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Lethal and sublethal cellular injury in multifraction irradiation
Europ. J. Cancer Vol. 11:, pp. 581-583. P e r g a m o n Press 1975. Printed in Great Britain
Lethal and Sublethal Cellular Injury in Multifraction Irradiation H. RODNEY W I T H E R S
Section of Experimental Radiotherapy, The University of Texas M. D. Anderson Hospital and Tumor Institute at Houston, 6723 Bertner Avenue, Houston, Texas, U.S.A. The dose Dr measured by Dutreix, W a m bersie and Bounik, and reported in their recent paper in this journal [1] is not the same as ( D N - - D 1 ) / ( N - - 1)which is the usual measure of recovery per fractionation interval and for which Dr would be a more apt symbol. The value measured by Dutreix et al would be better described as ~D r since they measured the increase in the dose, expressed as the incremental dose per fraction, required to achieve an iso-effect when the fraction number was doubled. The difference between Dr and ADr can be best illustrated by an, example. Assume a certain effect could be achieved with a single dose of 1350 rads, 2 doses of 800 rads, 4 doses of 450 rads or 8 doses of 240 rads. If there had been no additional sparing fi:om dividing the dose into 4 instead of 2 fractio:as, the dose schedule would have been 4 x 400 rads. Since the dose needed per fraction was 450rads, AD, = 50 rads. Similarly, had there been no additional recovery from dividing the dose into 8 fractions instead of 4, the do:~e per fraction would have been 1800/8 = 225rads: since a dose of 8 x 240 was needed, ADr = 15 fads for an increase from 4 to 8 fractions. It is not necessary that the number of dose fractions be doubled to measure AD,. Since it is the increase in dose per fraction needed for an iso-effect when the number of dose fractions is increased (from N t o N'), a more general expression is:
ADr =
DN,~D N
iV" Since the value for LxD, is not only dependent upon doses per fraction, but also upon the magnitude of change in fraction number, the expression will be written as: D N, ~ O N
ADr(N'/N) =
iV"
For comparison,
Dr = DN'--DI N'--I
or
DN--D1 N--1
The differences between D, and AD, for the hypothetical example used above are shown in Table 1.
Table 1 2N 2 4 8
D,(rads)
AD,(2N/~) (rads)
1 6 0 0 - 1350 - 250 1 1 8 0 0 - 1350 = 150 3 1 9 2 0 - 1350 - 93 7
1 6 0 0 - 1350 = 125" 2 1 8 0 0 - 1600 = 50 4 1 9 2 0 - 1800 -- 15 8
*This value is only conceptually valid if the single dose, 1350 rads, is considered to be two equal doses of 675 rads.
Although it is not shown in Table 1, the increase in dose-per-fraction if the fraction number were increased from 2 to 8 would be
Total dose in N" fractions N"
Ds--D2~ = 1920--1600 = 40 fads. 8
Total dose in N fractions iV"
8
Thus, insteadof replacing 2 × 800 fads by 8 x 200 rads, the new dose schedule for the same effect would be 8 × 240 rads. Since possible changes in fraction number are limitless, further discussion in this letter will be restricted, for convenience,
Accepted 10 O c t o b e r 1973. *This work was supported in part by Grants C A 11138 and C A 06294 from the National Institutes of Health.
