Predictive formulas expressing relationship among dose rate, duration of exposure and mortality probability in total body irradiation in humans

Author(s)
Sung Jang Chung

ABSTRACT

A clear and exact quantitative relationship between dose of radiation and mortality in humans is still not known because of lack of human data that would enable to determine LD50 for humans in total body irradiation. Analysis of human data has been primarily from radiation accidents, radiotherapy and the atomic bomb victims.The death rate equation derived from the 'probacent'-probability model of survival probability is employed in this study to construct the general formula of mortality probability as a function of dose rate and duration of exposure in total body irradiation in humans. There is a remarkable agreement between formula-predicted and published estimated LD50 and also between both mortality probabilities. The formulas of LD50 ans mortality probability in lethal radiation exposure for humans might be helpful in preventing radiation hazard and injury, and further for safety in radiotherapy.

A clear and exact quantitative relationship between dose of radiation and mortality in humans is still not known because of lack of human data that would enable to determine LD50 for humans in total body irradiation. Analysis of human data has been primarily from radiation accidents, radiotherapy and the atomic bomb victims.The death rate equation derived from the 'probacent'-probability model of survival probability is employed in this study to construct the general formula of mortality probability as a function of dose rate and duration of exposure in total body irradiation in humans. There is a remarkable agreement between formula-predicted and published estimated LD50 and also between both mortality probabilities. The formulas of LD50 ans mortality probability in lethal radiation exposure for humans might be helpful in preventing radiation hazard and injury, and further for safety in radiotherapy.

Cite this paper

nullChung, S. (2011) Predictive formulas expressing relationship among dose rate, duration of exposure and mortality probability in total body irradiation in humans.*Journal of Biomedical Science and Engineering*, **4**, 497-505. doi: 10.4236/jbise.2011.47063.

nullChung, S. (2011) Predictive formulas expressing relationship among dose rate, duration of exposure and mortality probability in total body irradiation in humans.

References

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[2] T. J. Jones, M. D. Morris, S. M. Wells and R. W. Young, “Animal Mortality Resulting From Uniform Exposures To Photon Radiations: Calculated LD50 and a Compilation of Experimental Data,” Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1986. doi:10.2172/6940829

[3] J. Nénot, “Radiation accidents over the last 60 years,” Journal of Radiological Protection, Vol. 29, 2009, pp. 301-320. doi:10.1088/0952-4746/29/3/R01

[4] S. Abrahamson, M.A. Bender, R. B. Boecker, et al., “Health Effect Models for Nuclear Power Plant Accident Consequence Analysis,” US Government Printing Office, Washington, D. C. 1993.

[5] E. H. Donnelly, J. B. Nemhauser, M. Smith, et al., “ Acute radiation syndrome: Assessment and management,” Southern Medical Journal, vol. 103, pp. 541-544. doi:10.1097/SMJ.0b013e3181ddd571

[6] Department of Radiology, University of Illinois, “Acute effects of whole body irradiation: Lesson from Chernobyl,” 1990. Internet Available: http//:www.uic.edu/com/uhrd/manuscript/section4/section4.html

[7] K. F. Baverstock, P. J. D. Ash, ”A review of radiation accidents involving whole body exposure and the relevance to the LD 50/60 for man,” British Journal of Radiology, Vol. 56, 1983, 837-849. doi:10.1259/0007-1285-56-671-837

[8] S. Warren, “The Pathology of Ionizing Radiation,” Charles C. Thomas Publisher, Springfield, 1961.

[9] L. Van Middlesworth, “Worldwide iodine fallout in animal thyroid, 1954-1987,” In: Radiation and the Thyroid, Excerpta Medica, Amsterdam-Prinston-Hong Kong-Tokyo-Sydney, 1989, pp. 36-56.

[10] L. Van Middlesworth, “ Effects of radiation on the thyroid gland,” Advanced Internal Medicine, Vol. 34, 1989, pp. 265-284.

[11] S. L. Simon, A. Bouville and C. E. Land, “Fallout from nuclear weapons tests and cancer risks,” American Scientist, vol. 94, 2006, pp. 48-57.

