

ORIGINAL ARTICLE 

Year : 2018  Volume
: 38
 Issue : 4  Page : 150159 

ComputerAssisted formulas predicting radiationexposureinducedcancer risk in interplanetary travelers: Radiation safety for astronauts in space flight to mars
Sung J Chung
MorristownHamblen Healthcare System, Morristown, TN, USA
Date of Submission  06Oct2017 
Date of Decision  01Jan2018 
Date of Acceptance  11Jan2018 
Date of Web Publication  27Jul2018 
Correspondence Address: Dr. Sung J Chung 3909 Vailwood Drive, Nashville, TN 37215 USA
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jmedsci.jmedsci_125_17
A clear quantitative relationship between the dose of total body ionizing radiation and mortality in humans is not known because of lack of human data that would enable us to determine the lethal dose for 50% of cases (LD_{50}) in total body irradiation on earth or in probable future interplanetary travels. Analysis of human data has been primarily from radiation accidents, radiotherapy, and the atomic bomb victims. The author published the general mathematical formula that predicts mortality probability as a function of dose rate and duration of exposure to acute ionizing radiation in humans on the basis of data presented by Cerveny et al., employing the author's mathematical probacent model. Further, the author applied the general formula to the data on dose versus cancer mortality risk published by the United Nations Scientific Committee on the effects of atomic radiation and other investigators to construct general formulas expressing a relationship between dose and solid cancer or leukemia mortality probability after exposure to acute lowdose ionizing radiation in humans on earth. There is a remarkable agreement between formuladerived and published values of dose and solid cancer or leukemia mortality probability (P > 0.99). In this study, the above mortality formulas are applied to the measurements of the Mars Science Laboratory spacecraft containing the Curiosity rover (2012–2013) in estimating radiation safety for astronauts in a future space flight to Mars planned by the National Aeronautics and Space Administration. Results of the estimation obtained with a mathematical approach are presented in this study. Keywords: Formula of LD_{50}, probacent model, radiation safety in interplanetary travelers, radiationexposureinducedcancer mortality, space flight to Mars, theory of everything, ultronlogotron theory
How to cite this article: Chung SJ. ComputerAssisted formulas predicting radiationexposureinducedcancer risk in interplanetary travelers: Radiation safety for astronauts in space flight to mars. J Med Sci 2018;38:1509 
How to cite this URL: Chung SJ. ComputerAssisted formulas predicting radiationexposureinducedcancer risk in interplanetary travelers: Radiation safety for astronauts in space flight to mars. J Med Sci [serial online] 2018 [cited 2018 Dec 19];38:1509. Available from: http://www.jmedscindmc.com/text.asp?2018/38/4/150/233535 
Introduction   
A clear quantitative relationship between the dose of radiation and mortality in humans is not known because of lack of human data that would enable us to determine LD_{50} for humans in total body irradiation. Analysis of human data has been primarily from radiation accidents, radiotherapy, and the atomic bomb victims.
Consequently, laboratory animals have been used to investigate the relationship between radiation exposure and biomedical effects in total body irradiation and further to possibly derive a general mathematical formula expressing a doseeffect curve.^{[1],[2],[3],[4]}
General Mathematical Model of ProbacentProbability Equation   
A mathematical model of the “probacent”probability equation, equation (1) was developed on the basis of animal experiments, clinical application, and mathematical reasoning to express a relationship among intensity of stimulus, duration of exposure and response in biological phenomena.^{[5],[6],[7],[8],[9]}
where i is intensity of stimulus, external stressor or noxious agent; t is duration of exposure; a, b, c, d and n are constants. P is “probacent” (abbreviation of percent probability), a relative amount of internal stress caused by an external stressor or a relative amount of loss of reserve for survival. Probacent values of 0, 50, and 100 correspond to (mean5 standard deviation [SD]), mean and (mean + 5 SD), respectively; the unit of “probacent” is 0.1 SD In addition, 0, 50, and 100 probacents seem to correspond to 0, 50, and 100 percent probability, respectively, in mathematical prediction problems in terms of percentage. Q is mortality probability (%). Survival probability (%) is (100Q). Equation (1) can be used for survival probability problems.
