International Journal of
Radiation Oncology biology
physics
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Clinical Investigation: Genitourinary Cancer
On the Sensitivity of a/b Prediction to Dose Calculation Methodology in Prostate Brachytherapy Hossein Afsharpour, PhD,*,y Sean Walsh, PhD,z,x Charles-Antoine Collins Fekete, MSc,* Eric Vigneault, MSc, MD,* Frank Verhaegen, PhD,z,{ and Luc Beaulieu, PhD* *Centre de Recherche sur le Cancer, Universite´ Laval and De´partement de Radio-Oncologie, Centre Hospitalier Universitaire de Que´bec, Que´bec, QC, Canada; yCentre Inte´gre´ de Cance´rologie de la Monte´re´gie, Hoˆpital Charles-LeMoyne, Greenfield Park, QC, Canada; zDepartment of Radiation Oncology Maastricht Radiation Oncology (MAASTRO), GROW, University Hospital Maastricht, Maastricht, The Netherlands; xGray Institute for Radiation Oncology and Biology, The University of Oxford, The United Kingdom; and {Medical Physics Unit, Department of Oncology, McGill University, Montre´al, Que´bec, Canada Received Jun 8, 2013, and in revised form Sep 16, 2013. Accepted for publication Nov 1, 2013.
Summary The aim of this work is to show the importance of using accurate dose calculation algorithms in brachytherapy from a radiobiological point of view. More specifically, the impact of heterogeneity corrections on the estimation of the a/b ratio for prostate cancer is investigated. Different dosimetry protocols in brachytherapy are used and compared for estimating this ratio.
Purpose: To study the relationship between the accuracy of the dose calculation in brachytherapy and the estimations of the radiosensitivity parameter, a/b, for prostate cancer. Methods and Materials: In this study, Monte Carlo methods and more specifically the code ALGEBRA was used to produce accurate dose calculations in the case of prostate brachytherapy. Equivalent uniform biologically effective dose was calculated for these dose distributions and was used in an iso-effectiveness relationship with external beam radiation therapy. Results: By considering different levels of detail in the calculations, the estimation for the a/b parameter varied from 1.9 to 6.3 Gy, compared with a value of 3.0 Gy suggested by the American Association of Physicists in Medicine Task Group 137. Conclusions: Large variations of the a/b show the sensitivity of this parameter to dose calculation modality. The use of accurate dose calculation engines is critical for better evaluating the biological outcomes of treatments. Ó 2014 Elsevier Inc.
Introduction Prostate cancer may not have the same doseeresponse sensitivity to radiation as tumors in general. Several authors have reported unusually low a/b ratios for prostate cancer (1) compared with other typical tumors (>9 Gy). However, these works do not agree on a Reprint requests to: Luc Beaulieu, PhD, Centre Hospitalier Universitaire de Que´bec Pavillon Carlton-Auger, De´partement de RadioOncologie, 11 cote du palais, Que´bec, QC, G1R 2J6, Canada. Tel: (418) 525-4444, ext. 15315; E-mail: [email protected] Int J Radiation Oncol Biol Phys, Vol. 88, No. 2, pp. 345e350, 2014 0360-3016/$ - see front matter Ó 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ijrobp.2013.11.001
unique consensus value and have reported a/b values ranging from 1.2 to 8 Gy (1). Brenner and Hall (2) obtained an a value of 0.036 Gy1 for prostate cancer by fitting the 3-year survival data with the reported D90 dose metric for brachytherapy (BT) patients. By fixing the a parameter, they used the survival rates of external beam radiation therapy (EBRT) to obtain a range for the a/b ratio extending from 0.8 Gy to 2.2 Gy, with a mean value of 1.5 Gy. King This work has been supported by grant 2011-700180 from the Canadian Cancer Society Research Institute. Conflict of interest: none.