[12] G. A. Sacher, “On the statistical nature of mortality, with especial reference to chronic radiation mortality,” Radiology, Vol. 67, 1956, pp. 250-257.

[13] G. A. Sacher, “On the relation of radiation lethality to radiation injury and its relevance for the prediction problem,” IX th International Congress of Radiology, 23 VII-30 VII, 1959 in München, Germany, Georg Thieme Verlag, Stuttgart, 1960, pp. 1223-1232.

[14] E. L. Travis, L. G. Peters, H. D. Thames, et al., “Effect of dose-rate on total body irradiation: Lethality and pathologic findings,” Radiotherapy and Oncology, vol. 4, 1985, pp. 341-351. doi:10.1016/S0167-8140(85)80122-5

[15] F. Ellington, “Influence of dose fractionation on the lethal X-ray effect produced by total body irradiation in mice,” Radiology, Vol. 47, 1947, pp. 238-241.

[16] D. Grahn, “Acute radiation response of mice from a cross between radio-sensitive and radio-resistant strains,” Genetics, Vol. 43, 1958, pp. 835-843.

[17] E. A. Komarova, R. V. Kondratov, K. Wang, et al., “Dual effect of p53 on radiation sensitivity in vivo: p53 promotes hematopoietic injury, but protects from gastro-intestinal syndrome in mice,” Oncogene, Vol. 23, 2004, pp. 3265-3271. doi:10.1038/sj.onc.1207494

[18] E. T. Lee and J. W. Wang, “Statistical Methods for Survival Data,” John Wiley & Sons, Hoboken, 2003, pp. 8-197. doi:10.1002/0471458546.ch2

[19] L. Heligman and J. H. Pollard, “The age pattern of mortality,” Journal of Inst. Actuaries, Vol. 107, 1980, pp. 49-80.

[20] B. Gompertz, “Parametric models,” I n: Statistical Methods in Medical Research, Blackwell Science, Cambridge, 1994, pp. 482-483.

[21] S. J. Chung, “Formulas expressing life expectancy, survival probability and death rate in life table at various ages in US adults,” International Journal of Bio-Medical Computing, Vol. 39, 1995, pp. 209-217. doi:10.1016/0020-7101(94)01068-C

[22] S. J. Chung, “Comprehensive life table of computer-assisted predictive mathematical relationship between age and life expectancy, survival probability or death rate in US adults,” Computer Methods and Programs in Biomedicine, Vol. 52, 1997, pp. 67-73. doi:10.1016/S0169-2607(96)01778-6

[23] S. J. Chung, “Computer-assisted predictive formulas expressing survival probability and life expectancy in US adults, men and women, 2001,” Computer Methods and Programs in Biomedicine, Vol. 86, 2007, pp. 197-209. doi:10.1016/j.cmpb.2007.02.009

[24] S. J. Chung, “Studies on a mathematical relationship between stress and response in biological phenomena,” Rep of Korea Journal of National Academy of Sciences, Vol. 2, 1960, pp. 115-162.

[25] S. J. Chung, “Computer-assisted predictive mathematical relationship among metrazol and time and mortality in mice,” Computer Methods and Programs in Biomedicine, Vol. 22, 1986, pp. 275-284. doi:10.1016/0169-2607(86)90004-0

[26] C. C. Kim and S. J. Chung, “Studies on a relationship between stress, duration of exposure and percentage of response in goldfish to single, double and triple stresses of acceleration, electroshock, heat, chemical and osmotic stimuli,” Republic of Korea Theses of Catholic Medical College, Vol. 5, 1962, pp. 257-336.

[27] S. J. Chung, ”Formula expressing carboxyhemoglobin resulting from carbon monoxide exposure,” Veterinary and Human Toxicology, Vol. 30, 1988, pp. 528-532.