The probacent model has been applied to data in biomedical literature to express a relationship among plasma acetaminophen concentration, time after ingestion, and occurrence of hepatotoxicity in man;^{[10]} to express survival probability in patients with heart transplantation;^{[11]} to express survival probability in patients with malignant melanoma;^{[12]} to express a relationship among blood levels of carboxyhemoglobin as a function of carbon monoxide concentration in air and duration of exposure,^{[13]} and to express a relationship among age, height, and weight, and percentile in Saudi and US children of ages 6–16 years.^{[14]}
The equation of death rate of the probacent model was applied to predict agespecific death rate in the US elderly population, 2001^{[7]} and to express the relationship between dose rate and survival probability in total body irradiation in humans.^{[8],[9]} The results of the above two studies revealed a close agreement between “probacent”formuladerived and publishedreported values of death rates in humans or survival probability in humans (P > 0.995).
Mehta and Joshi ^{[15]} successfully applied the probacentprobability equation model to use modelderived data as an input for radiation risk evaluation of the Indian adult population in their studies.
Formulas expressing a relationship among dose rate, duration of exposure, and mortality probability in total body irradiation in humans
A general formula was developed on the basis of the animalmodel predictions of lethal radiation doses for humans published by Cerveny, et al.^{[1]} The data are based on the extensive study of mortality resulting from radiation exposure and a compilation of animal experimental data published by Jones, Morris, Wells, and Young at the Oak Ridge National Laboratory.^{[2]} The LD_{50} for humans is mathematically predictable as a function of dose rate and duration of exposure. A remarkable agreement is present between values of formuladerived and animalmodelpredicted LD_{50} as well as mortality probabilities (P > 0.995).
The probacent model was applied to the data on dose versus solid cancer or leukemia mortality probabilities published by the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR,) and other investigators ^{[16],[17],[44],[45]} to construct general formulas expressing between dose and solid cancer or leukemia mortality probability after exposure to acute lowdose ionizing radiation in humans.^{[18]} There is a remarkable agreement between formuladerived and published values of dose and solid cancer or leukemia mortality probability (P > 0.99). The general formula might be helpful in preventing radiation hazard and injury in acute lowdose ionizing radiation, and for safety in radiotherapy and further in case of astronauts in a possible future long space flight to Mars by mathematically estimating their safety.^{[19]}
Space radiation in transit to Mars
Zeitlin et al.^{[20]} reported the measurements of energetic particle radiation made by the Radiation Assessment Detector (RAD) inside Mars Science Laboratory (MSL) spacecraft in transit to Mars (2011–2013). The RAD provides the data on the measurements of the radiation dose, dose equivalent, and linear energy transfer spectra. The dose equivalent for the shortest round trip with current propulsion system and comparable shielding is found to be 0.66 ± 0.12 sievert [Table 1].  Table 1: Radiation environment measured by Mars Science Laboratory/Radiation Assessment Detector (2012–2013) (galactic cosmic rays only)
Click here to view 
Radiation on Mars
Hassler et al.^{[21]} reported the measurements made by RAD on MSL's Curiosity rover (2012–2013). The measurements provide the data on the absorbed dose and dose equivalent from galactic cosmic rays and solar energetic particles on the surface of Mars that are 0.21 ± 0.04 mGr/day and 0.64 ± 0.12 mSv/day, respectively [Table 1]. We receive an average of 2 mSv/year from background radiation alone on Earth; 1 mSv of space radiation is approximately equivalent to receiving three chest Xrays.^{[22]}
Cancer risk from exposure to galactic cosmic rays in space flight
Cucinotta and Durante ^{[23]} reported that the oncogenic biological effects of highenergy ions in space radiation are poorly understood and an important barrier to exploration of Mars. The magnitude of cancer risk posed by exposure to radiation in space is subject to many uncertainties. The authors presented a review of recent worldwide research on oncogenic effects of galactic cosmic rays.
To my knowledge, there seems to be no general mathematical models in the literature that express the quantitative relationship among dose rate, duration of exposure, and cancer mortality risk after exposure to total body ionizing radiation. The author employs a mathematical approach to estimate radiationexposureinducedcancer death (REID) and radiation safety in the analysis of the measurements of the Curiosity rover of MSL spacecraft (2012–2013).
