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This article proposes chance-constrained formulations for the calibration of computational models given data subject to uncertainty. The uncertainty might be caused by a poor metrology system, measurement noise, model-form uncertainty or by the inability to directly measure the inputs and/or outputs of the model. The formulations developed, called Forward Maximum Likelihood and Inverse Maximum Likelihood, are applicable to datasets with and without uncertainty. The forward approach performs the calibration in the space of the model’s output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model’s parameters. The potential loss of performance incurred by this approach is often justified by a sizable reduction in computational cost. The ideas proposed are applied to the calibration of a radiation quality model used by NASA to assess cancer risk in future deep space missions. We calibrate several models in order to evaluate the extent by which data uncertainty, outliers, and the commonly made assumption of parameter independence cause conservatism in the resulting model prediction.

Ionizing radiation causes chromosome aberrations, which are possible biomarkers to assess space radiation cancer risks. Using the Monte Carlo codes Relativistic Ion Tracks (RITRACKS) and Radiation-Induced Tracks, Chromosome Aberrations, Repair and Damage (RITCARD), we investigated how geometrical properties of the cell nucleus, irradiated with ion beams of linear energy transfer (LET) ranging from 0.22 keV/μm to 195 keV/μm, influence the yield of simple and complex exchanges. We focused on the effect of (1) nuclear volume by considering spherical nuclei of varying radii; (2) nuclear shape by considering ellipsoidal nuclei of varying thicknesses; (3) beam orientation; and (4) chromosome intermingling by constraining or not constraining chromosomes in non-overlapping domains. In general, small nuclear volumes yield a higher number of complex exchanges, as compared to larger nuclear volumes, and a higher number of simple exchanges for LET < 40 keV/μm. Nuclear flattening reduces complex exchanges for high-LET beams when irradiated along the flattened axis. The beam orientation also affects yields for ellipsoidal nuclei. Reducing chromosome intermingling decreases both simple and complex exchanges. Our results suggest that the beam orientation, the geometry of the cell nucleus, and the organization of the chromosomes within are important parameters for the formation of aberrations that must be considered to model and translate in vitro results to in vivo risks.

Transport codes used for space radiation protection require accurate nuclear fragmentation cross sections as input. The fragmentation process is modeled in two stages: a fast step, called abrasion or knockout, and a slower step, called evaporation or ablation. In this work, the ablation step is calculated via Monte Carlo (MC) methods using the recently modified legacy EVAporation (EVA) code. The code is based on the Weisskopf-Ewing particle emission formalism and has been extensively overhauled and modernized. Updates include a new nuclear mass table and modifications to the nuclear level density expression. The new formulation enables calculated results to exhibit the odd-even effect observed in experimental measurements. The revised ablation code, EVAporation-University of Tennessee, Knoxville (EVA-UTK), has been coupled with the quantum multiple scattering abrasion formalism incorporated in the nuclear fragmentation code, Optical PoTential FRAGmentation (OPTFRAG), and resulted in substantial improvements in agreement between fragmentation cross section estimates and experimental measurements.

To understand the biological effects of radiation, it is important to determine how ionizing radiation deposits energy in micrometric targets. The energy deposited in a target located in an irradiated tissue is a function of several factors such as the radiation type and the irradiated volume size. We simulated the energy deposited by energetic ions in spherical targets of 1, 2, 4, and 8 µm radii encompassed in irradiated parallelepiped volumes of various sizes using the stochastic radiation track structure code Relativistic Ion Tracks (RITRACKS). Because cells are usually part of a tissue when they are irradiated, electrons originating from radiation tracks in neighboring volumes also contribute to energy deposition in the target. To account for this contribution, we used periodic boundary conditions in the simulations. We found that the single-ion spectra of energy deposition in targets comprises two components: the direct ion hits to the targets, which is identical in all irradiation conditions, and the contribution of hits from electrons from neighboring volumes, which depends on the irradiated volume. We also calculated an analytical expression of the indirect hit contributions using the local effect model, which showed results similar to those obtained with RITRACKS.

