1990, The British Journal of Radiology, 63, 114-119
Radiobiological rationale for compensation for gaps in radiotherapy regimes by post-gap acceleration of fractionation By T. E. Wheldon, BSc, PhD, FlnstP and A. Barrett, MRCS, MRCP, FFR Radiation Oncology Research Group, Beatson Oncology Centre, Western Infirmary, Glasgow G11 6NT and Department of Clinical Physics and Bio-Engineering, 11 West Graham Street, Glasgow G4 9LF
(Received April 1989 and in revised form September 1989)
Abstract. It is now recognized that clonogenic tumour cells may repopulate vigorously during radiotherapy. Gaps in treatment schedules which lead to prolongation of overall treatment time may therefore cause sparing of tumour. Acute-responding normal tissues will also be spared if repopulation by surviving stem cells takes place. However, it is unlikely that stem cells in lateresponding normal tissues repopulate significantly over the time-scale of a conventional treatment regime; these tissues will therefore experience little or no sparing as a result of a gap. This poses a dilemma since tumour cell repopulation implies that an increased therapeutic effect in the post-gap phase of treatment may be necessary to compensate for any prolongation of treatment time, but it is difficult to achieve increased tumour effect without also increasing damage to late-responding normal tissues. Neither increased total dose nor increased fraction size is able to achieve this. A possible solution is provided if total treatment time can be held constant, with unchanged total dose and fraction size, by use of twice-daily conventionally sized dose fractions administered after the gap. Provided the twice-daily fractions are sufficiently spaced (not less than 6-8 h apart), the result will be to offset repopulation in tumour and acute-responding normal tissues without additional impairment of late-responding normal tissues. The feasibility of the approach depends on being able to complete treatment by the time originally intended; it is therefore more readily applicable to gaps occurring early rather than late in a treatment schedule. The strategy should be especially advantageous for tumours with rapid repopulative potential in sites where risk of damage to late-responding normal tissues imposes limitation of dose.
In recent years, split-course radiotherapy regimes with a gap between two phases of conventionally fractionated treatment have become less popular. This is because of evidence of reduced therapeutic differential for regimes involving prolongation of total time and because of indirect kinetic evidence of rapid repopulation of surviving tumour cells during a course of treatment (Withers et al, 1988). Unplanned gaps, however, still occur. These may arise for two reasons. Firstly, an initially unintended gap may be imposed for clinical reasons, for example where a patient shows an unexpectedly severe mucosal reaction which must be allowed to decrease before treatment can be resumed. Secondly, gaps may occur for a variety of reasons unrelated to radiation reactions: these include patient illness, machine breakdown and public holidays. In the case of gaps in the first category, the continuation of the regime must be managed empirically. The total dose given will depend on what mucosal reactions will permit, and this will have to be reviewed throughout treatment. The second group of reasons for gaps pose a clinical dilemma of a different kind. Since the gap has not been forced by untoward radiation reactions, and evidence exists that time prolongation may reduce tumour curability, there is an implication that some form of compensation for the gap is required. What should this be? In practice, clinical strategies that are used include neglect of the gap, increased number of fractions and total dose or increased dose per fraction. 114
The purpose of this paper is to draw attention to an alternative strategy: post-gap acceleration of fractionation, which may be advantageous. Repopulation in normal tissues and tumours
It has long been known that prolongation of overall time, either by introduction of a gap, or by wider spacing of treatment fractions in a uniform regime, has a sparing effect (for given total dose) on acuteresponding tissues such as epidermis, gastrointestinal tract and oral mucosa and haemopoietic tissues. This is probably because of repopulation by surviving clonogenic cells. Evidence exists (Turesson & Notter, 1984) that basal cell repopulation in epidermis begins approximately 4 weeks after the start of treatment and is rapid thereafter. It is likely that other acute-responding tissues behave similarly, though with a tissue-specific time of onset of repopulation. Some attempts have been made to quantify the sparing effects of repopulation for acute-responding tissues by power-law isoeffect formulae of the nominal standard dose type (Ellis, 1969; Kirk et al, 1971; Orton & Ellis, 1973). However, it seems most unlikely that the mathematical form of power-functions is appropriate for doing this, and the corrections for time protraction predicted by these models are probably in error (Fowler, 1984). Similar attempts to incorporate a time-factor in the linear quadratic model run into difficulties such as the need to measure a and /J values individually (rather The British Journal of Radiology, February 1990
Post-gap acceleration of fractionation
than the ajfi ratio) as well as the relevant kinetic factors (Wheldon & Amin, 1988). The current status of the time-dependent formulation of the linear quadratic model has been included in the recent review by Fowler (1989). At present, it seems doubtful whether time factors are sufficiently well known to enable their clinical application. Although time protraction will usually result in some sparing of acute-responding normal tissues, quantitation of this remains unreliable. In contrast, it is likely that late-responding normal tissues are little spared by time prolongation within the time scales of conventional radiotherapy (Thames & Hendry, 1987; Hall, 1988). Theoretically, a prompt response of repopulation in late-responding tissues is not expected (Michalowski, 1981). It is possible that lung may be an exception in that time prolongation over a scale of weeks does seemingly result in modest sparing; this is attributed to the poorly understood phenomenon of "slow repair", but this has not been seen in other