The purpose of this study is to examine radiation hazards and safety in interplanetary travelers, especially for astronauts in a future space flight to Mars, applying the author's computerassisted formulas of REID.
Material and Methods   
Materials
Zeitlin et al.^{[20]} at Johnson Space Center, USA, Southwest Research Institute, USA, Christian Albrechts University, Germany, Jet Propulsion Laboratory, USA, German Aerospace Center, National Aeronautics and Space Administration (NASA) Headquarter and other institutes, reported that MSL spacecraft, containing the Curiosity rover launched to Mars on 26 November 2011 provided detailed measurements of energetic particle radiation environment inside the RAD, the radiation dose, dose equivalent, and dose rate.
Hassler et al.^{[21]} reported the measurements of the absorbed dose and dose equivalent from galactic cosmic rays and solar energetic particles on the Mars surface for up to 300 days of observations provided by MSL (2012–2013).
The measurements of both reports are shown in [Table 1] and used in this study to analyze radiation hazard and safety in the exploration of Mars.
Methods
Equations
In this study, equations (2) and (3) in the author's previous publication ^{[18]} are used to express the mortality probability (Q) of solid cancer and leukemia as a function of lethal dose (D) of radiation after exposure to acute low dose ionizing radiation in humans, respectively.
Where D = dose of radiation in mSv, P = probacent, and Q = solid cancer mortality probability (%).
Where D = dose in mSv, P = probacent, and Q = leukemia mortality probability (%).
The equations (2) and (3) are postulated to be applicable in case of use of millisylvert (mSv) unit, dose equivalent instead of milligray (mGy) unit.
Description of computer program
Computer programs are written in UBASIC to calculate equations. The computer program uses a formula of approximation instead of integral of equations (2b) and (3b) because the computer cannot perform integral.^{[6],[18],[24]} Calculation of equation (2)(6) is carried out with the author's computer programs as shown in [Figure 1] and [Figure 4].  Figure 1: Computer program for equations (4), (5), and (6) to calculate the radiationexposureinducedcancer death risk (mortality probability) as a function of dose rate and duration of exposure
Click here to view 
 Figure 4: Computer program for equations (2) and (3) to calculate the radiationexposureinducedcancer death risk (mortality probability) as a function of dose
Click here to view 
Statistical analysis
A Chisquare goodnessoffit test (logrank test) is used to test the fit of mathematical model to the data on dose versus mortality probability in acute ionizing radiation in humans.^{[9],[18]} The differences are considered statistically significant when P < 0.05.
Results   
Radiationexposureinducedsolidcancer death
[Table 2] shows the results of solid cancer mortality risk in percentage as a function of dose after exposure to acute lowdose total body ionizing radiation in humans. Solid cancer means excluding leukemia from total cancer developed in lifetime followup observations after exposure in the lifespan studies.  Table 2: Relationship between dose and solid cancer mortality probability after exposure to acute lowdose ionizing radiation in humans
Click here to view 
[Table 2] also shows comparison of formuladerived values with the reported data on acute low dose versus solid cancer mortality probability (%). Both values of formuladerived and reported solid cancer mortality probabilities in [Table 2] reveal a close agreement (P > 0.99). The maximum difference is 0.75% in exposure to 1000 mSv.