581
582
H. Rodney Withers
to examples in which the n u m b e r of fractions is doubled. Values for AD, and D, diverge rapidly at low doses-per-fraction (Table 1). A simple explanation of this is as follows: The amount of sublethal injury deposited is proportional to dose and hence, as dose is increased, so is the amount of sublethal injury deposited and repaired. Thus, D, increases with dose, even at very low doses. However, at low doses, when all sublethal damage is completely repaired and cell killing results only from non-repairable injury, decreasing the dose-per-fraction cannot increase the amount of sublethal injury repaired, and hence, cannot increase further the sparing effect of dose-fractionation. Therefore, at low dosesper-fraction, AD, approaches zero. As Dutreix et al. have emphasized, the absolute amount of sublethal injury repaired per fractionation interval (D,) is not as important to radiotherapists as the change in the amount repaired (AD,) when the dose-per-fraction is altered. ~ 9 , is a practical value and is the type of information radiotherapists seek from isoeffect formulae [2, 3]. In their Fig. 6, Dutreix et al. plotted values for AD, on the same graph as values of D, for skin and other tissues. Other data for AD, are presented here on the same graph (Fig. 1) as the data of Dutreix et al., for h u m a n skin. The value for AD, for h u m a n skin at a dose of 200 rads is shown as 25 rads or less, but it may be closer to 0 than 25 rads (1, 13). Thus the h u m a n and murine data may be more separated at low doses than suggested by the symbols in Fig. 1. Except for gastric mucosa [5] and bone AOr For Doubling N S
150-
J
"~ I00 o
d
~o
C p
o
•
L
H J,~ 0
o
2~o
46o'-doo
Dose Per Fraction
Fig. 1. The increase in dose (per fraction), ADr(2mN) necessary for an iso-effect when the number of dose fractions is increased from N to N" plotted as a function of the new (lower) dose-per-fractlon. The data were taken from experiments in which 3, 4, 5, 10 or 20 dose fractious were given and all ADr values relate to a doubling in the number of fractions. The tissues irradiated were human skin ([[]), hemoleucopoietic tissue (H), jejunum (J), descending colon (C), lung (L), callus-forming periosteal tissue (P), stomach (S) and a mouse mammary carcinoma ( A ) .
marrow (measured by LD~o/30 [6]), most values for AD, are not greatly different from those for h u m a n skin [1]. The overall treatment durations in experiments on gastric mucosa and hemoleucopoietic tissue were 9 and 11 days respectively and rapid repopulation probably increased AD, above that expected to result from repair of sublethal injury alone. T h e data for colon [7] and j e i u n u m [8] came from experiments using 3-hr fractionation intervals which minimized repopulation. Callus-forming tissue [9], lung [10] and h u m a n skin [1] would be expected to undergo minimal repopulation in the experiments from which the data in Fig. 1 were drawn. Repopulation was also excluded as a significant factor in the 5 and 10 dose fraction data obtained by Howes et al. [11] for mouse m a m m a r y carcinoma. Although the differences between data in Fig. 1 are small they could be significant, especially since they would be multiplied by fraction n u m b e r in clinical practice. The data in Fig. 1, derived from a variety of tissues, support the conclusion of Dutreix et al., that when a dose is divided into a large n u m b e r of fractions, further increase of fraction number is of less importance to tissue sparing than is suggested by the iso-effect formulae of Ellis [2] or Cohen [3]. This reflects the importance of non-repairable injury in determining the response of tissues to low doses. The other implication from the data in Fig. 1 is that the survival curve shape at low doses must be similar for the cells of the eight various tissues--that is, their sensitivity to nonrepairable damage must be similar as must their capacity for sublethal damage and its repair. Furthermore, there is no appreciable difference in ~ 9 , between normal tissues and the one malignant tissue for which data are available. This is similar to the data for D, [4, 12]. T h e data for stomach probably reflect the large effect of repopulation on the incremental dose necessary for an iso-effect in a rapidly proliferating tissue when the overall time is extended. Similar conclusions have been reached by Wambersie et al. [13] based on experiments in which mouse intestine and skin were exposed to multiple doses. In summary, although there is a critical divergence at low doses, the data for mouse tissues are similar to those given for h u m a n skin by Dutreix et al. [1] and support the conclusions: i. that the capacity of m a n y normal cells for accumulating and repairing sublethal radiation injury is probably not greatly different [4, 12].
Lethal and Sublethal Cellular Injury in Multifraction Irradiation
ii. that fixed exponents used for fraction number and time in iso-effect formulae [2, 3] are inappropriate. At low dosesper-fraction, repair of sublethal iniury is complete, or nearly so, and hence, additional fractionation of dose does not give appreciable additional sparing, whereas
rapidly-regenerating tissues, due to the lengthening of overall time, would continue being spared by repopulation.
