Stereotactic treatment of brain tumors with radioactive implants or external photon beams: radiobiophysical aspects

Radiotherapy and Oncology, 26 (1993) 11-18 © 1993 Elsevier Scientific Publishers Ireland Ltd. All rights reserved. 0167-8140/93/$06.00

11

RADION01091

Stereotactic treatment of brain tumors with radioactive implants external photon beams: radiobiophysical aspects

or

C. Clifton Ling a n d C h e n S. Chui Department of Medical Physics, Memorial Sioan Kettering Cancer Center, New York, USA (Received 20 May 1992, revision received 27 July 1992, accepted 18 August 1992)

Key words: Radiosurgery; Interstitial brain implant; Radiobiology

Summary We perform calculations, based on the linear-quadratic model, to assess the biologically effective doses (BED) of tumor and normal tissue in the stereotactic irradiation of brain tumors with either radioactive implants or radiosurgery techniques. Treatment protocols for radiosurgery and radioactive implants, as obtained from the literature, are reviewed and compared. A figure of merit is defined to be the ratio of tumor to normal tissue BED, expressed in units of Gy~0/Gy3. These comparisons indicate a clear radiobiological advantage for brachytherapy, unless the radiosurgery is to be delivered in a large number of fractions. The differences in dose uniformity, and in the volume of normal tissue encompassed by the high dose regions, are factors that may also influence clinical results.

Introduction The success of radiation treatment of cancers depends on the adequacy of dose, and on the temporal and spatial distributions of dose, relative to the characteristics of the tumor being treated. The physical attributes of the tumor, e.g. size, shape, extension and proximity to critical structures, directly affect the desired and achievable level of dose and the associated spatial distribution, and influence the probability of attaining tumor control within the constraint of acceptable normal tissue complication. The biological characteristics of the tumor, e.g. its intrinsic radioresponsiveness and environmental modulation, the kinetics of sublethal damage repair and regrowth, are also major determinants of the eventual treatment outcome, given a certain dose level and its temporal and spatial distribution. Radiation is a major modality in the treatment of tumors of the central nervous system. External beam radiotherapy is commonly used for brain tumors which are not suitable for surgery. For recurrent anaplastic astrocytomas and glioblastoma multiforme, workers at

the University of California, San Francisco, pioneered the use of stereotactic interstitial implants [24,33,34]. Subsequently, the technique has been extended to manage early stage primary lesions [33,34]. While the concept of interstitial implant has been widely embraced, variation exists among institutions in terms of the choice of radionuclides, the convention of source placement, and the temporal pattern of dose delivery, i.e. permanent or temporary implant. Temporary implants using 12sI seeds (tl/2 = 60 d)are well-accepted [4,13,17], while other clinicians use 192Ir (hi2 = 74 d) sources [ 1]. Permanent implants using 125I or ~°3pd (t1/2 = 17 d) are also being performed [28]. The use of radionuclides with low photon energies, i.e. 12sI and l°3Pd (20-35 keV), is attractive for the purpose of radiation safety [20,21,48,52]. In terms of maximizing tumor cell inactivation while minimizing tumor regrowth during radiation delivery, the higher dose rates associated with temporary implants (0.50.8 Gy/h) or with permanent implants using ~°3Pd (0.2 Gy/h initial dose rate) are believed to be more efficacious than that associated with permanent implants

Addressfor correspondence:C. Clifton Ling, Department of Medical Physics, Memorial Sloan Kettering Cancer Center, N.Y. 10021, USA.

