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??Original Contribution

NORMAL TISSUE COMPLICATION PROBABILITIES: VARIABLE DOSE PER FRACTION JOHN T. LYMAN, PH.D. Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 Because of the large amount of data generated by 3D treatment planning, new tools are being developed for the evaluation and optimization of the plans. Estimates of the probability of local control of the tumor and for the probability of specific normal tissue complications are among the new tools. The normal tissue complication probability (NTCP) is based on clinical estimates of the tolerance doses for specific tissues/organs. These tolerance doses are assumed to apply for uniform partial and full volume irradiations delivered at 2 Gy per fraction and 5 fractions per week. A different tolerance dose may apply when the dose is delivered at a different dose per fraction and over a diierent period of time. This study evaluates the maximum change expected in the NTCP when the normal structure receives the dose at a different dose per fraction than the target volume due to different choices in the delivery of the daily fraction. INTRODUCTION

Table 1 illustrates three different schemes that would result in the same DVH. Plan 1 represents a situation where the normal structure is within a region at risk for microscopic disease and receives the same dose as the minimum large volume dose, but is excluded from the cone-down field which is given at the end of the treatment period (the last 30% of the overall time). In plan 2 the structure is irradiated only on 70% of the fractions, but these fractions are distributed over the total treatment time (a port that delivers 30% of the total dose does not irradiate the structure). Plan 3 represents a situation where all fields are treated at each fraction, but the tissue is only receiving 70% of the target dose. Based on radiobiologic considerations, these three plans are expected to produce different biologic effects. Based on the NSD formulation (6), plan 1 would cause more normal tissue damage than plan 2 because of the shorter overall time. Plan 2 would cause more damage than plan 3 because of the larger dose per fraction. This is a study to investigate how the calculated NTCP might vary with different assumptions about the rate of dose delivery as measured by the dose per fraction (the situation described by plans 2 and 3).

Because of the large volume of data contained in a 3-dimensional treatment plan the results are often summarized by using dose-volume histograms (DVHs) (3, 4, 13). A radiation therapy treatment is usually designed to provide a fairly uniform dose throughout a small target volume, and to have all portions of the larger target volume receive a dose greater than a given minimal dose. With such a plan, the critical normal tissue volumes generally receive nonhomogeneous dose distributions. DVHs for the target volumes and for the critical normal tissues have been used to calculate estimates of the probabilities of local control and normal tissue complications (9). The normal tissue complication probability (NTCP) models in use (8, 11) convert by some algorithm a non-uniform DVH into a uniform DVH and then apply a tolerance dose for the uniform irradiation of the volume. NTCP calculations are based on tabulated tolerance dose data for a conventional fractionation scheme (2 Gy per fraction and 5 fractions per week) (7, 10). In the simplest implementation of the NTCP models, an implicit assumption is made that all portions of the structure are irradiated at the same dose per fraction and for the same overall time as the target volume. The DVHs and isodose distributions do not indicate how this non-uniform dose distribution was delivered. Even for a uniform irradiation, the normal tissue dose may be delivered at a different dose per fraction (dpf) than the target dose per fraction.

METHODS

AND MATERIALS

The procedure chosen to extend the basic NTCP calculation for different dose delivery schemes and fractionation

Presented at the NC1 workshop on “Potential Clinical Gains by Use of Superior Radiation Dose Distributions,” Bethesda, MD, 26-29 April, 1989. Reprint requests to: John T. Lyman, Ph.D., 10 Tanglewood Road, Berkeley, CA 94705.

work was supported in part by the National Cancer Institute grant CA 42940 and was conducted at the Lawrence Berkeley Laboratory (Department of Energy Contract DE-AC03-76FOOO98 to the University of California). Accepted for publication 24 June 1991.

Acknowledgements-This

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Volume 22, Number 2, 1992 Table 3. Three dose fractionation schedules for the NTCP evaluation

Table 1. Three different plans that could produce the dose-volume histogram

Plan

(%)

Fractions (%)

Overall time (“ro)

1

100

70

2 3

100 70

70 100

70 100 100

W

schedules is based on an isoeffect LQ + time formalism (14). The basic LQ formalism (1) uses alpha/beta (a/P> ratios to determine tolerance dose for differing dose per fraction values but for the same overall time. The effect of the variation in treatment time can be estimated by an additional time factor. For this study, only the dose per fraction within a structure is changed. The tolerance dose is assumed to depend only on the dose per fraction and is independent of the overall time. There are several ways that the effect of the dose per fraction come into the estimate of the NTCP. The first and obvious one is as the daily dose. If a treatment plan calls for a dose per fraction different than 2 Gy, and adjustment can be made to the tolerance dose data based on any of a number of different models (1, 5, 12). I have chosen (9) to use a method based on the LQ model because it can be tissue-specific. The second and more difficult effect to determine is the local dose per fraction in different regions of a critical structure. The DVH shows the result of the total treatment but does not indicate how the dose was delivered. If all ports are utilized at every fraction and with the same relative weighting as their final weighting, then portions of a structure that receive a low dose will receive that dose at a dose per fraction that can be determined by knowing the total dose and the number of fractions. Tolerance doses for partial uniform volume irradiations are determined from a power-law relationship (10). A modification is made to this formula to obtain the tolerance dose for different values of the dose per fraction and with different overall treatment times.