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and Mayo (3) questioned the validity of the results of Brenner and Hall, owing to its extremely low radiosensitivity (a) leading to an unrealistically low number of clonogens with no biological relevance. Brenner and Hall (4) responded with a fully heterogeneous linear-quadratic (LQ) model in which both a and b were represented by independent Gaussian distributions, resulting in an a/b of 2.1 Gy. In a short article, King and Fowler (5) assumed the iso-efficiency of the EBRT prescription dose of 70-74 Gy with the 145-Gy prescription dose of 125I BT to predict an a/b ratio of approximately 2 Gy (1.8 Gy if source decay and repair kinetic of cells are considered). In the same year, Fowler et al (6) proposed 3 methods to estimate the radiosensitivity parameter for prostate cancer. In the first method they compared the 3-year survival data of EBRT with BT, whereas in the second method they directly analyzed the outcome data and correlated them in a maximum likelihood estimation with prescription doses. Third, they analyzed the 2-year outcome data of high-dose-rate (HDR) and HDR boost treatments. Overall, the 3 methods agreed on an a/b ratio smaller than 2 Gy. They proposed an estimation of 1.5 Gy for the a/b ratio of prostate cancer derived from their second method. Brenner et al (7) used dose-escalation trials with EBRT in combination with HDR BT. The analysis of the outcomes led the authors to obtain an a/b value of 1.2 Gy for prostate cancer. On the basis of the assumption that EBRT and BT are biologically equivalent, Wang et al (8) reanalyzed the data used by Fowler et al (6) and included the effect of cell proliferation. They concluded that a is approximately 0.15 Gy1, which is in the range reported for in vitro values and is far more plausible than Brenner’s value (4-9). They estimated that the a/b is twice the value predicted by Fowler at approximately 3 Gy (8). In a later article, Wang and Li (10) confirmed the results of their former works by analyzing the survival data of HDR BT and EBRT treatments. On the basis of the works of Wang et al (8, 11, 12), American Association of Physicists in Medicine Task Group 137 (TG137) (13) recommends an a/b of 3.0 Gy to be used for prostate cancer. Contrary to the assumption of a low a/b, some authors insist that the response of prostate cancer to radiation is similar to other tumors and that its a/b ratio is not small. By performing in vitro radiobiological clonogenic assays, Nahum et al (9) obtained a mean a/b ratio of 8.3 Gy. Proclaiming that a low a/b value may be a calculation artefact due to the presence of hypoxic clonogens in approximately 20% of the prostate cancer cases, they claimed that the interpatient and intratumor variation in radiosensitivity should be considered in calculations (14). Different works tried to find the impact of interpatient or intratumor heterogeneity on the a/b estimates (15-18). Carlone et al (15, 16) investigated the issue of intratumor heterogeneity of clonogens but concluded with large uncertainties on the value of a/b. This suggests that the difference between homogeneous and heterogeneous models is not clinically detectable (17). Because its importance was also stressed by King and Mayo (3), Lindsay et al (18) studied the sensitivity of the estimation of a/b with the heterogeneity of dose distributions in BT. For a potential doubling time (Tpot) of 45 days and a Z 0.2 Gy1, they observed an overall a/b range from 1.1 to 12.3 Gy for clinical BT cases. Overall, the heterogeneous models add more degrees of freedom and uncertainties in determining the LQ parameters. All the above-mentioned works have one thing in common; they all correlate the clinical outcomes with the dose being the prescription dose or any dose metric from EBRT or BT treatments. Whatever the dose parameter used, it needs to be estimated with good accuracy. It is well known that current clinical
International Journal of Radiation Oncology Biology Physics dosimetry algorithms in BT neglect the heterogeneities of the medium, namely the tissue heterogeneity (TH) and the interseed attenuation (ISA) in the case of permanent seed implants. The dosimetric importance of taking the heterogeneities into account for low-dose-rate BT has already been reported in several articles (19-21). Nevertheless, the radiobiological impact of those heterogeneities has not been fully explored. In this work, we investigated the impact of dose heterogeneities on the estimations of the a/b parameter for prostate cancer. Following the first calculation method proposed by Fowler et al (6), an isoeffectiveness relation is used to compare the biological effect of BT and EBRT and to extract the a/b ratio for prostate cancer. Equivalent uniform BED (EUBED) (13) is used for BT, to better quantify the effect of large dose gradients of BT in the calculations.