12

USing 125I seeds (0.077 Gy/h initial dose rate) [41]. Permanent implants using l°3Pd seeds have some advantages: it may obviate the need for the somewhat lengthy hospital stay for temporary implant patients, it has a higher dose rate than 125I permanent implant, but retains the radiation safety advantages. The introduction of Gammaknife units [35] and the application of high energy proton beams [31 ] for the treatment of arterial venous malformation, followed by the adaptation and popularization of medical linacs using stereotactic approaches for the same purpose, has prompted the exploratory use of"radiosurgery" for malignant diseases of the brain [6,11,32,38,39,53,54]. This development is still embryonic, perhaps evinced by the plethora of time-dose-fraction schema used by different institutions, and the active research in the physical and technical aspects of such application [22,23,27,29,51]. Much clinical data need to be accumulated before the efficacy of this approach for treating malignant brain tumors can be validated. These two modalities described above, both use stereotactic techniques in localizing the target volume relative to the radiation delivery, and may involve the same equipment (e.g. the Brown Robert Wells stereotactic system). However, the similarity stops there. Stereotactic implant and stereotactic radiosurgery are two distinct modalities with vastly different spatial and temporal distributions of radiation dose. Given the importance of the time-dose factor and of spatial dose distribution in affecting clinical results, we compare the two modalities in terms of these radiobiophysical entities. The primary emphasis of this paper is on the influence of time-dose-fractionation, with some comments on the effect of spatial dose distribution, the latter being the subject of another investigation [2]. As indicated above, the time course of dose delivery influences radioresponse [25,26,43], i.e. the fractionation schedule in external beam radiotherapy and the dose rate in brachytherapy. Various models, based on radiobiological principles and clinical experience, have been proposed to aid our understanding of the timedose relationship encountered in radiation therapy [7,14-16,30,37,45,46]. The linear quadratic or a-/~ model, initially proposed to explain cell ,inactivation in experimental systems, has evolved in the past decade to be of utility to clinical radiotherapy in terms of assessing time-dose effects [12,18]. Dale has extended such analysis to protracted irradiation as encountered in brachytherapy, for both temporary and permanent implants [8,9]. Specifically, formulae have been derived,

in terms of extrapolated response dose (ERD) or biological effective dose (BED)*, which give a measure of the biological effect for a certain specific endpoint, independent of the time course of dose delivery. Using these formulae, one can account for the disparate timedose patterns, and estimate the relative radiobiological efficacies of the different brachytherapy approaches [8,9]. Another factor that has relevance is dose inhomogeneity, which is inherent to brachytherapy but usually avoided in treatment with external beam. Dose inhomogeneity, if consisting of regions of higher doses as in brachytherapy, is likely to contribute to additional tumor cell inactivation, relative to a uniform dose distribution with the same peripheral dose. As yet, we do not have an understanding of the quantitative impact of such dose heterogeneity, although theoretical considerations from a radiobiophysical perspective can be made. Materials and methods

The linear quadratic model of cell inactivation is useful as the basis for estimating the radiobiological response in radiotherapy [see ref. 18 for review]. For a course of external beam radiotherapy using n fractions, each of dose d, the biological effective dose to the tumor can be written as BED = n d [ 1 + d/(cx/fl)] - 0 . 6 9 3 T / ( a . T p )

(1)

and/~ are the linear and quadratic coefficients of the cell survival curve; Tp is tumor potential doubling time and T is the overall time of the treatment course. For late effect tissues, the second term can be omitted (i.e. Tp approaches infinity), because repopulation is of negligible consequence. The BED concept has been extended for application to low dose rate brachytherapy by Dale [8], but without incorporating the inverse dose rate effect [43]. Using the same nomenclature, the tumor BED produced by a constant low dose rate for time T can be approximated as BED = RT [1 + 2Rl{#.(~tlfl)}] - 0.693T/(a. Tp) (2) where R is the dose rate, and # the time constant of sublethal damage repair. For permanent implants with short half-life sources, the biologically effective dose at time t has been shown to be [9]

*ERD and BED are definedby the sameformulae,the nomenclatureis the onlydifference.