late-responding organs (Field et al, 1976). Since lateresponding tissues are usually dose-limiting in radiotherapy, and repopulation probably does not occur during a typical course, it seems unlikely that gaps of only a few days would enable higher doses of radiation to be given without increased risk of tissue injury. In the case of tumours, the recognition of high repopulative capacity in those which are slowly growing at the start of therapy has been an important development. Analysis of reduced therapeutic benefit in pro/onged or split-course regimes has provided evidence for actual doubling times of surviving clonogenic cells which are typically of the order of a few days (Thames & Hendry, 1987, pp. 124-127). Indirect evidence supports a proportionality relationship between recurrence time of irradiated tumours and the cell kinetic potential doubling time (Trott & Kummermehr, 1985) which may be a predictive parameter for tumours with high repopulative capacity. Potential doubling times of 3 or 4 days have been reported in several tumour types (Trott & Kummermehr, 1985) and as short as approximately 1-2 days in nephroblastoma (Aherne & Buck, 1971). Also, the potential doubling time may underestimate repopulation since an expansion of the clonogenic growth fraction (taken to be constant in calculations of potential doubling time) occurs in experimental tumours (Steel, 1977) and seems plausible for human tumours. These considerations have given rise to interest in the use of time-shortened (accelerated) treatment schedules as a means of improving the radiotherapy of at least some tumour types (Thames et al, 1983). The same considerations suggest that gaps of some days' duration are not necessarily negligible and that significant tumour repopulation might occur if remedial action is not taken. Neglect of gaps If a gap is simply neglected, the radiotherapy regime resumes when possible and ends at the same total dose level originally intended. The net effect will be that the total dose is delivered over an increased total time. The Vol. 63, No. 746
Logaithmic increase of tumour cell number ( A Log N ) 3 r
2 -
0
2 4 6 8 Prolongation of treatments (days)
10
Figure 1. Estimated change in tumour cell number (A log N) expected to result from treatment prolongation for tumour doubling times in the range 1-5 days.
effects on normal tissues will be sparing of acuteresponding tissues with negligible effects on lateresponding tissues. However, it is the possible sparing of tumours that gives rise to concern. This will, of course, vary from one tumour to another in accordance with its radiobiological and kinetic properties. Some idea of the importance of gaps in terms of tumour repopulation is given by Fig. 1, which shows the net increase of tumour cell number, for doubling times in the range 1-5 days, as a function of the magnitude of prolongation of the treatment regime resulting from the gap. It is worth noticing that this calculation does not require the tumour cells to be proliferating at this rate during the gap. The importance of the gap is that it prolongs overall treatment time. If increased tumour cell proliferation takes place as a result of prolongation (for example starting after the gap) then prolongation will reduce the net effect of treatment on the tumour. Significant increases of tumour cell number could be facilitated by gaps of only a few days. The implication is that such gaps cannot be neglected without increased risk of tumour recurrence. Compensation by increased total dose A possible strategy of gap compensation is to give additional treatment i.e. by adding conventionally sized 115
T. E. Wheldon and A. Barrett
Compensatory dose (Gy) ( 2 G y fractions) 30
Compensatory dose (Gy) (2 Gy fractions) 30
20
10
TD=5days
0
Prolongation (days) (a)
Prolongation (days) (b)
Figure 2. Estimated dose (given as 2Gy fractions) to compensate for tumour proliferation during treatment prolongation for doubling times in the range 1-5 days for (a) radiosensitive tumour cell populations (S2 = 0.22) and (b) radioresistant tumour cell population (S2 = 0.58). The S2 values are those given by Fertil and Malaise (1985) as the mean for the most sensitive and the most resistant of six groups of tumour cell lines ranked for radiosensitivity in vitro. It should be noted that doses to compensate for tumour proliferation will not necessarily result in equal effects on normal tissues.
treatment fractions. There is however, a two-fold difficulty. First, little sparing of late-responding tissues is likely to have resulted from the gap. If the originally intended treatment came close to tolerance for lateresponding tissues, there may be no safe margin for further increase of dose. Secondly, the additional dose which should be given to compensate for tumour repopulation will depend on tumour survival curve parameters as well as repopulation kinetics and will vary not only from one tumour type to another but from patient to patient. Some idea of the magnitude of compensatory dose increments required for gaps may be gained by a calculation which makes use of the in vitro tumour radiosensitivity data of Fertil and Malaise (1985). These authors summarized data on a large number of human tumour cell lines, dividing these into six categories, ranked for radiosensitivity. Conveniently, cell line radiosensitivity may be represented by the S2 value: the surviving fraction following a 2Gy radiation dose. Fertil and Malaise reported that the most resistant group has a mean S2 value of 0.58 and the most sensitive group a mean S2 value of 0.22. The compensatory dose 116
(given as 2Gy fractions) has been calculated for the most resistant and most sensitive groups, for doubling times ranging from 1-5 days, as a function of prolongation caused by a gap. Figure 2 shows the results of these calculations and demonstrates the wide range of compensatory doses that would be required. This form of compensation is accompanied by the difficulty of knowing whether the dose compensation used is appropriate for the individual tumour, and whether there will be an increased risk of injury to late-responding tissues. Compensation by increased dose per fraction