[28] S. J. Chung, “Computer-assisted predictive mathematical relationship among plasma acetaminophen concentration and time after ingestion and occurrence of hepatotoxicity in man,” Computer Methods and Programs in Biomedicine, Vol. 28, 1989, pp. 37-43. doi:10.1016/0169-2607(89)90179-X

[29] S. J. Chung, “Formula predicting survival probability in patients with heart transplantation,” International Journal of Biomedical Computing, Vol. 32, 1993, pp. 211-221. doi:10.1016/0020-7101(93)90015-X

[30] S. J. Chung, ”Formulas expressing relationship among lesion thickness, time after diagnosis, and survival probability in patients with malignant melanoma,” International Journal of Biomedical Computing, Vol. 37, 1994, pp. 171-180. doi:10.1016/0020-7101(94)90139-2

[31] S. J. Chung, “Formulas expressing relationship among age, height and weight, and percentile in Saudi and US children of ages 6-16 years,” International Journal of Biomedical Computing, Vol. 37, 1994, pp. 259-272. doi:10.1016/0020-7101(94)90124-4

[32] S. C. Mehta and H. C. Joshi, “Model based point estimates of survival/death rates: An input for radiation risk evaluation in Indian context,” Indian Journal of Nuclear Medicine, Vol. 19, 2004, pp. 16-18

[33] S. J. Chung, “Predictive formulas expressing mathematical relationship between dose rate of total body irradiation and survival time in mice,” unpublished, 2011.

[34] S. J. Chung, “Seeking a New World: a New Philosophy of Confucius and Kim Hang,” iUniverse, Bloomington, 2009, pp. 69-76.

[35] W. J. Dixon and F. S. Massey Jr., “χ2 test for goodness-of-fit”, In: Introduction to Statistical Analysis, MacGraw-Hill, New York, 1957, pp. 226-227.

[36] I. Damjanov and J. Linder, Ed. “Anderson’s Pathology”, 10th Edition, Mosby, New York, 1996, pp. 484-512.

[37] S. G. Levin, R. W. Young and R. L. Stohler, “Estimation of median human lethal radiation dose computed from data on occupants of reinforced concrete structure in Nagasaki, Japan,” Health Physics, Vol. 63, 1992, pp. 522-531. doi:10.1097/00004032-199211000-00003

[38] S. Fujita, H. Kato and W. J. Schull, “The LD50 associated with exposure to the atomic bombing of Hiroshima,” Journal of Radiation Research (Tokyo), Vol. 30, 1989, pp. 359-381. doi:10.1269/jrr.30.359

[39] Y. Cui, H. Hisha, G. Yang, et al., “Optimal protocol for total body irradiation for allogeneic bone marrow transplantation in mice,” Bone Marrow Transplantation, Vol. 30, 2002, pp. 843-849. doi:10.1038/sj.bmt.1703766

[40] N. Gibbs, “The 9.0 quake that hit Japan on March 11 was powerful enough to shift the earth on its axis and make it spin a little faster, shortening the day by 1.8 millionths of a second,” Time, March 28, 2011, p. 26.

[41] Donga Ilbo, “A Strong Earthquake in the East Japan”, http:// www.donga.com, March 18. 2011.

[42] A. Morse, ”Behind Reactor Battle, a Legion of Grunts,” The Wall Street Journal, March 24, 2011, p. A7.

[1] T.J. Cerveny, T. J. MacVittie and R. W. Young, “Acute radiation syndrome in humans,” In: R. I. Walker and T. J. Cerveny, Ed., Medical Consequences of Nuclear Warfare, TMM Publications, Office of the Surgeon General, Falls Church, Virginia, 1989, pp. 15-36.

[2] T. J. Jones, M. D. Morris, S. M. Wells and R. W. Young, “Animal Mortality Resulting From Uniform Exposures To Photon Radiations: Calculated LD50 and a Compilation of Experimental Data,” Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1986. doi:10.2172/6940829

[3] J. Nénot, “Radiation accidents over the last 60 years,” Journal of Radiological Protection, Vol. 29, 2009, pp. 301-320. doi:10.1088/0952-4746/29/3/R01

[4] S. Abrahamson, M.A. Bender, R. B. Boecker, et al., “Health Effect Models for Nuclear Power Plant Accident Consequence Analysis,” US Government Printing Office, Washington, D. C. 1993.