mvm =

TD(V&J~)

x WP + d,,) -

Vy/p(q, - 0

cd@ + d

(v/v,)”



1 2 3

Fractions

dpf

Days

35 30 25

2.00 2.33 2.8

47 40 33

(2 Gy), d is the new dose-per-fraction, CX,p are the tissue dependent parameters of the LQ model for the tissue, y is the tissue dependent parameter for the overall time correction, f, is the assumed reference treatment time, and t is the new treatment time (for this study, t = to). This formula is used in an extended NTCP model to test the effect of a variable dose per fraction in different portions of the DVH. The results are compared with a standard model NTCP assuming a constant dose per fraction. From equation 1, it can be seen that the largest variation in tolerance dose due to changes in the dose per fraction will be seen in structures with the smallest a/p ratio. Barendsen (1) identified three groups of tissues for which an average value of a/p can be used. 1. Skin and intestine; the average cxy/pis 10 Gy. 2. Late effects in skin as a result of connective tissue damage and late CNS effects as a result of demyelination; the average (Y/P is 5 Gy. 3. Third group of tissues for which the influence of fractionation is larger. These tissues include lung, kidney, white matter, and the vascular system of the CNS and possibly other tissues in which cells are characterized by a high degree of differentiation and low regenerative capacity; the average a/p is 2.5 Gy . Table 2 lists some critical tissues and the tolerance dose for a 50% complication probability when a full volume irradiation is delivered at 2.0 Gy/fraction and the u/p ratio. Based on the above considerations these tissues are the most likely to benefit from a treatment delivery schedule that lowers the dose per fraction in the normal tissue.

(1) RESULTS

where TD is the tolerance dose for the uniform irradiation of the specified tissue, d, is the reference dose-per-fraction

Table 2. Tissues with low a/p ratios and/or with a low tolerance dose Tissue Heart Kidney Liver Lung

Schedule

48

2.5

28 40 24.5

2.5 2.5 2.5

Three different DVHs representing partial-volume uniform irradiations were evaluated. The irradiated volumes represented 40, 50, and 60% of the liver. Three different dose fractionation schedules were assumed (Table 3). The schedules were chosen only because they all delivered 70 Gy in either 5, 6, or 7 weeks and therefore are expected to produce a broad range of complication probabilities. It is not the intent to compare the different schedules, but only the variations between the two NTCP algorithms for a given schedule. Table 4. gives the NTCPs based on both a constant and a variable dose per fraction. The NTCP for the variable

Normal tissue complication

Table 4. NTCP values for the uniform partial volume irradiation of the liver Schedule DVH (%)

Method

1

40

Constant Variable Constant Variable Constant Variable

.019 .OOO .175 .014 .583 ,156

50 60

2

3 .147 .002 .637 .066 .960 .490

.049 .OOO .343 .028 .801 .274

dose per fraction is always much less than the result assuming a constant dose per fraction. The reduction of NTCP as determined by the ratio of the variable/constant is greatest for the smallest volume histograms because this histogram has the greatest change in dose per fraction in the variable calculation. DISCUSSION A few generalizations

can be made from this study.

0 This dose per fraction effect will be greater for low o@ ratio tissues. This also means that the effect will not be as important for high LET radiations (RBE>l) because the RBE increase is related to higher values of 42); therefore the tissue CX/~ ratio is expected to be higher with high LET radiations. The effect will be very dependent on the shape of the DVH, coupled with the characteristics of the structure such as the value of the TD,,,, and the volume dependency of the tolerance dose. 0 If portions of the structure are irradiated at a lower dose per fraction, the tissue may be better able to tolerate the dose, but only if the dose in this region makes a significant contribution to the NTCP. 0 In structures with low volume dependency, the NTCP is