13 BED = D {1 + 2 (Ro'2)(fl/~)"

g/~

-

2)}

(3)

- 0.693t/(a. Tp)

with g = [1/(1 - ~)].{(1 - e2)/22- [1 - ~.exp( - ~)]/ ~ + 2)}; D = the total dose delivered; Ro = the initial dose rate; 2 = the decay constant of the radioactive source; # = the repair constant of sublethal damage; = exp( - 20. For tumors that exhibit regrowth delay of a period Td, the second term in Eqns. (1) and (2) is replaced with 0.693(T-Td)/(~.Tp), and in Eqn. (3) with 0.693(t- Td)/(ct'Tp), respectively, when T> T d or t > Td. No regrowth delay is included in our subsequent calculations, however, since the clinical situations encountered do not warrant it, nor will its inclusion affect the conclusions of our investigation. For permanent implants, the combined effect of source decay and tumor regrowth is to produce a maximum BED at a certain effective time (Tear), at which the rate of cell repopulation is equal to that of cell inactivation. Beyond T¢~, the BED actually decreases and the number of clonogens increases, even though additional radiation dose continues to be delivered. The value of Tearcan be obtained by taking the derivative of Eqn. (3) with respect to time, and approximating, giving T~r = (1/2) In [1.44 Ro.cx. Tp]

(4)

The exact derivation of this equation is detailed by Dale [9]. The value of Tear is dependent on the prescribed dose (which determines the initial dose rate Ro) and the tumor potential doubling time Tp. For our calculations, we adopt Ro that correspond to clinically prescribed doses of 120 and 160 Gy for l°3pd and 1251 implants, with respective R o values of 0.20, and 0.077 Gy/h. The values of ct/fl (in units of Gy) of 10 and 3 are used for acute reacting tissues (including tumors) and late responding tissues, respectively. The value of ct for tumors is taken to be 0.3 G y - ~, in the middle of the range of radiosensitivity, as derived from clinical and

laboratory data. These values correspond to a surviving fraction for the tumor of about 0.5 for a 2 Gy fraction of external beam radiotherapy. The repair time constant is assumed to be the same for both acute and late reacting tissues, with a value of 0.693 h - 1, such that half of the sublethal damage is repaired in one hour. Although there have been reports [47,57] indicating possible differences between the repair kinetics of acute and late responding tissues, the generalization and application of these findings to the clinical situation may not be warranted at this time. As for the potential tumor doubling time, To, we will consider a range of values, for both fast and slowly growing tumors, of 3-10 days [3,58,59]. For fractionated stereotactic radiosurgery, we shall use Eqn. (1) to calculate the biologically effective dose, in units of GyIo for the tumor and early responding tissues, and in units of Gy3 for late reacting tissues, with the subscript indicating the value of the ~t/fl ratio adopted. For temporary implants using 1251or 192Ir, we shall use the clinical prescription of the various institutions along with Eqn. (2) to calculate the BED. For permanent implants using 1251and ~°3Pd, we shall first compute the Ton of each modality, and then the associated BED. The possibly different radiobiological effectiveness (RBE) for the radiation qualities of the radionuclides are recognized, but not considered in the comparison on account of the large range of reported values for 125I [ 10,19,41], and because no data is as yet available for X°3pd. Results Using Eqn. (2) and the radiobiological parameters stated above, the tumor BED is calculated for temporary implants delivering 70 Gy at 0.6 Gy/h [33,34]. The computed values are 78 Gyl0 and 81 GYlo for Tp of 3 and 10 days, respectively, as listed in Table I. That the calculated BED is somewhat insensitive to the choice of Tp is due to the relative short duration of the implant. BED for late responding tissues is similarly calculated and presented in Table I; note that Tp is assumed to be

TABLE I Technique

Dose schedule

Tp (d)

Acute BED (GYlo)

Late BED (Gy3)

Temporaryimplant

70 Gy at 0.6 Gy/h 160 Gy

Permanent ~°3Pdimplant

120 Gy

78 81 36 100 69 100

110

Permanent 125Iimplant

3 10 3 10 3 10

166 131

14 TABLE II Reference

Dose schedule

23 50 53 27

12 x 3.5 Gy 2 x 20 Gy 6 x 7 Gy [ext. RT 33 Gy*] radiosurgery 2 x 6 Gy 2 x 25 Gy 30x2 Gy 25 x 2 Gy [ext. RT 15 x 2 Gy] radio, surgery 1 x 20 Gy I x 50 Gy 1 x 30 Gy

