Health risks from galactic cosmic rays (GCR) in space travel above low earth orbit remain a concern. For many years accelerator experiments investigating space radiation induced prevalence of murine Harderian gland (HG) tumorigenesis have been performed to help estimate GCR risks. Most studies used acute, relatively low fluence, exposures. Results on a broad spectrum of individual ions and linear energy transfers (LETs) have become available. However, in space, the crew are exposed simultaneously to many different GCR. Recent upgrades at the Brookhaven NASA Space Radiation Laboratory (NSRL) now allow mixtures in the form of different one-ion beams delivered in rapid sequence. This paper uses the results of three two-ion mixture experiments to illustrate conceptual, mathematical, computational, and statistical aspects of synergy analyses and also acts as an interim report on the mixture experiments' results. The results were interpreted using the following: (a) accumulated data from HG one-ion accelerator experiments; (b) incremental effect additivity synergy theory rather than simple effect additivity synergy theory; (c) parsimonious models for one-ion dose-effect relations; and (d), computer-implemented numerical methods encapsulated in freely available open source customized software. The main conclusions are the following. As yet, the murine HG tumorigenesis experimental studies show synergy in only one case out of three. Moreover, some theoretical arguments suggest GCR-simulating mixed beams are not likely to be synergistic. However, more studies relevant to possible synergy are needed by various groups that are studying various endpoints. Especially important is the possibility of synergy among high-LET radiations, since individual high-LET ions have large relative biological effectiveness for many endpoints.

Selected terminology, symbols, and abbreviations. DER – dose-effect relation; E(d) – DER of a one-ion beam, where d is dose; HG prevalence p – in this paper, p is the number of mice with at least one Harderian gland tumor divided by the number of mice that are at risk of developing Harderian gland tumors (so that in this paper prevalence p can never, conceptually speaking, be greater than 1); IEA – incremental effect additivity synergy theory; synergy level – a specification, exemplified in Fig. 5, of how clear-cut an observed synergy is; mixmix principle – a consistency condition on a synergy theory which insures that the synergy theory treats mixtures of agent mixtures in a mathematically self-consistent way; NTE – non-targeted effect(s); NSNA – neither synergy nor antagonism; SEA – simple effect additivity synergy theory; TE – targeted effect(s); β* – ion speed relative to the speed of light, with 0 < β* < 1; SLI – swift light ion(s).

低地球轨道上方的太空旅行中来自银河系宇宙射线（GCR）的健康风险仍然令人担忧。多年来，已经进行了加速器实验，以研究太空辐射引起的鼠类哈德氏腺（HG）肿瘤发生率，以帮助估计GCR风险。大多数研究使用急性，相对低通量的暴露量。广泛的单个离子和线性能量转移（LET）的结果已可供使用。但是，在太空中，机组人员同时暴露于许多不同的GCR。Brookhaven NASA太空辐射实验室（NSRL）的最新升级现在允许以快速序列传送不同单离子束形式的混合物。本文使用三个两离子混合实验的结果来说明概念，数学，计算，和协同分析的统计方面，还可以作为混合物实验结果的临时报告。使用以下方法解释结果：（a）HG单离子加速器实验的累积数据；（b）增量效应可加协同理论而不是简单效应可加协同理论；（c）一离子剂量效应关系的简约模型；（d）封装在免费提供的开源定制软件中的计算机实现的数值方法。主要结论如下。迄今为止，鼠类HG肿瘤发生实验研究显示只有三分之一的病例具有协同作用。此外，一些理论论据表明，模拟GCR的混合光束不太可能具有协同作用。然而，研究各种终点的各个小组还需要进行更多与可能的协同作用相关的研究。特别重要的是在高LET辐射之间产生协同作用的可能性，因为单个高LET离子对许多终点都具有较大的相对生物学有效性。

选定的术语，符号和缩写。DER –剂量效应关系；E（d）–单离子束的DER，其中d为剂量；HG患病率p –在本文中，p是具有至少一种哈德氏腺瘤的小鼠数除以有发生哈德氏腺瘤风险的小鼠数（因此，本文患病率p从概念上讲，永远不能大于1）；IEA –增量效应可加协同理论；协同水平–规范，如图5所示，观察到的协同作用有多清晰；mixmix原理–协同理论的一致性条件，可确保协同理论以数学上自洽的方式处理代理混合物的混合物；NTE –非目标效应；NSNA –既不协同也不拮抗；SEA –简单效应可加协同理论；TE –目标效果；β * –离子相对于光速的速度，0 < β * <1；SLI –快速的轻离子。