Methods and Materials We base our analysis on the methodology of Fowler et al (6). By analyzing the outcome data of BT and EBRT from different institutions, Fowler et al (6) estimated that a prescription dose of 145 Gy in 125I BT is iso-effective to an EBRT dose of 71 Gy administered in a 2-Gy-per-fraction regime. This means that for these prescription doses, both modalities are clinically equivalent. Following the LQ model, BED can be used to compare the biological effect of different treatment modalities (22). The expression relating the BED of BT with EBRT is called the biological iso-effectiveness relation. BED BT;125 I; 145 Gy Z BEDðEBRT; 71= 2 GyÞ ½1 The BED for BT is calculated as (22) Teff BED tZTeff ZD Teff RE Teff ln2 aTpot where g 1 Teff Z ln l alD0 D Teff ZD0 1 elTeff
½2
½3 ½4
2 1 1 2l D0 b 1 elTeff 1 e2lTeff RE Teff Z1 þ ml a 2l ½5 1 Teff ðmþlÞ 1e lþm a/b characterizes the intrinsic radiosensitivity of the LQ model, g is the repopulation constant of tumor cells, l is the decay constant of the implanted radionuclide (4.812 104 h1 for 125 I), m is the repair rate of tumor cells (m Z log(2)/Tr), and D0 is the total absorbed dose. In the case of EBRT, BED is calculated by (22) ( ) d T logð2Þ BEDZnd 1 þ . ½6 a Tpot a b where the second term accounts for the repopulation given that a treatment is administered over n fractions of dose d (35 fractions of 2 Gy in this case) for an overall treatment time of T Z 1.4 n (5 days per week). By solving Eq. 1, an estimation of a/b value can be found. However, a major deficiency in this way of proceeding is that the prescription dose is used to calculate the BED for BT. However,
Sensitivity of a/b to dose calculation
Volume 88 Number 2 2014 the prescription dose is just a planned dose value and does not fully represent the dose received by the prostate. Indeed, the geometry of an implant changes owing to different effects, such as edema, seed migration, or anatomic changes (13). The implant quality is usually characterized using a specific dose metric, such as the D90 (23, 24). Some investors may also use D0 Z D90 in Eqs. 3 and 4 to evaluate BED of prostate BT and to correlate it with the clinical outcome data (25-28). In an attempt to make the iso-effectiveness relation more realistic, we will replace the D0 in Eq. 3 with the postimplant D90 extracted from the postimplant dosimetry of a cohort of 287 intermediate-risk prostate cancer patients (29). This metric is first calculated using an American Association of Physicists in Medicine Task Group 43 (TG43)based calculation protocol, and an estimation of the a/b parameter is obtained from the iso-effectiveness relation. In the next step, a correction is made to this estimation by using Monte Carlo (MC) dose distributions obtained using ALGEBRA (30), a patientspecific dosimetry tool for calculating postimplant dose distributions in BT. The MC-calculated D90 metric is then used in Eq. 2 to give an estimate of a/b ratio. This way, the effects of TH and ISA can also be considered. Another deficiency of the iso-effectiveness relation in its current format (Eq. 1) stems from the fact that BED might not be appropriate for BT. Dose distributions are rather uniform in EBRT, but this is not the case for BT. As shown in the literature (31), BED does not account for the spatial heterogeneity of dose distributions because of using a single metric from a doseevolume histogram (eg, D90). Additionally, by neglecting the large dose gradients of BT, the BED over- or underestimates the biological efficiency of treatments. A more appropriate model was introduced in TG137 (13): EUBED, which generalizes the concept of BED to heterogeneous dose distributions (Eq. 7). ! X 1 a:BEDi ni e EUBEDZ ln ½7
a
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repair half-times of 0.25, 0.50, 1.0, and 2.0 hours are considered, to include the half-time values reported by both authors and to cover some values in between. The left and right sides of the iso-effectiveness relation are plotted in Figure 1a for different a/b values. A 95% confidence interval is also calculated for BED of EBRT and is presented in the same figure as dashed curves. The value of a/b at which the BT and EBRT curves intersect gives an estimate of prostate cancer radiosensitivity. It can be seen that the 2 curves intersect at a/b values between 1.6 and 2.3 Gy, with a best estimate of 1.9 Gy for Tr Z 0.25 hours, chosen for direct comparison with Wang et al (8). This range of a/b is in broad agreement with the results of Fowler et al (6) and Brenner and Hall (2). Wang et al (8) criticized the results of Fowler et al (6) for not taking into account the effect of clonogen repopulation on BED for both BT and EBRT. The clonogenic repopulation can be taken into account for the calculation of BED through Eqs. 2-4. The potential doubling time Tpot of 42 days is used in our analysis as per TG137 (13) recommendations. It can be seen in Figure 1b that for Tr Z 0.25 hours both curves intersect at a/b Z 3.1 Gy,