A related strategy is to increase fraction size in the post-gap phase of treatment to keep overall treatment time the same. This has the merit that no estimation of tumour repopulation seems to be required: since the overall treatment time remains the same, the contribution to net tumour survival made by repopulation will be unchanged. The problem is that if the gap provides no sparing of late-responding tissues, these tissues will experience greater damage than originally intended if fraction size is increased without change of total of dose. The British Journal of Radiology, February 1990
Post-gap acceleration offractionation Table I. Treatment schedules incorporating increased fraction size following a gap to give unchanged treatment time and unchanged radiobiological effect on typical tumour
Total Dose Equivalent ( 2 Gy Fractions) For Late-responding Tissue
Duration of gap (days)
8CH
76-
Post-gap phase of treatment schedule Early stage gap
Mid-stage gap
23x2.16 Gy 21x2.34Gy 19x2.57 Gy 17x2.84 Gy 15x3.17Gy
13x2.28 Gy 3x3.17Gy llx2.65Gy 1 x 7.89 Gy 9x3.17 Gy 7 x 3.94 Gy 5 x 5.23 Gy
Late stage gap
Mid Gap 7268-
Early Gap
2 4 6 8 10
Notes. (1) The originally intended regime (without gaps) was taken to be 30 x 2 Gy in 6 weeks. (2) Gap position was denned as follows: early stage—gap 60 commencing after 1 week of therapy (5x2 Gy given); 2 4 6 8 10 mid-stage—gap commencing after 3 weeks of therapy Gap Length (15x2 Gy given) and late stage—gap commencing after 5 ( Days) weeks of therapy (25 x 2 Gy given). (3) Fraction number in the post-gap phase was taken to be Figure 3. The diagram depicts the biological effect on latethe number of treatment days remaining (within the 6 responding normal tissues (expressed as equivalent total dose week time period originally intended) following the gap. given as 2 Gy fractions) which would result from attempting to For the late stage gap, with gap duration > 5 days, the 6 compensate for gaps of varying size, occurring at three week period is exceeded by the gap; hence this procedure different positions in the schedule, by the strategy of increased cannot be used to give unchanged treatment time and fraction size. The schedule originally intended was taken to be unchanged effect on tumour. 30 x 2 Gy over 6 weeks. Gap position was denned as at 1 week (4) Fraction size in the post-gap phase was calculated from (early stage), 3 weeks (mid-stage) or 5 weeks (late stage) after the linear quadratic model with a//? = 20 Gy ("typical" the commencement of therapy. The number of fractions in the value for a tumour) such that the post-gap phase, together compensatory post-gap phase of treatment was taken to be the with treatment already given, should have equivalent number of treatment days remaining within the 6 week period tumour effect to the originally intended regime. and the fraction size was chosen such that the composite regime should have the same effect on a typical tumour (a//? = 20 Gy on the linear quadratic model) as the originally intended regime (Table I). The calculation of equivalent total dose (given as 2 Gy fractions) for damage to late-responding normal tissues used the linear quadratic model with a//? = 3 Gy. 64-
The magnitude of this effect varies from one situation to another but may be illustrated by some examples. Consider the situation in which a conventional radical regime (30 x 2 Gy, 6 weeks) is interrupted by a gap of variable length which can occur anywhere within the schedule. Specifically, we shall consider an early stage gap (after the first week of therapy), a mid-stage gap (after the third week of therapy) and a late stage gap (after the fifth week of therapy). In each case, suppose the fraction size of remaining treatments is increased to keep overall time the same and the radiobiological effect on the tumour as originally intended. The choice of fraction size, if radiobiological effects on the tumour are to be unchanged, requires knowledge of the radiobiological properties of each individual tumour. For example, if the linear quadratic model is used to calculate isoeffective doses, the a/j5 ratio for the tumour must be known. Usually, this information will not be available. However, studies of experimental tumours have suggested that an a//? ratio of approximately 20 Gy may be typical, at least for murine tumours, although conVol. 63, No. 746
siderable variation is seen (Williams et al, 1985). Adopting this as a representative value, it is theoretically possible to compute fraction size increases that just compensate for the occurrence of the gap in terms of effects on the tumour. Table I shows how the regimen would have to be modified in its post-gap phase to give equal effects on the tumour. Unfortunately, the effect on late-responding normal tissues is no longer the same. This phenomenon is illustrated in Fig. 3, which shows how the resultant biological effect on late-responding tissue increases with gap length for each of the three gap positions considered. The effect on late-responding normal tissues is expressed in terms of a "conventional schedule equivalent", i.e. the total dose (given as 2 Gy fractions) which would have the same effect on the tissue concerned as the actual regime. These results show that the biological effects on late-responding normal tissues would be greater than originally intended (60 Gy as 2Gy fractions). This shows that appropriate compensation, to give the same effects as originally intended on both tumour and late-responding tissues, is not possible even if the relevant a/j5 ratio values are all known. The strategy of increased fraction size cannot therefore 117
T. E. Wheldon and A. Barrett
time unchanged. The strategy described involves a change in time-structure to compensate for a time effect (the gap), and does not require a "trade-off" of time and dose. General equivalence Of course, the strategy is only feasible in the case of The time gap problem is a special case of the problem of "general equivalence" i.e. the conditions under which gaps that are sufficiently short in relation to the treattwo schedules of differing fractionation structure can ment time remaining such that it is still possible to keep have identical effects on all tissues irradiated. Recently, the total time constant. Large gaps, which cause the Deehan and O'Donoghue (1988) have discussed the original treatment time to be exceeded before therapy conditions for general equivalence of two schedules resumes, cannot be completely allowed for in this way which are given in the same overall time. Here, the although the therapeutic disadvantage could be reduced. problem is