The complex and inaccessible space radiation environment poses an unresolved risk to astronaut cardiovascular health during long-term space exploration missions. To model this risk, healthy male c57BL/6 mice aged six months (corresponding to an astronaut of 34 years) were exposed to simplified galactic cosmic ray (GCR

The space radiation environment is qualitatively different from Earth, and its radiation hazard is generally quantified relative to photons using quality factors that allow assessment of biologically-effective dose. Two approaches exist for estimating radiation quality factors in complex radiation environments: One is a fluence-based risk cross-section approach, which requires very detailed in silico characterization of the radiation field and biological cross sections, and thus cannot realistically be used for in situ monitoring. By contrast, the microdosimetric approach, using measured (or calculated) distributions of microdosimetric energy deposition together with empirical biological weighting functions, is conceptually and practically simpler. To demonstrate feasibility of the microdosimetric approach, we estimated a biological weighting function for one specific endpoint, heavy-ion-induced tumorigenesis in APC1638N/+ mice, which was unfolded from experimental results after a variety of heavy ion exposures together with corresponding calculated heavy-ion microdosimetric energy deposition spectra. Separate biological weighting functions were unfolded for targeted and non-targeted effects, and these differed substantially. We folded these biological weighting functions with microdosimetric energy deposition spectra for different space radiation environments, and conclude that the microdosimetric approach is indeed practical and, in conjunction with in-situ measurements of microdosimetric spectra, can allow continuous readout of biologically-effective dose during space flight.

I.AbstractA new approach to NASA space radiation risk modeling has successfully extended the current NASA probabilistic cancer risk model to an ensemble framework able to consider sub-model parameter uncertainty as well as model-form uncertainty associated with differing theoretical or empirical formalisms. Ensemble methodologies are already widely used in weather prediction, modeling of infectious disease outbreaks, and certain terrestrial radiation protection applications to better understand how uncertainty may influence risk decision-making. Applying ensemble methodologies to space radiation risk projections offers the potential to efficiently incorporate emerging research results, allow for the incorporation of future models, improve uncertainty quantification for underlying sub-models, and reduce the impact of subjective bias on risk projections. Moreover, risk forecasting across an ensemble of multiple predictive models can provide stakeholders additional information on risk acceptance if current health/medical standards cannot be met for future space exploration missions, such as human missions to Mars. In this work, ensemble risk projections implementing multiple sub-models of radiation quality, dose and dose-rate effectiveness factors, excess risk, and latency as ensemble members are presented. Initial consensus methods for ensemble model weights and correlations to account for individual model bias are discussed. In these analyses, the ensemble forecast compares well to results from NASA’s current operational cancer risk projection model used to assess permissible mission durations for astronauts. However, a large range of projected risk values are obtained at the upper 95th confidence level where models must extrapolate beyond available biological data sets. Closer agreement is seen at the median + one sigma due to the inherent similarities in available models. Identification of potential new models, epidemiological data, and methods for statistical correlation between predictive ensemble members are discussed. Alternate ways of communicating risk and acceptable uncertainty with respect to NASA’s current permissible exposure limits are explored.

With exciting new NASA plans for a sustainable return to the moon, astronauts will once again leave Earth’s protective magnetosphere only to endure higher levels of radiation from galactic cosmic radiation (GCR) and the possibility of a large solar particle event (SPE). Gateway, lunar landers, and surface habitats will be designed to protect crew against SPEs with vehicle optimization, storm shelter concepts, and/or active dosimetry; however, the ever penetrating GCR will continue to pose the most significant health risks especially as lunar missions increase in duration and as NASA sets its aspirations on Mars. The primary risks of concern include carcinogenesis, central nervous system (CNS) effects resulting in potential in-mission cognitive or behavioral impairment and/or late neurological disorders, degenerative tissue effects including circulatory and heart disease, as well as potential immune system decrements impacting multiple aspects of crew health. Characterization and mitigation of these risks requires a significant reduction in the large biological uncertainties of chronic (low-dose rate) heavy-ion exposures and the validation of countermeasures in a relevant space environment. Historically, most research on understanding space radiation-induced health risks has been performed using acute exposures of monoenergetic single-ion beams. However, the space radiation environment consists of a wide variety of ion species over a broad energy range. Using the fast beam switching and controls systems technology recently developed at the NASA Space Radiation Laboratory (NSRL) at Brookhaven National Laboratory, a new era in radiobiological research is possible. NASA has developed the “GCR Simulator” to generate a spectrum of ion beams that approximates the primary and secondary GCR field experienced at human organ locations within a deep-space vehicle. The majority of the dose is delivered from protons (approximately 65%–75%) and helium ions (approximately 10%–20%) with heavier ions (Z ≥ 3) contributing the remainder. The GCR simulator exposes state-of-the art cellular and animal model systems to 33 sequential beams including 4 proton energies plus degrader, 4 helium energies plus degrader, and the 5 heavy ions of C, O, Si, Ti, and Fe. A polyethylene degrader system is used with the 100 MeV/n H and He beams to provide a nearly continuous distribution of low-energy particles. A 500 mGy exposure, delivering doses from each of the 33 beams, requires approximately 75 minutes. To more closely simulate the low-dose rates found in space, sequential field exposures can be divided into daily fractions over 2 to 6 weeks, with individual beam fractions as low as 0.1 to 0.2 mGy. In the large beam configuration (60 × 60 cm2), 54 special housing cages can accommodate 2 to 3 mice each for an approximately 75 min duration or 15 individually housed rats. On June 15, 2018, the NSRL made a significant achievement by completing the first operational run using the new GCR simulator. This paper discusses NASA’s innovative technology solution for a ground-based GCR simulator at the NSRL to accelerate our understanding and mitigation of health risks faced by astronauts. Ultimately, the GCR simulator will require validation across multiple radiogenic risks, endpoints, doses, and dose rates., This study describes how NASA’s new earth-based galactic cosmic ray simulator is being used to accelerate our understanding of the effects of space radiation exposure on astronauts and to validate countermeasures for exploration missions. For the first time, research teams can study mixed field ion and dose rate effects in a simulated space environment.