i
Here, ni is the fractional volume that receives BEDi. The EUBED is able to consider the effect of dose heterogeneity for calculating the biological efficiency of a BT plan. In the final part of this work, EUBED replaces BED of BT in the iso-effectiveness relation (Eq. 8). This way, a new estimation of the a/b value is made that corrects for the effect of spatial dose heterogeneity. By estimating the average EUBED from MC dose distributions, the medium heterogeneities, namely the ISA and the TH effects, can also be taken into account. BEDðEBRT; 2Gy 35ÞZEUBEDðBTÞ ½8 Unlike BT, the use of BED for EBRT in Eq. 8 is still a valid approximation because the dose distributions are much more uniform in EBRT that in BT (10). Furthermore, EUBED reduces simply to BED for uniform dose distributions.
Results and Discussion Methodology validation To verify the validity of the calculations, we first reproduce the previous values of a/b predicted by Fowler et al (6) and by Wang et al (8). Fowler et al (6) reported the first estimate of the repair halftime for sublethal damage in human prostate tumors, Tr Z 1.9 hours. A separate analysis by Wang et al (8), also derived from clinical outcomes data, resulted in a much lower value of 16 minutes for repair half-time. For the purposes of this work, 4 sublethal damage
Fig. 1. Both sides of Eq. 1 are plotted for varying a/b values without (a) and with cell repopulation (b). The biologically effective dose (brachytherapy, BT) is calculated with 4 Tr values, ranging from 15 minutes to 2 hours. EBRT Z external beam radiation therapy.
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International Journal of Radiation Oncology Biology Physics
with a range of 2.8-3.6 Gy, in agreement with the results of Wang et al (8).
New a/b calculation The first step in this study is to use the postimplant D90 in Eq. 2 to estimate BED for BT and to use it in the iso-effectiveness equation (Eq. 1). Unfortunately, no detailed dosimetry data are available for the patient cohorts considered by Fowler et al (6). To overcome this data shortage, we use a set of 287 clinical cases of intermediate-risk prostate cancer patients treated with 125I BT as a monotherapy, for which dosimetry data were available (29). This method enables an estimate of the typical postimplant D90 for prostate patients. Dosimetry based on TG43 was performed, and a mean D90 metric was determined to be 170 Gy for this cohort (V100 Z 96%). The equivalence between BT and EBRT can now be reconsidered using the mean D90 metric. It can be seen from Figure 2 that if Tr Z 0.25 hours, BT and EBRT will be isoeffective for a/b Z 2.0 Gy and if Tr Z 2 hours, a/b Z 1.5 Gy. It is worth mentioning that because there is a direct relationship between BED for BT and D90 (D0 in Eq. 2), if D90 increases (decreases), BED for BT will also increase (decrease). This will cause the intersection between BT and EBRT curves to occur sooner, and a/b becomes smaller. The TG43-based dosimetry algorithm neglects the effect of TH and ISA on dose distributions. It was shown that the dosimetric accuracy can be greatly enhanced by using MC dose calculation techniques that consider the TH and ISA effects on the energy fluence of photon beams. In the studied cohort, the average MC D90 is evaluated to be 157 Gy, which is approximately 13 Gy lower than the estimated value from TG43. The analysis was repeated using this value for D90 and is plotted in Figure 3. By comparing Figure 2 with Figure 3, it is possible to determine the impact of TH and ISA on the estimates of a/b. It can be seen that the combined effects of TH and ISA increase a/b from 2.0 Gy to 2.54 Gy for Tr Z 0.25 hours, and if Tr Z 2 hours, a/b rises from 1.5 to 2.0 Gy. We can conclude that a/b rises by approximately 30% as an effect of considering TH and ISA in models.