49 51 11 39 40 54

seeds, with tumor BED of 35 and 100 G y l 0 for the two values of Tp. Even for l ° 3 p d implants, the tumor BED varies from 69 to 100 Gylo. Again, the late effect has an infinite Tp, and for these implants the late effect BED are numerically similar to the total physical dose. The latter point is characteristic for protracted irradiation at very low dose rates. The Gylo/Gy 3 ratios are 0.22-0.62 for permanent implants USing 125I, and 0.53-0.76 for those with l°3pd, respectively. Table II contains a compilation, from the literature, of the time-dose-fractionation protocols used in the radiosurgery of tumors [ 11,23,27,38,39,40,44,4951,53,54]. Based on these schedules, Eqn. (1) is used to calculate the BED for acute and late tissues. When a protocol includes conventional external beam therapy, the biologically effective dose of that portion of the treatment is also included. For the sake of simplicity, the effect of tumor repopulation is ignored in these calculations. However, this approximation will not affect the primary aim of this Table, which is to show the variation in time-dose-fractionation schedules and the correspondingly large ranges of the tumor and the late effect BED. For the treatment re~mens included in this compilation, there are substantial variations, by more than a factor of 4, in the BED values for both the tumor and the late response tissues. It would be difficult to reconcile these differences by invoking variations in Tp or in other radiobiological parameters, if the disease conditions and treatment objectives are common for these trials. In terms of the GyIo/Gy3 ratios, there are also large variations, with a range of 0.36-0.72. It should be noted that the linear-quadratic formulism may not be appropriate for large doses per fraction; some entries in Table II should therefore he considered within this context. Adopting temporary implants using 125I (70 Gy at 0.6 Gy/h to give 80 Gyxo) as the reference we calculate l o n g e r - l i v e d 1251

Acute BED (GYlo)

Late BED (GY3)

56.7 120 71.,1

91 307 140

[40] + 19.2 175 72 60

[55] + 36 467 100 83

[36] + 60 300 120

[50] + 153 883 330

*Fraction size not given, assumed to be 2 Gy.

infinity for such tissues. The late effect BED for such implants, taken as the reference point for subsequent comparisons, is 110 Gy3. The ratio of the BEDs for acute and late effects, designated the Gylo/Gy3 ratio, will be used as a figure of merit for subsequent discussion. For the temporary implant discussed above, the Gy~o/GY3 ratio is 80/110, or 0.73. Strictly speaking, the use of Gy~o/Gy3 ratio as a figure of merit in comparing different treatment techniques is only appropriate if either the tumor response BED or the late reaction BED is kept constant. Nevertheless, even when that is not the case, the concept is useful as a tool. Calculations are performed using Eqn. (3) to obtain BED of the tissues, for permanent 125I and ~°apd implants with prescribed total doses of 160 Gy and 120 Gy, respectively. The values obtained are also given in Table I for Tp of 3 and 10 days. In contrast to what is observed for the temporary implants, the tumor BED of permanent implants depends strongly on Tp. This is particularly significant for applications involving the

TABLE III Technique

Dose schedule

Radiosurgery

3 × 12.2 Gy 5 x 8.8 7x7.2 9 x 6.1 15 x 4.4 3 x 12.1 Gy 5 x 8.7 7 x 6.9 9 x 5.8 15 x 4.0

Tp (d)

Acute BED (Gylo)

Late BED (GY3)

