2013. R: A Language and Environment for Statistical Computing. Technical report, R Foundation for Statistical Computing, Vienna, Austria. URL 〈http://www.r-project.org/〉.
[53] Schmitt, A., Guichard, J., Mass, J.M., Debili, N., Cramer, E.M., 2001. Of mice and men: comparison of the ultrastructure of megakaryocytes and platelets. Exp. Hematol. 29 (November (11)) 1295-1302. ISSN 0301-472X. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/11698125〉.
[54] Scholz, M., Gross, A., Loeffler, M., 2010. A biomathematical model of human thrombopoiesis under chemotherapy. J. Theor. Biol. 264 (May (2)), 287-300. ISSN 1095-8541. http://dx.doi.org/10.1016/j.jtbi.2009.12.032. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/20083124〉. · Zbl 1406.92277
[55] Skomorovski, K., Harpak, H., Ianovski, A., Vardi, M., Visser, T.P., Hartong, S.C.C., van Vliet, H.H.D.M., Wagemaker, G., Agur, Z., 2003. New TPO treatment schedules of increased safety and efficacy: pre-clinical validation of a thrombopoiesis simulation model. Br. J. Haematol. 123 (November (4)), 683-691. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/14616973〉.
[56] Smirnova, O.A., 2010. Environmental Radiation Effects on Mammals. Springer, New York, New York, NY. ISBN 978-1-4419-7212-5. http://dx.doi.org/10.1007/978-1-4419-7213-2. URL 〈http://link.springer.com/10.1007/978-1-4419-7213-2〉.
[57] Smirnova, O.A., 2012. Comparative analysis of the dynamics of thrombocytopoietic, granulocytopoietic, and erythropoietic systems in irradiated humans: a modeling approach. Health Phys. 103 (December (6)), 787-801. ISSN 1538-5159. http://dx.doi.org/10.1097/HP.0b013e31826021bb. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/23111526〉.
[58] Soetaert, K.; Petzoldt, T., Inverse modelling, sensitivity and Monte Carlo analysis in R using package FME, J. Stat. Softw., 330, 0, 1-28, (2010), URL 〈http://www.jstatsoft.org/v33/i03/〉
[59] Soetaert, K., Petzoldt, T., Setzer, R.W., 2010. Solving differential equations in R: Package deSolve. J. Stat. Softw. 33(9), 1-25. ISSN 1548-7660. URL 〈http://www.jstatsoft.org/v33/i09〉.
[60] Starr, C., Taggart, R., 1989. Biology: The Unity and Diversity of Life, 5 ed. Wadsworth Publishing Co Inc., Belmont, California.
[61] Stavem, P., Brgger, A., Devik, F., Flatby, J., van der Hagen, C.B., Henriksen, T., Hoel, P.S., Hst, H., Kett, K., Petersen, B., 1985. Lethal acute gamma radiation accident at Kjeller, Norway: report of a case. Acta Oncol. 24 (1), 61-63. ISSN 0349-652X. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/2984904〉.
[62] Sullivan, L.W., Adams, W.H., Liu, Y.K., 1977. Induction of thrombocytopenia by thrombopheresis in man: patterns of recovery in normal subjects during ethanol ingestion and abstinence. Blood 49 (February (2)), 197-207. ISSN 0006-4971. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/831873〉.
[63] UNSCEAR, 1988. Sources, Effects, and Risks of Ionizing Radiation. 1988 Report to the General Assembly. United Nations Scientific Committee on the Effects of Atomic Radiation, New York
[64] Usacheva, I.N., Raeva, N.V., 1963. Normal indices of the peripheral blood and bone marrow for the monkey macacus rhesus. Bull. Exp. Biol. Med. 54 (November (5)) 1285-1287. ISSN 0007-4888. http://dx.doi.org/10.1007/BF00785609. URL 〈http://link.springer.com/10.1007/BF00785609〉.
[65] Valentin, J., 2002. Basic anatomical and physiological data for use in radiological protection: reference values. ICRP Publication 89. Ann. of ICRP 32(3-4), 1-277.
[66] Wang, Y., Tang, H.-T., Xia, Z.-F., Zhu, S.-H., Ma, B., Wei, W., Sun, Y., Lv, K.-Y., 2010. Factors affecting survival in adult patients with massive burns. Burns: J. Int. Soc. Burn Injur. 36 (February (1)), 57-64. ISSN 1879-1409. http://dx.doi.org/10.1016/j.burns.2009.04.014. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/19487080〉.
[67] Weisbach, V., Friedlein, H., Glaser, A., Zingsem, J., Zimmermann, R., Eckstein, R., 1999. The influence of automated plateletpheresis on systemic levels of hematopoietic growth factors. Transfusion 39 (August (8)) 889-894. ISSN 0041-1132. http://dx.doi.org/10.1046/j.1537-2995.1999.39080889.x. URL 〈http://www.ncbi.nlm.nih.gov/pubmed/10504126〉.
[68] Wentz, J.; Oldson, D.; Stricklin, D., Modeling the thrombopoietic effects of burn, Lett. Biomath., 1, 1, (2014)
[69] Wentz, J., Oldson, D., Stricklin, D., 2014b. Mathematical Models of Human Hematopoiesis Following Acute Radiation Exposure. Technical Report DTRA-TR-14-31, Defense Threat Reduction Agency, Fort Belvoir, VA. URL 〈http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA602115〉.
[70] World Book Inc., Staff. 1998. Blood. In: World Book Encyclopedia. World Book, Chicago, p. 407.
[71] Yarmonenko, S. P., Radiation sickness in man, Radiobiology of Humans and Animals, 153-170, (1988), Mir Publishers Moscow, URL http://www.getcited.org/pub/102915198
[72] Yeaman, M.R., 2010. Platelets in defense against bacterial pathogens. Cell. Mol. Life Sci.: CMLS 67 (February(4)) 525-544. ISSN 1420-9071. http://dx.doi.org/10.1007/s00018-009-0210-4. URL 〈http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2809947&tool=pmcentrez&rendertype=abstract〉.
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