The radiation environment in space, and on the Moon and the distant planets, is qualitatively and quantitatively very different from that on the Earth’s surface1–3. It consists of mixture of different radiation types and energies that include protons, neutrons and heavy ions. Astronauts are exposed to this complex radiation environment, the components of which can differ dramatically in their relative biological effectiveness2,4,5. For example, densely-ionizing energetic heavy ions and neutrons can have much higher biological effectiveness per unit dose than sparsely-ionizing x or γ rays6,7.
In practice, these increased health risks from exposure to space radiation are quantified using radiation quality factors8,9 or radiation weighting factors10,11, which are effectively multiplicative scaling factors used to characterize the increased health risks of densely ionizing radiations relative to the better quantified x- or γ-ray risks. For example, at low radiation doses, the radiation quality factor, Q, represents a multiplicative factor to scale from the physical quantity radiation dose (D, in Gray) to the dose equivalent (H, in Sieverts)8,9:
Currently, two potential approaches exist to estimate radiation quality factors, and thus dose equivalents, in a complex radiation environment such as in space. One is the fluence-based risk cross-section approach13–15, which is used in the current NASA cancer risk model16. This method requires an extremely detailed characterization of the radiation field, including energy spectra and physical and biological action cross sections for every important radiation type that contributes to the overall radiation field. By contrast, the microdosimetric approach is both conceptually and practically simpler. In short, this approach generates quality factors using measured or calculated microdosimetric spectra (distributions of energy depositions within cellular-sized volumes) that are weighted with an empirically determined biological weighting function. Because microdosimetric energy distributions can be easily and continuously measured in space environments17–20, and assuming that an appropriate biological weighting function is available (the subject of this paper), then radiation quality factors, and thus, corresponding dose equivalents, can be continuously assessed in situ in space environments. This microdosimetric approach, originally suggested by Zaider and Brenner21 and Bond et al.22, and endorsed in the International Commission on Radiation Units and Measurements (ICRU) Report 409, has been used extensively in other radiation exposure contexts22–33.
Both the fluence-based cross section approach and the microdosimetric approach have been extensively reviewed in a National Council on Radiation Protection and Measurements (NCRP) Report34. Direct intercomparisons there of these approaches suggest that they produce quality factor predictions that are within ~ 30% of each other.
In the present paper we examine the utility and practicality of the microdosimetric approach for characterizing radiation quality factors in space environments, by generating relevant biological weighting functions, in this example for an intestinal cancer endpoint. This approach can be applied to other relevant radiation-induced cancer (and potentially non-cancer) endpoints, provided there are experimental data available to calibrate it, allowing ultimately for the generation of a consensus average quality factor.
The Microdosimetric Approach
The microdosimetric approach can be used to calculate the mean quality factor based on the measured (or calculated) distribution of microdosimetric energy depositions. This energy deposition distribution is then weighted using a biological weighting function to produce a mean quality factor. The logic behind this approach is that differences in biological effectiveness between different radiations at the same dose can only be caused by differences in the patterns of energy deposition on the microscopic scale, such as within cellular and sub-cellular targets. For example, the spatially-dense pattern of energy depositions from heavy ions more frequently generates severe, difficult to repair biological damage (e.g., complex DNA double strand breaks) per unit dose than does the pattern of spatial energy depositions from photons35–37. Relative health risks from exposure to different radiation types are thus determined by the corresponding different initial physical energy deposition patterns at the microscopic level, and these in turn can be characterized by the microdosimetric distribution of energy depositions.
Based on these considerations, the microdosimetric approach for calculating the mean quality factor, \(\stackrel{-}{Q}\), can be written as follows21:
$$\stackrel{-}{Q}=\int Q\left(y\right) d\left(y\right) dy,$$
2
where y is the stochastic quantity lineal energy, defined as the energy deposited in a defined microscopic site by a single radiation track, divided by the mean path length in that site, d(y) is the normalized dose distribution (probability density) from single-event lineal energy depositions (the measured or calculated microdosimetric energy deposition distribution)38, and Q(y) is an empirical consensus-determined biological weighting function21.
The normalized dose distribution d(y) from single-event lineal energy depositions is, of course, radiation specific. It is based on the measured (or calculated) probability distribution of lineal energies deposited by each radiation type i, which is denoted by fi(y)21. The normalized dose-weighted lineal energy distribution di(y) is derived from this frequency-weighted distribution fi(y) as follows38:
$${d}_{i}\left(y\right)=y {f}_{i}\left(y\right)/\int y {f}_{i}\left(y\right) dy$$
3
.
Here fi(y) and di(y) represent probability densities of lineal energy frequencies and dose contributions, respectively38, and thus the total integral of each of these distributions over y is, by definition, unity.
In a space environment, d(y) can be continuously measured using a compact tissue-equivalent proportional counter17,18,20 or a silicon microdosimeter19,39. Thus, given an empirical consensus biological weighting function, Q(y), the mean quality factor, \(\stackrel{-}{Q}\), can be continuously assessed using Eq. (2), and thus the dose equivalent can be continuously assessed using Eq. (1).
Clearly, the key to this microdosimetric approach is to estimate the empirical consensus biological weighting function, Q(y) (see Eq. 2). As with all quality factors and radiation weighting factors, this function will represent a consensus “averaged” over a variety of relevant biological endpoints and health effects21. The notation that we use here, taken from Zaider and Brenner, 198521, is that the corresponding biological weighting function for a specific biological or health effect, ε, is denoted by the lower case function, qε(y)21, and the consensus weighted average over a variety of “relevant” qε(y) functions is denoted by the upper case notation Q(y). In the present study we demonstrate the concept by estimating qε(y) for the endpoint of radiation-induced induction of intestinal tumors in APC1638N/+ mice.
Estimation of q ε (y), for a Specific Biological Endpoint,ε
As described below, we analyzed the results of a series of experiments with a given biological endpoint, ε. We define the metric Ei to represent the relative yield at low doses (vs. γ rays) of the given endpoint, ε, induced by a given radiation type i, which is characterized by microdosimetric spectra di(y) (Eq. 3).
Using these definitions, the quality function qε(y) for endpoint ε can be unfolded from the following set of Fredholm equations21 for different radiation types i:
E i \(=\int {q}_{\varepsilon }\left(y\right){d}_{i}\left(y\right)dy / \int {q}_{\varepsilon }\left(y\right){d}_{\gamma }\left(y\right)dy\). (4)
The denominator in Eq. (4), which contains the γ-ray lineal energy spectrum dγ(y), is the same for each radiation type i. Because we are interested only in the shape of the qε(y) function, we can simplify these equations as
E i \(=k\int {q}_{\varepsilon }\left(y\right){d}_{i}\left(y\right)dy\) , (5)
where k is a constant, set to 1 for simplicity.
In this study the endpoint, ε, is intestinal tumors in tumor-prone adenomatous-polyposis-coli APC(1638N/+) mice, and the data are tumor yields (number of tumors per mouse) after exposure to space-relevant doses of energetic 1H, 4He, 12C, 16O, 28Si, or 56Fe ions40. These data, kindly provided by our collaborators at Georgetown University, are described below. Since this work is focused on densely-ionizing radiations, our dose-response formalism7 used to estimate the low-dose effect metrics, Ei, separately includes both targeted effects (TE) due to direct traversals of cells by ionizing tracks, and non-targeted effects (NTE) caused by release of signals from directly-hit cells6,41,42. The other inputs needed for unfolding Eq. (5) are single-event lineal energy distributions, di(y), for each relevant ion-energy combination, as described below.