[5] E. H. Donnelly, J. B. Nemhauser, M. Smith, et al., “ Acute radiation syndrome: Assessment and management,” Southern Medical Journal, vol. 103, pp. 541-544. doi:10.1097/SMJ.0b013e3181ddd571

[6] Department of Radiology, University of Illinois, “Acute effects of whole body irradiation: Lesson from Chernobyl,” 1990. Internet Available: http//:www.uic.edu/com/uhrd/manuscript/section4/section4.html

[7] K. F. Baverstock, P. J. D. Ash, ”A review of radiation accidents involving whole body exposure and the relevance to the LD 50/60 for man,” British Journal of Radiology, Vol. 56, 1983, 837-849. doi:10.1259/0007-1285-56-671-837

[8] S. Warren, “The Pathology of Ionizing Radiation,” Charles C. Thomas Publisher, Springfield, 1961.

[9] L. Van Middlesworth, “Worldwide iodine fallout in animal thyroid, 1954-1987,” In: Radiation and the Thyroid, Excerpta Medica, Amsterdam-Prinston-Hong Kong-Tokyo-Sydney, 1989, pp. 36-56.

[10] L. Van Middlesworth, “ Effects of radiation on the thyroid gland,” Advanced Internal Medicine, Vol. 34, 1989, pp. 265-284.

[11] S. L. Simon, A. Bouville and C. E. Land, “Fallout from nuclear weapons tests and cancer risks,” American Scientist, vol. 94, 2006, pp. 48-57.

[12] G. A. Sacher, “On the statistical nature of mortality, with especial reference to chronic radiation mortality,” Radiology, Vol. 67, 1956, pp. 250-257.

[13] G. A. Sacher, “On the relation of radiation lethality to radiation injury and its relevance for the prediction problem,” IX th International Congress of Radiology, 23 VII-30 VII, 1959 in München, Germany, Georg Thieme Verlag, Stuttgart, 1960, pp. 1223-1232.

[14] E. L. Travis, L. G. Peters, H. D. Thames, et al., “Effect of dose-rate on total body irradiation: Lethality and pathologic findings,” Radiotherapy and Oncology, vol. 4, 1985, pp. 341-351. doi:10.1016/S0167-8140(85)80122-5

[15] F. Ellington, “Influence of dose fractionation on the lethal X-ray effect produced by total body irradiation in mice,” Radiology, Vol. 47, 1947, pp. 238-241.

[16] D. Grahn, “Acute radiation response of mice from a cross between radio-sensitive and radio-resistant strains,” Genetics, Vol. 43, 1958, pp. 835-843.

[17] E. A. Komarova, R. V. Kondratov, K. Wang, et al., “Dual effect of p53 on radiation sensitivity in vivo: p53 promotes hematopoietic injury, but protects from gastro-intestinal syndrome in mice,” Oncogene, Vol. 23, 2004, pp. 3265-3271. doi:10.1038/sj.onc.1207494

[18] E. T. Lee and J. W. Wang, “Statistical Methods for Survival Data,” John Wiley & Sons, Hoboken, 2003, pp. 8-197. doi:10.1002/0471458546.ch2

[19] L. Heligman and J. H. Pollard, “The age pattern of mortality,” Journal of Inst. Actuaries, Vol. 107, 1980, pp. 49-80.

[20] B. Gompertz, “Parametric models,” I n: Statistical Methods in Medical Research, Blackwell Science, Cambridge, 1994, pp. 482-483.

[21] S. J. Chung, “Formulas expressing life expectancy, survival probability and death rate in life table at various ages in US adults,” International Journal of Bio-Medical Computing, Vol. 39, 1995, pp. 209-217. doi:10.1016/0020-7101(94)01068-C

[22] S. J. Chung, “Comprehensive life table of computer-assisted predictive mathematical relationship between age and life expectancy, survival probability or death rate in US adults,” Computer Methods and Programs in Biomedicine, Vol. 52, 1997, pp. 67-73. doi:10.1016/S0169-2607(96)01778-6

[23] S. J. Chung, “Computer-assisted predictive formulas expressing survival probability and life expectancy in US adults, men and women, 2001,” Computer Methods and Programs in Biomedicine, Vol. 86, 2007, pp. 197-209. doi:10.1016/j.cmpb.2007.02.009

[24] S. J. Chung, “Studies on a mathematical relationship between stress and response in biological phenomena,” Rep of Korea Journal of National Academy of Sciences, Vol. 2, 1960, pp. 115-162.