to derive schedule parameters such that a Greater importance consequently attaches to gaps sequence of two (or more) fractionated schedules are occurring later rather than earlier in treatment, since the simultaneously equivalent for all tissues to a particular opportunity for post-gap adjustment of the time-strucuniform schedule (i.e. independent of cc/fi ratios). In the ture will be less. circumstances described in this paper, we have the degeThe feasibility of the strategy may also be limited by nerate case where the "intended" schedule and the practical considerations. Where a gap involving many schedule already given have the same fraction size. The patients occurs as a result of machine breakdown, it equations for general equivalence have the solutions may be impractical to institute post-gap acceleration for such that: all such patients. Patients might then be selected for (1) The schedule remaining to be given must also post-gap acceleration on the basis of potential doubling time of tumour type (Trott & Kummermehr, 1985). have the same fraction size. (2) It must have the number of fractions that is the difference between the intended schedule and the Radiobiological processes other than repopulation The consequences of gaps in treatment cannot be schedule already given. If the schedule remaining to be given has any other considered exclusively in terms of repopulation. Redisfraction size or fraction number, general equivalence is tribution is also likely to be an important process, with impossible and the best that can be achieved is an gaps allowing increasing time for reassortment of equivalence for only one value of a//?. This means that surviving clonogenic cells in both normal tissues and general equivalence between the originally intended tumours. It is possible that clonogenic cells in lateschedule and the schedule including a time-gap usually responding tissues reassort relatively slowly. Gaps cannot be achieved by increased total dose or dose per would then be relatively disadvantageous to such tissues and accelerated fractionation relatively sparing. It is fraction. also conceivable that gaps might allow increased time for tumour reoxygenation. The generally poor theraRationale for post-gap acceleration The above considerations lead to disappointing peutic effects of treatment time prolongation (Thames & conclusions in terms of compensating for gaps. A diffi- Hendry, 1987) do not suggest that this is likely to be an culty with some compensation strategies is that they important factor. However, the possibility that post-gap attempt a "trade-off" between time and dose or dose per acceleration might allow insufficient time for reoxygenafraction. Even if all the relevant radiobiological para- tion during this phase of treatment cannot yet be meters are known, this trade-off differs between normal excluded. Accumulating evidence on the efficacy of tissues and tumours making any dose compensation regimes that are uniformly accelerated throughout strategies incapable of achieving the same overall effects should provide relevant evidence. Mitotic delay is not expected to be an important factor on the basis of in as the originally intended schedule. An alternative approach is to try to keep the overall vitro evidence, but should it prove greater than time constant, despite the gap, but without changing expected, this would tend to favour the strategy of posteither dose or dose per fraction. Simply, fractions would gap acceleration, which would preferentially stop repobe given more frequently after the gap than before it i.e. pulation in the tumour and acute-responding tissues, the post-gap phase of treatment would be accelerated, with little effect on non-repopulating, late-responding though the regimen as a whole would not. This could be tissues. There seem to be no strong grounds for done by giving two rather than one conventionally sized expecting post-gap acceleration to be therapeutically fractions daily following the gap for as many days as is disadvantageous rather than otherwise. necessary to ensure total time remains constant. Current evidence implies that an interval of at least 6h (and Conclusions preferably more) should be allowed between any two Evidence exists that implies that unintended gaps fractions to avoid increased damage to normal tissues. leading to increased total time may be important in Provided this is ensured, the effect on late-responding facilitating tumour repopulation. Compensatory stratetissues should be little altered by changes of time- gies involving changes in total dose or dose per fraction structure, whilst additional repopulation in tumours and are beset by problems. A strategy of post-gap accelin acute-responding tissues is offset by keeping the total eration of fractionation involves fewer radiobiological provide a satisfactory solution to the problem of gap compensation.
118
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Post-gap acceleration of fractionation
difficulties; this strategy is most clearly indicated for tumours likely to be capable of fast repopulation occurring in sites where dose limitation is imposed by tolerance of late-responding normal tissues. References AHERNE, W. & BUCK, P., 1971. The potential cell doubling time in neuroblastoma and nephroblastoma. British Journal of Cancer, 25, 691-696. ELLIS, F., 1969. Dose, time and fractionation: a clinical hypothesis. Clinical Radiology, 20, 1-7. DEEHAN,
C.
&
O'DONOGHUE,
J.
A.,
1988.
Biological
equivalence between fractionated radiotherapy treatments using the linear quadratic model. British Journal of Radiology, 61, 1187-1188. FERTIL, B. & MALAISE, E. P., 1985. Intrinsic radiosensitivity of
human cell lines is correlated with radioresponsiveness of human tumours. An analysis of 101 published survival curves. International Journal of Radiation Oncology, Biology, Physics, 11, 1699-1707. FIELD, S. B., HORNSEY, S. & KUTSUTANI, Y., 1976. Effects of
fractionated irradiation on mouse lung and a phenomenon of slow repair. British Journal of Radiology, 49, 700-707. FOWLER, J. F., 1984. What next in fractionated radiotherapy? British Journal of Cancer, 49, Supplement vi, 285-300. FOWLER, J. F., 1989. The linear quadratic model and progress in fractionated radiotherapy. British Journal of Radiology, 62, 679-694. HALL, E. J., 1988. Radiobiology for the Radiologist, 3rd edn (J. B. Lippincott, Philadelphia).