3

80 80 81 81 81

185 173 171 166 162

10

80 80 80 80 80

182 169 159 153 140

15 the combinations of the fraction number n, and the dose per fraction d, which would yield the same tumor BED of about 80 Gylo (see Table I). The calculations are carried out for Tp of 3 and 10 d, with the assumptions that daily fractions are given, and that treatments are delivered five times weekly, with the first session on a Monday. (The effect of using other schedules will be addressed in the Discussion.) The combinations of n and d, and the corresponding late effect BED are listed in Table III, and presented in graphical form in Figs. 1 and 2. (By design, the acute effect BED is 80 GYlo, the slight variation noted in Table III is due to the effect of rounding off, to the first decimal point, of the value of d in Gy.) Comparing Tables I and III, and using the Gyx0/Gy3 ratio as an index, we note that radiosurgery generally engenders a lesser figure of merit than temporary implants, unless the number of fractions is sufficiently large. Radiosurgery is also inferior to permanent implants with ~°3pd in that regard. It appears more advantageous than permanent ~25I implants, but only for a small Tp (e.g. 3 d).

~

12

U. 8

i 4

2

4

6

8

10

12

14

16

Number of Fractions Fig. 1. Combinations of number of fraction n, and dose per fraction d, which yield the same tumor BED as an temporary 125I implant delivering 70 Gy at 0.6 Gy/h. For each n, two values of d are Oven, for Tp of 3 and 10 d, respectively.

190 180

A a 0 m

~

Tp

130

.

.

.

.

i

5

~Tp:3d

Discussion

"AlS : 10 d

"A~"'~,,,A

.

.

.

.

i

10

.

.

.

.

Consistent with current understanding, for a given acute (or tumor) BED, late effect decreases with an increase in the number of fractions. For a Tp of 10 d, the late effect BED is reduced from 182 Gy3 to 140 Gy3, as n varies from 3 to 15. However, for the smaller value of Tp of 3 d, the reduction reaches a plateau at about 160 Gy3. This is because, in order to compensate for the rapid tumor repopulation with longer treatment time, the radiation dose d needs to be increased, halting the decrease in late effect BED. In the comparisons above, the differences in the volume-dose distributions of an implant and of radiosurgery application are not considered. Indeed, such comparison based on the linear-quadratic concept are appropriate primarily for similar spatial dose patterns. However, we reason that our general conclusion would not be compromised, but rather would be strengthened, based on the following considerations. Preliminary resuits from an ongoing study indicate that an inhomogeneous dose distribution, typical of an 125Iimplant for brain tumors, is much more effective in cell inactivation than an uniform one with the same peripheral dose [2]. The enhancement factor, defined as the ratio of the two BED values corresponding to the different levels of cell inactivation for the two types of dose distributions, is about 1.4. This means that the "effective" early effect BED values may be 40% higher than those listed in Table I. (This value probably depends on the type and geometry of an implant, these factors are currently under study.) The late effect BED may also need to be altered, but the overall enhancement will depend on the volume of normal stroma included in the high dose region s. For radiosurgery to achieve the same level of early effect BED, the dose per fraction in Table III needs to be appropriately increased, with concomitant and proportionately higher increase in late effect BED due to the "curvier" dose response of such tissues [56]. Given that the dose distribution achievable with brachytherapy is more conforming to the target contour (than current radiosurgical approaches), the overall effect of the associated inhomogeneity will probably be an advantage.

i

.

.

15

.

.

20

Number of Fractions Fig. 2. Calculated late effect BED as a function of n, for the combinations of n and d given in Fig. 1.

We emphasize that the calculated results of this study are theoretical considerations based on the following major assumptions: (1)the linear-quadratic model of radiation-induced cell killing is applicable to fractionated high dose-rate external beam radiotherapy and low dose-rate brachytherapy, (2) the ~//~ratio of late effects is about one-third that o f early responding tissues, and