Prolonged exposure to the galactic cosmic ray (GCR) environment is a potentially limiting factor for manned missions in deep space. Evaluating the risk associated with the expected GCR environment is an essential step in planning a deep space mission. This requires an understanding of how the local interstellar spectrum is modulated by the heliospheric magnetic field (HMF) and how observed solar activity is manifested in the HMF over time. While current GCR models agree reasonably well with measured observations of GCR flux on the first matter, they must rely on imperfect or loose correlations to describe the latter. It is more accurate to use dose rates directly measured by instruments in deep space to quantify the GCR condition for a given period of time. In this work, dose rates observed by the Cosmic Ray Telescope for the Effects of Radiation (CRaTER) instrument are used to obtain the local GCR intensity and composition as a function of time. A response function is constructed that relates observed dose rates to solar modulation potential using a series of Monte Carlo radiation transport calculations. The record of observed solar modulation potential vs. time is then used to calculate a recent historical record of permissible mission duration (PMD) according to NASA's permissible exposure limits (PEL). Tables are provided for extreme values of PMD. Additional tables include risk of exposure-induced death (at upper 95% confidence interval) accrual rates and NASA effective dose rates as a function of solar modulation potential, astronaut age, sex, and shielding thickness. The significance of the PMD values reported in relation to likely transit duration requirements for future exploration missions is discussed. There is general agreement between CRaTER observations and the prescription of solar modulation vs. time given by the Badhwar-O'Neill 2014 GCR model. However, CRaTER observations do capture the effects of significant heliospheric transients, among other features, that are missing from the prescription of solar modulation potential vs. time.

Background: Radiation induces DNA double-strand breaks (DSBs), and chromosome aberrations (CA) form during the DSBs repair process. Several methods have been used to model the repair kinetics of DSBs including the bi-exponential model, i.e., N(t) = N1exp(&minus, t/&tau, 1) + N2exp(&minus, 2), where N(t) is the number of breaks at time t, and N1, N2, &tau, 1 and &tau, 2 are parameters. This bi-exponential fit for DSB decay suggests that some breaks are repaired rapidly and other, more complex breaks, take longer to repair. Methods: The bi-exponential repair kinetics model is implemented into a recent simulation code called RITCARD (Radiation Induced Tracks, Chromosome Aberrations, Repair, and Damage). RITCARD simulates the geometric configuration of human chromosomes, radiation-induced breaks, their repair, and the creation of various categories of CAs. The bi-exponential repair relies on a computational algorithm that is shown to be mathematically exact. To categorize breaks as complex or simple, a threshold for the local (voxel) dose was used. Results: The main findings are: i) the curves for the kinetics of restitution of DSBs are mostly independent of dose, ii) the fraction of unrepaired breaks increases with the linear energy transfer (LET) of the incident radiation, iii) the simulated dose&ndash, response curves for simple reciprocal chromosome exchanges that are linear-quadratic, iv) the alpha coefficient of the dose&ndash, response curve peaks at about 100 keV/&micro, m.

