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Impact of Fraction Size on Lung Radiation Toxicity: Hypofractionation may be Beneficial in Dose Escalation of Radiotherapy for Lung Cancers
Int. J. Radiation Oncology Biol. Phys., Vol. 76, No. 3, pp. 782–788, 2010 Copyright Ó 2010 Elsevier Inc. Printed in the USA. All rights reserved 0360-3016/10/$–see front matter
doi:10.1016/j.ijrobp.2009.02.079
CLINICAL INVESTIGATION
Lung
IMPACT OF FRACTION SIZE ON LUNG RADIATION TOXICITY: HYPOFRACTIONATION MAY BE BENEFICIAL IN DOSE ESCALATION OF RADIOTHERAPY FOR LUNG CANCERS JIN-YUE JIN, PH.D.,* FENG-MING KONG, M.D., PH.D., M.P.H.,yz INDRIN J. CHETTY, PH.D.,* MUNTHER AJLOUNI, M.D.,* SAMUEL RYU, M.D.,* RANDALL TEN HAKEN, PH.D.,y AND BENJAMIN MOVSAS, M.D.* * Department of Radiation Oncology, Henry Ford Hospital, Detroit, MI; y Department of Radiation Oncology, University of Michigan, Ann Arbor, MI; and z Department of Radiation Oncology, Veteran’s Hospital, Ann Arbor, MI Purpose: To assess how fraction size impacts lung radiation toxicity and therapeutic ratio in treatment of lung cancers. Methods and Materials: The relative damaged volume (RDV) of lung was used as the endpoint in the comparison of various fractionation schemes with the same normalized total dose (NTD) to the tumor. The RDV was computed from the biologically corrected lung dose–volume histogram (DVH), with an a/b ratio of 3 and 10 for lung and tumor, respectively. Two different (linear and S-shaped) local dose-effect models that incorporated the concept of a threshold dose effect with a single parameter DL50 (dose at 50% local dose effect) were used to convert the DVH into the RDV. The comparison was conducted using four representative DVHs at different NTD and DL50 values. Results: The RDV decreased with increasing dose/fraction when the NTD was larger than a critical dose (DCR) and increased when the NTD was less than DCR. The DCR was 32–50 Gy and 58–87 Gy for a small tumor (11 cm3) for the linear and S-shaped local dose-effect models, respectively, when DL50 was 20–30 Gy. The DCR was 66–97 Gy and 66–99 Gy, respectively, for a large tumor (266 cm3). Hypofractionation was preferred for small tumors and higher NTDs, and conventional fractionation was better for large tumors and lower NTDs. Hypofractionation might be beneficial for intermediate-sized tumors when NTD = 80–90 Gy, especially if the DL50 is small (20 Gy). Conclusion: This computational study demonstrated that hypofractionated stereotactic body radiotherapy is a better regimen than conventional fractionation in lung cancer patients with small tumors and high doses, because it generates lower RDV when the tumor NTD is kept unchanged. Ó 2010 Elsevier Inc. Hypofraction, Stereotactic body radiotherapy, Non–small-cell lung cancer, Radiobiology, Normal tissue complication probability.
Because normal lung tissue usually has a relatively lower a/b ratio than does tumor tissue, traditionally, hypofractionation is not considered beneficial in terms of normal tissue sparing. However, the newly emerging technique of hypofractionated stereotactic body radiotherapy (SBRT) has achieved improved tumor control with minimal lung toxicity for the treatment of inoperable Stage I non–small-cell lung cancers (NSCLC) (1–8). Stereotactic body radiotherapy has also been used in the treatment of tumors in many other body sites (9–11). Do the successful clinical results in SBRT contradict the conventional wisdom that hypofractionation is not beneficial for normal tissue sparing? In other words, is there an underlying principle supporting that hypo-
fractionated SBRT is superior to conventional fractionated treatment? In addition, is there an optimal fractionation scheme for maximizing the therapeutic ratio? Can hypofractionation be applied to lung cancer patients with larger tumors? And in which situations is hypofractionation preferred? This study aimed to answer these questions by evaluating the impact of fraction size on lung radiation toxicity and therapeutic ratio. The combination of a linear-quadratic model in radiobiology and a dose–volume histogram (DVH)-based lung toxicity model was used in the study. In particular, considering that the lung is a parallel organ consisting of many individual lung function units, new local dose-effect functions that incorporated the concepts of a threshold dose effect and a partial damage effect were used to calculate lung toxicity.
Reprint requests to: Jian-Yue Jin, Ph.D., Department of Radiation Oncology, Henry Ford Hospital, 2799 W. Grand Blvd., Detroit, MI 48202. Tel: (313) 916-0234; Fax: (313) 916-3235;
E-mail: [email protected] Conflict of interest: none. Received Jan 4, 2009. Accepted for publication Feb 24, 2009.
INTRODUCTION
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Hypofractionation may reduce lung toxicity for dose escalation d J.-Y. JIN et al.
was from an opposing anterior-to-posterior (AP) and posterior-toanterior (PA) plan of the same large central lesion (GTV = 266 cm3).
120 100
Percentage Volume (%)
783
DVH1
Converting physical DVHs into normalized biologic equivalent DVHs
DVH2 80
DVH3 DVH4
Each lung DVH was converted to the normalized biologic equivalent (NBE) DVH for various fractionation schemes, assuming that the target received the same NTD for each fractionation scheme. Alpha/beta ratios of 10 and 3 were used for tumor and normal lung tissue, respectively. Table 1 lists the doses per fraction for some selected fractionation schemes with the same NTD of 60, 80, 100, and 120 Gy. For a particular fractionation scheme, NTD was calculated using the following equation:
60 40 20 0 0
20
40
60
80
100
120
NTD ¼ DF n
Percentage Dose (%)
Fig. 1. Four representative dose–volume histograms (DVHs) used for the analysis. DVH1 was from a stereotactic body radiotherapy plan of a small gross tumor volume (GTV) (11 cm3). DVH2 was from a similar hypothetical seven-field intensity-modulated radiotherapy plan of a relatively large peripheral tumor (GTV = 224 cm3). DVH3 was from a seven-field plan of a large central lesion (GTV = 266 cm3). DVH4 was from an anteroposterior/posteroanterior plan of the same large central lesion.
ð1 þ DF =10GyÞ ¼ BED=1:2 ð1 þ 2Gy=10GyÞ
where DF is the dose per fraction, n is the number of fractions, 10Gy is the a/b ratio of the tumor, 2Gy is the dose per fraction for conventional fractionation, and BED is the biologic equivalent dose. We assumed that the original lung DVH was expressed as the volume vs. the percentage dose, with the percentage dose divided into many percentage dose bins (Di%). Thus, the lung NBE-DVH was computed by converting each Di% into the NBE dose bin (NBEDi) using the following equation:
METHODS AND MATERIALS
NBEDi ¼ DF Di % n
We first set the normalized total dose (NTD) (12) to the same value for the various fractionation schemes. Thus, the lung toxicity reflected the therapeutic ratio, because the tumor control was the same for the same NTD to the target. The relative damaged volume (RDV) (13) or fraction of damaged subfunction units (fdam) (14) was then calculated from the lung DVH and the local dose-effect functions to represent the lung toxicity. Therefore, the optimal fractionation scheme can be determined by comparing the RDVs of different fractionation sizes. To determine the optimal fractionation scheme in various situations, such comparisons were performed for different NTD values, various parameters used in the lung toxicity models, and four representative lung DVHs with different tumor sizes, locations, and planning techniques.
