Joiner M C, Rojas A, Michael B D
CRC Gray Laboratory, Mount Vernon Hospital, Northwood, Middlesex, U.K.
Int J Radiat Biol. 1990 Jan;57(1):143-62. doi: 10.1080/09553009014550411.
Current interest in determining the rate of recovery of damage between radiation doses in fractionated treatments has resulted in the development of several experimental designs and methods of analysis to address this. One approach is where two or more fractions are given with a varying interval. Isoeffect doses are then determined from the dose-response curves for each interval, and these are plotted on a logarithmic axis against time on a linear scale. An estimate of the rate of dose recovery can then be made if the data show monoexponential or well-defined multiexponential kinetics. However, three problems can be identified in this simple protocol. First, most repair models (e.g. Thames' IR and Curtis' LPL) assume that between two doses loge (cell survival), i.e. underlying effect, not dose itself, recovers exponentially with time. Experimental data support this assumption. Since underlying effect and dose are not linearly related, recovery measured from the change in isoeffect dose can appear substantially slower (depending on dose per fraction) than the true underlying recovery rate of damage. This artifact is avoided by converting dose increments into changes in underlying effect (with the linear-quadratic model) or by measuring underlying effect more directly in 'top-up' experiments. The use of (neutron) top-up experiments is preferred, as it enables recovery between constant X-ray doses per fraction to be studied, and makes no prior assumptions regarding either the shape of the X-ray dose-response curve or how recovery takes place, although the shape of the neutron dose-response curve must be known. Second, plotting log (unrecovered damage) against time can overestimate recovery half-times, because such plots cannot handle negative values and therefore become naturally weighted in favour of the data from the longer time intervals where the difference from complete recovery is smallest. This problem is managed by using nonlinear regression to fit the values of unrecovered damage expressed on a linear scale against interval. Third, experiments using three or more evenly spaced fractions, 'concertina'-style, permit interaction between non-adjacent fractions. If this is not taken account of, then recovery appears to be initially faster and multiexponential, even though the underlying recovery may be actually monoexponential. Thus concertina experiments are poor at resolving the precise shape of recovery-kinetics profiles and are less suited for measuring any dependence of recovery rate on dose per fraction compared with approaches using either just two fractions, or two fractions per day.
当前对于确定分次治疗中不同辐射剂量间损伤恢复速率的兴趣，促使人们开发了多种实验设计和分析方法来解决这一问题。一种方法是给予两个或更多分次，间隔时间不同。然后从每个间隔的剂量-反应曲线确定等效应剂量，并将这些剂量在对数轴上绘制，而时间在线性尺度上。如果数据呈现单指数或明确的多指数动力学，那么就可以对剂量恢复速率进行估计。然而，在这个简单的方案中可以识别出三个问题。首先，大多数修复模型（例如泰晤士河的IR模型和柯蒂斯的LPL模型）假定在两次剂量之间，自然对数（细胞存活），即潜在效应，而非剂量本身，随时间呈指数恢复。实验数据支持这一假设。由于潜在效应和剂量并非线性相关，从等效应剂量变化测量得到的恢复可能显得比损伤的真实潜在恢复速率慢得多（取决于每次分次的剂量）。通过将剂量增量转换为潜在效应的变化（使用线性二次模型）或在“补充”实验中更直接地测量潜在效应，可以避免这种假象。使用（中子）补充实验更为可取，因为它能够研究每次分次恒定X射线剂量之间的恢复情况，并且对于X射线剂量-反应曲线的形状或恢复如何发生无需预先假设，尽管必须知道中子剂量-反应曲线的形状。其次，将对数（未恢复损伤）与时间作图可能会高估恢复半衰期，因为这样的图无法处理负值，因此自然会偏向较长时间间隔的数据，在这些间隔中与完全恢复的差异最小。通过使用非线性回归来拟合线性尺度上表示的未恢复损伤值与间隔的关系来解决这个问题。第三，使用三个或更多等间隔分次的“手风琴式”实验允许非相邻分次之间的相互作用。如果不考虑这一点，那么恢复最初似乎更快且呈多指数形式，尽管潜在恢复实际上可能是单指数形式。因此，与仅使用两个分次或每天两个分次的方法相比，手风琴式实验在解析恢复动力学曲线的精确形状以及测量恢复速率对每次分次剂量的任何依赖性方面表现较差。
