Half-times of irradiation recovery in accelerated partialbreast irradiation : Incomplete recovery as a potentially dangerous enhancer of radiation damage

Purpose: To compare clinical results from accelerated partial breast irradiation with predictions from different half-times of recovery of radiation damage. Method: Three published results of excessive late complications led to an editorial [1] which was a “wake up call” to the possible hazards of fractions spaced close together such as two fractions of 3.85 Gy a day on five consecutive days. These results are re-examined here using linear quadratic modelling with mono-exponential and bi-exponential recovery kinetics. Results: Although clinical results showed rather high proportions of severe complications, only in one of the three studies discussed in reference [1] complications were severe enough to cause it to be terminated. Since then other studies with the same doses have reported acceptable results. However, none of these complication rates are predicted to be tolerable, if mono-exponential kinetics with a single T 1⁄2 of ~4 hours is assumed. Conclusions: Better matches to clinical results can be found by assuming bi-exponential recovery with 50%50% components of 0.3 hand 4 h, and  = 3 Gy, for late complications. There is continuing need for data from more clinical results, especially concerning various tumour types.


Introduction
In 2010 a warning was published [1] that accelerated radiotherapy schedules using two fractions a day for only five days to irradiate partial breast could lead to a high risk of late complications.This warning was accompanied by a calculation of an excessively high dose, due to unrecovered dose, that assumed only a single halftime of recovery (T½) as long as 4.4 h.However a wide discrepancy from the quoted clinical results in their own editorial [1] invites a reconsideration of their specific model of T½= 4.4 h monotonic exponential recovery in accelerated partial breast irradiation.
It has been established [2] that recovery does not have unique half-times but they increase with the increase in interfraction interval.This proves the presence of more than one recovery rate.It is obvious if a shorter component of recovery of significantly less than 4.4 h is present, then the problem of incomplete recovery will be less important.This paper explores that possibility.
A recent thorough review of all aspects of radiation recovery drew attention to the bi-exponential nature of recovery in late normal-tissue complications [3].It is obvious that the presence of a significant proportion of rapid recovery would reduce the disadvantage of incomplete recovery on schedules with two fractions a day.

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Some results from accelerated partial breast irradiation allow this to be demonstrated particularly clearly.
Bentzen et al. reported evidence for long half-times of recovery: 4.9 h for laryngeal oedema, 3.8 h for skin telangiectasia, and 4.4 h for subcutaneous fibrosis, so that an average T½ of four hours appeared to be a reasonable starting assumption for their warning calculations [4].These calculations must be questioned because no shorter intervals between fractions than 6 hours were available in the CHART schedule.normal-tissue complications were most likely, but found no evidence for more than one T½ in tumour data [3].
First, not the entire dose delivered is capable of recovery in the LQ formulation.It is generally assumed that recovery from radiation damage occurs in the two-hit or multi-hit component of the damage, which is not the linear singlehit part of the damage [6][7][8][9][10].The proportion of each dose fraction that is recoverable is shown in figure 1.This diagram is important because it shows how the recovery proportion rises to high values for the larger doses per fraction.Next, evidence is summarised for the presence of a range of short half-times of 0.1 -1 h (Figure 2), and for longer half-times of 1.5 to 7 h (Figure 3), in various animal data and one human data set.All these references are tabulated in the reference [5].The bi-exponential half-times have often been summarised and used as 0.3 h and 4 h [5].
Figure 2 The longer of the two components [5] Figure 3 The shorter components of the concomitant pairs (Table 1 and reference 5).