Representative DVHs for analysis Four representative lung DVHs (Fig. 1) were used for the analysis. DVH1 was from an SBRT plan for a patient with a relatively small gross tumor volume (GTV) (11 cm3). Intensity-modulated radiotherapy (IMRT) planning with seven coplanar fields was used for the SBRT treatment plan (15). DVH2 was from a similar seven-field IMRT plan for a patient with a larger peripheral tumor (GTV = 224 cm3); DVH3 was from a seven-field IMRT plan for a patient with a large central lesion (GTV = 266 cm3); and DVH4
(1)
ð1 þ DF Di %=3GyÞ ð1 þ 2Gy Di %=3GyÞ
(2)
where 3Gy is the a/b ratio for the lung tissue.
Lung complication models There are many DVH-based normal tissue toxicity models in the literature (13, 14, 16–21), and these can be grouped into two categories according to how the DVH is reduced into a single parameter (16): (1) the equivalent dose model, in which a lung DVH is converted into an equivalent dose to the whole lung with specific conversion functions, and (2) the effective volume model, in which the lung DVH is converted into an equivalent RDV using a local effective dose function, E(D). The effective volume model can also be called the ‘‘parallel functional subunit model,’’ and the RDV is the fraction of damaged functional subunits (fdam) (14). Because the lung is considered a parallel organ consisting of many individual lung function units, the effective volume model should better reflect the lung toxicity mechanism than the equivalent dose model. Mathematically, this model can be expressed as: X RDV ¼ EðDi Þ Vi (3) i
where Vi is the percentage of lung volume receiving a dose (Di) from the lung DVH. The simple threshold model such as the V20 model is
Table 1. Dose per fraction for different numbers of fractions to achieve the same NTD of 60, 80, 100 and 120 Gy at 2-Gy fractions Dose per fraction for hypofractionation with different number of fractions (Gy) NTD (Gy)
Conventional fractionation
60 80 100 120
2 Gy 30 F 2 Gy 40 F 2 Gy 50 F 2 Gy 60 F
1F
2F
3F
4F
5F
6F
10 F
20 F
22.30 26.39 30 33.28
14.62 17.47 20 22.29
11.28 13.57 15.62 17.47
9.32 11.28 13.03 14.62
8 9.73 11.28 12.69
7.04 8.60 10 11.28
4.85 6 7.04 8
2.81 3.54 4.22 4.85
Abbreviations: NTD = normalized tumor dose; F = fraction(s).
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old models: the linear effective dose and S-shaped effective dose models. As shown in Fig. 2, a single parameter, DL50 (i.e., the dose at the local dose effect of 50%), was assumed for both models. These models incorporated the concept of the threshold dose effect from the simple threshold model and the concept of partial damage from the MLD-V model. When the radiation dose increases to DPla = 2DL50, the lung functional subunit is considered completely damaged and the local dose effect reaches a plateau of 100% in both models. In the dose range of 0 to DPla, the linear model shows a linear increase of the local damage effect with the radiation dose, and the S-shaped model shows an S-shaped response. Mathematically, E(D) of the linear and S-shaped models can be expressed as:
Effective dose function E(D)
1
0.8
0.6
0.4
Linear (LED) model S-shaped (SED) model Simple threshold model MLD-V model Logistic model
0.2
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0 DL50
EðDÞ ¼ D=2DL50 when D \ 2DL50
(8A)
EðDÞ ¼ 100% when D $ 2DL50
(8B)
DPla
Dose
Fig. 2. Graphic illustration of the local dose effect, E(D), for various models. The linear and S-shaped models have only one parameter, DL50, the dose causing 50% of local effect. When the dose D is 2DL50 (= DPla), E(D) reaches a plateau. The simple threshold model has also only one parameter, DThr = DL50 = DPla. The mean lung dose converted equivalent volume (MLD-V) model has no parameters. The logistic function model has two parameters. k = 2 was used in this plot. an example of a lung effective volume model (13). In this model, the E(D) can be expressed as: EðDÞ ¼ 0 when D \ 20 Gy; and
(4A)
EðDÞ ¼ 100% when D $ 20 Gy;
(4B)
where D is the dose received by a functional unit. The equivalent uniform dose and mean lung dose (MLD) models are two examples of the equivalent dose model (13). The MLD can be calculated as: X Di Vi : (5) MLD ¼ i
Comparing Eqs. 3 and 5, if we assume an effective dose function EðDÞ ¼ D=100Gy:
(6)
the MLD model can be considered as an equivalent volume mode mathematically, and RDV ¼ MLD=100Gy:
(7)
We named this MLD-converted equivalent volume model as the MLD-V model. The MLD and MLD-V models should behave similarly because they share a similar DVH reduction formula. The simple threshold model reflects an important characteristic of radiation-induced lung radiation toxicity (i.e., a local lung functional subunit is completely damaged after irradiation with a threshold dose); therefore, further increase in the dose will not further damage that subunit. However, the simple threshold model may be inaccurate because it suggests that doses less than the threshold dose inflict no damage. The MLD-V model reflects the concept of partial damage (i.e., a linear increase in damage with an increase in dose) of a local lung functional subunit. However, it is also not theoretically sound because it shows a damage effect of >1 when the doses are >100 Gy. In this study, we proposed two more-sophisticated effective dose models as an extension of the MLD-V and simple thresh-
and EðDÞ ¼
D=DL50 1 1 þ ðD=DL50 1Þ2
þ 1=2 when D \ 2DL50
EðDÞ ¼ 100% when D $2DL50
(9A)
(9B)
respectively, where D is the dose received by a functional subunit. A logistic function model had also been used by other investigators (16, 18). The E(D) of the logistic function model is: (10) EðDÞ ¼ 1= 1 þ ðDL50 =DÞk where k is another parameter representing the steepness of the curve. The logistic model with k = 2 is shown in Fig. 2 for comparison. It assumes a shape very similar to that of the S-shaped model except for the plateau part. In this model the damage effect will always be <1 (complete damage for the subunit) even for an infinitely large dose. In addition, two parameters are used in this model, in comparison with the single parameter for the linear, S-shaped, and simple threshold models and no parameters for the MLD model. Therefore, the logistic model will not be used for this study. Although many studies of dose correlation with functional imaging, CT density, and clinical symptoms have suggested that the lung dose response is similar to the linear, S-shaped, or logistic function models, there are no consistent data showing the value of DL50 for lung tissue (22–25). In this study, we assumed that the DL50 was a parameter that could vary with patients. Hypothetical DL50 values of 20, 30, and 40 Gy were used in the study for both models.
Analysis of lung RDV The lung RDVs were computed for various fractionation schemas for four representative DVHs at different hypothetical DL50 values and at different prescription doses (NTD, 50–120 Gy). The comparisons and analysis were performed at the following levels. Analysis 1. The correlation of RDV and the fraction size (dose/ fraction) was first analyzed to determine whether there is an optimal fraction size and whether a larger fraction is better than a conventional fraction for a fixed prescription dose (NTD = 100 Gy, typically for SBRT) and for various other parameters. Analysis 2. On the basis of the results of Analysis 1 that there was a monotonic relationship between RDV and the fraction size, the percentage difference of RDVs (or percentage reduction of RDV)
Hypofractionation may reduce lung toxicity for dose escalation d J.-Y. JIN et al. 35 DVH1, SED model DVH2, SED model DVH3, SED model DVH4, SED model
60
DVH1, LED model DVH2, LED model DVH3, LED model DVH4, LED model
Relative Damaged Lung Volume (%)
Relative Damaged Lung Volume (%)
70
785
50 40 30 20 10
30 25 20 15
Linear model, DL50 = 20Gy S-shape model, DL50= 20Gy Linear model, DL50 = 30Gy S-shape model, DL50 = 30GY Linear model, DL50 = 40Gy S-shape model, DL50 = 40Gy
10 5 0
0 0
5
10
15
20
25
30
Dose Per Fraction (Gy)(NTD=100Gy)
Fig. 3. Correlation of lung relative damage volume with dose per fraction for four dose–volume histograms (DVHs) for both linear and S-shaped models when normalized total dose (NTD) = 100 Gy and DL50 = 20 Gy. SED = S-shaped effective dose; LED = linear effective dose.
between the conventional fractionation and the single-fraction scheme was used as the parameter to represent the correlation of RDV with the fraction size. The correlation of the percentage RDV difference to NTD was then analyzed for various parameters. Analysis 3. On the basis of the results of Analysis 2 that the percentage RDV reduction increased monotonically with NTD, a critical prescription dose (DCR) was defined as the NTD value when the RDV reduction equaled zero. Therefore, when NTD > DCR , the RDV reduction was positive and a single fraction had a smaller RDV than did conventional fractionation, and vice verse. This critical prescription dose was calculated and analyzed for various DVHs under different parameters.