The energetic particle environment on the Martian surface is influenced by solar and heliospheric modulation and changes in the local atmospheric pressure (or column depth). The Radiation Assessment Detector (RAD) on board the Mars Science Laboratory rover Curiosity on the surface of Mars has been measuring this effect for over four Earth years (about two Martian years). The anticorrelation between the recorded surface Galactic Cosmic Ray-induced dose rates and pressure changes has been investigated by Rafkin et al. (2014) and the long-term solar modulation has also been empirically analyzed and modeled by Guo et al. (2015). This paper employs the newly updated HZETRN2015 code to model the Martian atmospheric shielding effect on the accumulated dose rates and the change of this effect under different solar modulation and atmospheric conditions. The modeled results are compared with the most up-to-date (from 14 August 2012 to 29 June 2016) observations of the RAD instrument on the surface of Mars. Both model and measurements agree reasonably well and show the atmospheric shielding effect under weak solar modulation conditions and the decline of this effect as solar modulation becomes stronger. This result is important for better risk estimations of future human explorations to Mars under different heliospheric and Martian atmospheric conditions.

Galactic cosmic rays enter Earth's atmosphere after interacting with the geomagnetic field. The primary galactic cosmic rays spectrum is fundamentally changed as it interacts with Earth's atmosphere through nuclear and atomic interactions. At points deeper in the atmosphere, such as at airline altitudes, the radiation environment is a combination of the primary galactic cosmic rays and the secondary particles produced through nuclear interactions. The RaD-X balloon experiment measured the atmospheric radiation environment above 20 km during 2 days in September 2015. These experimental measurements were used to validate and quantify uncertainty in physics-based models used to calculate exposure levels for commercial aviation. In this paper, the Badhwar-O'Neill 2014, the International Organization for Standardization 15390, and the German Aerospace Company galactic cosmic ray environment models are used as input into the same radiation transport code to predict and compare dosimetric quantities to RaD-X measurements. In general, the various model results match the measured tissue equivalent dose well, with results generated by the German Aerospace Center galactic cosmic ray environment model providing the best comparison. For dose equivalent and dose measured in silicon, however, the models were compared less favorably to the measurements.

Accurate galactic cosmic ray (GCR) models are required to assess crew exposure during long-duration missions to the Moon or Mars. Many of these models have been developed and compared to available measurements, with uncertainty estimates usually stated to be less than 15%. However, when the models are evaluated over a common epoch and propagated through to effective dose, relative differences exceeding 50% are observed. This indicates that the metrics used to communicate GCR model uncertainty can be better tied to exposure quantities of interest for shielding applications. This is the first of three papers focused on addressing this need. In this work, the focus is on quantifying the extent to which each GCR ion and energy group, prior to entering any shielding material or body tissue, contributes to effective dose behind shielding. Results can be used to more accurately calibrate model-free parameters and provide a mechanism for refocusing validation efforts on measurements taken over important energy regions. Results can also be used as references to guide future nuclear cross-section measurements and radiobiology experiments. It is found that GCR with Z>2 and boundary energies below 500 MeV/n induce less than 5% of the total effective dose behind shielding. This finding is important given that most of the GCR models are developed and validated against Advanced Composition Explorer/Cosmic Ray Isotope Spectrometer (ACE/CRIS) measurements taken below 500 MeV/n. It is therefore possible for two models to very accurately reproduce the ACE/CRIS data while inducing very different effective dose values behind shielding.

This is the last of three papers focused on quantifying the uncertainty associated with galactic cosmic rays (GCR) models used for space radiation shielding applications. In the first paper, it was found that GCR ions with Z>2 and boundary energy below 500 MeV/nucleon induce less than 5% of the total effective dose behind shielding. This is an important finding since GCR model development and validation have been heavily biased toward Advanced Composition Explorer/Cosmic Ray Isotope Spectrometer measurements below 500 MeV/nucleon. Weights were also developed that quantify the relative contribution of defined GCR energy and charge groups to effective dose behind shielding. In the second paper, it was shown that these weights could be used to efficiently propagate GCR model uncertainties into effective dose behind shielding. In this work, uncertainties are quantified for a few commonly used GCR models. A validation metric is developed that accounts for measurements uncertainty, and the metric is coupled to the fast uncertainty propagation method. For this work, the Badhwar-O'Neill (BON) 2010 and 2011 and the Matthia GCR models are compared to an extensive measurement database. It is shown that BON2011 systematically overestimates heavy ion fluxes in the range 0.5-4 GeV/nucleon. The BON2010 and BON2011 also show moderate and large errors in reproducing past solar activity near the 2000 solar maximum and 2010 solar minimum. It is found that all three models induce relative errors in effective dose in the interval [-20%, 20%] at a 68% confidence level. The BON2010 and Matthia models are found to have similar overall uncertainty estimates and are preferred for space radiation shielding applications.