16 (3) the repair kinetics of the different types of tissues are similar. In addition, the model prediction is probably invalid when the number of fractions is small and the dose per fraction is high. Within these limitations, the theoretical considerations yield certain insights concerning the comparative radiobiological efficacy of treatments with different temporal dose patterns. As new radiobiological and clinical data emerge, studies such as this can be appropriately modified to reflect the more realistic assumptions. For the purpose of comparison, temporary 1251implants are adopted as the reference, based in part on the substantial clinical experience of treating intracranial lesions with this technique. Using the calculated BED values (Table I) and the associated Gylo/Gy3 ratios as a criterion, permanent implants with 125I is clearly less efficacious, whereas l°3Pd applied permanently may be comparable for tumors with Tp approaching or larger than 10 d. Concerning the use of radiosurgery in treating intracranial lesions, current practice as derived from the literature presents a mosaic of time-dose patterns, as judged by the computed BED for both early responding and late reaction tissues. Except for the two centers using 25-30 fractions, the other time-dose schedules yield Gylo/Gy3 ratios considerably less desirable than that of the standard implant. This is not surprising. The concept of a smaller u//~ ratio for late reacting tissues relative to early responding tissues (including tumor) is the rationale for hyperfractionation in external beam radiotherapy, with the hope of minimizing late complication while keeping constant the tumoricidal effect [55]. Low dose rate irradiation, in delivering small increments of radiation dose continuously, is perhaps the ultimate form of hyperfractionation. Thus, in substituting LDR implants with high dose rate fractionated treatment with large d, it should be expected that late effect would increase for the same early response, unless the fraction number is sufficiently large. Brenner et al. emphasized this same point in their recent paper [51. The same conclusion can be drawn from Table III and Figs. 1 and 2, results of our systematic consideration. Any n and d combination, which matches the tumor BED, elicits more severe late effect than the standard temporary implant, with Gy~o/Gy3 ratios that are generally less than 0.5 except for n values greater than 15. This overall conclusion is also independent of our choices of daily fraction and 5 weekly treatments; other fractionation schema would unveil the same resuits - a case of "can't fool mother nature". This exercise again bespeaks the intuition that protracted dose delivery of 10 Gy/d as employed in temporary implants,

in combining accelerated treatment and the ultimate of hyperfractionation, is most advantageous radiobiologically [26]. As was observed in a related paper [36], Tp influences the comparative radiobiological efficacy of different time-dose re~mes. A slow delivery to a large t'mal dose (e.g. permanent implant using 1251 seeds) can be quite effective for very slow-growing tumors with Tp> 10-15 d, and protraction is most desirable for the preferential sparing of late reacting tissue. In contrast, the eradication of a tumor with a small Tp value requires that a sufficiently high dose is given in a brief span of time. Even for this instance, low dose rate irradiation (e.g. temporary implant) can prevent the ravages on normal tissues, that could result from large dose per fraction of fractionated delivery. If low dose rate approaches are contraindicated, treatment with a sufficient number of fractions is the next alternative, to yield the best therapeutic efficacy. Aside from radiobiological considerations, other important factors must also be considered in selecting a radiotherapeutic approach. Some of these are briefly mentioned below. The invasiveness of the procedure is a disadvantage of brachytherapy. Whereas prevailing radiosurgical techniques are mildly invasive to insure reproducibility of set-up, there are developments in patient immobilization which may overcome this difficulty. Logistically, both interstitial implant and radiosurgery are labor intensive. The necessity for radionuclides in implants and the associated radiation safety issues are negatives. Another factor is the amount of normal tissues included in the high dose region [42]; no comparative study has been performed to contrast this aspect of these procedures. Finally, we note that this paper reviews the concepts that underlie the radiobiological effects of various stereotactic radiation treatments of CNS tumors, and provides examples for examining various time-dosefractionation schema. We emphasize that direct application of the results of this study to clinical situations may be inappropriate because the applicable radiobiological parameters could be quite different. Rather, these discussions are meant to provide perspectives with regard to the careful considerations needed in adopting or extending clinical protocol from existing ones.

Acknowledgement This work is supported in part by grants from the American Cancer Society ( P D T # 334), and from NIH/ NCI (CA52713), Department of Health and Human Services.

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