RESULTS Correlation of RDV with fraction size for a fixed NTD Figure 3 shows the lung RDV vs. fraction size for all four DVHs for both linear and S-shaped models when NTD = 100 Gy and DL50 = 20 Gy. The RDV reduced monotonically with increasing dose per fraction for all DVHs. DVH4, which was from a simple AP/PA plan for a large central tumor, showed a relatively slower reduction in the RDV with the fraction size, in comparison with the other three DVHs. Therefore, increasing fraction size (hypofractionation) tended to reduce the lung RDV compared with conventional fractionation (2 Gy per fraction) for the same NTD given to the tumor when DL50 was relatively low and NTD was relatively high. Figure 4 shows the lung RDV varying with the fraction size for DVH2 with NTD = 100 Gy to the tumor for three DL50 values. The lung RDV decreased monotonically with increasing fraction size for both the linear and S-shaped models when DL50 = 20 Gy and for the linear model when DL50 = 30 Gy. However, the RDV increased monotonically with increasing fraction size for the S-shaped model when DL50 = 40 Gy. The RDV tended to vary minimally for different fraction sizes for the linear model when DL50 = 40 Gy and for the S-shaped model when DL50 = 30 Gy.
0
5
10
15
20
25
30
Dose Per Fraction (Gy)(NTD=100Gy)
Fig. 4. Correlation of lung relative damage volume with dose per fraction for Dose–Volume Histogram 2 for various dose-effect models at various DL50 value when normalized total dose (NTD) = 100 Gy.
These data showed that the RDV either increased or decreased monotonically or stayed relatively constant with the change in dose per fraction for different situations. There were no optimal numbers of fractions between conventional and single fractionation that would lead to less lung toxicity. Therefore, the difference between conventional fractionation and the single fraction (such as the percentage RDV reduction from conventional fractionation to the single fraction) seems to be a parameter to indicate the preference of fractionation schemes. A positive difference means that the RDV decreases with the fraction size and hypofractionation is preferred. A negative difference indicates that the RDV increases with the fraction size and conventional fractionation is preferred. Correlation of RDV difference with NTD Figure 5 shows the percentage RDV difference vs. the NTD for various DVHs and DL50 values of the two models. The percentage RDV difference increased monotonically with the NTD for all four DVHs and DL50 values of the two lung toxicity models. The percentage RDV difference tended to be negative when NTD was low and became positive when the NTD was larger than a critical value. This critical NTD value was defined as the critical dose (DCR). Therefore, this DCR can be used as a parameter to determine whether hypofractionation is better than conventional fractionation for a specific treatment plan. The critical dose Table 2 shows the DCR in various situations for the four DVH examples. Generally, the DCR increased with the DL50 value and the tumor volume. The S-shaped model had a larger DCR than the linear model for the same DL50 value. The DCR value was 32–50 Gy and 58–87 Gy for the linear and S-shaped models, respectively, when DL50 varied from 20 to 30 Gy for the DVH of a small tumor (11 cm3). This indicates that the hypofractionation scheme, for which the
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DISCUSSION
20
0
LED20 LED30 LED40 SED20 SED30 SED40
-20
Lung RDV reduction (%)
-40 20
0
-20
Lung RDV reduction (%)
-40 20
0
-20
-40
Lung RDV reduction (%)
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20
0
-20
-40 40
50
60
70
80
90
100
110
120
130
Normalized total dose to the tumor (Gy)
Fig. 5. Percentage difference of the relative damage volume (RDV) between conventional fractionation and a single fraction varies with the normalized total dose for different dose-effect models, DL50 value, and dose–volume histograms (DVHs). (A) DVH1, (B) DVH2, (C) DVH3, (D) DVH4. SED = S-shaped effective dose; LED = linear effective dose.
prescription dose is usually large (NDT > 90 Gy), may be the preferred choice to reduce the lung RDV in such situations. On the other hand, the corresponding DCR was 66–97 Gy and 66–99 Gy for the DVH of the largest tumor with a seven-field IMRT plan (DVH3). Therefore, traditional fractionation may be preferred in this situation, in which the prescription dose is relatively small (NTD = 60–70 Gy). The corresponding DCR was 52–80 Gy and 60–90 Gy for the DVH of an intermediate-sized peripheral tumor (DVH2). In this situation, hypofractionation may be beneficial when a prescription dose of NTD = 70–90 Gy can be given, especially for the linear lung toxicity model or small DL50 value (20 Gy).
This computational study showed that hypofractionation was associated with less lung RDV than was conventional fractionation for very high prescription doses. On the other hand, conventional fractionation tended to be associated with less lung RDV when a relatively low dose was delivered to the target. The finding that hypofractionation caused less lung damage than did conventional fractionation seems to contradict our traditional belief, because lung tissue has a lower a/b ratio. However, this new observation could be explained by the fact that both our traditional beliefs and clinical experience mostly come from the two-dimensional era, during which the radiation dose was low, the radiation fields were large, the radiation was mostly confined to the irradiated volume, and the dose distribution within the irradiated volume was relatively uniform (i.e., equal to the prescription dose). The situation could be quite different today in the context of modern three-dimensional conformal radiotherapy, especially with regard to SBRT. For SBRT, the irradiation target is relatively small, but low doses could spread out to a much larger volume, with only a relatively small portion of the lung receiving high doses. However, for those lung volumes receiving high doses of radiation, although hypofractionation would increase the BED, the lung functional units were already totally damaged, and thus increasing the dose would not worsen the damage. However, for most lung volumes receiving relatively low doses of radiation, hypofractionation actually reduces the BED. For example, for the volume receiving 10% of the prescription dose of 120 Gy NTD, the actual physical dose is 3.3 Gy per fraction for single-fraction treatment, which has a BED of 6.9 Gy (assuming a/b = 3 Gy), whereas for conventional fractionation the actual dose is 0.2 Gy in 60 fractions, which has a BED of 13.2 Gy. The use of the DVH-based models helps us to better understand the cumulative effect of these complicated phenomena. Interestingly, the results of this study seem to support the current clinical practice. For a larger target volume (normally limited to lower prescription dose), conventional fractionation has a lower RDV and is thus preferred. For a small target volume and high prescription dose, hypofractionation is often preferred, which agrees with the clinical toxicity outcome in patients with inoperable Stage I NSCLC treated with SBRT (1–8). These agreements suggest that the proposed DVH reduction models are conceptually reasonable. The results suggest that the fractionation scheme (large or small fractionation) could be another important parameter to consider for the individualized radiation treatment of lung cancers to minimize lung damage and hence to improve the therapeutic ratio. For example, using singlefraction treatment would reduce lung RDVs by 24% and 17% from the conventional fractionation for the linear model and by 22% and 12% for the S-shaped model when DL50 = 20 and 30 Gy, respectively, for DVH1 and an NTD of 120 Gy. On the other hand, conventional fractionation would be associated with 9% and 20% less lung RDV than the single fraction for the linear and S-shaped
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Table 2. Critical prescription dose for different DVHs, dose effect models, and DL50 values Critical prescription dose S-shaped model for various DL50 values
Linear model for various DL50 values DVH
GTV (cm3)
Plan
20 Gy
30 Gy
40 Gy
20 Gy
30 Gy
40 Gy
DVH1 DVH2 DVH3 DVH4
11 224 266 266
7-field SBRT 7-Field IMRT 7-field IMRT 2D
32 52 66 45
50 80 97 65
65 105 >120 87
58 60 66 61
87 90 99 91
116 120 >120 120
Abbreviations: DVH = dose–volume histogram; SBRT = stereotactic body radiotherapy; IMRT = intensity-modulated radiotherapy; 2D = two-dimensional.
