1990, The British Journal of Radiology, 63, 290-294
The use of small fraction numbers in high dose-rate gynaecological afterloading: some radiobiological considerations By R. G. Dale, PhD, FlnstP, FIPSM Department of Radiation Physics, Charing Cross Hospital, London W6 8RF (Received July 1989 and in revised form October 1989) Abstract. Using commonly assumed a//? ratios for tumours and late-reacting tissues, the linear-quadratic (LQ) model has been used to compare low dose-rate (LDR) gynaecological treatment with high dose-rate (HDR) techniques given in small fraction numbers. Even in the absence of relatively favourable tissue recovery constants (fi values) it is shown that, provided a modest extra amount of geometrical sparing of critical tissues is available (by means of spacing or shielding), HDR treatment in a small number of fractions may be used in place of an LDR regime without loss of therapeutic ratio. This general result, although not universally true, does indicate that HDR treatment delivered in a small number of fractions may be more feasible than is sometimes thought. These findings do not contradict currently accepted radiobiological philosophy, which cautions against the use of small numbers of high-dose fractions. Primarily they serve to emphasize the importance of the recommendations of the ICRU (1985), which stress the need to consider the complete time-dose pattern of radiation delivery to all the critical tissues in an intracavitary treatment.
+ 10% over the range of dose-rates tested (Liversage, 1969; Liversage & Dale, 1978; Turesson, 1978). Although the original LDR regime will deliver different total doses to the various tissues (because of the dose-gradients), provided the LDR and HDR geometries are similar then the equivalence relationship between the two treatments remains true at all sites throughout the treatment volume. The possible effects of tumour and acute normaltissue proliferation are ignored in these formulae; for the equations to be strictly valid the N fractions would therefore need to be delivered in the same overall treatment time as the original LDR regime, i.e. in T hours. Although this would not be feasible in the majority of cases, it is clear from equations (1) and (2) that the theoretical number of HDR fractions would, in any case, usually be relatively large. For example, an LDR regime delivering 60 Gy in 72 h would need to be replaced by a fractionated regime that gives 60 Gy in approximately 18 ( = 72/4) fractions. In general, therefore, the satisfactory delivery of an HDR regime would appear to require a fraction number N= which is large enough to negate many of the logistic benefits of using such a treatment, and which is likely to 2{\-[\-QXP(-HT)]/HT} ( i) be distressing for patients. where /J. is the recovery constant, assumed to be the For fraction numbers less than that theoretically same for all the tissues. Liversage used a value for /J. of 0.46 h"1 (corresponding to a recovery half-life of 1.5 h). calculated from equation (2), Liversage (1969, 1987) For relatively large values of T this equation simplifies predicted that a loss in therapeutic ratio (relative to the and, for the particular half-life chosen by Liversage, the LDR regime) is to be expected, and the development of the linear-quadratic (LQ) formulation has enabled this derived relationship is better remembered as: aspect to be further quantified. It has been shown that N ~ T/4 (2). the Liversage General Formula may be regarded as a This general formula for equating N and T has been special case of a more complex LQ relationship, the tested against experimental results for a variety of very latter taking account of the tissue tx/f} ratios, in addition different biological end points, at a variety of different to their recovery constants (Dale, 1985, 1988). These dose-rates, and has been shown to be valid to within aspects have been further discussed by Fowler (1989a). The radiobiological assessment of gynaecological brachytherapy treatments continues to be a subject of considerable interest. Although high dose-rate (HDR) afterloading units have been available for many years (e.g. O'Connell et al, 1967; Joslin et al, 1972), the growing availability of more sophisticated treatment machines has generated a concommitant requirement for a fuller understanding of the radiobiological pitfalls that might be associated with this form of treatment. Much remains to be properly understood, but the question of the optimal number of fractions to use is always of particular significance. An in-depth appraisal of the possible link between low and high dose-rate treatments was undertaken by Liversage (1969). That analysis showed that, if a protracted low dose-rate (LDR) treatment lasting T hours is to be replaced by a HDR regime consisting of N fractions, the condition whereby the therapeutic ratio remains unchanged is that the same total dose is given in each case, with TV being calculated from T by the relationship:
290
The British Journal of Radiology, April 1990
Small fraction numbers in high dose-rate gynaecological afterloading
Although the clinical value of using HDR gynaecological afterloading alone remains to be seen, many clinicians have found little difficulty in replacing, with fractionated HDR, the LDR intercavitary component of combined intracavitary/external beam treatments, and with significantly fewer intracavitary fractions than radiobiological calculations predict are necessary. It is therefore appropriate to assess quantitatively the possible reasons for this. In this paper the nature of the inter-relationship between the geometrical sparing of the normal tissues and the fraction number will be examined in the light of the basic LQ formulation. The more complex case of intermediate dose-rate therapy is not addressed here. Method
For fractionated HDR therapy, the standard LQ equation of Barendsen (1982), linking extrapolated response dose (ERD), relative effectiveness per unit dose (RE) and total dose (TD) is ERD = TD x RE (3). Using Barendsen's definition of RE we have (4) ERD = Ndx[\ + d/(u/P)] where N fractions of magnitude d are used. Since the a//? ratio is characteristic of the tissue under consideration it follows that RE, and hence ERD, is also tissue specific. Therefore, even in a uniformly irradiated block comprising several different tissues, there will be separate ERD values that characterize the effects of the given dose on the individual tissues. In general, late-reacting tissues are characterized by lower a//? ratios than are tumours (Fowler, 1989b). Equation (4) therefore shows why, for any given value of d, RE will usually be larger for late-reacting tissues than for tumours. Thus, reducing the dose/fraction has proportionately more effect on the late-reacting RE than on the tumour RE. This gives rise to the now well known argument that, where tumour and lateresponding normal-tissue doses are the same, preferential sparing of the latter is more likely to be achieved with small doses/fraction. In the case of a gynaecological application, there will almost certainly be large differences between the doses received by the tumour and the critical normal tissues, because of the large dose-gradients that exist. Although this is a seemingly obvious observation, there is still a common tendency to assess the efficacy of such treatments in terms of a nominal dose at an arbitrary reference point. It is therefore important that radiobiological calculations are not made on the assumption that both the tumour and late-reacting tissues each receive the same total dose, and hence the same dose/fraction (or dose-rate). For the reasons outlined above, this assumption will invariably lead to the prediction that a relatively large number of HDR fractions will be required if a satisfactory therapeutic ratio is to be maintained. Vol. 63, No. 748
If the dose to a late-reacting critical tissue (the rectum, say) is some known fraction (/) of the true tumour dose, then we may write separate ERD equations for both the HDR and LDR cases. In the HDR case, (a) for the tumour: P)tum]
(5)
(b) for the late-reacting critical tissue: ERDlate = fNd x [1 +/
The use of small fraction numbers in high dose-rate gynaecological afterloading: some radiobiological considerations By R. G. Dale, PhD, FlnstP, FIPSM Department of Radiation Physics, Charing Cross Hospital, London W6 8RF (Received July 1989 and in revised form October 1989) Abstract. Using commonly assumed a//? ratios for tumours and late-reacting tissues, the linear-quadratic (LQ) model has been used to compare low dose-rate (LDR) gynaecological treatment with high dose-rate (HDR) techniques given in small fraction numbers. Even in the absence of relatively favourable tissue recovery constants (fi values) it is shown that, provided a modest extra amount of geometrical sparing of critical tissues is available (by means of spacing or shielding), HDR treatment in a small number of fractions may be used in place of an LDR regime without loss of therapeutic ratio. This general result, although not universally true, does indicate that HDR treatment delivered in a small number of fractions may be more feasible than is sometimes thought. These findings do not contradict currently accepted radiobiological philosophy, which cautions against the use of small numbers of high-dose fractions. Primarily they serve to emphasize the importance of the recommendations of the ICRU (1985), which stress the need to consider the complete time-dose pattern of radiation delivery to all the critical tissues in an intracavitary treatment.