[Figure 3] illustrates the relationship between dose and solid cancer mortality probability after exposure to acute lowdose ionizing radiation in humans. The closed circles of data points fall on or appear to fall close to the solid curved line expressed by equation (2). Dashed lines below and above beyond the endpoints of the solid curved line of equation (2) represent extrapolation of equation (2)expressed solid line.  Figure 3: Relationship between dose and solid cancer mortality probability after exposure to acute lowdose ionizing radiation in humans. The abscissa represents dose in mGy (log scale). The ordinate on the left side represents “probacent” (p) corresponding to mortality probability (Q) in percentage in a lognormal probability graph. The data points of closed circles of reportedestimated solid cancer mortality probabilities after exposure to dose of 30, 100, and 10000 mGy shown in Table 2 appear to fall on or very close to the solid curved line representing equation (2)
Click here to view 
Radiationexposureinducedleukemia death
[Table 3] shows the results of leukemia mortality risk in percentage as a function of dose after exposure to acute lowdose total body ionizing radiation in humans. Comparison of both values of formuladerived and reported estimated mortality probabilities reveals a close agreement without statistical significant differences (P > 0.995).  Table 3: Relationship between dose and leukemia mortality probability after exposure to acute lowdose ionizing radiation in humans
Click here to view 
[Figure 2] illustrates the relationship between dose and leukemia mortality probability after exposure to acute lowdose ionizing radiation in humans. The closed circles of data points of Reference 16, 17, and 25 in [Table 3] are the basis on which equation (3) is constructed. There is a close agreement between formuladerived and reported lethal radiation doses (P > 0.995).  Figure 2: Relationship between dose and leukemia mortality probability of lifetime risk after exposure to acute lowdose ionizing radiation in humans. The abscissa represents dose in mGy (log scale). The ordinate on the right side represents leukemia mortality probability (q) in percentage. The ordinate on the left side represents “probacent” (p) corresponding to mortality probability (q) in a lognormal probability graph. The data points of closed circles of reportedestimated leukemia mortality probabilities after exposure to 30, 100, and 1000 mGy of References 16 and 17 shown in Table 3 appear to fall on the solidcurved line representing equation (3). The other data points of reported estimated leukemia mortalities for 1000 mGy of Reference 25 in Table 3 are not plotted but if plotted would fall very close to the solid line of equation 3
Click here to view 
The data points on which equation (3) are based fall on the solid curved line. The other points of Reference 25 in [Table 3] are not plotted in [Figure 2] but, if plotted, would fall very close to the solid curved line at 1000 mSv expressed by equation (3).
Radiationexposureinducedcancer death
REID (Q_{REID)} is equal to the sum of radiationexposureinducedsolidcancer death (REISCD) (Q_{REISCD}) + radiationexposureinducedleukemia death (REILD) (Q_{REILD}). Therefore, equations (4), (5), and (6) are newly constructed to express REID as a function of dose rate and duration of exposure in total body ionizing radiation in humans.
Where D = dose rate (mSv/min), T = duration of exposure (minute), P = probacent and Q_{REISCD} = mortality probability of REISCD.
Where D = dose rate (mSv/min), T = duration of exposure (minute), P = probacent and Q_{REILD} = mortality probability of REILD.
Equation (6) can be readily calculated with the computer program shown in [Figure 1].
The REISCD, REILD, and REID at the radiation dose of 30 mSv are 0.05%, 0.005%, and 0.55%; at the dose of 100 mSv, 0.565%, 0.04%, and 0.605%; at the dose of 1000 mSv, 5.75%, 0.8%, and 6.55%, respectively, as shown in the computer program [Figure 4], The REID of 391 mSv is associated with 3% of REID that is suggested to be PEL of NASA ^{[26],[27]} from the standpoint of the mathematical approach. The REID of 662 mSv is 4.76%. The average effective dose for the approximately 6month missions of the 19 astronauts of the international space station (ISS) was 72 mSv. The REID of 72 mSv is 0.36% in this study of a mathematical approach.^{[27]}
Relationship among dose rate of 1.84 mSv/day during the round trip to Mars or 0.64 mSv/day during stay on Mars, duration of exposure, and radiationexposureinducedcancer death (%)
The author presents general formulas, equations (4), (5), and (6) that predict the relationship among dose rate of 1.84 mSv/day during the round trip to Mars or dose rate of 0.64 mSv/day during the stay on Mars, duration of exposure to radiation, and REID (%).
[Table 4] shows the relationship among the durations of round trip and stay on Mars and REID in various conditions of missions. In case of the fastest round trip (240 days) and the shortest stay on Mars (100 days), its REID would be 3.65%. This REID is still >3% of NASA's PEL.
[Figure 5] illustrates graphically the relationship among dose rate, duration of exposure, and REID.  Figure 5: Relationships among dose rate of 1.84 mSv or o. 64 mSv, duration of exposure in days and radiationexposureinducedcancer death in total body ionizing irradiation in interplanetary space or on Mars surface. Closed circles represent values of REID at different durations of exposure, 100–1000 days in interplanetary space (1.84 mSv) or on Mars surface (0.64 mSv)
Click here to view 
3% radiationexposureinducedcancer death
The Russian Space Agency, European Space Agency and Canadian Space Agency have adopted 1 Sv as the astronaut career exposure limit.^{[20]} NASA proposed 3% REID risk as PEL.^{[26],[27]}
In this study with the mathematical approach and the computer program of [Figure 4], the dose of 391 mSv would correspond to the NASA's PEL of 3%. The REID of 1 Sv is 6.55%.