models, respectively, when NTD is 60 Gy for the tumor of DVH3 if DL50 = 30 Gy. Hypofractionation could be beneficial for some intermediate-sized or large peripherally located tumors, for which high-dose escalation (NTD = 80– 100 Gy) can be performed with some risk of lung toxicity (14, 18, 26). For example, a single fraction would have a 16% and 8% reduction in lung RDV compared with conventional fractionation for the linear model, and this would be 16% and 4% for the S-shaped model, when DL50 = 20 and 30 Gy, respectively, for the tumor of the example DHV2 if an NTD of 100 Gy was given. Although qualitatively the results indicate that hypofractionation may be preferred for a higher prescription dose and conventional fractionation for a lower prescription dose, it is beyond the scope of this study to pinpoint the exact cut-off (critical) prescription dose, because it depends on many factors, such as the lung damage model and its parameter, the radiobiologic model and its parameters, and the DVH shape, which in turn depends on the target volume and the treatment planning. Understanding the mechanism of radiation-induced lung toxicity is particularly important to determine the maximal tolerable prescription dose to the target and, based on that, the fractionation scheme to minimize the lung damage. We have used the linear and S-shaped local radiation dose-response models to simulate the relative lung damage volume. Each of these models requires only one parameter, the DL50 value. However, there were no reliable data available to determine the value for each patient. A correlation study of clinical lung toxicity data with the calculated RDV using the models, similar to that done by Kwa et al. (19), might be able to determine this value for the general population. The local radiation dose response (effect) of lung has been studied using three-dimensional CT imaging for the lung density change and lung fibrosis (22) and using single photon emission computed tomography (SPECT) for the lung function changes (lung perfusion) after irradiation (23–25). Linear-plateau, S-shaped-plateau, and logistic function radiation responses were reported (23–25). However, large variations among different patients and studies were noted. For example, Garipagaoglu et al. (24) reported that the overall plateau dose was approximately 60–65 Gy, suggesting that DL50 z 30 Gy. On the other hand, Theuws et al. (25) reported a DL50 of 55 Gy for lung perfusion after
radiotherapy. Generally, CT and SPECT studies suggest that the DL50 value for local lung damage is relatively high. However, the radiologic response could be quite different from the clinical manifestations. Analysis of DVH and the radiation-induced lung pneumonitis data showed that the DL50 could be much smaller. Using a logistic dose-effect function, it was reported that the parameters that best fit the clinical pneumonitis data were DL50 = 20.3 Gy and k = 2.83 (14, 16). Kwa et al. (19) also showed that if the simple threshold model for the dose effective function was used, the bestfitting threshold dose would be 13 Gy, or DL50 would be in the range of 6.5–13 Gy. Threshold doses of 20 Gy (V20) and 5 Gy (V5) have also been shown to best relate to radiation-induced lung toxicity (14, 21), suggesting that lung tissue would be injured at a very low dose. Therefore, the DL50 value of 20–30 Gy could be a reasonable choice and could be patient dependent and pneumonitis-grade dependent. Our results showed that the RDV monotonically decreased with increasing dose per fraction when the prescription dose was larger than the critical dose, suggesting that a single fraction has a greater benefit than 2–4 fractions. This result was based on the simple linear-quadratic model for the radiobiologic effect, which does not fully reflect the repair, redistribution, repopulation, and reoxygenation (the ‘‘four Rs’’) of radiobiology. Specifically, the tumor cells redistribute in a cell cycle, and the proportion of hypoxic cells readjust after irradiation. This means that the radiosensitivities of cells in different phases of the cell cycle and in the hypoxic state are very different. For example, a single fraction or 2 fractions may not effectively kill the low-sensitivity cells in the hypoxic state and in the S phase. Therefore, 3 to 4 fractions might be the better clinical choice. Further clinical studies are needed to better understand these important issues. CONCLUSION This study conceptually demonstrated that hypofractionation tended to be associated with less lung toxicity or a high therapeutic ratio compared with conventional fractionation when very high radiation doses were delivered to the tumor. On the other hand, conventional fractionation tended to be associated with less lung toxicity when relatively low radiation doses were delivered to the tumor.
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REFERENCES 1. Nagata Y, Negoro Y, Aoki T, et al. Clinical outcomes of 3D conformal hypofractionated single high-dose radiotherapy for one or two lung tumors using a stereotactic body frame. Int J Radiat Oncol Biol Phys 2002;52:1041–1046. 2. Timmerman R, Papiez L, McGarry R, et al. Extracranial stereotactic radioablation: Results of a phase I study in medically inoperable stage I non-small cell lung cancer. Chest 2003;124: 1946–1955. 3. Onishi H, Araki T, Shirato H, et al. Stereotactic hypofractionated high-dose irradiation for stage I nonsmall cell lung carcinoma: Clinical outcomes in 245 subjects in a Japanese multiinstitutional study. Cancer 2004;101:1623–1631. 4. Zimmermann FB, Geinitz H, Schill S, et al. Stereotactic hypofractionated radiotherapy in stage I (T1-2 N0 M0) non-smallcell lung cancer (NSCLC). Acta Oncol 2006;45:796–801. 5. Hoyer M, Roed H, Hansen AT, et al. Prospective study on stereotactic radiotherapy of limited-stage non-small-cell lung cancer. Int J Radiat Oncol Biol Phys 2006;66:S128–S135. 6. Beitler JJ, Badine EA, El-Sayah D, et al. Stereotactic body radiation therapy for nonmetastatic lung cancer: An analysis of 75 patients treated over 5 years. Int J Radiat Oncol Biol Phys 2006;65:100–106. 7. Matsuo Y, Takayama K, Nagata Y, et al. Interinstitutional variations in planning for stereotactic body radiation therapy for lung cancer. Int J Radiat Oncol Biol Phys 2007;68:416–425. 8. Guckenberger M, Heilman K, Wulf J, et al. Pulmonary injury and tumor response after stereotactic body radiotherapy (SBRT): Results of a serial follow-up CT study. Radiother Oncol 2007;85:435–442. 9. Kavanagh BD, Scheftera TE, Wersa¨ll PJ. Liver, renal, and retroperitoneal tumors: Stereotactic radiotherapy. Front Radiat Ther Oncol 2007;40:415–426. 10. Timmerman RD, Kavanagh BD, Cho LC, et al. Stereotactic body radiation therapy in multiple organ sites. J Clin Oncol 2007;25:947–952. 11. Jin JY, Chen Q, Jin R, et al. Technical and clinical experience with spine radiosurgery: A new technology for management of localized spine metastases. Technol Cancer Res Treat 2007;6:127–133. 12. Fowler JF, Tome´ WA, Fenwick JD, et al. A challenge to traditional radiation oncology. Int J Radiat Oncol Biol Phys 2004; 60:1241–1256. 13. Seppenwoolde Y, Lebesque JV, de Jaeger K, et al. Comparing different NTCP models that predict the incidence of radiation pneumonitis. Normal tissue complication probability. Int J Radiat Oncol Biol Phys 2003;55:724–735. 14. Yorke ED, Jackson A, Rosenzweig KE, et al. Correlation of dosimetric factors and radiation pneumonitis for non-small-