+ 10% over the range of dose-rates tested (Liversage, 1969; Liversage & Dale, 1978; Turesson, 1978). Although the original LDR regime will deliver different total doses to the various tissues (because of the dose-gradients), provided the LDR and HDR geometries are similar then the equivalence relationship between the two treatments remains true at all sites throughout the treatment volume. The possible effects of tumour and acute normaltissue proliferation are ignored in these formulae; for the equations to be strictly valid the N fractions would therefore need to be delivered in the same overall treatment time as the original LDR regime, i.e. in T hours. Although this would not be feasible in the majority of cases, it is clear from equations (1) and (2) that the theoretical number of HDR fractions would, in any case, usually be relatively large. For example, an LDR regime delivering 60 Gy in 72 h would need to be replaced by a fractionated regime that gives 60 Gy in approximately 18 ( = 72/4) fractions. In general, therefore, the satisfactory delivery of an HDR regime would appear to require a fraction number N= which is large enough to negate many of the logistic benefits of using such a treatment, and which is likely to 2{\-[\-QXP(-HT)]/HT} ( i) be distressing for patients. where /J. is the recovery constant, assumed to be the For fraction numbers less than that theoretically same for all the tissues. Liversage used a value for /J. of 0.46 h"1 (corresponding to a recovery half-life of 1.5 h). calculated from equation (2), Liversage (1969, 1987) For relatively large values of T this equation simplifies predicted that a loss in therapeutic ratio (relative to the and, for the particular half-life chosen by Liversage, the LDR regime) is to be expected, and the development of the linear-quadratic (LQ) formulation has enabled this derived relationship is better remembered as: aspect to be further quantified. It has been shown that N ~ T/4 (2). the Liversage General Formula may be regarded as a This general formula for equating N and T has been special case of a more complex LQ relationship, the tested against experimental results for a variety of very latter taking account of the tissue tx/f} ratios, in addition different biological end points, at a variety of different to their recovery constants (Dale, 1985, 1988). These dose-rates, and has been shown to be valid to within aspects have been further discussed by Fowler (1989a). The radiobiological assessment of gynaecological brachytherapy treatments continues to be a subject of considerable interest. Although high dose-rate (HDR) afterloading units have been available for many years (e.g. O'Connell et al, 1967; Joslin et al, 1972), the growing availability of more sophisticated treatment machines has generated a concommitant requirement for a fuller understanding of the radiobiological pitfalls that might be associated with this form of treatment. Much remains to be properly understood, but the question of the optimal number of fractions to use is always of particular significance. An in-depth appraisal of the possible link between low and high dose-rate treatments was undertaken by Liversage (1969). That analysis showed that, if a protracted low dose-rate (LDR) treatment lasting T hours is to be replaced by a HDR regime consisting of N fractions, the condition whereby the therapeutic ratio remains unchanged is that the same total dose is given in each case, with TV being calculated from T by the relationship:
290
The British Journal of Radiology, April 1990
Small fraction numbers in high dose-rate gynaecological afterloading
Although the clinical value of using HDR gynaecological afterloading alone remains to be seen, many clinicians have found little difficulty in replacing, with fractionated HDR, the LDR intercavitary component of combined intracavitary/external beam treatments, and with significantly fewer intracavitary fractions than radiobiological calculations predict are necessary. It is therefore appropriate to assess quantitatively the possible reasons for this. In this paper the nature of the inter-relationship between the geometrical sparing of the normal tissues and the fraction number will be examined in the light of the basic LQ formulation. The more complex case of intermediate dose-rate therapy is not addressed here. Method
For fractionated HDR therapy, the standard LQ equation of Barendsen (1982), linking extrapolated response dose (ERD), relative effectiveness per unit dose (RE) and total dose (TD) is ERD = TD x RE (3). Using Barendsen's definition of RE we have (4) ERD = Ndx[\ + d/(u/P)] where N fractions of magnitude d are used. Since the a//? ratio is characteristic of the tissue under consideration it follows that RE, and hence ERD, is also tissue specific. Therefore, even in a uniformly irradiated block comprising several different tissues, there will be separate ERD values that characterize the effects of the given dose on the individual tissues. In general, late-reacting tissues are characterized by lower a//? ratios than are tumours (Fowler, 1989b). Equation (4) therefore shows why, for any given value of d, RE will usually be larger for late-reacting tissues than for tumours. Thus, reducing the dose/fraction has proportionately more effect on the late-reacting RE than on the tumour RE. This gives rise to the now well known argument that, where tumour and lateresponding normal-tissue doses are the same, preferential sparing of the latter is more likely to be achieved with small doses/fraction. In the case of a gynaecological application, there will almost certainly be large differences between the doses received by the tumour and the critical normal tissues, because of the large dose-gradients that exist. Although this is a seemingly obvious observation, there is still a common tendency to assess the efficacy of such treatments in terms of a nominal dose at an arbitrary reference point. It is therefore important that radiobiological calculations are not made on the assumption that both the tumour and late-reacting tissues each receive the same total dose, and hence the same dose/fraction (or dose-rate). For the reasons outlined above, this assumption will invariably lead to the prediction that a relatively large number of HDR fractions will be required if a satisfactory therapeutic ratio is to be maintained. Vol. 63, No. 748
If the dose to a late-reacting critical tissue (the rectum, say) is some known fraction (/) of the true tumour dose, then we may write separate ERD equations for both the HDR and LDR cases. In the HDR case, (a) for the tumour: P)tum]
(5)
(b) for the late-reacting critical tissue: ERDlate = fNd x [1 +/