Fig. 2. Iso-effective curves for external beam radiation therapy (EBRT) and brachytherapy (BT) using the average D90 dose metric calculated using the American Association of Physicists in Medicine Task Group 43 formalism. The biologically effective dose (BT) is calculated with 4 Tr, ranging from 0.25 hours to 2 hours.
Fig. 3. Iso-effective curves for external beam radiation therapy (EBRT) and brachytherapy (BT) using the average D90 from Monte Carlo calculations. The biologically effective dose (BT) is calculated with 4 Tr, ranging from 0.25 hours to 2 hours. To consider the effect of dose heterogeneity in BT, we use the new iso-effectiveness relation (Eq. 8). To obtain an estimation of the average EUBED over a typical cohort of BT 125I, the same cohort of patients is again used here. Dose distributions are generated in full geometry MC (TH and ISA), and the dose scoring is to water. For now, a is set to 0.15 Gy1 in conformity with the TG137 (13) recommendations. The main interest of this work is to study the effect of the heterogeneity of dose distributions on the estimation of a/b. It is critical to have a good estimation of a to determine a/b. It is nevertheless reasonable to fix a to reduce the degrees of freedom of the formalism and to isolate the effect of heterogeneities (medium and dose distribution) on a/ b ratio. A sensitivity analysis between the value of a and the evaluation of a/b is going to be performed at the end of this section. For now we take a Z 0.15 Gy1 as determined by Wang et al (8) to observe how consideration of the heterogeneities changes the a/b ratio for the specific a used. It can be seen from
Fig. 4. Iso-effectiveness relation between external beam radiation therapy (EBRT) using biologically effective dose and brachytherapy (BT) using equivalent uniform biologically effective dose as showed in Eq. 8.
Sensitivity of a/b to dose calculation
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Figure 4 that the equivalence between BED for EBRT and EUBED for BT occurs at a/b Z 6.2 Gy. The estimation of a/b can change depending on the Tr chosen, but the variation is small. In the case of the last calculation with EUBED, it can go from 5.8 to 6.2 Gy when Tr is considered to be 2 or 0.25 hours. The impact is similar when BED is used. In vitro experiments confirm that Tr for prostate cancer may be smaller than 26 minutes (32).
This required us to use a different cohort of 287 BT patients to provide a descriptor of the average implant quality instead of the same patient cohorts reported by Fowler et al (6). To some extent, the results of this study are also limited to the number of patients studied. Larger cohorts from various centers may lead to more accurate representation of the average implant quality and lower the uncertainties of the estimation for the a/b value.
Dependence to the choice of a
Conclusion
Note that to calculate EUBED, a was fixed to 0.15 Gy1 (similar to what was used by Wang et al [8]). As a first approach, this was a reasonable approximation because our initial goal was to illustrate by how much the estimation of a/b is affected when the dose heterogeneity is considered in the calculations. It is nevertheless important to perform a sensitivity analysis of a/b versus the choice of a. In other words, we need to determine the sensitivity of our model to the choice of initial constants such as a. In vitro studies of the intrinsic radiosensitivity of human prostate tumors have reported that a values range between 0.062 Gy1 and 0.487 Gy1 (33, 34). For that reason, the average EUBED is recalculated with a Z {0.03, 0.05, 0.075, 0.1, 0.15, 0.2} Gy1, and the analysis is repeated with Tr set to 15 minutes. Figure 5 illustrates the variation of a/b with a for BED- and EUBED-based calculations. The calculations of a/b versus a behave very differently when BED or EUBED is used. When using BED, small values of a lead to large a/b, whereas for large a, a/b tends to become smaller, which is also trivially derived from Eq. 6. When EUBED-based calculations are used, the monotonously decreasing function is not apparent anymore; a/b Z 2.8 Gy when a Z 0.03 Gy1, and it increases with increasing a until attaining 7.9 Gy for a Z 0.2 Gy1.