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cell lung cancer patients in a recently completed dose escalation study. Int J Radiat Oncol Biol Phys 2005;63:672–682. Jin JY, Ajlouni M, Chen Q, et al. Quantification of incidental dose to potential clinical target volume (CTV) under different stereotactic body radiation therapy (SBRT) techniques for non-small cell lung cancer—tumor motion and using internal target volume (ITV) could improve dose distribution in CTV. Radiother Oncol 2007;85:267–276. Kwa SL, Theuws JC, Wagenaar A, et al. Evaluation of two dose-volume histogram reduction models for the prediction of radiation pneumonitis. Radiother Oncol 1998;48:61–69. Rodrigues G, Lock M, D’Souza D, et al. Prediction of radiation pneumonitis by dose-volume histogram parameters in lung cancer—a systematic review. Radiother Oncol 2004;71:127–138. Yorke ED, Jackson A, Rosenzweig KE, et al. Dose-volume factors contributing to the incidence of radiation pneumonitis in non-small-cell lung cancer patients treated with three-dimensional conformal radiation therapy. Int J Radiat Oncol Biol Phys 2002;54:329–339. Kwa SL, Lebesque JV, Theuws JC, et al. Radiation pneumonitis as a function of mean lung dose: An analysis of pooled data of 540 patients. Int J Radiat Oncol Biol Phys 1998;42:1–9. Rancati T, Wennberg B, Lind P, et al. Early clinical and radiological pulmonary complications following breast cancer radiation therapy: NTCP fit with four different models. Radiother Oncol 2007;82:308–316. Tucker SL, Liu HH, Wang S, et al. Dose-volume modeling of the risk of postoperative pulmonary complications among esophageal cancer patients treated with concurrent chemoradiotherapy followed by surgery. Int J Radiat Oncol Biol Phys 2006; 66:754–761. Rosen II, Fischer TA, Antolak JA, et al. Correlation between lung fibrosis and radiation therapy dose after concurrent radiation therapy and chemotherapy for limited small cell lung cancer. Radiology 2001;221:614–622. Marks LB, Munley MT, Spencer DP, et al. Quantification of radiation-induced regional lung injury with perfusion imaging. Int J Radiat Oncol Biol Phys 1997;38:399–409. Garipagaoglu M, Munley MT, Hollis D, et al. The effect of patient-specific factors on radiation-induced regional lung injury. Int J Radiat Oncol Biol Phys 1999;45:331–338. Theuws JC, Kwa SL, Wagenaar AC, et al. Dose-effect relations for early local pulmonary injury after irradiation for malignant lymphoma and breast cancer. Radiother Oncol 1998;48:33–43. Kong FM, Hayman JA, Griffith KA, et al. Final toxicity results of a radiation-dose escalation study in patients with non-smallcell lung cancer (NSCLC): Predictors for radiation pneumonitis and fibrosis. Int J Radiat Oncol Biol Phys 2006;65:1075–1086.
doi:10.1016/j.ijrobp.2009.02.079
CLINICAL INVESTIGATION
Lung
IMPACT OF FRACTION SIZE ON LUNG RADIATION TOXICITY: HYPOFRACTIONATION MAY BE BENEFICIAL IN DOSE ESCALATION OF RADIOTHERAPY FOR LUNG CANCERS JIN-YUE JIN, PH.D.,* FENG-MING KONG, M.D., PH.D., M.P.H.,yz INDRIN J. CHETTY, PH.D.,* MUNTHER AJLOUNI, M.D.,* SAMUEL RYU, M.D.,* RANDALL TEN HAKEN, PH.D.,y AND BENJAMIN MOVSAS, M.D.* * Department of Radiation Oncology, Henry Ford Hospital, Detroit, MI; y Department of Radiation Oncology, University of Michigan, Ann Arbor, MI; and z Department of Radiation Oncology, Veteran’s Hospital, Ann Arbor, MI Purpose: To assess how fraction size impacts lung radiation toxicity and therapeutic ratio in treatment of lung cancers. Methods and Materials: The relative damaged volume (RDV) of lung was used as the endpoint in the comparison of various fractionation schemes with the same normalized total dose (NTD) to the tumor. The RDV was computed from the biologically corrected lung dose–volume histogram (DVH), with an a/b ratio of 3 and 10 for lung and tumor, respectively. Two different (linear and S-shaped) local dose-effect models that incorporated the concept of a threshold dose effect with a single parameter DL50 (dose at 50% local dose effect) were used to convert the DVH into the RDV. The comparison was conducted using four representative DVHs at different NTD and DL50 values. Results: The RDV decreased with increasing dose/fraction when the NTD was larger than a critical dose (DCR) and increased when the NTD was less than DCR. The DCR was 32–50 Gy and 58–87 Gy for a small tumor (11 cm3) for the linear and S-shaped local dose-effect models, respectively, when DL50 was 20–30 Gy. The DCR was 66–97 Gy and 66–99 Gy, respectively, for a large tumor (266 cm3). Hypofractionation was preferred for small tumors and higher NTDs, and conventional fractionation was better for large tumors and lower NTDs. Hypofractionation might be beneficial for intermediate-sized tumors when NTD = 80–90 Gy, especially if the DL50 is small (20 Gy). Conclusion: This computational study demonstrated that hypofractionated stereotactic body radiotherapy is a better regimen than conventional fractionation in lung cancer patients with small tumors and high doses, because it generates lower RDV when the tumor NTD is kept unchanged. Ó 2010 Elsevier Inc. Hypofraction, Stereotactic body radiotherapy, Non–small-cell lung cancer, Radiobiology, Normal tissue complication probability.
Because normal lung tissue usually has a relatively lower a/b ratio than does tumor tissue, traditionally, hypofractionation is not considered beneficial in terms of normal tissue sparing. However, the newly emerging technique of hypofractionated stereotactic body radiotherapy (SBRT) has achieved improved tumor control with minimal lung toxicity for the treatment of inoperable Stage I non–small-cell lung cancers (NSCLC) (1–8). Stereotactic body radiotherapy has also been used in the treatment of tumors in many other body sites (9–11). Do the successful clinical results in SBRT contradict the conventional wisdom that hypofractionation is not beneficial for normal tissue sparing? In other words, is there an underlying principle supporting that hypo-
fractionated SBRT is superior to conventional fractionated treatment? In addition, is there an optimal fractionation scheme for maximizing the therapeutic ratio? Can hypofractionation be applied to lung cancer patients with larger tumors? And in which situations is hypofractionation preferred? This study aimed to answer these questions by evaluating the impact of fraction size on lung radiation toxicity and therapeutic ratio. The combination of a linear-quadratic model in radiobiology and a dose–volume histogram (DVH)-based lung toxicity model was used in the study. In particular, considering that the lung is a parallel organ consisting of many individual lung function units, new local dose-effect functions that incorporated the concepts of a threshold dose effect and a partial damage effect were used to calculate lung toxicity.
Reprint requests to: Jian-Yue Jin, Ph.D., Department of Radiation Oncology, Henry Ford Hospital, 2799 W. Grand Blvd., Detroit, MI 48202. Tel: (313) 916-0234; Fax: (313) 916-3235;
E-mail: [email protected] Conflict of interest: none. Received Jan 4, 2009. Accepted for publication Feb 24, 2009.
INTRODUCTION
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was from an opposing anterior-to-posterior (AP) and posterior-toanterior (PA) plan of the same large central lesion (GTV = 266 cm3).