In order to assess the astronaut exposure received within vehicles or habitats, accurate models of the ambient galactic cosmic ray (GCR) environment are required. Many models have been developed and compared to measurements, with uncertainty estimates often stated to be within 15%. However, intercode comparisons can lead to differences in effective dose exceeding 50%. This is the second of three papers focused on resolving this discrepancy. The first paper showed that GCR heavy ions with boundary energies below 500 MeV/n induce less than 5% of the total effective dose behind shielding. Yet, due to limitations on available data, model development and validation are heavily influenced by comparisons to measurements taken below 500 MeV/n. In the current work, the focus is on developing an efficient method for propagating uncertainties in the ambient GCR environment to effective dose values behind shielding. A simple approach utilizing sensitivity results from the first paper is described and shown to be equivalent to a computationally expensive Monte Carlo uncertainty propagation. The simple approach allows a full uncertainty propagation to be performed once GCR uncertainty distributions are established. This rapid analysis capability may be integrated into broader probabilistic radiation shielding analysis and also allows error bars (representing boundary condition uncertainty) to be placed around point estimates of effective dose.

Chromosome aberrations (CAs) are one of the effects of radiation exposure and can have implications for human health in the space environment, since they are related to cancer risk. In radiation research, chromosome aberrations are a convenient biomarker for carcinogenesis. To shed light on the formation and quality of chromosome aberrations in the space environment, many experiments and simulations have been performed using chromosome aberrations in human cells, induced by heavy ions, which are present in galactic cosmic rays (GCRs). In this work, the new simulation program, radiation-induced tracks, chromosome aberrations, repair and damage (RITCARD), is presented. This software program is based on the algorithm used in the NASA Radiation Track Image (NASARTI) model with some improvements. NASARTI and RITCARD are both comprised of four parts: a random walk (RW) algorithm for simulating chromosomes in a nucleus; a deoxyribonucleic acid (DNA) damage algorithm; a break repair process; and a function to assess and count chromosome aberrations. Prior to running RITCARD, the code, relativistic ion tracks (RITRACKS), is used to simulate detailed radiation track structure and calculate time-dependent differential voxel dose maps in a parallelepiped centered on a cell nucleus. The RITCARD program reads the pre-calculated voxel dose and locates the intersections between the voxels and the chromosomes that were simulated by random walk. Radiation-induced breaks occur strictly at these intersections with a probability that is a function of the voxel dose. When a break occurs in the random walk, the corresponding chromosome piece is cut into two fragments where each has a free end at the position of the break. RITCARD generates a collection of all fragments, free ends, and enlists free end pairs. In the next step, the algorithm simulates the time-dependent rejoining of free end pairs, using different probabilities for pairs originating from a given break (proper) or from different breaks (improper), which results in the formation of fragment sequences. By grouping these sequences, the program determines the number and types of aberrations, based on the same criteria used in our experiment. The new program is used to assess the yields of various types of chromosome aberrations in human fibroblast cells for several ions (1H+, 4He2+, 12C6+, 16O8+, 20Ne10+, 28Si14+, 48Ti22+ and 56Fe26+) with energies varying from 10 to 1,000 MeV/n. The results show linear and linear-quadratic dose dependence for most chromosome aberrations types. The calculation results were compared with those obtained by fluorescence in situ hybridization (FISH) experiments that were performed by our group. The simulations and experiments are in better agreement at lower LET. Regarding the simulation results, the coefficient of the linear part of the dose-dependence curve also peaks at an LET value of approximately 100 keV/lm, which evokes a relative biological effectiveness (RBE) peak found by other researchers.

Recent work has indicated that pion production and the associated electromagnetic (EM) cascade may be an important contribution to the total astronaut exposure in space. Recent extensions to the deterministic space radiation transport code, HZETRN, allow the production and transport of pions, muons, electrons, positrons, and photons. In this paper, the extended code is compared to the Monte Carlo codes, Geant4, PHITS, and FLUKA, in slab geometries exposed to galactic cosmic ray (GCR) boundary conditions. While improvements in the HZETRN transport formalism for the new particles are needed, it is shown that reasonable agreement on dose is found at larger shielding thicknesses commonly found on the International Space Station (ISS). Finally, the extended code is compared to ISS data on a minute-by-minute basis over a seven day period in 2001. The impact of pion/EM production on exposure estimates and validation results is clearly shown. The Badhwar–O’Neill (BO) 2004 and 2010 models are used to generate the GCR boundary condition at each time-step allowing the impact of environmental model improvements on validation results to be quantified as well. It is found that the updated BO2010 model noticeably reduces overall exposure estimates from the BO2004 model, and the additional production mechanisms in HZETRN provide some compensation. It is shown that the overestimates provided by the BO2004 GCR model in previous validation studies led to deflated uncertainty estimates for environmental, physics, and transport models, and allowed an important physical interaction (π/EM) to be overlooked in model development. Despite the additional π/EM production mechanisms in HZETRN, a systematic under-prediction of total dose is observed in comparison to Monte Carlo results and measured data.