Lethal doses of LD_{3}, LD_{5}, LD_{10}, LD_{50}, LD_{90,} and LD_{95} of total body irradiation in humans.
[Table 5] and [Figure 6] show the relationship among dose rate of radiation, duration of exposure and lethal dose, LD_{5}, LD_{10}, LD_{50,} LD_{90,} and LD_{95} in total body irradiation in humans.^{[9]} Formulas of LD_{5}, LD_{10}, LD_{50}, LD_{90,} and LD_{95} that express the above relationship are published in the author's previous publication.^{[9]} [Figure 7] illustrates LD_{3} of lethal dose of 3% REID_{.} Each of the 6 lines in both [Figure 6] and [Figure 7] reveals a straight line in exposure to acute low, moderate, and high doses of ionizing radiation in humans.  Table 5: Comparison of formuladerived and animalmodelpredicted lethal radiation doses to humans
Click here to view 
 Figure 6: Relationship among dose of radiation, duration of exposure and lethal radiation dose LD_{5}, LD_{10,}LD_{50}, LD_{90,}and LD_{95}in total body irradiation in humans. The abscissa represents duration of exposure in minutes (log scale). The ordinate represents dose rate in rad/min (log scale). Data points indicate lethal doses of LD_{5,}_{10,}_{50,}_{90,}_{and}_{95}appear to fall on the five formulapredicted straight lines in each group, respectively (see text)
Click here to view 
 Figure 7: Relationship between dose rate and duration of exposure for 3% radiationexposureinducedcancer death, LD_{3}. The zone below the straight line represents radiationexposureinducedcancer death <3% radiationexposureinducedcancer death, and the zone above the line represents radiationexposureinducedcancer death >3% radiationexposureinducedcancer death
Click here to view 
Discussion   
[Table 2], [Table 3], and [Figure 2], [Figure 3] reveal a remarkable agreement between formuladerived and reportedestimated data on solid cancer (P > 0.99) or leukemia (P > 0.995) mortalities after exposure to acute lowdose ionizing radiation in humans. This study is primarily based on the report (2010) of UNSCEAR.^{[16]} The UNSCEAR has been undertaking reviews and evaluations of global and regional exposures to radiation and also evaluates evidence of radiationinduced health effects including cancers and deaths in exposed groups, including survivors of the atomic bombings in Japan. The UNSCEAR provides international standards for the protection of the general public and workers against ionizing radiation.^{[16]}
A quantitative doseresponse relationship in lethal ionizing radiation exposure in humans is not known.^{[1]} Several investigators have derived hypothetical doseresponse curve based on experiences with reactor accidents and the atomic exposure in Japan. From these observations, LD_{50} for humans exposed to single dose of radiation delivered over a period of less than 24 h is believed to be in the range of 2.504.0 Gy.^{[28]} Levin, Young and Stohler ^{[29]} published an estimate of the median lethal dose on humans exposed to total body ionizing radiation and not subsequently treated for the radiation sickness. The median lethal dose was estimated from calculated doses to young adults who were inside two reinforced concrete buildings that remained standing in Nagasaki, Japan, after the atomic detonation. Median dose estimates were calculated using both logarithmic (2.9 Gy) and linear (3.9 Gy) dose scales. Both calculations supported previous estimates of the median lethal dosebased solely on human data, which clustered around 3 Gy. The LD_{50} of 2.9 Gy was surprisingly consistent with estimates made by other researchers; 2.45 Gy by Langham, 2.86 Gy by Lushbaugh et al, 2.652.70 Gy by Bond and Robertson.^{[29]}
Fujita, Kato, and Schull ^{[30]} reported the LD_{50} of 2.32.6 Gy that is noticeably in a good agreement with the value of LD_{50} shown in [Table 5]. There is a remarkable agreement between the formuladerived LD_{50} in [Table 5] and the abovedescribed publishedestimated LD_{50}.^{[28],[29],[30]}
The doseresponse relation in human exposure to ionizing radiation reveals a linear relationship in both high and lowdose rates as shown in [Figure 6] and [Figure 7] if the dose rate and duration of exposure are plotted on a log–log graph paper.