120 100
Percentage Volume (%)
783
DVH1
Converting physical DVHs into normalized biologic equivalent DVHs
DVH2 80
DVH3 DVH4
Each lung DVH was converted to the normalized biologic equivalent (NBE) DVH for various fractionation schemes, assuming that the target received the same NTD for each fractionation scheme. Alpha/beta ratios of 10 and 3 were used for tumor and normal lung tissue, respectively. Table 1 lists the doses per fraction for some selected fractionation schemes with the same NTD of 60, 80, 100, and 120 Gy. For a particular fractionation scheme, NTD was calculated using the following equation:
60 40 20 0 0
20
40
60
80
100
120
NTD ¼ DF n
Percentage Dose (%)
Fig. 1. Four representative dose–volume histograms (DVHs) used for the analysis. DVH1 was from a stereotactic body radiotherapy plan of a small gross tumor volume (GTV) (11 cm3). DVH2 was from a similar hypothetical seven-field intensity-modulated radiotherapy plan of a relatively large peripheral tumor (GTV = 224 cm3). DVH3 was from a seven-field plan of a large central lesion (GTV = 266 cm3). DVH4 was from an anteroposterior/posteroanterior plan of the same large central lesion.
ð1 þ DF =10GyÞ ¼ BED=1:2 ð1 þ 2Gy=10GyÞ
where DF is the dose per fraction, n is the number of fractions, 10Gy is the a/b ratio of the tumor, 2Gy is the dose per fraction for conventional fractionation, and BED is the biologic equivalent dose. We assumed that the original lung DVH was expressed as the volume vs. the percentage dose, with the percentage dose divided into many percentage dose bins (Di%). Thus, the lung NBE-DVH was computed by converting each Di% into the NBE dose bin (NBEDi) using the following equation:
METHODS AND MATERIALS
NBEDi ¼ DF Di % n
We first set the normalized total dose (NTD) (12) to the same value for the various fractionation schemes. Thus, the lung toxicity reflected the therapeutic ratio, because the tumor control was the same for the same NTD to the target. The relative damaged volume (RDV) (13) or fraction of damaged subfunction units (fdam) (14) was then calculated from the lung DVH and the local dose-effect functions to represent the lung toxicity. Therefore, the optimal fractionation scheme can be determined by comparing the RDVs of different fractionation sizes. To determine the optimal fractionation scheme in various situations, such comparisons were performed for different NTD values, various parameters used in the lung toxicity models, and four representative lung DVHs with different tumor sizes, locations, and planning techniques.
Representative DVHs for analysis Four representative lung DVHs (Fig. 1) were used for the analysis. DVH1 was from an SBRT plan for a patient with a relatively small gross tumor volume (GTV) (11 cm3). Intensity-modulated radiotherapy (IMRT) planning with seven coplanar fields was used for the SBRT treatment plan (15). DVH2 was from a similar seven-field IMRT plan for a patient with a larger peripheral tumor (GTV = 224 cm3); DVH3 was from a seven-field IMRT plan for a patient with a large central lesion (GTV = 266 cm3); and DVH4
(1)
ð1 þ DF Di %=3GyÞ ð1 þ 2Gy Di %=3GyÞ
(2)
where 3Gy is the a/b ratio for the lung tissue.
Lung complication models There are many DVH-based normal tissue toxicity models in the literature (13, 14, 16–21), and these can be grouped into two categories according to how the DVH is reduced into a single parameter (16): (1) the equivalent dose model, in which a lung DVH is converted into an equivalent dose to the whole lung with specific conversion functions, and (2) the effective volume model, in which the lung DVH is converted into an equivalent RDV using a local effective dose function, E(D). The effective volume model can also be called the ‘‘parallel functional subunit model,’’ and the RDV is the fraction of damaged functional subunits (fdam) (14). Because the lung is considered a parallel organ consisting of many individual lung function units, the effective volume model should better reflect the lung toxicity mechanism than the equivalent dose model. Mathematically, this model can be expressed as: X RDV ¼ EðDi Þ Vi (3) i
where Vi is the percentage of lung volume receiving a dose (Di) from the lung DVH. The simple threshold model such as the V20 model is
Table 1. Dose per fraction for different numbers of fractions to achieve the same NTD of 60, 80, 100 and 120 Gy at 2-Gy fractions Dose per fraction for hypofractionation with different number of fractions (Gy) NTD (Gy)
Conventional fractionation
60 80 100 120
2 Gy 30 F 2 Gy 40 F 2 Gy 50 F 2 Gy 60 F
1F
2F
3F
4F
5F
6F
10 F
20 F
22.30 26.39 30 33.28
14.62 17.47 20 22.29
11.28 13.57 15.62 17.47
9.32 11.28 13.03 14.62
8 9.73 11.28 12.69
7.04 8.60 10 11.28
4.85 6 7.04 8
2.81 3.54 4.22 4.85
Abbreviations: NTD = normalized tumor dose; F = fraction(s).
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old models: the linear effective dose and S-shaped effective dose models. As shown in Fig. 2, a single parameter, DL50 (i.e., the dose at the local dose effect of 50%), was assumed for both models. These models incorporated the concept of the threshold dose effect from the simple threshold model and the concept of partial damage from the MLD-V model. When the radiation dose increases to DPla = 2DL50, the lung functional subunit is considered completely damaged and the local dose effect reaches a plateau of 100% in both models. In the dose range of 0 to DPla, the linear model shows a linear increase of the local damage effect with the radiation dose, and the S-shaped model shows an S-shaped response. Mathematically, E(D) of the linear and S-shaped models can be expressed as:
Effective dose function E(D)
1
0.8
0.6
0.4
Linear (LED) model S-shaped (SED) model Simple threshold model MLD-V model Logistic model
0.2
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0 DL50
EðDÞ ¼ D=2DL50 when D \ 2DL50
(8A)
EðDÞ ¼ 100% when D $ 2DL50
(8B)
DPla
Dose
Fig. 2. Graphic illustration of the local dose effect, E(D), for various models. The linear and S-shaped models have only one parameter, DL50, the dose causing 50% of local effect. When the dose D is 2DL50 (= DPla), E(D) reaches a plateau. The simple threshold model has also only one parameter, DThr = DL50 = DPla. The mean lung dose converted equivalent volume (MLD-V) model has no parameters. The logistic function model has two parameters. k = 2 was used in this plot. an example of a lung effective volume model (13). In this model, the E(D) can be expressed as: EðDÞ ¼ 0 when D \ 20 Gy; and
(4A)
EðDÞ ¼ 100% when D $ 20 Gy;
(4B)
where D is the dose received by a functional unit. The equivalent uniform dose and mean lung dose (MLD) models are two examples of the equivalent dose model (13). The MLD can be calculated as: X Di Vi : (5) MLD ¼ i
Comparing Eqs. 3 and 5, if we assume an effective dose function EðDÞ ¼ D=100Gy:
(6)
the MLD model can be considered as an equivalent volume mode mathematically, and RDV ¼ MLD=100Gy:
(7)
We named this MLD-converted equivalent volume model as the MLD-V model. The MLD and MLD-V models should behave similarly because they share a similar DVH reduction formula. The simple threshold model reflects an important characteristic of radiation-induced lung radiation toxicity (i.e., a local lung functional subunit is completely damaged after irradiation with a threshold dose); therefore, further increase in the dose will not further damage that subunit. However, the simple threshold model may be inaccurate because it suggests that doses less than the threshold dose inflict no damage. The MLD-V model reflects the concept of partial damage (i.e., a linear increase in damage with an increase in dose) of a local lung functional subunit. However, it is also not theoretically sound because it shows a damage effect of >1 when the doses are >100 Gy. In this study, we proposed two more-sophisticated effective dose models as an extension of the MLD-V and simple thresh-
and EðDÞ ¼
D=DL50 1 1 þ ðD=DL50 1Þ2
þ 1=2 when D \ 2DL50
EðDÞ ¼ 100% when D $2DL50
(9A)
(9B)
respectively, where D is the dose received by a functional subunit. A logistic function model had also been used by other investigators (16, 18). The E(D) of the logistic function model is: (10) EðDÞ ¼ 1= 1 þ ðDL50 =DÞk where k is another parameter representing the steepness of the curve. The logistic model with k = 2 is shown in Fig. 2 for comparison. It assumes a shape very similar to that of the S-shaped model except for the plateau part. In this model the damage effect will always be <1 (complete damage for the subunit) even for an infinitely large dose. In addition, two parameters are used in this model, in comparison with the single parameter for the linear, S-shaped, and simple threshold models and no parameters for the MLD model. Therefore, the logistic model will not be used for this study. Although many studies of dose correlation with functional imaging, CT density, and clinical symptoms have suggested that the lung dose response is similar to the linear, S-shaped, or logistic function models, there are no consistent data showing the value of DL50 for lung tissue (22–25). In this study, we assumed that the DL50 was a parameter that could vary with patients. Hypothetical DL50 values of 20, 30, and 40 Gy were used in the study for both models.