This study concludes that depending on the dose calculation method used in BT, the estimation of a/b for prostate cancer is subject to variations. Keeping in mind that the study does not pretend to set a definitive value for a/b, the a/b predicted here is larger than the current recommendations of the TG137 (13) (if Tr Z 0.25 hours) but still smaller than typical tumors. Provided the a/b ratio for prostate cancer is not above that for late rectal damage (approximately 3 Gy), hypofractionation will be safe and will diminish the total required dose, rendering the EBRT costeffective and convenient for patients. The results of this study emphasize the importance of using accurate dose calculation algorithms in BT to account for the heterogeneities.
Limitation Analysis As mentioned before, detailed dosimetry data for the patient cohorts presented in the study of Fowler et al (6) are not available.
Fig. 5. Variation of a/b with a using biologically effective dose and equivalent uniform biologically effective dose for evaluating the biological effectiveness of brachytherapy.
References 1. Oliveira SM, Teixeira NJ, Fernandes L. What do we know about the a/b for prostate cancer? Med Phys 2012;39:3189-3201. 2. Brenner DJ, Hall EJ. Fractionation and protraction for radiotherapy of prostate carcinoma. Int J Radiat Oncol Biol Phys 1999;43:1095-1101. 3. King CR, Mayo CS. Is the prostate alpha/beta ratio of 1.5 from Brenner and Hall a modeling artifact? Int J Radiat Oncol Biol Phys 2000;47:536-538. 4. Brenner DJ, Hall EJ. In response to Drs. King and Mayo: Low a/b values for prostate appear to be independent of modeling details. Int J Radiat Oncol Biol Phys 2000;47:538-539. 5. King CR, Fowler JF. A simple analytic derivation suggests that prostate cancer alpha/beta ratio is low. Int J Radiat Oncol Biol Phys 2001;51:213-214. 6. Fowler J, Chappell R, Ritter M. Is alpha/beta for prostate tumors really low? Int J Radiat Oncol Biol Phys 2001;50:1021-1031. 7. Brenner DJ, Martinez AA, Edmundson GK, et al. Direct evidence that prostate tumors show high sensitivity to fractionation (low alpha/beta ratio), similar to late-responding normal tissue. Int J Radiat Oncol Biol Phys 2002;52:6-13. 8. Wang JZ, Guerrero M, Li XA. How low is the alpha/beta ratio for prostate cancer? Int J Radiat Oncol Biol Phys 2003;55:194-203. 9. Nahum AE, Movsas B, Horwitz EM, et al. Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: Implications for the alpha/beta ratio. Int J Radiat Oncol Biol Phys 2003;57:391-401. 10. Wang JZ, Li XA. Evaluation of external beam radiotherapy and brachytherapy for localized prostate cancer using equivalent uniform dose. Med Phys 2003;30:34-40. 11. Wang JZ, Li XA. Impact of tumor repopulation on radiotherapy planning. Int J Radiat Oncol Biol Phys 2005;61:220-227. 12. Wang JZ, Mayr NA, Nag S, et al. Effect of edema, relative biological effectiveness, and dose heterogeneity on prostate brachytherapy. Med Phys 2006;33:1025-1032. 13. Nath R, Bice WS, Butler WM, et al. AAPM recommendations on dose prescription and reporting methods for permanent interstitial brachytherapy for prostate cancer: Report of Task Group 137. Med Phys 2009;36:5310-5322.