A©l~xowledgements--I am indebted to Dr. A. E. Howes for permitting me to use unpublished data.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
583
J. I)UTREIX,A. WAMBERSIEand C. BOUNIK,Cellular recovery in human skin reactions: Application to dose fraction number overall time relationship in radiotherapy. Europ. d. Cancer 9, 159 (1973). F. ELLIS,Nominal standard dose and the ret. Br. d. Radio l. 44, 101 (1971). L. COHEN, The statistical prognosis in radiation therapy. Amer. d. Roentgenol. 84, 741 (1960). H . R . WITHERS,Recovery in normal and malignant tissues. IVth International Congress of Radiation Research, Evian, France (1970). K.Y. CHENand H. R. WITHERS,Survival characteristics of stem-cells of gastric mucosa exposed to localized gamma irradiation in C3H mice. Int. d. Radiat. Biol. 21, 521 (1972). T . L . PHILLIPS and E. J. AINSWORTH, Altered split-dose recovery in mice irr~diated under hypoxic conditions. Radiat. Res, 39, 317 (1969). H . R . WITI-IERSand K. MASON,The kinetics of recovery in irradiated colonic mucosa of the mouse. Cancer 34, 896 (1974). H . R . WITHERS,A. M. CHU and B. O. REID (In preparation.) S. HAYASmand H. D. SUIT, Effect of fractionation of radiation dose on callus formation at site of fracture. Radiology 101' 181 (1971). T . L . PHInLIPS,'Split-dose recovery in euoxic and hypoxic normal and tumor cells. Radiology 105, 127 (1972). A.E. HowEs and H. D. SUIT,personal communication. H . R . WITHERS, Capacity for repair in cells of normal and malignant tissues. In Time & Dose Relationships in Radiation Biology as Applied to Radiotherapy, Brookhaven National Laboratory Report 50203 (C-57), 1970, pp. 54-69. A ]~AMBERSIE,J. DUTREIX,J. GUEULETTE and J. LELLOUCH, Early recovery for intestinal stem cells, as a function of dose per fraction, evaluated by survival rate after fracfionated irradiation of the abdomen of mice Radiat. Res. 58, 498 (1974).
Lethal and Sublethal Cellular Injury in Multifraction Irradiation H. RODNEY W I T H E R S
Section of Experimental Radiotherapy, The University of Texas M. D. Anderson Hospital and Tumor Institute at Houston, 6723 Bertner Avenue, Houston, Texas, U.S.A. The dose Dr measured by Dutreix, W a m bersie and Bounik, and reported in their recent paper in this journal [1] is not the same as ( D N - - D 1 ) / ( N - - 1)which is the usual measure of recovery per fractionation interval and for which Dr would be a more apt symbol. The value measured by Dutreix et al would be better described as ~D r since they measured the increase in the dose, expressed as the incremental dose per fraction, required to achieve an iso-effect when the fraction number was doubled. The difference between Dr and ADr can be best illustrated by an, example. Assume a certain effect could be achieved with a single dose of 1350 rads, 2 doses of 800 rads, 4 doses of 450 rads or 8 doses of 240 rads. If there had been no additional sparing fi:om dividing the dose into 4 instead of 2 fractio:as, the dose schedule would have been 4 x 400 rads. Since the dose needed per fraction was 450rads, AD, = 50 rads. Similarly, had there been no additional recovery from dividing the dose into 8 fractions instead of 4, the do:~e per fraction would have been 1800/8 = 225rads: since a dose of 8 x 240 was needed, ADr = 15 fads for an increase from 4 to 8 fractions. It is not necessary that the number of dose fractions be doubled to measure AD,. Since it is the increase in dose per fraction needed for an iso-effect when the number of dose fractions is increased (from N t o N'), a more general expression is:
ADr =
DN,~D N
iV" Since the value for LxD, is not only dependent upon doses per fraction, but also upon the magnitude of change in fraction number, the expression will be written as: D N, ~ O N
ADr(N'/N) =
iV"
For comparison,
Dr = DN'--DI N'--I
or
DN--D1 N--1
The differences between D, and AD, for the hypothetical example used above are shown in Table 1.