Analysis of lung RDV The lung RDVs were computed for various fractionation schemas for four representative DVHs at different hypothetical DL50 values and at different prescription doses (NTD, 50–120 Gy). The comparisons and analysis were performed at the following levels. Analysis 1. The correlation of RDV and the fraction size (dose/ fraction) was first analyzed to determine whether there is an optimal fraction size and whether a larger fraction is better than a conventional fraction for a fixed prescription dose (NTD = 100 Gy, typically for SBRT) and for various other parameters. Analysis 2. On the basis of the results of Analysis 1 that there was a monotonic relationship between RDV and the fraction size, the percentage difference of RDVs (or percentage reduction of RDV)
Hypofractionation may reduce lung toxicity for dose escalation d J.-Y. JIN et al. 35 DVH1, SED model DVH2, SED model DVH3, SED model DVH4, SED model
60
DVH1, LED model DVH2, LED model DVH3, LED model DVH4, LED model
Relative Damaged Lung Volume (%)
Relative Damaged Lung Volume (%)
70
785
50 40 30 20 10
30 25 20 15
Linear model, DL50 = 20Gy S-shape model, DL50= 20Gy Linear model, DL50 = 30Gy S-shape model, DL50 = 30GY Linear model, DL50 = 40Gy S-shape model, DL50 = 40Gy
10 5 0
0 0
5
10
15
20
25
30
Dose Per Fraction (Gy)(NTD=100Gy)
Fig. 3. Correlation of lung relative damage volume with dose per fraction for four dose–volume histograms (DVHs) for both linear and S-shaped models when normalized total dose (NTD) = 100 Gy and DL50 = 20 Gy. SED = S-shaped effective dose; LED = linear effective dose.
between the conventional fractionation and the single-fraction scheme was used as the parameter to represent the correlation of RDV with the fraction size. The correlation of the percentage RDV difference to NTD was then analyzed for various parameters. Analysis 3. On the basis of the results of Analysis 2 that the percentage RDV reduction increased monotonically with NTD, a critical prescription dose (DCR) was defined as the NTD value when the RDV reduction equaled zero. Therefore, when NTD > DCR , the RDV reduction was positive and a single fraction had a smaller RDV than did conventional fractionation, and vice verse. This critical prescription dose was calculated and analyzed for various DVHs under different parameters.
RESULTS Correlation of RDV with fraction size for a fixed NTD Figure 3 shows the lung RDV vs. fraction size for all four DVHs for both linear and S-shaped models when NTD = 100 Gy and DL50 = 20 Gy. The RDV reduced monotonically with increasing dose per fraction for all DVHs. DVH4, which was from a simple AP/PA plan for a large central tumor, showed a relatively slower reduction in the RDV with the fraction size, in comparison with the other three DVHs. Therefore, increasing fraction size (hypofractionation) tended to reduce the lung RDV compared with conventional fractionation (2 Gy per fraction) for the same NTD given to the tumor when DL50 was relatively low and NTD was relatively high. Figure 4 shows the lung RDV varying with the fraction size for DVH2 with NTD = 100 Gy to the tumor for three DL50 values. The lung RDV decreased monotonically with increasing fraction size for both the linear and S-shaped models when DL50 = 20 Gy and for the linear model when DL50 = 30 Gy. However, the RDV increased monotonically with increasing fraction size for the S-shaped model when DL50 = 40 Gy. The RDV tended to vary minimally for different fraction sizes for the linear model when DL50 = 40 Gy and for the S-shaped model when DL50 = 30 Gy.
0
5
10
15
20
25
30
Dose Per Fraction (Gy)(NTD=100Gy)
Fig. 4. Correlation of lung relative damage volume with dose per fraction for Dose–Volume Histogram 2 for various dose-effect models at various DL50 value when normalized total dose (NTD) = 100 Gy.
These data showed that the RDV either increased or decreased monotonically or stayed relatively constant with the change in dose per fraction for different situations. There were no optimal numbers of fractions between conventional and single fractionation that would lead to less lung toxicity. Therefore, the difference between conventional fractionation and the single fraction (such as the percentage RDV reduction from conventional fractionation to the single fraction) seems to be a parameter to indicate the preference of fractionation schemes. A positive difference means that the RDV decreases with the fraction size and hypofractionation is preferred. A negative difference indicates that the RDV increases with the fraction size and conventional fractionation is preferred. Correlation of RDV difference with NTD Figure 5 shows the percentage RDV difference vs. the NTD for various DVHs and DL50 values of the two models. The percentage RDV difference increased monotonically with the NTD for all four DVHs and DL50 values of the two lung toxicity models. The percentage RDV difference tended to be negative when NTD was low and became positive when the NTD was larger than a critical value. This critical NTD value was defined as the critical dose (DCR). Therefore, this DCR can be used as a parameter to determine whether hypofractionation is better than conventional fractionation for a specific treatment plan. The critical dose Table 2 shows the DCR in various situations for the four DVH examples. Generally, the DCR increased with the DL50 value and the tumor volume. The S-shaped model had a larger DCR than the linear model for the same DL50 value. The DCR value was 32–50 Gy and 58–87 Gy for the linear and S-shaped models, respectively, when DL50 varied from 20 to 30 Gy for the DVH of a small tumor (11 cm3). This indicates that the hypofractionation scheme, for which the
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DISCUSSION
20
0
LED20 LED30 LED40 SED20 SED30 SED40
-20
Lung RDV reduction (%)
-40 20
0
-20
Lung RDV reduction (%)
-40 20
0
-20
-40
Lung RDV reduction (%)
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20
0
-20
-40 40
50
60
70
80
90
100
110
120
130
Normalized total dose to the tumor (Gy)
Fig. 5. Percentage difference of the relative damage volume (RDV) between conventional fractionation and a single fraction varies with the normalized total dose for different dose-effect models, DL50 value, and dose–volume histograms (DVHs). (A) DVH1, (B) DVH2, (C) DVH3, (D) DVH4. SED = S-shaped effective dose; LED = linear effective dose.
prescription dose is usually large (NDT > 90 Gy), may be the preferred choice to reduce the lung RDV in such situations. On the other hand, the corresponding DCR was 66–97 Gy and 66–99 Gy for the DVH of the largest tumor with a seven-field IMRT plan (DVH3). Therefore, traditional fractionation may be preferred in this situation, in which the prescription dose is relatively small (NTD = 60–70 Gy). The corresponding DCR was 52–80 Gy and 60–90 Gy for the DVH of an intermediate-sized peripheral tumor (DVH2). In this situation, hypofractionation may be beneficial when a prescription dose of NTD = 70–90 Gy can be given, especially for the linear lung toxicity model or small DL50 value (20 Gy).