[25] S. J. Chung, “Computer-assisted predictive mathematical relationship among metrazol and time and mortality in mice,” Computer Methods and Programs in Biomedicine, Vol. 22, 1986, pp. 275-284. doi:10.1016/0169-2607(86)90004-0

[26] C. C. Kim and S. J. Chung, “Studies on a relationship between stress, duration of exposure and percentage of response in goldfish to single, double and triple stresses of acceleration, electroshock, heat, chemical and osmotic stimuli,” Republic of Korea Theses of Catholic Medical College, Vol. 5, 1962, pp. 257-336.

[27] S. J. Chung, ”Formula expressing carboxyhemoglobin resulting from carbon monoxide exposure,” Veterinary and Human Toxicology, Vol. 30, 1988, pp. 528-532.

[28] S. J. Chung, “Computer-assisted predictive mathematical relationship among plasma acetaminophen concentration and time after ingestion and occurrence of hepatotoxicity in man,” Computer Methods and Programs in Biomedicine, Vol. 28, 1989, pp. 37-43. doi:10.1016/0169-2607(89)90179-X

[29] S. J. Chung, “Formula predicting survival probability in patients with heart transplantation,” International Journal of Biomedical Computing, Vol. 32, 1993, pp. 211-221. doi:10.1016/0020-7101(93)90015-X

[30] S. J. Chung, ”Formulas expressing relationship among lesion thickness, time after diagnosis, and survival probability in patients with malignant melanoma,” International Journal of Biomedical Computing, Vol. 37, 1994, pp. 171-180. doi:10.1016/0020-7101(94)90139-2

[31] S. J. Chung, “Formulas expressing relationship among age, height and weight, and percentile in Saudi and US children of ages 6-16 years,” International Journal of Biomedical Computing, Vol. 37, 1994, pp. 259-272. doi:10.1016/0020-7101(94)90124-4

[32] S. C. Mehta and H. C. Joshi, “Model based point estimates of survival/death rates: An input for radiation risk evaluation in Indian context,” Indian Journal of Nuclear Medicine, Vol. 19, 2004, pp. 16-18

[33] S. J. Chung, “Predictive formulas expressing mathematical relationship between dose rate of total body irradiation and survival time in mice,” unpublished, 2011.

[34] S. J. Chung, “Seeking a New World: a New Philosophy of Confucius and Kim Hang,” iUniverse, Bloomington, 2009, pp. 69-76.

[35] W. J. Dixon and F. S. Massey Jr., “χ2 test for goodness-of-fit”, In: Introduction to Statistical Analysis, MacGraw-Hill, New York, 1957, pp. 226-227.

[36] I. Damjanov and J. Linder, Ed. “Anderson’s Pathology”, 10th Edition, Mosby, New York, 1996, pp. 484-512.

[37] S. G. Levin, R. W. Young and R. L. Stohler, “Estimation of median human lethal radiation dose computed from data on occupants of reinforced concrete structure in Nagasaki, Japan,” Health Physics, Vol. 63, 1992, pp. 522-531. doi:10.1097/00004032-199211000-00003

[38] S. Fujita, H. Kato and W. J. Schull, “The LD50 associated with exposure to the atomic bombing of Hiroshima,” Journal of Radiation Research (Tokyo), Vol. 30, 1989, pp. 359-381. doi:10.1269/jrr.30.359

[39] Y. Cui, H. Hisha, G. Yang, et al., “Optimal protocol for total body irradiation for allogeneic bone marrow transplantation in mice,” Bone Marrow Transplantation, Vol. 30, 2002, pp. 843-849. doi:10.1038/sj.bmt.1703766

[40] N. Gibbs, “The 9.0 quake that hit Japan on March 11 was powerful enough to shift the earth on its axis and make it spin a little faster, shortening the day by 1.8 millionths of a second,” Time, March 28, 2011, p. 26.

[41] Donga Ilbo, “A Strong Earthquake in the East Japan”, http:// www.donga.com, March 18. 2011.

[42] A. Morse, ”Behind Reactor Battle, a Legion of Grunts,” The Wall Street Journal, March 24, 2011, p. A7.