International Journal of Radiation Oncology*Biology*Physics
Biology contributionThe low α/β ratio for prostate cancer: What does the clinical outcome of HDR brachytherapy tell us?
Introduction
Radiobiologic parameters (for example, the α/β ratio of the linear-quadratic [LQ] model) play an important role in planning and optimizing radiotherapy treatments for human cancer. Recently, the α/β ratio for prostate cancer has become a highly debated topic in the radiation therapy community 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21. Accumulating evidence from clinical studies suggests that prostate cancer has a low α/β ratio (1.2–3.1 Gy), which is significantly different from typical α/β values for tumors (≥8 Gy). Such a low α/β value should have a significant impact on the treatment design of radiation therapy. Typical fractionated treatment schemes based on large α/β ratios may not be optimal for the radiotherapeutic management of prostate cancer 4, 7, 8, 13. As a result, alternative treatment strategies have been designed based on such low α/β values. At the current time, it is critical to clinically verify that the α/β ratio is, indeed, low for prostate cancer.
In earlier studies, Brenner et al. 1, 3 and Fowler et al. (10) derived an α/β ratio of 1.5 Gy from the compiled clinical data. Unfortunately such an α/β ratio was always linked with an extremely low radiosensitivity (α ≈ 0.04 Gy−1) and extremely low clonogen numbers (in the order of 10 to 100) 1, 3, 5, 6, 10. By taking into account the effect of tumor proliferation, Wang et al. (2) have analyzed several reported clinical studies, including the external beam radiotherapy (EBRT) dose-escalation study from Memorial Sloan-Kettering Cancer Center (MSKCC) 22, 23. A self-consistent set of LQ parameters: α = 0.15 Gy−1, α/β = 3.1 Gy and a repair time Tr = 16 min was obtained in their analysis (2). In addition, the puzzle for the extremely low clonogen numbers was also naturally solved in their study. The numbers of clonogens were estimated to be 106−107 depending on the risk level of prostate patient groups (2).
Although much effort has been spent on deriving and confirming the α/β ratio for prostate cancer, several challenging issues still remain 5, 6, 11, 14, 15, 16, 17, 18, 19, 20, 21. Most of the previous data modeling was based on the clinical finding that EBRT and permanent brachytherapy with certain dosing regimes are equivalent in treatment outcome. Some investigators have questioned this equivalence in terms of the definition of tumor control and the prescribed dose (11). Others have raised the issue that the relative biologic effectiveness (RBE) may play a role in the permanent brachytherapy since low-energy photons are used in 125I and 103Pd implants (14). This RBE effect was ignored in several previous important studies presented in Refs. 1, 2, 3, 10, 12. There are also concerns about the systematic uncertainties of the clinical data collected from different institutions for multiple modalities (EBRT vs. brachytherapy), which may ultimately question the definitive results yielded from these earlier studies 1, 2, 3, 10, 12.
Recently, Brenner et al. (1) have compiled and analyzed the clinical study conducted at the William Beaumont Hospital (WBH) using EBRT plus high-dose-rate (HDR) brachytherapy boost for prostate cancer 24, 25. In the HDR boost treatment, both 3-fraction and 2-fraction schemes with a total boost dose escalated from 16.5 Gy to 21 Gy were used. Because no permanent brachytherapy was involved in this study, it provides us an opportunity to address the issues mentioned above. Using this data set to derive the α/β ratio is not subject to any equivalence in the comparison between EBRT and permanent brachytherapy. The issue of RBE effect is less important because the photon energies of the HDR source (192Ir) are much higher than those used in the permanent brachytherapy and only one type of source is involved. Furthermore, the variation of multi-institutional and multimodality results is not a concern, because the data were collected from a single institution using a single modality.
Based on the LQ and tumor control probability (TCP) models, Brenner et al. (1) have analyzed the WBH data and derived a set of radiobiological parameters for prostate cancer: α = 0.026 Gy−1, α/β = 1.2 Gy, clonogen number K = 138 cells. However, several limitations compromised their analysis: (i) The Brenner et al. analysis was based on the endpoint of 3-year post-treatment time. However, one data point (2 × 8.25 Gy) used in their study was a value beyond 3.7 years which was inconsistent with the other data points. While the 3-year biochemical control rate for this data point is about 95%, the value used in their analysis was about 87%, corresponding to a post-treatment time equal or longer than 3.7 years (Refer to Fig. 1, Fig. 2 of Ref. 1). (ii) One data point used in their analysis was in an unstable phase. The biochemical control rate for the 3 × 5.5 Gy data point changed from 64% at 3 years to 54.5% at 3.1 years and to 45.5% at 3.3 years (Refer to Fig. 1a of Ref. 1). Because such dramatic changes occurred within 3 months, the 3-year data would not be mature enough for data modeling. (iii) Due to the small number of patients sampled in each group, the statistical uncertainties are very large; therefore, it is hard to derive any definitive and unique values for the LQ parameters from such a single data set. Because of these limitations, a more rigorous analysis on this data set is necessary to address the challenging issues and to obtain more accurate estimation of radiobiological parameters.
In this study, we have reanalyzed the WBH data with a different approach. The endpoint of 4-year post-treatment time was chosen to allow for maturity and stability in the data. By combining with the results obtained with MSKCC clinical data in another study (2), we have derived a new set of LQ parameters, which is independent of any permanent brachytherapy of prostate cancer. The results obtained in this work are compared with the LQ parameters obtained in earlier investigations.
Section snippets
LQ and TCP models for EBRT and HDR
The general LQ model, extended to include the effects of dose rate, repair of sublethal damage, and clonogen proliferation 26, 27, 28, was used in this study. In this model, the surviving fraction S of cells irradiated to a total dose D within an overall treatment time T is given by where α and β characterize intrinsic radiosensitivity, G is the dose protraction factor, γ is the effective tumor repopulation rate [γ = ln (2)/Td, and Td is the potential tumor doubling time]. A
Fitting to the WBH clinical data
To search for the minimum chi-square value (χmin2) in the fitting to the WBH data, we varied parameter α from 0 to 0.5 Gy−1 and parameter α/β from 0 to 20 Gy. It was found that the χmin2 occurred at α = 0 (α/β = 0), β = 0.044 Gy−2, and χmin2 = 0.7. This result indicates that the linear term in the LQ formalism is negligible and only the quadratic term contributes significantly to cell killing. We did not search the χmin2 value for α < 0, because a negative α value has no physical meaning in
Conclusion and discussion
In this study, we have revisited the clinical data collected at WBH (1) and have derived a new set of LQ parameters in conjunction with the clinical data collected at MSKCC (22). The current study provides further evidence to support that prostate cancer has a low α/β ratio. The estimated values of LQ parameters (α = 0.14 ± 0.5 Gy−1, α/β = 3.1−1.6+2.6 Gy) from the current analysis are consistent with the previous results derived from the compiled EBRT and permanent brachytherapy data (2). The
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