This computational study showed that hypofractionation was associated with less lung RDV than was conventional fractionation for very high prescription doses. On the other hand, conventional fractionation tended to be associated with less lung RDV when a relatively low dose was delivered to the target. The finding that hypofractionation caused less lung damage than did conventional fractionation seems to contradict our traditional belief, because lung tissue has a lower a/b ratio. However, this new observation could be explained by the fact that both our traditional beliefs and clinical experience mostly come from the two-dimensional era, during which the radiation dose was low, the radiation fields were large, the radiation was mostly confined to the irradiated volume, and the dose distribution within the irradiated volume was relatively uniform (i.e., equal to the prescription dose). The situation could be quite different today in the context of modern three-dimensional conformal radiotherapy, especially with regard to SBRT. For SBRT, the irradiation target is relatively small, but low doses could spread out to a much larger volume, with only a relatively small portion of the lung receiving high doses. However, for those lung volumes receiving high doses of radiation, although hypofractionation would increase the BED, the lung functional units were already totally damaged, and thus increasing the dose would not worsen the damage. However, for most lung volumes receiving relatively low doses of radiation, hypofractionation actually reduces the BED. For example, for the volume receiving 10% of the prescription dose of 120 Gy NTD, the actual physical dose is 3.3 Gy per fraction for single-fraction treatment, which has a BED of 6.9 Gy (assuming a/b = 3 Gy), whereas for conventional fractionation the actual dose is 0.2 Gy in 60 fractions, which has a BED of 13.2 Gy. The use of the DVH-based models helps us to better understand the cumulative effect of these complicated phenomena. Interestingly, the results of this study seem to support the current clinical practice. For a larger target volume (normally limited to lower prescription dose), conventional fractionation has a lower RDV and is thus preferred. For a small target volume and high prescription dose, hypofractionation is often preferred, which agrees with the clinical toxicity outcome in patients with inoperable Stage I NSCLC treated with SBRT (1–8). These agreements suggest that the proposed DVH reduction models are conceptually reasonable. The results suggest that the fractionation scheme (large or small fractionation) could be another important parameter to consider for the individualized radiation treatment of lung cancers to minimize lung damage and hence to improve the therapeutic ratio. For example, using singlefraction treatment would reduce lung RDVs by 24% and 17% from the conventional fractionation for the linear model and by 22% and 12% for the S-shaped model when DL50 = 20 and 30 Gy, respectively, for DVH1 and an NTD of 120 Gy. On the other hand, conventional fractionation would be associated with 9% and 20% less lung RDV than the single fraction for the linear and S-shaped
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Table 2. Critical prescription dose for different DVHs, dose effect models, and DL50 values Critical prescription dose S-shaped model for various DL50 values
Linear model for various DL50 values DVH
GTV (cm3)
Plan
20 Gy
30 Gy
40 Gy
20 Gy
30 Gy
40 Gy
DVH1 DVH2 DVH3 DVH4
11 224 266 266
7-field SBRT 7-Field IMRT 7-field IMRT 2D
32 52 66 45
50 80 97 65
65 105 >120 87
58 60 66 61
87 90 99 91
116 120 >120 120
Abbreviations: DVH = dose–volume histogram; SBRT = stereotactic body radiotherapy; IMRT = intensity-modulated radiotherapy; 2D = two-dimensional.
models, respectively, when NTD is 60 Gy for the tumor of DVH3 if DL50 = 30 Gy. Hypofractionation could be beneficial for some intermediate-sized or large peripherally located tumors, for which high-dose escalation (NTD = 80– 100 Gy) can be performed with some risk of lung toxicity (14, 18, 26). For example, a single fraction would have a 16% and 8% reduction in lung RDV compared with conventional fractionation for the linear model, and this would be 16% and 4% for the S-shaped model, when DL50 = 20 and 30 Gy, respectively, for the tumor of the example DHV2 if an NTD of 100 Gy was given. Although qualitatively the results indicate that hypofractionation may be preferred for a higher prescription dose and conventional fractionation for a lower prescription dose, it is beyond the scope of this study to pinpoint the exact cut-off (critical) prescription dose, because it depends on many factors, such as the lung damage model and its parameter, the radiobiologic model and its parameters, and the DVH shape, which in turn depends on the target volume and the treatment planning. Understanding the mechanism of radiation-induced lung toxicity is particularly important to determine the maximal tolerable prescription dose to the target and, based on that, the fractionation scheme to minimize the lung damage. We have used the linear and S-shaped local radiation dose-response models to simulate the relative lung damage volume. Each of these models requires only one parameter, the DL50 value. However, there were no reliable data available to determine the value for each patient. A correlation study of clinical lung toxicity data with the calculated RDV using the models, similar to that done by Kwa et al. (19), might be able to determine this value for the general population. The local radiation dose response (effect) of lung has been studied using three-dimensional CT imaging for the lung density change and lung fibrosis (22) and using single photon emission computed tomography (SPECT) for the lung function changes (lung perfusion) after irradiation (23–25). Linear-plateau, S-shaped-plateau, and logistic function radiation responses were reported (23–25). However, large variations among different patients and studies were noted. For example, Garipagaoglu et al. (24) reported that the overall plateau dose was approximately 60–65 Gy, suggesting that DL50 z 30 Gy. On the other hand, Theuws et al. (25) reported a DL50 of 55 Gy for lung perfusion after
radiotherapy. Generally, CT and SPECT studies suggest that the DL50 value for local lung damage is relatively high. However, the radiologic response could be quite different from the clinical manifestations. Analysis of DVH and the radiation-induced lung pneumonitis data showed that the DL50 could be much smaller. Using a logistic dose-effect function, it was reported that the parameters that best fit the clinical pneumonitis data were DL50 = 20.3 Gy and k = 2.83 (14, 16). Kwa et al. (19) also showed that if the simple threshold model for the dose effective function was used, the bestfitting threshold dose would be 13 Gy, or DL50 would be in the range of 6.5–13 Gy. Threshold doses of 20 Gy (V20) and 5 Gy (V5) have also been shown to best relate to radiation-induced lung toxicity (14, 21), suggesting that lung tissue would be injured at a very low dose. Therefore, the DL50 value of 20–30 Gy could be a reasonable choice and could be patient dependent and pneumonitis-grade dependent. Our results showed that the RDV monotonically decreased with increasing dose per fraction when the prescription dose was larger than the critical dose, suggesting that a single fraction has a greater benefit than 2–4 fractions. This result was based on the simple linear-quadratic model for the radiobiologic effect, which does not fully reflect the repair, redistribution, repopulation, and reoxygenation (the ‘‘four Rs’’) of radiobiology. Specifically, the tumor cells redistribute in a cell cycle, and the proportion of hypoxic cells readjust after irradiation. This means that the radiosensitivities of cells in different phases of the cell cycle and in the hypoxic state are very different. For example, a single fraction or 2 fractions may not effectively kill the low-sensitivity cells in the hypoxic state and in the S phase. Therefore, 3 to 4 fractions might be the better clinical choice. Further clinical studies are needed to better understand these important issues. CONCLUSION This study conceptually demonstrated that hypofractionation tended to be associated with less lung toxicity or a high therapeutic ratio compared with conventional fractionation when very high radiation doses were delivered to the tumor. On the other hand, conventional fractionation tended to be associated with less lung toxicity when relatively low radiation doses were delivered to the tumor.
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