21 years of biologically effective dose

Abstract

In 1989 the British Journal of Radiology published a review proposing the term biologically effective dose (BED), based on linear quadratic cell survival in radiobiology. It aimed to indicate quantitatively the biological effect of any radiotherapy treatment, taking account of changes in dose-per-fraction or dose rate, total dose and (the new factor) overall time. How has it done so far? Acceptable clinical results have been generally reported using BED, and it is in increasing use, although sometimes mistaken for "biologically equivalent dose", from which it differs by large factors, as explained here. The continuously bending nature of the linear quadratic curve has been questioned but BED has worked well for comparing treatments in many modalities, including some with large fractions. Two important improvements occurred in the BED formula. First, in 1999, high linear energy transfer (LET) radiation was included; second, in 2003, when time parameters for acute mucosal tolerance were proposed, optimum overall times could then be "triangulated" to optimise tumour BED and cell kill. This occurs only when both early and late BEDs meet their full constraints simultaneously. New methods of dose delivery (intensity modulated radiation therapy, stereotactic body radiation therapy, protons, tomotherapy, rapid arc and cyberknife) use a few large fractions and obviously oppose well-known fractionation schedules. Careful biological modelling is required to balance the differing trends of fraction size and local dose gradient, as explained in the discussion "How Fractionation Really Works". BED is now used for dose escalation studies, radiochemotherapy, brachytherapy, high-LET particle beams, radionuclide-targeted therapy, and for quantifying any treatments using ionising radiation.

Figure 1

Estimated tumour log cell kill plotted vs tumour cell doubling time Tp during radiotherapy of the four schedules in the Radiation Therapy Oncology Group 90-03 clinical trial [27, 28]. The start of repopulation Tk was assumed to be 21 days. The rapid decrease of tumour effect as doubling time decreases is obvious, with two pairs of the schedules predicted to give identical results at two different levels of cell kill, but both at Tp = 2 days only, at the crossover points. Redrawn from log cell kill Figure 7 of Fowler 1989 [1].

Figure 2

The lack of any obvious optimum overall time in head and neck radiotherapy with radiation only. The square points show the estimated tumour log₁₀ cell kill for schedules used in 14 centres worldwide and the schedule of 2 Gy×35F = 70 Gy in 7 weeks commonly used as control. The best schedules are predicted to give 11.0 to 11.2 logs of cell kill assuming α/β = 10 Gy, α = 0.35 Gy⁻¹, Tk = 21 days, Tp = 3 days.

Figure 3

Estimated biochemical recurrence-free survival of patients treated with an imaginary series of schedules with 2F given on each of 5 days a week, up to 60F in 6 weeks (39 days), calculated from Equation (1) assuming Tp = 4 days doubling time and Tk = 14 days. The fraction size for each schedule was adjusted to deliver always the same late constraint biologically effective dose in Gy₃ or total EQD_3/2. The 2-day gaps at weekends are obvious, but the accumulated effect on tumours continues to rise with successive weeks. (Replotted from Arvidson et al [47].

Figure 4

Each schedule is represented by one X (tumour equivalent dose (EQD)_10/2) and one O (acute mucosal EQD_10/2 below it), plotted against fraction number only. The circles show the maximum estimated acute mucosal EQDs given by choosing overall times according to 1F or 2F on weekdays only, and then extending overall time where necessary to the shortest “practical OvT” that keeps the acute mucosal EQD _10/2 not greater than 51.0 Gy. (Reproduced from Fowler 2008 [42]). The separate families of points for 1F or 2F per day were then obvious.

Figure 5

The same data as in Figure 4 plotted against practical overall time (the minimum overall time that keeps acute mucosal equivalent dose (EQD)_10/2 at or below 51 Gy). X, Tumour EQD; O, acute mucosal EQD. Optimum tumour EQDs for 2F/day are higher than those for 1F/day by 4 Gy EQD and 0.3 log₁₀ cell kill. The plotted curves fall when the late constraint dose is reached (Reproduced from Fowler [42] 2008).

Figure 6

The same data for tumour EQD and log-cell kill as in Figures 4 and 5, cleaned up and the best schedules labelled. They are also listed in Table 6 slightly more legibly with mandatory minimum overall times listed too. It is interesting how much better we can do than with 35 factions of 2 Gy in 7 weeks, even without adding chemotherapy.