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1054 I.J. Radiation Oncology Biology Physics May 1988, Volume 14, Number 5

2. "The analysis included patients improperly assigned to treatment

Response: Fifty-five patients were assigned to radiation therapy. Three patients refused radiation therapy and demanded surgery. These three patients, as they received surgery, were analyzed as if they were random- ized to receive surgery. Forty-two patients were randomized to receive radical surgery. Four patients refused radical surgery and demanded ra- diation. These four patients who received radiation were analyzed as if they had been randomized to radiation therapy. Thus the two populations which were ultimately randomized were the 55 who were randomized to radiation therapy, minus the three who demanded surgery, plus the four randomized to surgery who demanded radiation for a total of 56. The number for radical surgery are calculated as follows: 42 minus 4 plus 3 for a total of 41. The statistician for the study debated as to whether the patients who were randomized to one treatment but who received another should be analyzed according to their randomization or analyzed by their treatment received. The decision was made to analyze by the treatment received since the study was to examine the relative impact of the two treatments rather than the relative impact of the randomization assignment.

3. "There were unacceptable deletions from the surgical arm."

Response. Local recurrence did not constitute failure in this study. Patients who received radiation who had biopsy proven persistent disease after definitive radiation therapy, were not identified as failures.

4. "'There was an unacceptabh, rate of lost patients."

Response: Further follow-up at 80 months continued to demonstrate relative benefit of surgery over radiation.

5. "'The input of the uro-oncology group radiation therapy committee

Response The protocol did not require blind biopsies of patients ran- domized to surgery to determine whether or not local disease was present. It does not seem proper to blindly biopsy patients following radical surgery when they can be adequately monitored by digital examination for local recurrent disease. Furthermore, local disease did not constitute failure.

6. "The endpoint selected was inappropriate to evaluate the . . . "

Response." The use of first evidence of disease recurrence has become an accepted modality for evaluating impact of treatment designed for control of early stage disease. As first evidence of distant disease recurrence was equivalently applied to both treatment groups, to deny that the endpoint selected was inappropriate serves only to support the bias of the radio- therapist.

7. "The rate of metastasis in the radiation group was cons is tent . . . "

Response" One can only state that the volume of diseasc was equivalent in both the radiation therapy arm and the radical prostatectomy arm. It is interesting that a later publication from this same cooperative group that examined the impact of radiation therapy vs. no treatment for node negative stage disease indicated that the failure rates were equivalent in both the actively treated by radiation therapy arm and the arm that did not receive treatment but which was observed only (Paulson, D. F., Hodge, G. B. Jr., Hinshaw, W. and Uro-Oncology Research Group: Radiation therapy vs. delayed androgen deprivation for stage C carcinoma of the prostate. J Urol 131: 901-902, 1984). These studies would indicate that the reported impact of radiation may be nothing other than the observed natural history of node negative Stage T3 adenocarcinoma of the prostate.

8. "The results obtained with the surgical group are similar o r . . . " Response: The studies referred to in reference 6 are studies in which the patients were selected retrospectively to optimize their treatment response. Similarly selected patients who underwent radical surgery demonstrate a benefit to radical surgery greater than that achieved in the randomized arm. This only serves to confirm that retrospective analysis of a patient population can produce treatment results equivalent to the bias of the authors.

9..','Morbidity was not reported in this study which is quoted as . . . "

Response: Morbidity was not analyzed.

DAVID F. PAULSON, M.D. Div. of Urologic Surgery Duke University Med. Ctr. Durham, NC 27710

RADIOBIOLOGICAL IMPLICATIONS OF FRACTIONATED LOW DOSE RATE IRRADIATION

To the Editor." Recently, Pierquin and coworkers 5 presented updated results from a trial on low dose rate (LDR) irradiation of the oropharynx. 4 In this trial a comparison was made between conventional high dose rate (HDR) fractionated irradiation (45 Gy given as 25 fractions in 35 days, followed at day 40 by a boost of 25 Gy in 18 fractions), and frac- tionated LDR irradiation (also 45 Gy, but now given as 7 fractions of 6-7 Gy at approximately 1 Gy/hr in 10 days, again followed at day 40 by a LDR boost of 25 Gy in 4 fractions). Their main finding was that less recurrences and more late normal-tissue damage were seen in the patients treated with LDR than in the group treated with conventional HDR radiotherapy.