Safe and efficient mission operations in space require an accurate understanding of the physical interactions of space radiation. As the primary space radiation interacts with intervening materials, the composition and spectrum of the radiation environment changes. The production of secondary particles can make a significant contribution to radiation exposure. In this work, the NASA space radiation transport code, HZETRN, is extended to include the transport of electrons, positrons, and photons. The production of these particles is coupled to the initial cosmic ray radiation environment through the decay of neutral pions, which produce high energy photons, and through the decay of muons, which produce electrons and positrons. The photons, electrons, and positrons interact with materials producing more photons, electrons and positrons generating an electromagnetic cascade. The relevant cross sections, transport equation, and solution method are introduced. Electron and positron production in Earth’s atmosphere is investigated and compared to experimental balloon-flight measurements. Reasonable agreement is seen between HZETRN and data.

There is growing interest in flying biological experiments beyond low-Earth orbit (LEO) to measure biological responses potentially relevant to those expected during a human mission to Mars. Such experiments could be payloads onboard precursor missions, including unmanned private-public partnerships, as well as small low-cost spacecraft (satellites) designed specifically for biosentinel-type missions. It is the purpose of this paper to provide physical cosmic-ray interaction data and related information useful to biologists who may be planning such experiments. It is not the objective here to actually design such experiments or provide radiobiological response functions, which would be specific for each experiment and biological endpoint. Nuclide-specific flux and dose rates were calculated using OLTARIS and these results were used to determine particle traversal rates and doses in hypothetical biological targets. Comparisons are provided between GCR in interplanetary space and inside the ISS. Calculated probabilistic estimates of dose from solar particle events are also presented. Although the focus here is on biological experiments, the information provided may be useful for designing other payloads as well if the space radiation environment is a factor to be considered.

In March 2016 accelerator-based experiments colliding protons (0.4 and 0.8 GeV), helium (0.4 AGeV) and iron (0.4 and 0.8 AGeV) on thick aluminum targets with surface densities of 20, 40, and 60 g/cm2 were performed at the National Aeronautics and Space Administration Space Radiation Laboratory (NSRL) at Brookhaven National Laboratory. Two targets were utilized in each experimental configuration. Hydrogen and helium ions were detected using organic liquid scintillators in conjunction with thin plastic scintillators at 10°, 30°, 45°, 60°, 80°, and 135° from beam axis. Time-of-flight techniques and pulse shape discrimination were used to identify light ion species in order to generate double differential energy spectra of the light ion fragments. Comparisons of these measured yields were compared with Monte Carlo calculations generated by MCNP6. These yields will be used to quantify uncertainty in radiation transport codes utilized in risk assessment for spaceflight missions with prolonged exposures to galactic cosmic rays.

The Badhwar-O'Neill (BON) Galactic Cosmic Ray (GCR) flux model has been used by NASA to certify microelectronic systems and in the analysis of radiation health risks for human space flight missions. Of special interest to NASA is the kinetic energy region below 4.0 GeV/n due to the fact that exposure from GCR behind shielding (e.g., inside a space vehicle) is heavily influenced by the GCR particles from this energy domain. The BON model numerically solves the Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration under the assumption of a spherically symmetric heliosphere. The model utilizes a comprehensive database of GCR measurements from various particle detectors to determine boundary conditions. By using an updated GCR database and improved model fit parameters, the new BON model (BON14) is significantly improved over the previous BON models for describing the GCR radiation environment of interest to human space flight.

During the design process, the configuration of space vehicles and habitats changes frequently and the merits of design changes must be evaluated. Methods for rapidly assessing astronaut exposure are therefore required. Typically, approximations are made to simplify the geometry and speed-up the evaluation of each design. In this work, the error associated with two common approximations used to simplify space radiation vehicle analyses, scaling into equivalent materials and material reordering, are investigated. Over thirty materials commonly found in spacesuits, vehicles, and human bodies are considered. Each material is placed in a material group (aluminum, polyethylene, or tissue), and the error associated with scaling and reordering was quantified for each material. Of the scaling methods investigated, range scaling is shown to be the superior method, especially for shields less than 30 g/cm2 exposed to a solar particle event. More complicated, realistic slabs are examined to quantify the separate and combined effects of using equivalent materials and reordering. The error associated with material reordering is shown to be at least comparable to, if not greater than, the error associated with range scaling. In general, scaling and reordering errors were found to grow with the difference between the average nuclear charge of the actual material and average nuclear charge of the equivalent material. Based on this result, a different set of equivalent materials (titanium, aluminum, and tissue) are substituted for the commonly used aluminum, polyethylene, and tissue. The realistic cases are scaled and reordered using the new equivalent materials, and the reduced error is shown.