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14. Fowler JF, Nahum AE, Orton CG. The best radiotherapy for the treatment of prostate cancer involves hypofractionation. Med Phys 2006;33:3081-3084. 15. Carlone M, Wilkins D, Nyiri B, et al. TCP isoeffect analysis using a heterogeneous distribution of radiosensitivity. Med Phys 2004;31: 1176-1182. 16. Carlone M, Wilkins D, Nyiri B, et al. Comparison of alpha/beta estimates from homogeneous (individual) and heterogeneous (population) tumor control models for early stage prostate cancer. Med Phys 2003;30:2832-2848. 17. Macias V, Biete A. Hypofractionated radiotherapy for localised prostate cancer. Review of clinical trials. Clin Transl Oncol 2009;11: 437-445. 18. Lindsay PE, Moiseenko VV, Dyk JV, et al. The influence of brachytherapy dose heterogeneity on estimates of alpha/beta for prostate cancer. Phys Med Biol 2003;48:507-522. 19. Rivard MJ, Venselaar JLM, Beaulieu L. The evolution of brachytherapy treatment planning. Med Phys 2009;36:2136-2153. 20. Beaulieu L, Tedgren AC, Carrier JF, et al. Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: Current status and recommendations for clinical implementation. Med Phys 2012;39:6208-6236. 21. Carrier JF, Beaulieu L, Therriault-Proulx F, et al. Impact of interseed attenuation and tissue composition for permanent prostate implants. Med. Phys 2006;33:595-604. 22. Dale R, Jones B. The clinical radiobiology of brachytherapy. Br J Radiol 1998;71:465-483. 23. Stock RG, Stone NN, Lo YC, et al. Postimplant dosimetry for 125I prostate implants: Definitions and factors affecting outcome. Int J Radiat Oncol Biol Phys 2000;48:899-906. 24. Potters L, Cao Y, Calugaru E, et al. A comprehensive review of CTbased dosimetry parameters and biochemical control in patients treated with permanent prostate brachytherapy. Int J Radiat Oncol Biol Phys 2001;50:605-614.
International Journal of Radiation Oncology Biology Physics 25. Stock RG, Stone NN, Cesaretti JA, et al. Biologically effective dose values for prostate brachytherapy: Effects on PSA failure and posttreatment biopsy results. Int J Radiat Oncol Biol Phys 2006;64:527533. 26. Miles EF, Nelson JW, Alkaissi AK, et al. Biologically effective dose (BED) correlation with biochemical control after low-dose rate prostate brachytherapy for clinically low-risk prostate cancer. Int J Radiat Oncol Biol Phys 2010;77:139-146. 27. Stone NN, Stock RG, Cesaretti JA, et al. Local control following permanent prostate brachytherapy: Effect of high biologically effective dose on biopsy results and oncologic outcomes. Int J Radiat Oncol Biol Phys 2010;76:355-360. 28. Butler WM, Stewart RR, Merrick GS. Evaluation of radiobiologic biochemical control in a large permanent prostate brachytherapy population from a single institution using AAPM TG-137 parameters. Brachytherapy 2011;10:16-28. 29. Zebentout O, Apardian R, Beaulieu L, et al. Evolution clinique des patients atteints d’un cancer prostatique de risque intermediaire traites par implants permanents d’iode-125: l’experience de l’Hotel-Dieu de Quebec. Cancer/Radiother 2010;14:183-188. 30. Afsharpour H, Landry G, D’Amours M, et al. ALGEBRA: Heterogeneous dosimetry algorithm based on GEANT4 for brachytherapy. Phys Med Biol 2012;57:3273-3280. 31. Afsharpour H, Reniers B, Landry G, et al. Consequences of dose heterogeneity on the biological efficiency of 103Pd permanent breast seed implants. Phys Med Biol 2012;57:809-823. 32. Wang JZ, Rhee JG, Shi P, et al. In vitro determination of radiation sensitivity parameters for DU-145 prostate cancer cells. Int J Radiat Biol 2008;84:515-522. 33. Algan O, Stobbe CC, Helt AM, et al. Radiation inactivation of human prostate cancer cells: The role of apoptosis. Radiat Res 1996;146:267-275. 34. Deweese TL, Shipman JM, Dillehay LE, et al. Sensitivity of human prostatic carcinoma cell lines to low dose rate radiation. J Urol 1998; 159:591-598.