probabilities

0 J. T. LYMAN

249

dominated by the volume that gets the high dose with no additional contribution from a larger volume that gets a much lower dose. The high-dose region will be irradiated at a relatively high dose per fraction and the portion at the lower dose per fraction doesn’t contribute to the NTCP even without a dose per fraction correction. 0 For fairly uniform partial volume irradiations, the effect will be important if treating close to the tolerance dose and the tolerance dose is less than the tumor dose. 0 For any dose limiting tissue, a good strategy is to lower the NTCP by spreading, in time, the radiation dose to the tissue over the full course of therapy. The goal would be to make the daily isodose the same as the final isodose by treating all ports at each fraction (this represents the situation assumed by the extended NTCP model). For photons, use partial shields for the total treatment instead of a total shield for some portion of treatment to protect critical structures. Use partial shielding of the large target volume instead of cone-down ports or use a concomitant boost. Use any strategy to decrease the tissue dose relative to the tolerance dose by: (a) decrease the maximum normal tissue dose by spreading the dose over a larger volume; (b) decrease the volume (increases the tolerance dose) by a better choice of beam directions; (c) decrease the dose per fraction (increases the tolerance dose).

CONCLUSIONS NTCP calculations for both a variable and for a constant dose per fraction are useful as an aid to the evaluation of possible improvement in patient outcome that might be achieved by modifications in the radiation delivery schedule. This study was designed to explore the greatest variation in the NTCP values. More typical DVHs derived from 3D treatment plans suggest that the variable dose per fraction NTCP is usually not more than a factor of two less than the constant dose per fraction NTCP.

REFERENCES 1. Barendsen, G. W. Dose fractionation, dose rate and iso-effeet relationships for normal tissue responses. Int. J. Radiat. Oncol. Biol. Phys. 8:1981-1997; 1982. 2. Chapaman, J. D.; Blakely, E. A.; Smith, K. C.; Urtasun, R. C.; Lyman, J. T.; Tobias, C. A. Radiation biophysical studies with mammalian cells and a modulated carbon ion beam. Radiat. Res. 74: 101-l 10; 1978. 3. Chen, G. T. Y.; Austin-Seymour, M.; Castro, J. R.; Collier, J. M.; Lyman, J. T.; Pitluck, S.; Saunders, W. M.; Zink, S. R. Dose volume histograms in treatment planning evaluation of carcinoma of the pancreas. Eighth Int’l. Conf. on Uses of Computer in Radiation Therapy. Toronto, Canada: IEEE; 1984:264-268. 4. Chin, L. M.; Kijewski, P. K.; Svensson, G. K.; Bjtigard, B. E. Dose optimization with computer-controlled gantry rotation, collimator motion and dose-rate variation. Int. J. Radiat. Oncol. Biol. Phys. 9: 723-729; 1983. 5. Cohen, L.; Scott, M. J. Fractionation procedures in radiation

6.

7.

8.

9. 10. 11.

therapy: a computerized approach to evaluation. Brit. J. Radiol. 41:529-533; 1968. Ellis, F. Fractionation in radiotherapy. In Deeley, W., ed. Modem trends in radiotherapy. London: Butterworths; 1967: 34-51. Emami, B.; Lyman, J.; Brown, A.; Coia, L.; Gotein, M.; Munzenrider, J. E.; Shank, B.; Solin, L. J.; Wesson, M. Tolerance of normal tissue of therapeutic irradiation. Int. J. Radiat. Oncol. Biol. Phys. 21:109-122; 1991. Kutcher, G. J.; Burman, C. Calculation of complication probability factors for non-uniform normal tissue irradiation: the effective volume method. Int. J. Radiat. Oncol. Biol. Phys. 16:1623-1630; 1989. Lyman, J. T. Complication probabilities as assessed from dose-volume histograms. Radiat. Res. 104:S13-S19; 1985. Lyman, J. T. Tolerance doses for treatment planning. Lawrence Berkeley Laboratory; 1985:LBL-22700. Lyman, J. T.; Wolbarst, A. B. Optimization of radiation

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therapy IV: A dose-volume histogram reduction algorithm. Int. J. Radiat. Oncol. Biol. Phys. 17:433-436; 1989. 12. Orton, C. G.; Ellis. F. A simplification in the use of the NSD concept in practical radiotherapy. Brit. J. Radiol. 46: 529-537; 1973. 13. Shipley, W. U.; Tepper, J. E.; Trout, G. R.; Verhey, L. J.;

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Mendiodo, 0. A.; Goitein, M.; Koehler, A. M.; Suit, H. D. Proton radiation as boost therapy for localized prostatic carcinema. JAMA 241:1912-1915; 1979. 14. Travis, E.; Tucker, S. Isoeffect models and fractionated radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 13:283-287; 1987.

Normal tissue complication probabilities: variable dose per fraction.

Because of the large amount of data generated by 3D treatment planning, new tools are being developed for the evaluation and optimization of the plans...
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