The On-Line Tool for the Assessment of Radiation In Space (OLTARIS) is a World Wide Web based tool that assesses the effects of space radiation to humans in items such as spacecraft, habitats, rovers, and spacesuits. This document explains the basis behind the interface and framework used to input the data, perform the assessment, and output the results to the user as well as the physics, engineering, and computer science used to develop OLTARIS. The physics is based on the HZETRN2005 and NUCFRG2 research codes. The OLTARIS website is the successor to the SIREST website from the early 2000 s. Modifications have been made to the code to enable easy maintenance, additions, and configuration management along with a more modern web interface. Over all, the code has been verified, tested, and modified to enable faster and more accurate assessments. The next major areas of modification are more accurate transport algorithms, better uncertainty estimates, and electronic response functions. Improvements in the existing algorithms and data occur continuously and are logged in the change log section of the website.

The protection of astronauts and instrumentation from galactic cosmic rays and solar particle events is one of the primary constraints associated with mission planning in low earth orbit or deep space. To help satisfy this constraint, several computational tools have been developed to analyze the effectiveness of various shielding materials and structures exposed to space radiation. These tools are now being carefully scrutinized through a systematic effort of verification, validation, and uncertainty quantification. In this benchmark study, the deterministic transport code HZETRN is compared to the Monte Carlo transport codes HETC-HEDS and FLUKA for a 30 g/cm 2 water target protected by a 20 g/cm 2 aluminum shield exposed to a parameterization of the February 1956 solar particle event. Neutron and proton fluences as well as dose and dose equivalent are compared at various depths in the water target. The regions of agreement and disagreement between the three codes are quantified and discussed, and recommendations for future work are given.

The HZETRN deterministic radiation code is one of several tools developed to analyze the effects of harmful galactic cosmic rays (GCR) and solar particle events on mission planning and shielding for astronauts and instrumentation. This paper is a comparison study involving the two Monte Carlo transport codes, HETC–HEDS and FLUKA and the deterministic transport code, HZETRN. Each code is used to transport an ion from the 1977 solar minimum GCR spectrum impinging upon a 20 g/cm 2 aluminum slab followed by a 30 g/cm 2 water slab. This research is part of a systematic effort of verification and validation to quantify the accuracy of HZETRN and determine areas where it can be improved. Comparisons of dose and dose equivalent values at various depths in the water slab are presented in this report. This is followed by a comparison of the proton and forward, backward and total neutron flux at various depths in the water slab. Comparisons of the secondary light ion 2 H, 3 H, 3 He and 4 He fluxes are also examined.

The deterministic transport code HZETRN was developed for research scientists and design engineers studying the effects of space radiation on astronauts and instrumentation protected by various shielding materials and structures. In this work, several aspects of code verification are examined. First, a detailed derivation of the light particle (A= 4) numerical marching algorithms used in HZETRN is given. References are given for components of the derivation that already exist in the literature, and discussions are given for details that may have been absent in the past. The present paper provides a complete description of the numerical methods currently used in the code and is identified as a key component of the verification process. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of round-off error is also given, and the impact of this error on previously predicted exposure quantities is shown. Finally, a coupled convergence study is conducted by refining the discretization parameters (step-size and energy grid-size). From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is determined that almost all of the discretization error in HZETRN is caused by the use of discretization parameters that violate a numerical convergence criterion related to charged target fragments below 50AMeV. Total discretization errors are given for the old and new algorithms to 100g/cm^2 in aluminum and water, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons between the old and new algorithms are given for one, two, and three layer slabs of 100g/cm^2 of aluminum, polyethylene, and water. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Long term human presence in space requires the inclusion of radiation constraints in mission planning and the design of shielding materials, structures, and vehicles. In this paper, the numerical error associated with energy discretization in HZETRN is addressed. An inadequate numerical integration scheme in the transport algorithm is shown to produce large errors in the low energy portion of the neutron and light ion fluence spectra. It is further shown that the errors result from the narrow energy domain of the neutron elastic cross section spectral distributions, and that an extremely fine energy grid is required to resolve the problem under the current formulation. Two numerical methods are developed to provide adequate resolution in the energy domain and more accurately resolve the neutron elastic interactions. Convergence testing is completed by running the code for various environments and shielding materials with various energy grids to ensure stability of the newly implemented method.