Hematopoietic cells of bone marrow, intestinal tract, and central nervous system are most vulnerable for radiation effects.^{[31],[32],[33]}
It is the current understanding in the studies of the development of cancer after radiation exposure that the process starts by the mutation of one or more genes of the DNA of a single “stemlike” cell in a body organ contributes to cancer development unless affected cells have repaired the DNA. Body responses to radiation exposure reflect status of living body in which physiologic response, repair and regeneration of recovery, pathologic changes, and aging process are concurrently occurring.^{[3],[28],[34],[35],[36]} There is a strong epidemiological evidence that exposure of humans to radiation at moderate and high levels can lead to excess incidence of solid tumors in many organs and of leukemia.^{[23]}
Cucinotta et al. at NASA, Lyndon B. Johnson Space Center, Wyle Laboratory Life Science Group and U. S. R. A. Division of Space Life Sciences reported radiation damages in blood cells (lymphocytes) in the 19 astronauts of the ISS after approximately 6month missions.^{[27]}
Elon Musk, Chief Executive Officer of the rocket company, SpaceX, and the autopilot car company, Tesla, recently published his vision to colonize Mars and save humanity.^{[46]} If it is real and true that a 160day round trip to Mars, a 100day stay on Mars surface and a 1000day stay in the radiationshielded building and/or the underground shelterlike gimme shelter caves with a skylight opening ^{[47]} of Mars,^{[48]} then the REID of the planned space flight to Mars would be 2.86% with dose 371 mSv that is <3% of the NASA's PEL of dose 391 mSv ^{[47]} in the mathematical analysis of this study (see equation 7).
The dose rate of radiation in the radiationshielded building and the underground shelter of Mars is assumed to be 1/50 of the dose rate of Mars surface (1.64/50 = 0.0128). When the abovedescribed advancements in technologies are achieved, space flights to Mars would be safe for astronauts against cosmic ray.
The probacent formula gave a special momentum to the author to develop the hypothesis of the ultronlogotron theory related to mind and matter, consciousness, and quantum physics (Theory of Everything), and further, the possible deeper structure of leptons and quarks on the basis of quantum physics and Confucian philosophy.^{[37],[38]}
It has been recently discovered that electrons split into two separable parts: A spinon (a neutral magnet behaving as a tiny compass needle) and an orbiton carrying its electron motion (negative electrical charge) around the nucleus.^{[38],[40],[41]} The spinon and orbiton seem to correspond to the neutral part of yinand yangultrons composite and the negative part of yinultron as predicted in the ultronlogotron theory, respectively. Yinand yangultrons in a spinon are postulated to line up in a tiny series magnet with a south and a north pole in one direction that can generate spin. This substructure of electron suggests that a quark in a proton is likewise composed of two separable particles, a magnetic (of yinand yangultrons composite), and an electrical particle (of yinor yangultrons).^{[38],[42],[43]}
This study regarding radiation hazards and safety in total body irradiation in humans in a space trip is based on reported data and the mathematical approach and analysis. Further, research would be needed for the verification of the findings and propositions in this study.
Conclusions   
The author published a general formula that predicts mortality probability of solid cancer or leukemia death as a function of lethal dose in acute lowdose total body ionizing irradiation in humans. The formula was constructed by applying the author's general mathematical model of “probacent”probability equation that expresses relationships among intensity of stimulus, duration of exposure, and response in biomedical phenomena. New formulas of tolerance in total body irradiation that expresses the radiationexposureinducedcancer death (REID) as a function of radiation dose rate and duration of exposure in total body ionizing irradiation in humans are constructed. In this study, the new formulas are applied to the measurements of the MSL spacecraft containing the Curiosity rover (2012–2013) to estimate radiation safety for astronauts in a future space flight to Mars. The following findings and conclusions in the author's mathematical approach are proposed:
 New general equations, equation, (4) (5) and (6) that express the REID as a function of lethal dose rate and duration of exposure are constructed from both equations, equations (2) and (3) of the author's previous publication ^{[18]} that predict mortality probabilities of solid cancer death and leukemia death risk in total body irradiation in humans
 Estimates of REID in various circumstances of missions for astronauts in space flights to Mars are calculated and shown in [Table 4]. In case of the fastest round trip (240 days) and the shortest stay on Mars (100 days), its REID would be 3.65%. This REID is still >3% of the NASA's permissible exposure limit (PEL)
 A lethal dose of 391 mSv seems to correspond to the NASA's PEL 3% of REID
 Results of this study suggest that a future space flight to Mars would need increase in propulsion power for a faster speed and a shortened round trip, and increase in protective radiation shielding to reduce radiation dose rate, and a shortened stay on Mars for the astronauts' radiation safety in a future space flight to Mars. When the abovedescribed advancements in technologies are achieved, the space flight to Mars would be safe for astronauts against cosmic ray.