In this note we present radiobiological considerations, based upon the linear-quadratic (LQ) model,l which may explain some of these results, and highlight a potential danger from this sort of LDR treatment. This seems appropriate, because Pierquin et al. 4"5 touch only lightly on the radiobiological differences between the two treatment modalities. Frac- tionated LDR irradiation as used by Pierquin et al. 4'5 has two conflicting characteristics. On the one hand LDR irradiation can be regarded as the limit of hyperfractionation, and hence it should preferentially spare tissues with low a/fl ratios (late responding normal tissue or NT), compared to tissues with high a/fl values (tumor tissue or TT). On the other hand, a fractionated LDR treatment can also be considered as consisting of large

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Fig. I. (a) Effective dose of the considered conventional fractionation (high dose rate) schedule 4 as a function of repair halftime of the tissue (log scale). Curves are drawn for values ofa/B = 2 Gy (normal tissue or NT) and a/~ = l0 Gy (tumor tissue or TT). If the repair halftime is long, not all sublethal damage is repaired between doses and the effective dose increases. (b) Effective dose of the low dose rate schedule. 4 The effective dose is very dependent on the repair halftime, especially for low ~/3 tissue.

Correspondence 1055

fractions (7 fractions of 6.4 Gy in the considered case), which would tend to increase, preferentially, damage to low a i r tissues. This apparent contradiction disappears if the rate of repair of sublethal damage (SLD) is taken into account. If the repair process is very slow, the LDR fractions are equivalent to large HDR fractions, because the sublethal damage is hardly repaired during an LDR session. If the repair process is very fast, however, in comparison to the length of the LDR session, the effect of LDR irradiation resembles that of a hyperfractionated treatment, because all inflicted SLD is repaired almost instantaneously. We have quantitated these remarks and applied them to the trial of Pierquin et al. The approach of Dale 2'3 has been used to compare the relative effectiveness of LDR and conventional HDR fractionation. To simplify the calculation we have discussed only the initial 45-Gy treatment. The conclusions from our calculations are also valid for the total irradiation schemes including the successive boosts. Two types of tissue are considered, characterized by a/fl = 2 Gy (late responding NT) and a/fl = 10 Gy (TT), respectively. Qualitatively similar results would be obtained if other values for a/fl were assumed, as long as the a/fl ratio of the TT is larger than the one of the NT. Note that, the effectiveness of the different treatment modalities depends strongly on the rates of repair of SLD in NT and TT. The little quantitative information that is available on halftimes of repair suggests values of around 0.8 hr for early responding (high a/fl) NT and of around 1.4 hr for late responding (low a/fl) NT. s

The Effective Dose (ED) of the conventionally fractionated HDR treatment is given in the LQ model by:

ED = D(1 + d/(a/fl)), (1)

where D is the total dose and d the dose per fraction. For 45 Gy in 25 fractions 4 this amounts to ED = 85.5 Gy for a/fl = 2 Gy (NT) and ED = 53.1 Gy for c~/fl = 10 Gy (TT). This equation is only valid if the halftime of repair (Tu2) of SLD is much shorter than the time between successive fractions (24 hr in this case). If for a certain tissue Tt/2 is longer than, say, 6 hr, not all SLD inflicted during a fraction is repaired before the next fraction is given and the Effective Dose becomes higher. 3'7 Figure la shows the variation of ED as a function of T~/2 both for NT (a/fl = 2 Gy) and for TT (a/fl = 10 Gy). For damage to late responding tissue, ED lies between 85.5 Gy for Tu2 = 0.1 hr and 99.9 Gy for Tu2 = 10 hr, whereas for tumor the range of values is smaller.

The Effective Dose ED corresponding to fractionated LDR treat- ment is2:

ED = D{ 1 + (2R/lz)(fl/a)[1 - { 1 - exp(-u.T)}/(u.T)]}, (2)

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Fig. 2. Relative effective dose (RED), that is, the effective dose of the low-dose rate schedule divided by the effective dose of the conventional schedule. For a tissue with repair halflime of 0.75 hr, both schedules are equally effective. If the repair halftime is longer than 0.75 hr, the low dose rate schedule inflicts more damage than the conventional fraction- ation schedule.

with D the total dose, R the dose rate, T the total time of a fraction (so D = n.R.T, with n the number of fractions) and u the repair rate constant (# = ln(2)/Tu2 ). Again, in this formula the interaction between successive fractions is neglected and therefore it is strictly valid only if the Tt/2 is much shorter than the interval between fractions (here 24 hr); for T~/2 longer than approximately 6 hr the interaction needs to be taken into account. Figure lb shows the value of the ED for the LDR treatment schedule of Pierquin et aL 4 (7 daily fractions of 6.4 Gy at 1 Gy/h) as a function of the halftime of repair T,/2. It is seen that for NT (a/fl = 2 Gy) the Effective Dose ranges between 51.3 Gy for Tu2 = 0.1 hr and 210.4 Gy for Tu2 = 10 hr.