To estimate astronaut health risk due to space radiation, one must have the ability to calculate various exposure-related quantities that are averaged over specific organs and tissue types. Such calculations require computational models of the ambient space radiation environment, particle transport, nuclear and atomic physics, and the human body. While significant efforts have been made to verify, validate, and quantify the uncertainties associated with many of these models and tools, relatively little work has focused on the uncertainties associated with the representation and utilization of the human phantoms. In this study, we first examine the anatomical properties of the Computerized Anatomical Man (CAM), Computerized Anatomical Female (CAF), Male Adult voXel (MAX), and Female Adult voXel (FAX) models by comparing the masses of various model tissues used to calculate effective dose to the reference values specified by the International Commission on Radiological Protection (ICRP). The MAX and FAX tissue masses are found to be in good agreement with the reference data, while major discrepancies are found between the CAM and CAF tissue masses and the reference data for almost all of the effective dose tissues. We next examine the distribution of target points used with the deterministic transport code HZETRN (High charge ( Z ) and Energy TRaNsport) to compute mass averaged exposure quantities. A numerical algorithm is presented and used to generate multiple point distributions of varying fidelity for many of the effective dose tissues identified in CAM, CAF, MAX, and FAX. The point distributions are used to compute mass averaged dose equivalent values under both a galactic cosmic ray (GCR) and solar particle event (SPE) environment impinging isotropically on three spherical aluminum shells with areal densities of 0.4 g/cm 2 , 2.0 g/cm 2 , and 10.0 g/cm 2 . The dose equivalent values are examined to identify a recommended set of target points for each of the tissues and to further assess the differences between CAM, CAF, MAX, and FAX. It is concluded that the previously published CAM and CAF point distributions were significantly under-sampled and that the set of point distributions presented here should be adequate for future studies involving CAM, CAF, MAX, or FAX. It is also found that the errors associated with the mass and location of certain tissues in CAM and CAF have a significant impact on the mass averaged dose equivalent values, and it is concluded that MAX and FAX are more accurate than CAM and CAF for space radiation analyses.

For the evaluation of organ dose and dose equivalent of astronauts on space shuttle and the International Space Station (ISS) missions, the CAMERA models of CAM (Computerized Anatomical Male) and CAF (Computerized Anatomical Female) of human tissue shielding have been implemented and used in radiation transport model calculations at NASA. One of new human geometry models to meet the “reference person” of International Commission on Radiological Protection (ICRP) is based on detailed Voxel (volumetric and pixel) phantom models denoted for male and female as MAX (Male Adult voXel) and FAX (Female Adult voXel), respectively. We compared the CAM model predictions of organ doses to those of MAX model, since the MAX model represents the male adult body with much higher fidelity than the CAM model currently used at NASA. Directional body-shielding mass was evaluated for over 1500 target points of MAX for specified organs considered to be sensitive to the induction of stochastic effects. Radiation exposures to solar particle event (SPE), trapped protons, and galactic cosmic ray (GCR) were assessed at the specific sites in the MAX phantom by coupling space radiation transport models with the relevant body-shielding mass. The development of multiple-point body-shielding distributions at each organ made it possible to estimate the mean and variance of organ doses at the specific organ. For the estimate of doses to the blood forming organs (BFOs), data on active marrow distributions in adult were used to weight the bone marrow sites over the human body. The discrete number of target points of MAX organs resulted in a reduced organ dose and dose equivalent compared to the results of CAM organs especially for SPE, and should be further investigated. Differences of effective doses between the two approaches were found to be small (

Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light particle transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Most accelerator-based space radiation experiments have been performed with single ion beams at fixed energies. However, the space radiation environment consists of a wide variety of ion species with a continuous range of energies. Due to recent developments in beam switching technology implemented at the NASA Space Radiation Laboratory (NSRL) at Brookhaven National Laboratory (BNL), it is now possible to rapidly switch ion species and energies, allowing for the possibility to more realistically simulate the actual radiation environment found in space. The present paper discusses a variety of issues related to implementation of galactic cosmic ray (GCR) simulation at NSRL, especially for experiments in radiobiology. Advantages and disadvantages of different approaches to developing a GCR simulator are presented. In addition, issues common to both GCR simulation and single beam experiments are compared to issues unique to GCR simulation studies. A set of conclusions is presented as well as a discussion of the technical implementation of GCR simulation.