MICHALOWSKI, A., 1981. Effects of radiation on normal tissues: hypothetical mechanisms of limitations of in situ assays of clonogenicity. Radiation Environmental Biophysics, 19, 157-172. ORTON, C. G. & ELLIS, F., 197?. A simplification in the use of
the NSD concept in practical radiotherapy. British Journal of Radiology, 46, 529-537. STEEL, G. G., 1977. Growth Kinetics of Tumours (Clarendon Press, Oxford). THAMES, H. D., PETERS, L. J., WITHERS, H. R. & FLETCHER, G.
H., 1983. Accelerated fractionation versus hyperfractionation: rationales for several treatments per day. International Journal of Radiation Oncology, Biology, Physics, 9, 127-138. THAMES, H. D. & HENDRY, J. H.,
1987. Fractionation in
Radiotherapy (Taylor & Francis, London). TROTT, K. R. & KUMMERMEHR, J., 1985. What is known about tumour proliferation rates to choose between accelerated fractionation or hyperfractionation? Radiotherapy and Oncology, 3, 1-9. TURESSON, I. & NOTTER, G., 1984. The influence of the overall
treatment time in radiotherapy on the acute reaction: comparison of the effects of daily and once-a-week fractionation on human skin. International Journal of Radiation Oncology, Biology, Physics, 10, 593-598. WHELDON, T. E. & AMIN, A. E., 1988. The linear-quadratic
model. British Journal of Radiology, 61, 700-702. WILLIAMS, M. V., DENEKAMP, J. & FOWLER, J. F., 1985. A
review of a//? values for experimental tumours: implications for clinical studies of altered fractionation. International Journal of Radiation Oncology, Biology, Physics, 11, 87-96.
KIRK, J., GRAY, W. M. & WATSON, E. R., 1971. Cumulative
WITHERS, H. R., TAYLOR, J. M. G. & MACIEJEWSKI, B., 1988.
radiation effect. Part 1: Fractionated treatment regimes. Clinical Radiology, 26, 159-176.
The hazard of accelerated tumour clonogen repopulation during radiotherapy. Ada Oncologica, 27, 131-146.
Vol. 63, No. 746
119
Radiobiological rationale for compensation for gaps in radiotherapy regimes by post-gap acceleration of fractionation By T. E. Wheldon, BSc, PhD, FlnstP and A. Barrett, MRCS, MRCP, FFR Radiation Oncology Research Group, Beatson Oncology Centre, Western Infirmary, Glasgow G11 6NT and Department of Clinical Physics and Bio-Engineering, 11 West Graham Street, Glasgow G4 9LF
(Received April 1989 and in revised form September 1989)
Abstract. It is now recognized that clonogenic tumour cells may repopulate vigorously during radiotherapy. Gaps in treatment schedules which lead to prolongation of overall treatment time may therefore cause sparing of tumour. Acute-responding normal tissues will also be spared if repopulation by surviving stem cells takes place. However, it is unlikely that stem cells in lateresponding normal tissues repopulate significantly over the time-scale of a conventional treatment regime; these tissues will therefore experience little or no sparing as a result of a gap. This poses a dilemma since tumour cell repopulation implies that an increased therapeutic effect in the post-gap phase of treatment may be necessary to compensate for any prolongation of treatment time, but it is difficult to achieve increased tumour effect without also increasing damage to late-responding normal tissues. Neither increased total dose nor increased fraction size is able to achieve this. A possible solution is provided if total treatment time can be held constant, with unchanged total dose and fraction size, by use of twice-daily conventionally sized dose fractions administered after the gap. Provided the twice-daily fractions are sufficiently spaced (not less than 6-8 h apart), the result will be to offset repopulation in tumour and acute-responding normal tissues without additional impairment of late-responding normal tissues. The feasibility of the approach depends on being able to complete treatment by the time originally intended; it is therefore more readily applicable to gaps occurring early rather than late in a treatment schedule. The strategy should be especially advantageous for tumours with rapid repopulative potential in sites where risk of damage to late-responding normal tissues imposes limitation of dose.
In recent years, split-course radiotherapy regimes with a gap between two phases of conventionally fractionated treatment have become less popular. This is because of evidence of reduced therapeutic differential for regimes involving prolongation of total time and because of indirect kinetic evidence of rapid repopulation of surviving tumour cells during a course of treatment (Withers et al, 1988). Unplanned gaps, however, still occur. These may arise for two reasons. Firstly, an initially unintended gap may be imposed for clinical reasons, for example where a patient shows an unexpectedly severe mucosal reaction which must be allowed to decrease before treatment can be resumed. Secondly, gaps may occur for a variety of reasons unrelated to radiation reactions: these include patient illness, machine breakdown and public holidays. In the case of gaps in the first category, the continuation of the regime must be managed empirically. The total dose given will depend on what mucosal reactions will permit, and this will have to be reviewed throughout treatment. The second group of reasons for gaps pose a clinical dilemma of a different kind. Since the gap has not been forced by untoward radiation reactions, and evidence exists that time prolongation may reduce tumour curability, there is an implication that some form of compensation for the gap is required. What should this be? In practice, clinical strategies that are used include neglect of the gap, increased number of fractions and total dose or increased dose per fraction. 114
The purpose of this paper is to draw attention to an alternative strategy: post-gap acceleration of fractionation, which may be advantageous. Repopulation in normal tissues and tumours
