The influence of experimental design and data analysis on the determination of recovery kinetics of radiation damage between acute dose-rate treatments in vivo.

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.