Further research would be needed for verification of the above presentations and propositions.
Acknowledgments
The author is grateful to Dr. C. W. Sheppard for his teaching in computer science and biophysics and his valuable advice and encouragements in my research. I would like to thank Dr. Lester Van Middlesworth for his outstanding research on radiation and thyroid, and for his teaching and advice in my researchrelated to thyroid physiology, using ^{131} I radioisotope at the Department of Physiology and Biophysics, the University of Tennessee.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Cerveny TJ, MacVittie TJ, Young RW. Acute radiation syndrome in humans. In: Walker RJ, Cerveny TJ, editors. Medical Consequences in Nuclear Warfare. Falls Church, Virginia: TMM Publications, Office of the Surgeon General; 1989. p. 1536. 
2.  Jones TJ, Morris MD, Wells SM, Young RW. Animal Mortality Resulting from Uniform Exposures to Photon Radiation: Calculated LD50 and a Compilation of Experimental Data. Oak Ridge, Tennessee: Oak Ridge National Laboratory; 1986. 
3.  Sacher GA. On the relation of radiation lethality to radiation injury and its relevance for the prediction problem. 19 ^{th} International Congress of Radiation, 2330 July, 1959. Berlin: Georg Thieme Verlag;1960. p. 122332. 
4.  Travis EL, Peters LJ, McNeill J, Thames HD Jr., Karolis C. Effect of doserate on total body irradiation: Lethality and pathologic findings. Radiother Oncol 1985;4:34151. 
5.  Chung SJ. Studies on a mathematical relationship between stress and response in biological phenomena. J Natl Acad Sci Rep Korea 1960;2:11562. 
6.  Chung SJ. Computerassisted predictive mathematical relationship among Metrazol dose and time and mortality in mics. Comput Methods Programs Biomed 1986;22:27584. 
7.  Chung SJ. Computerassisted predictive formulas expressing survival probability and life expectancy in US adults, men and women, 2001. Comput Methods Programs Biomed 2007;86:197209. 
8.  Chung SJ. Mathematical relationship of “probacent”probability equation among exogenous stressor, stress and response in biological phenomena. Int J Educ Res 2013;1:132. 
9.  Chung SJ. Predictive formulas expressing relationship among dose rate, duration of exposure and mortality probability in total body irradiation in humans. J Biomed Sci Eng 2011;4:497505. 
10.  Chung SJ. Computerassisted predictive mathematical relationship among plasma acetaminophen concentration and time after ingestion and occurrence of hepatotoxicity in man. Comput Methods Programs Biomed 1989;28:3743. 
11.  Chung SJ. Formulas predicting survival in patients with heart transplantation. Int J Biomed Comput 1993;32:21121. 
12.  Chung SJ. Formula expressing a relationship among lesion thickness and time after diagnosis and survival probability in patients with malignant melanoma. Int J Biomed Comput 1994;37:17180. 
13.  Chung SJ. Formulas predicting carboxyhemoglobin resulting from carbon monoxide exposure. Vet Hum Toxicol 1988;30:52832. 
14.  Chung SJ. Formulas expressing relationship among age, height and weight, and percentile in Saudi and US children aged 616 years. Int J Biomed Comput 1994;37:25972. 
15.  Mehta SC, Joshi HC. Model based estimates of survival/death rates: An input for radiation risk evaluation in Indian context. Indian J Nucl Med 2004;19:168. 