It has long been known that prolongation of overall time, either by introduction of a gap, or by wider spacing of treatment fractions in a uniform regime, has a sparing effect (for given total dose) on acuteresponding tissues such as epidermis, gastrointestinal tract and oral mucosa and haemopoietic tissues. This is probably because of repopulation by surviving clonogenic cells. Evidence exists (Turesson & Notter, 1984) that basal cell repopulation in epidermis begins approximately 4 weeks after the start of treatment and is rapid thereafter. It is likely that other acute-responding tissues behave similarly, though with a tissue-specific time of onset of repopulation. Some attempts have been made to quantify the sparing effects of repopulation for acute-responding tissues by power-law isoeffect formulae of the nominal standard dose type (Ellis, 1969; Kirk et al, 1971; Orton & Ellis, 1973). However, it seems most unlikely that the mathematical form of power-functions is appropriate for doing this, and the corrections for time protraction predicted by these models are probably in error (Fowler, 1984). Similar attempts to incorporate a time-factor in the linear quadratic model run into difficulties such as the need to measure a and /J values individually (rather The British Journal of Radiology, February 1990
Post-gap acceleration of fractionation
than the ajfi ratio) as well as the relevant kinetic factors (Wheldon & Amin, 1988). The current status of the time-dependent formulation of the linear quadratic model has been included in the recent review by Fowler (1989). At present, it seems doubtful whether time factors are sufficiently well known to enable their clinical application. Although time protraction will usually result in some sparing of acute-responding normal tissues, quantitation of this remains unreliable. In contrast, it is likely that late-responding normal tissues are little spared by time prolongation within the time scales of conventional radiotherapy (Thames & Hendry, 1987; Hall, 1988). Theoretically, a prompt response of repopulation in late-responding tissues is not expected (Michalowski, 1981). It is possible that lung may be an exception in that time prolongation over a scale of weeks does seemingly result in modest sparing; this is attributed to the poorly understood phenomenon of "slow repair", but this has not been seen in other late-responding organs (Field et al, 1976). Since lateresponding tissues are usually dose-limiting in radiotherapy, and repopulation probably does not occur during a typical course, it seems unlikely that gaps of only a few days would enable higher doses of radiation to be given without increased risk of tissue injury. In the case of tumours, the recognition of high repopulative capacity in those which are slowly growing at the start of therapy has been an important development. Analysis of reduced therapeutic benefit in pro/onged or split-course regimes has provided evidence for actual doubling times of surviving clonogenic cells which are typically of the order of a few days (Thames & Hendry, 1987, pp. 124-127). Indirect evidence supports a proportionality relationship between recurrence time of irradiated tumours and the cell kinetic potential doubling time (Trott & Kummermehr, 1985) which may be a predictive parameter for tumours with high repopulative capacity. Potential doubling times of 3 or 4 days have been reported in several tumour types (Trott & Kummermehr, 1985) and as short as approximately 1-2 days in nephroblastoma (Aherne & Buck, 1971). Also, the potential doubling time may underestimate repopulation since an expansion of the clonogenic growth fraction (taken to be constant in calculations of potential doubling time) occurs in experimental tumours (Steel, 1977) and seems plausible for human tumours. These considerations have given rise to interest in the use of time-shortened (accelerated) treatment schedules as a means of improving the radiotherapy of at least some tumour types (Thames et al, 1983). The same considerations suggest that gaps of some days' duration are not necessarily negligible and that significant tumour repopulation might occur if remedial action is not taken. Neglect of gaps If a gap is simply neglected, the radiotherapy regime resumes when possible and ends at the same total dose level originally intended. The net effect will be that the total dose is delivered over an increased total time. The Vol. 63, No. 746
Logaithmic increase of tumour cell number ( A Log N ) 3 r
2 -
0
2 4 6 8 Prolongation of treatments (days)
10
Figure 1. Estimated change in tumour cell number (A log N) expected to result from treatment prolongation for tumour doubling times in the range 1-5 days.
effects on normal tissues will be sparing of acuteresponding tissues with negligible effects on lateresponding tissues. However, it is the possible sparing of tumours that gives rise to concern. This will, of course, vary from one tumour to another in accordance with its radiobiological and kinetic properties. Some idea of the importance of gaps in terms of tumour repopulation is given by Fig. 1, which shows the net increase of tumour cell number, for doubling times in the range 1-5 days, as a function of the magnitude of prolongation of the treatment regime resulting from the gap. It is worth noticing that this calculation does not require the tumour cells to be proliferating at this rate during the gap. The importance of the gap is that it prolongs overall treatment time. If increased tumour cell proliferation takes place as a result of prolongation (for example starting after the gap) then prolongation will reduce the net effect of treatment on the tumour. Significant increases of tumour cell number could be facilitated by gaps of only a few days. The implication is that such gaps cannot be neglected without increased risk of tumour recurrence. Compensation by increased total dose A possible strategy of gap compensation is to give additional treatment i.e. by adding conventionally sized 115
T. E. Wheldon and A. Barrett
Compensatory dose (Gy) ( 2 G y fractions) 30
Compensatory dose (Gy) (2 Gy fractions) 30
20
10
TD=5days
0
Prolongation (days) (a)
Prolongation (days) (b)
Figure 2. Estimated dose (given as 2Gy fractions) to compensate for tumour proliferation during treatment prolongation for doubling times in the range 1-5 days for (a) radiosensitive tumour cell populations (S2 = 0.22) and (b) radioresistant tumour cell population (S2 = 0.58). The S2 values are those given by Fertil and Malaise (1985) as the mean for the most sensitive and the most resistant of six groups of tumour cell lines ranked for radiosensitivity in vitro. It should be noted that doses to compensate for tumour proliferation will not necessarily result in equal effects on normal tissues.