Table 1 2N 2 4 8
D,(rads)
AD,(2N/~) (rads)
1 6 0 0 - 1350 - 250 1 1 8 0 0 - 1350 = 150 3 1 9 2 0 - 1350 - 93 7
1 6 0 0 - 1350 = 125" 2 1 8 0 0 - 1600 = 50 4 1 9 2 0 - 1800 -- 15 8
*This value is only conceptually valid if the single dose, 1350 rads, is considered to be two equal doses of 675 rads.
Although it is not shown in Table 1, the increase in dose-per-fraction if the fraction number were increased from 2 to 8 would be
Total dose in N" fractions N"
Ds--D2~ = 1920--1600 = 40 fads. 8
Total dose in N fractions iV"
8
Thus, insteadof replacing 2 × 800 fads by 8 x 200 rads, the new dose schedule for the same effect would be 8 × 240 rads. Since possible changes in fraction number are limitless, further discussion in this letter will be restricted, for convenience,
Accepted 10 O c t o b e r 1973. *This work was supported in part by Grants C A 11138 and C A 06294 from the National Institutes of Health.
581
582
H. Rodney Withers
to examples in which the n u m b e r of fractions is doubled. Values for AD, and D, diverge rapidly at low doses-per-fraction (Table 1). A simple explanation of this is as follows: The amount of sublethal injury deposited is proportional to dose and hence, as dose is increased, so is the amount of sublethal injury deposited and repaired. Thus, D, increases with dose, even at very low doses. However, at low doses, when all sublethal damage is completely repaired and cell killing results only from non-repairable injury, decreasing the dose-per-fraction cannot increase the amount of sublethal injury repaired, and hence, cannot increase further the sparing effect of dose-fractionation. Therefore, at low dosesper-fraction, AD, approaches zero. As Dutreix et al. have emphasized, the absolute amount of sublethal injury repaired per fractionation interval (D,) is not as important to radiotherapists as the change in the amount repaired (AD,) when the dose-per-fraction is altered. ~ 9 , is a practical value and is the type of information radiotherapists seek from isoeffect formulae [2, 3]. In their Fig. 6, Dutreix et al. plotted values for AD, on the same graph as values of D, for skin and other tissues. Other data for AD, are presented here on the same graph (Fig. 1) as the data of Dutreix et al., for h u m a n skin. The value for AD, for h u m a n skin at a dose of 200 rads is shown as 25 rads or less, but it may be closer to 0 than 25 rads (1, 13). Thus the h u m a n and murine data may be more separated at low doses than suggested by the symbols in Fig. 1. Except for gastric mucosa [5] and bone AOr For Doubling N S
150-
J
"~ I00 o
d
~o
C p
o
•
L
H J,~ 0
o
2~o
46o'-doo
Dose Per Fraction
Fig. 1. The increase in dose (per fraction), ADr(2mN) necessary for an iso-effect when the number of dose fractions is increased from N to N" plotted as a function of the new (lower) dose-per-fractlon. The data were taken from experiments in which 3, 4, 5, 10 or 20 dose fractious were given and all ADr values relate to a doubling in the number of fractions. The tissues irradiated were human skin ([[]), hemoleucopoietic tissue (H), jejunum (J), descending colon (C), lung (L), callus-forming periosteal tissue (P), stomach (S) and a mouse mammary carcinoma ( A ) .