Figure 2 shows the Relative Effective Dose (RED) of the LDR schedule compared with the conventional HDR schedule, that is, the quotient of the ED values in Figure la (Eq. 1) and Figure lb (Eq. 2): RED = (EI~DR)/ (EDHDR)- We note that the RED is not dependent on the total dose (Eqs. 1 and 2) and therefore our conclusions will also be valid for the total LDR and HDR schedules of Pierquin et al., 4 including the boost dose. When RED is greater than one, the LDR schedule results in a higher effective dose than the HDR schedule. For a tissue with Tu2 = 0.75 hr, the LDR schedule is seen to be equally effective as the HDR schedule (RED = 1), independent of the a/fl value of the tissue. For tissues with repair halftimes less than 0.75 hr, the LDR schedule inflicts less damage than the HDR schedule. In addition, if the repair halftimes of two tissues are equal, the LDR schedule preferentially spares the low-a/fl tissue (NT). In other words for tissues with Tl/2 less than 0.75 hr the hyperfractionation properties of the LDR schedule dominate. If, however, Tu2 is greater than 0.75 hr, the opposite is true: the LDR fractions resemble HDR fractions of the same size and the LDR schedule produces more damage than the HDR schedule. Then, under the assumption of equal T,/2 for NT (low air) and TT (high air), the tumor is preferentially spared. Note that the exact shape of all the curves and therefore also the position of the cross-over point (RED = 1), depend on the details of the irradiation schedules, that is fraction size and number of fractions of the HDR schedule, and fraction size, number of fractions and dose rate of the LDR schedule.

In general, the values of T~/2 may be different for TT and for NT. In addition, the values of the computed Effective Dose obtain clinical rel- evance only if dose-response curves of the considered tissue are available. Unfortunately these data are not available for many effects on normal tissues and tumors. Still, some conclusions can be drawn pertaining to the two schedules of Pierquin et al. 4'5 Firstly, if both for tumor and for late responding normal tissues the halftimes of SLD repair are longer than 0.75 hr, the LDR schedule will be more damaging than the HDR schedule for both types of tissue. This may explain the higher local- control rate and the increased NT damage observed by Pierquin et a[. 4"5 when using the LDR schedule. Secondly, for dose rates higher than 1 Gy/hr, the similarity between a LDR treatment and an HDR treatment with large fraction size increases. Hence, the Effective Dose of a LDR treatment is larger for higher dose rates. This may explain the occurrence of more normal tissue damage for a dose rate above 1.5 Gy/hr, as observed by Pierquin et al. 4'5 Thirdly, the LQ model suggests that a preferable alternative exists to the LDR schedule used by Pierquin et al., 4 if the values of the repair halftimes of NT and of TT are such that REDrr is less than REDNT. Figure 2 shows this to be almost always the case if these halftimes are longer than 0.75 hr which, according to the available literature seems not unlikely. 6'8

Take as an example values ofTu2 = 2 hr for both TT and NT. Then, the Effective Doses are for the conventional HDR treatment 85.5 Gy (NT) and 53.1 Gy (TT), and for the LDR schedule ED = 122.8 Gy (NT) and ED = 60.6 Gy (TT). If such an ED of 122.8 Gy is clinically acceptable for NT, it may also be delivered as a conventionally fractionated HDR schedule of 25 fractions of 2.3 Gy; this would have the advantage of augmenting the effective dose to the tumor with respect to the LDR schedule by 17% to 70.7 Gy.

For other numerical values of the repair halftimes a similar conclusion can be drawn, provided that REDrr < REDrcr. The LDR-schedule of Pierquin et al. is, according to these calculations, inferior to a conven- tionally fractionated HDR schedule with higher doses per fraction. Con- ditions for the applicability of the present calculations are that the LQ model may be applied to the considered schedules and tissues and that the effects of late normal tissue damage can be characterized with a lower a/fl value than the effects on the t...