treatment fractions. There is however, a two-fold difficulty. First, little sparing of late-responding tissues is likely to have resulted from the gap. If the originally intended treatment came close to tolerance for lateresponding tissues, there may be no safe margin for further increase of dose. Secondly, the additional dose which should be given to compensate for tumour repopulation will depend on tumour survival curve parameters as well as repopulation kinetics and will vary not only from one tumour type to another but from patient to patient. Some idea of the magnitude of compensatory dose increments required for gaps may be gained by a calculation which makes use of the in vitro tumour radiosensitivity data of Fertil and Malaise (1985). These authors summarized data on a large number of human tumour cell lines, dividing these into six categories, ranked for radiosensitivity. Conveniently, cell line radiosensitivity may be represented by the S2 value: the surviving fraction following a 2Gy radiation dose. Fertil and Malaise reported that the most resistant group has a mean S2 value of 0.58 and the most sensitive group a mean S2 value of 0.22. The compensatory dose 116
(given as 2Gy fractions) has been calculated for the most resistant and most sensitive groups, for doubling times ranging from 1-5 days, as a function of prolongation caused by a gap. Figure 2 shows the results of these calculations and demonstrates the wide range of compensatory doses that would be required. This form of compensation is accompanied by the difficulty of knowing whether the dose compensation used is appropriate for the individual tumour, and whether there will be an increased risk of injury to late-responding tissues. Compensation by increased dose per fraction
A related strategy is to increase fraction size in the post-gap phase of treatment to keep overall treatment time the same. This has the merit that no estimation of tumour repopulation seems to be required: since the overall treatment time remains the same, the contribution to net tumour survival made by repopulation will be unchanged. The problem is that if the gap provides no sparing of late-responding tissues, these tissues will experience greater damage than originally intended if fraction size is increased without change of total of dose. The British Journal of Radiology, February 1990
Post-gap acceleration offractionation Table I. Treatment schedules incorporating increased fraction size following a gap to give unchanged treatment time and unchanged radiobiological effect on typical tumour
Total Dose Equivalent ( 2 Gy Fractions) For Late-responding Tissue
Duration of gap (days)
8CH
76-
Post-gap phase of treatment schedule Early stage gap
Mid-stage gap
23x2.16 Gy 21x2.34Gy 19x2.57 Gy 17x2.84 Gy 15x3.17Gy
13x2.28 Gy 3x3.17Gy llx2.65Gy 1 x 7.89 Gy 9x3.17 Gy 7 x 3.94 Gy 5 x 5.23 Gy
Late stage gap
Mid Gap 7268-
Early Gap
2 4 6 8 10
Notes. (1) The originally intended regime (without gaps) was taken to be 30 x 2 Gy in 6 weeks. (2) Gap position was denned as follows: early stage—gap 60 commencing after 1 week of therapy (5x2 Gy given); 2 4 6 8 10 mid-stage—gap commencing after 3 weeks of therapy Gap Length (15x2 Gy given) and late stage—gap commencing after 5 ( Days) weeks of therapy (25 x 2 Gy given). (3) Fraction number in the post-gap phase was taken to be Figure 3. The diagram depicts the biological effect on latethe number of treatment days remaining (within the 6 responding normal tissues (expressed as equivalent total dose week time period originally intended) following the gap. given as 2 Gy fractions) which would result from attempting to For the late stage gap, with gap duration > 5 days, the 6 compensate for gaps of varying size, occurring at three week period is exceeded by the gap; hence this procedure different positions in the schedule, by the strategy of increased cannot be used to give unchanged treatment time and fraction size. The schedule originally intended was taken to be unchanged effect on tumour. 30 x 2 Gy over 6 weeks. Gap position was denned as at 1 week (4) Fraction size in the post-gap phase was calculated from (early stage), 3 weeks (mid-stage) or 5 weeks (late stage) after the linear quadratic model with a//? = 20 Gy ("typical" the commencement of therapy. The number of fractions in the value for a tumour) such that the post-gap phase, together compensatory post-gap phase of treatment was taken to be the with treatment already given, should have equivalent number of treatment days remaining within the 6 week period tumour effect to the originally intended regime. and the fraction size was chosen such that the composite regime should have the same effect on a typical tumour (a//? = 20 Gy on the linear quadratic model) as the originally intended regime (Table I). The calculation of equivalent total dose (given as 2 Gy fractions) for damage to late-responding normal tissues used the linear quadratic model with a//? = 3 Gy. 64-
The magnitude of this effect varies from one situation to another but may be illustrated by some examples. Consider the situation in which a conventional radical regime (30 x 2 Gy, 6 weeks) is interrupted by a gap of variable length which can occur anywhere within the schedule. Specifically, we shall consider an early stage gap (after the first week of therapy), a mid-stage gap (after the third week of therapy) and a late stage gap (after the fifth week of therapy). In each case, suppose the fraction size of remaining treatments is increased to keep overall time the same and the radiobiological effect on the tumour as originally intended. The choice of fraction size, if radiobiological effects on the tumour are to be unchanged, requires knowledge of the radiobiological properties of each individual tumour. For example, if the linear quadratic model is used to calculate isoeffective doses, the a/j5 ratio for the tumour must be known. Usually, this information will not be available. However, studies of experimental tumours have suggested that an a//? ratio of approximately 20 Gy may be typical, at least for murine tumours, although conVol. 63, No. 746