marrow (measured by LD~o/30 [6]), most values for AD, are not greatly different from those for h u m a n skin [1]. The overall treatment durations in experiments on gastric mucosa and hemoleucopoietic tissue were 9 and 11 days respectively and rapid repopulation probably increased AD, above that expected to result from repair of sublethal injury alone. T h e data for colon [7] and j e i u n u m [8] came from experiments using 3-hr fractionation intervals which minimized repopulation. Callus-forming tissue [9], lung [10] and h u m a n skin [1] would be expected to undergo minimal repopulation in the experiments from which the data in Fig. 1 were drawn. Repopulation was also excluded as a significant factor in the 5 and 10 dose fraction data obtained by Howes et al. [11] for mouse m a m m a r y carcinoma. Although the differences between data in Fig. 1 are small they could be significant, especially since they would be multiplied by fraction n u m b e r in clinical practice. The data in Fig. 1, derived from a variety of tissues, support the conclusion of Dutreix et al., that when a dose is divided into a large n u m b e r of fractions, further increase of fraction number is of less importance to tissue sparing than is suggested by the iso-effect formulae of Ellis [2] or Cohen [3]. This reflects the importance of non-repairable injury in determining the response of tissues to low doses. The other implication from the data in Fig. 1 is that the survival curve shape at low doses must be similar for the cells of the eight various tissues--that is, their sensitivity to nonrepairable damage must be similar as must their capacity for sublethal damage and its repair. Furthermore, there is no appreciable difference in ~ 9 , between normal tissues and the one malignant tissue for which data are available. This is similar to the data for D, [4, 12]. T h e data for stomach probably reflect the large effect of repopulation on the incremental dose necessary for an iso-effect in a rapidly proliferating tissue when the overall time is extended. Similar conclusions have been reached by Wambersie et al. [13] based on experiments in which mouse intestine and skin were exposed to multiple doses. In summary, although there is a critical divergence at low doses, the data for mouse tissues are similar to those given for h u m a n skin by Dutreix et al. [1] and support the conclusions: i. that the capacity of m a n y normal cells for accumulating and repairing sublethal radiation injury is probably not greatly different [4, 12].
Lethal and Sublethal Cellular Injury in Multifraction Irradiation
ii. that fixed exponents used for fraction number and time in iso-effect formulae [2, 3] are inappropriate. At low dosesper-fraction, repair of sublethal iniury is complete, or nearly so, and hence, additional fractionation of dose does not give appreciable additional sparing, whereas
rapidly-regenerating tissues, due to the lengthening of overall time, would continue being spared by repopulation.
A©l~xowledgements--I am indebted to Dr. A. E. Howes for permitting me to use unpublished data.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
583
J. I)UTREIX,A. WAMBERSIEand C. BOUNIK,Cellular recovery in human skin reactions: Application to dose fraction number overall time relationship in radiotherapy. Europ. d. Cancer 9, 159 (1973). F. ELLIS,Nominal standard dose and the ret. Br. d. Radio l. 44, 101 (1971). L. COHEN, The statistical prognosis in radiation therapy. Amer. d. Roentgenol. 84, 741 (1960). H . R . WITHERS,Recovery in normal and malignant tissues. IVth International Congress of Radiation Research, Evian, France (1970). K.Y. CHENand H. R. WITHERS,Survival characteristics of stem-cells of gastric mucosa exposed to localized gamma irradiation in C3H mice. Int. d. Radiat. Biol. 21, 521 (1972). T . L . PHILLIPS and E. J. AINSWORTH, Altered split-dose recovery in mice irr~diated under hypoxic conditions. Radiat. Res, 39, 317 (1969). H . R . WITI-IERSand K. MASON,The kinetics of recovery in irradiated colonic mucosa of the mouse. Cancer 34, 896 (1974). H . R . WITHERS,A. M. CHU and B. O. REID (In preparation.) S. HAYASmand H. D. SUIT, Effect of fractionation of radiation dose on callus formation at site of fracture. Radiology 101' 181 (1971). T . L . PHInLIPS,'Split-dose recovery in euoxic and hypoxic normal and tumor cells. Radiology 105, 127 (1972). A.E. HowEs and H. D. SUIT,personal communication. H . R . WITHERS, Capacity for repair in cells of normal and malignant tissues. In Time & Dose Relationships in Radiation Biology as Applied to Radiotherapy, Brookhaven National Laboratory Report 50203 (C-57), 1970, pp. 54-69. A ]~AMBERSIE,J. DUTREIX,J. GUEULETTE and J. LELLOUCH, Early recovery for intestinal stem cells, as a function of dose per fraction, evaluated by survival rate after fracfionated irradiation of the abdomen of mice Radiat. Res. 58, 498 (1974).