Results
Referring to figure 1,3.85 Gy given twice a day, gives a proportion of 0.56 in the recovery "beta" term, so that each day's treatment of 2F × 3.85 Gy at six hours apart leads to a nominal overdose of 36% × 0.56 = 20.2% of the delivered dose.That is, 10.1% for each of the two fractions and therefore a nominal overdose of 10.1% for the whole prescribed dose, because the same dose is administered for every day of treatment.
But there is overnight decay occurring too, not falling to a negligible dose until the weekend (two days of no irradiation).Each 24 h interval leads to 2.52% nominal overdose, plus 0.91% for the 18h interval from the second fraction per day, giving 3.43% nominal overdose for each treatment day.These overnight increments accumulate on successive nights, giving (1.0343) 4 from Monday night to Friday morning, when the week's cycle is terminated by the Friday afternoon dose.A total of 14.4% nominal overdose has to be added to the 10.1% daytime overdose described above for the whole week.
Together, these two parts of the day yield 1.101 × 1.144 = 1.2595 x prescribed dose; a nominal overdose of 26%, assuming T½ = 4 h only.How does this compare with the clinical observations reported from accelerated partial breast irradiation by Bentzen and Yarnold [1]?This 26% extra predicted dose causes the biologically equivalent total dose in 2-Gy fractions (EQD) of the 38.5 Gy treatments to be increased from a modest 52 Gy (in 2 Gy equivalent fractions) to a much greater 65 Gy.In reference [1] T½ of 4.4 h was used, predicting an even higher EQD of 68 Gy, so we agree with the estimate in reported [1].This gave a predicted incidence of moderate-to-severe skin reactions of 75-82% [1], which is certainly excessive.Fortunately the clinical results observed were nowhere near this level (Table 1 in reference 1), and that is the point of this paper.
Although the last two reports [11,12] cited by Bentzen and Yarnold [1] had shorter follow-up, that was the opposite of reassuring, but moderate-to-severe reactions were nowhere near the 75-82% stated in reference [1], when the T½ was assumed to be ~ 4 h only.It is not simply a coincidence that real 13% result in the third study [13] cited by Bentzen and Yarnold [1] is half that of the modelled, when T½ was similarly assumed to be ~4 h 26% nominal overdose described above; it is what we would expect if the real T½ was half of the assumed T½ of ~4 h, that is, bi-exponential with the other component much smaller than ~4 h.
The trend is to support the concept from the many in situ experiments in Table 1 of reference [4] that approximately half of recovery does indeed have a T½ of ~4h, and the remainder has much shorter T½.This is illustrated in the following block diagrams where the modal value of each experimental in situ recovery result reported is plotted from the Table 1 in reference [4]: the longer of the two components in the present figure 2 and the shorter ones in figure 3. The two distributions of modal values at 4 h and 0.3 h are more clearly shown here than in the referenced tabulation [5].It is the presence of the shorter ones too that the present paper is all about.
The concept of the two distributions with modal halftimes of 4 h and 0.3 h, possibly approximating more complex spectra of many half-times [13,14], is then obvious.It is clear from Figure 2 that a long component of recovery is present in all the animal tissues tested and one human tissue, as indeed reported by Bentzen et al. [4].Figure 3 shows the simultaneous shorter component in each tissue, plotted from the experimental results cited in reference [4].The proportions of long versus short half-times were between 40% to 60% (or 60% to 40%) of each component, which we approximate here by assuming 50% to 50%.
It is a logical step to propose that a similar pair of T½ values is present in other normal tissues and this assumption brings the dangers of late damage into much closer correspondence with the clinical observations than assuming that the only T½ is the long one of about 4 h in the 2F/day schedules made in [1].Wang et al. [16] have proposed many times that the only T½ present is ~0.3 h -0.8 h, and this is equally incorrect.The statements made in [1] that "changes in skin appearance would be expected to be 75%-82% compared with 31% after 50 Gy in 2-Gy fractions" were obtained by the assumption of a single T½ of ~4 h only.We simply find that the inclusion of the shorter vales of T½ in both the daily pair of doses, and to a less extent the overnight pair, decrease the 26% overdose predicted by Bentzen and Yarnold [1], to just 13%.It is unlikely to be a coincidence that a 13% incidence of poorto-fair cosmesis is the clinical result reported for the only set of patients that has adequate follow-up of 4.2 years (Table 1, in reference 1).
We are then ready to look harder at the problem of extra radiation damage that may occur in other schedules that have been proposed and used for other cancer sites.Table 2 summarises the present author's results for two fractions per day from accelerated partial breast irradiation schedules and for other bi-exponential schedules used to treat head and neck cancers.The bottom line of Table 2 contain my best estimates, which might be tested until any better results for T½ values are obtained.Better T½ values should be sought but are challenging to obtain.

Discussion
Berrang et al. [16] from Canada reported 3-year results of their multicentre trial with a range of doses per fraction from 3.5 Gy to 3.85 Gy twice a day in 5 days for ductal carcinoma in situ or node-negative margins, less than 3 cm in diameter.They reported grade-1 toxicities in most normal tissues at 3 years follow-up.
Even more convincing is the report of Bourgier et al. [17] who treated between October 2007 and September 2008 25 breast cancer patients in an IMRT conformal trial, using 10 hypofractionated doses of 4 Gy each fraction, given twice daily in 5 days.They delivered an "en face" electron field plus two mini-tangents.

Conclusion
The conclusion was that this level of dose was acceptable, and that no patients had yet failed.Later results, as they mature, might comment on the relative frequency of the shorter versus longer components in either normal tissues or the tumours.[23], or the originator of the 2F × 1.6 Gy per day schedules, Wang [24].It is unlikely that 2F/d schedules employing doses per fraction less than 1.6 per fraction would present problems of excess late complications due to incomplete recovery, but the large doses used in stereotactic body radiation therapy should indeed be checked, using the two half-times described here until any more definitive values for T½ can beobtained.

Figure 1
Figure 1 Barendsen-type Biologically Effective Dose (BED) is defined as Total Dose x Relative Effectiveness (RE), where where d is the dose-per-fraction, and  and  are the linear and quadratic coefficients of log e cell kill per Gy and per Gy2 respectively [8,9].In the defining expression RE it is only the recoverable term that can change with time; so its proportion of the whole BED is plotted in figure 1 as an index of how large is the proportion of recoverable damage as late complications in normal tissues ( = 3 Gy), as a function of doseper-fraction.It rises above 50% for doses per fraction greater than 3 Gy, and as you see, it becomes very large for stereotactic body radiation therapy or ablative doses in radiotherapy.

Table 1 in
Fowler et al. summarized animal and some human evidence for two different rates of repair of radiation damage (or possibly multiple rates) in their NobleResearch www.nobleresearch.orgreference [5].Ling et al. in their comprehensive review of incomplete repair accepted that two components for

Table 2
Incomplete recovery with two fractions a day (2F/day) of various doses per fraction: Two doses delivered daily with an interval of 6 h between fractions, assumed bi-exponential recovery with 50% recoverable damage with a halftime (T½) of 0.3 h and the remaining 50% with a halftime of 4 h.
[22]e2lists the present accelerated partial breast irradiation schedule and three commonly used 2F/ day head and neck radiotherapy schedules together with the estimations of the excess percentage-dose assuming bi-exponential recovery of 50% with T½= 4 h and 50% with T½= 0.3 h.It is not surprising that several attempts to use 2F x 2 Gy per day have been tried and all have been given up as too damaging for clinical late effects fromJackson et al. in Vancouver [19]toBourhis et al.in Paris[20]: they reported 9% extra dose --larger dose errors than many protocols would allow anyway.In contrast the prediction of 7.6% extra dose for 2F × 1.6 Gy per day did not result in complaints from Fu et al.[21], Trotti et al.[22], Leborgne et al.