siderable variation is seen (Williams et al, 1985). Adopting this as a representative value, it is theoretically possible to compute fraction size increases that just compensate for the occurrence of the gap in terms of effects on the tumour. Table I shows how the regimen would have to be modified in its post-gap phase to give equal effects on the tumour. Unfortunately, the effect on late-responding normal tissues is no longer the same. This phenomenon is illustrated in Fig. 3, which shows how the resultant biological effect on late-responding tissue increases with gap length for each of the three gap positions considered. The effect on late-responding normal tissues is expressed in terms of a "conventional schedule equivalent", i.e. the total dose (given as 2 Gy fractions) which would have the same effect on the tissue concerned as the actual regime. These results show that the biological effects on late-responding normal tissues would be greater than originally intended (60 Gy as 2Gy fractions). This shows that appropriate compensation, to give the same effects as originally intended on both tumour and late-responding tissues, is not possible even if the relevant a/j5 ratio values are all known. The strategy of increased fraction size cannot therefore 117
T. E. Wheldon and A. Barrett
time unchanged. The strategy described involves a change in time-structure to compensate for a time effect (the gap), and does not require a "trade-off" of time and dose. General equivalence Of course, the strategy is only feasible in the case of The time gap problem is a special case of the problem of "general equivalence" i.e. the conditions under which gaps that are sufficiently short in relation to the treattwo schedules of differing fractionation structure can ment time remaining such that it is still possible to keep have identical effects on all tissues irradiated. Recently, the total time constant. Large gaps, which cause the Deehan and O'Donoghue (1988) have discussed the original treatment time to be exceeded before therapy conditions for general equivalence of two schedules resumes, cannot be completely allowed for in this way which are given in the same overall time. Here, the although the therapeutic disadvantage could be reduced. problem is to derive schedule parameters such that a Greater importance consequently attaches to gaps sequence of two (or more) fractionated schedules are occurring later rather than earlier in treatment, since the simultaneously equivalent for all tissues to a particular opportunity for post-gap adjustment of the time-strucuniform schedule (i.e. independent of cc/fi ratios). In the ture will be less. circumstances described in this paper, we have the degeThe feasibility of the strategy may also be limited by nerate case where the "intended" schedule and the practical considerations. Where a gap involving many schedule already given have the same fraction size. The patients occurs as a result of machine breakdown, it equations for general equivalence have the solutions may be impractical to institute post-gap acceleration for such that: all such patients. Patients might then be selected for (1) The schedule remaining to be given must also post-gap acceleration on the basis of potential doubling time of tumour type (Trott & Kummermehr, 1985). have the same fraction size. (2) It must have the number of fractions that is the difference between the intended schedule and the Radiobiological processes other than repopulation The consequences of gaps in treatment cannot be schedule already given. If the schedule remaining to be given has any other considered exclusively in terms of repopulation. Redisfraction size or fraction number, general equivalence is tribution is also likely to be an important process, with impossible and the best that can be achieved is an gaps allowing increasing time for reassortment of equivalence for only one value of a//?. This means that surviving clonogenic cells in both normal tissues and general equivalence between the originally intended tumours. It is possible that clonogenic cells in lateschedule and the schedule including a time-gap usually responding tissues reassort relatively slowly. Gaps cannot be achieved by increased total dose or dose per would then be relatively disadvantageous to such tissues and accelerated fractionation relatively sparing. It is fraction. also conceivable that gaps might allow increased time for tumour reoxygenation. The generally poor theraRationale for post-gap acceleration The above considerations lead to disappointing peutic effects of treatment time prolongation (Thames & conclusions in terms of compensating for gaps. A diffi- Hendry, 1987) do not suggest that this is likely to be an culty with some compensation strategies is that they important factor. However, the possibility that post-gap attempt a "trade-off" between time and dose or dose per acceleration might allow insufficient time for reoxygenafraction. Even if all the relevant radiobiological para- tion during this phase of treatment cannot yet be meters are known, this trade-off differs between normal excluded. Accumulating evidence on the efficacy of tissues and tumours making any dose compensation regimes that are uniformly accelerated throughout strategies incapable of achieving the same overall effects should provide relevant evidence. Mitotic delay is not expected to be an important factor on the basis of in as the originally intended schedule. An alternative approach is to try to keep the overall vitro evidence, but should it prove greater than time constant, despite the gap, but without changing expected, this would tend to favour the strategy of posteither dose or dose per fraction. Simply, fractions would gap acceleration, which would preferentially stop repobe given more frequently after the gap than before it i.e. pulation in the tumour and acute-responding tissues, the post-gap phase of treatment would be accelerated, with little effect on non-repopulating, late-responding though the regimen as a whole would not. This could be tissues. There seem to be no strong grounds for done by giving two rather than one conventionally sized expecting post-gap acceleration to be therapeutically fractions daily following the gap for as many days as is disadvantageous rather than otherwise. necessary to ensure total time remains constant. Current evidence implies that an interval of at least 6h (and Conclusions preferably more) should be allowed between any two Evidence exists that implies that unintended gaps fractions to avoid increased damage to normal tissues. leading to increased total time may be important in Provided this is ensured, the effect on late-responding facilitating tumour repopulation. Compensatory stratetissues should be little altered by changes of time- gies involving changes in total dose or dose per fraction structure, whilst additional repopulation in tumours and are beset by problems. A strategy of post-gap accelin acute-responding tissues is offset by keeping the total eration of fractionation involves fewer radiobiological provide a satisfactory solution to the problem of gap compensation.
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Post-gap acceleration of fractionation
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