16.  
17.  Wall BF, Kendall GM, Edwards AA, Bouffler S, Muirhead CR, Meara JR, et al. What are the risks from medical Xrays and other low dose radiation? Br J Radiol 2006;79:28594. 
18.  Chung SJ. Computerassisted formulas predicting cancer mortality risk after exposure to acute low dose ionizing radiation in humans. J Biomed Sci Eng 2012;5:17685. 
19.  Chung SJ. Comparison of mathematical equations applicable to tolerance of total body irradiation in humans and decay of isotopes, uranium and thorium: Differences and similarity. J Biomed Sci Eng 2017;10:27386. 
20.  Zeitlin C, Hassler DM, Cucinotta FA, Ehresmann B, WimmerSchweingruber RF, Brinza DE, et al. Measurements of energetic particle radiation in transit to mars on the mars science laboratory. Science 2013;340:10804. 
21.  Hassler DM, Zeitlin C, WimmerSchweingruber RF, Ehresmann B, Rafkin S, Eigenbrode JL, et al. Mars' surface radiation environment measured with the mars science laboratory's curiosity rover. Science 2014;343:1244797. 
22.  
23.  Cucinotta FA, Durante M. Cancer risk from exposure to galactic cosmic rays: Implications for space exploration by human beings. Lancet Oncol 2006;7:4315. 
24.  Hastings C Jr. Approximation for Digital Computer. Princeton MJ: Princeton University Press; 1955. p. 185. 
25.  
26.  
27.  Cucinotta FA, Kim MH, Willingham V, George KA. Physical and biological organ dosimetry analysis for international space station astronauts. Radiat Res 2008;170:12738. 
28.  Damjanov I, Linda J. Anderson's Pathology. 10 ^{th} ed. New York: Mosby; 1996. 
29.  Levin SG, Young RW, Stohler RL. Estimation of median human lethal radiation dose computed from data on occupants of reinforced concrete structures in Nagasaki, Japan. Health Phys 1992;63:52231. 
30.  Fujita S, Kato H, Schull WJ. The LD50 associated with exposure to the atomic bombing of Hiroshima. J Radiat Res 1989;30:35981. 
31.  Warren S. The Pathology of Ionizing Radiation. Springfield: Charles C Thomas Publisher; 1961. 
32.  Komarova EA, Kondratov RV, Wang K, Christov K, Golovkina TV, Goldblum JR, et al. Dual effect of p53 on radiation sensitivity in vivo: P53 promotes hematopoietic injury, but protects from gastrointestinal syndrome in mice. Oncogene 2004;23:326571. 
33.  Cui YZ, Hisha H, Yang GX, Fan TX, Jin T, Li Q, et al. Optimal protocol for total body irradiation for allogeneic bone marrow transplantation in mice. Bone Marrow Transplant 2002;30:8439. 
34.  Abrahamson S, Bender MA, Becker RB, Gilbert ES, Scott BR. Health Effect Models for Nuclear Power Plant Accident Consequence Analysis. Washington DC: US Government Printing Office; 1993. 
35.  
36.  Heligman I, Pollard JH. The age pattern of mortality. J InstActuar 1980;107:4980. 
37.  Chung SJ. Parallels between Confucian philosophy and quantum physics. Open J Philos 2014;4:192206. 
38.  Chung SJ. On the possible structure of leptons and quarks: A review of the “ultron””logotron” theory. Open J Philos 2015;5:30214. 
39.  Palus S. Electrons 'Split' in New Form of Matter. Discover. Oak Ridge, TN: Oak Ridge National Laboratory; 2017. p. 27. 
40.  Piazza BD, Mourigal M, Christensen NB, Nilsen GJ, TregennaPiggott P, Perring TG, et al. Fractional excitations in the square lattice quantum antiferromagnet. Nat Phys 2015;11:628. 
41.  
42.  Chung SJ. A review of the ultronlogotron theory: Consciousness and quantum physics. Int J Humanit Soc Sci 2017;7:1532. 
43.  
44.  
45.  
46.  
47.  Haynes K. Surviving Space: The Solution, Gimme Shelter. Discover. Waukesha, Wisconsin: Kalmbach Publishing Co; 2017. p. 72. 
48.  
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