Radiation Oncology biology
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Clinical Investigation: Genitourinary Cancer
On the Sensitivity of a/b Prediction to Dose Calculation Methodology in Prostate Brachytherapy Hossein Afsharpour, PhD,*,y Sean Walsh, PhD,z,x Charles-Antoine Collins Fekete, MSc,* Eric Vigneault, MSc, MD,* Frank Verhaegen, PhD,z,{ and Luc Beaulieu, PhD* *Centre de Recherche sur le Cancer, Universite´ Laval and De´partement de Radio-Oncologie, Centre Hospitalier Universitaire de Que´bec, Que´bec, QC, Canada; yCentre Inte´gre´ de Cance´rologie de la Monte´re´gie, Hoˆpital Charles-LeMoyne, Greenfield Park, QC, Canada; zDepartment of Radiation Oncology Maastricht Radiation Oncology (MAASTRO), GROW, University Hospital Maastricht, Maastricht, The Netherlands; xGray Institute for Radiation Oncology and Biology, The University of Oxford, The United Kingdom; and {Medical Physics Unit, Department of Oncology, McGill University, Montre´al, Que´bec, Canada Received Jun 8, 2013, and in revised form Sep 16, 2013. Accepted for publication Nov 1, 2013.
Summary The aim of this work is to show the importance of using accurate dose calculation algorithms in brachytherapy from a radiobiological point of view. More specifically, the impact of heterogeneity corrections on the estimation of the a/b ratio for prostate cancer is investigated. Different dosimetry protocols in brachytherapy are used and compared for estimating this ratio.
Purpose: To study the relationship between the accuracy of the dose calculation in brachytherapy and the estimations of the radiosensitivity parameter, a/b, for prostate cancer. Methods and Materials: In this study, Monte Carlo methods and more specifically the code ALGEBRA was used to produce accurate dose calculations in the case of prostate brachytherapy. Equivalent uniform biologically effective dose was calculated for these dose distributions and was used in an iso-effectiveness relationship with external beam radiation therapy. Results: By considering different levels of detail in the calculations, the estimation for the a/b parameter varied from 1.9 to 6.3 Gy, compared with a value of 3.0 Gy suggested by the American Association of Physicists in Medicine Task Group 137. Conclusions: Large variations of the a/b show the sensitivity of this parameter to dose calculation modality. The use of accurate dose calculation engines is critical for better evaluating the biological outcomes of treatments. Ó 2014 Elsevier Inc.
Introduction Prostate cancer may not have the same doseeresponse sensitivity to radiation as tumors in general. Several authors have reported unusually low a/b ratios for prostate cancer (1) compared with other typical tumors (>9 Gy). However, these works do not agree on a Reprint requests to: Luc Beaulieu, PhD, Centre Hospitalier Universitaire de Que´bec Pavillon Carlton-Auger, De´partement de RadioOncologie, 11 cote du palais, Que´bec, QC, G1R 2J6, Canada. Tel: (418) 525-4444, ext. 15315; E-mail: [email protected] Int J Radiation Oncol Biol Phys, Vol. 88, No. 2, pp. 345e350, 2014 0360-3016/$ - see front matter Ó 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ijrobp.2013.11.001
unique consensus value and have reported a/b values ranging from 1.2 to 8 Gy (1). Brenner and Hall (2) obtained an a value of 0.036 Gy1 for prostate cancer by fitting the 3-year survival data with the reported D90 dose metric for brachytherapy (BT) patients. By fixing the a parameter, they used the survival rates of external beam radiation therapy (EBRT) to obtain a range for the a/b ratio extending from 0.8 Gy to 2.2 Gy, with a mean value of 1.5 Gy. King This work has been supported by grant 2011-700180 from the Canadian Cancer Society Research Institute. Conflict of interest: none.
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and Mayo (3) questioned the validity of the results of Brenner and Hall, owing to its extremely low radiosensitivity (a) leading to an unrealistically low number of clonogens with no biological relevance. Brenner and Hall (4) responded with a fully heterogeneous linear-quadratic (LQ) model in which both a and b were represented by independent Gaussian distributions, resulting in an a/b of 2.1 Gy. In a short article, King and Fowler (5) assumed the iso-efficiency of the EBRT prescription dose of 70-74 Gy with the 145-Gy prescription dose of 125I BT to predict an a/b ratio of approximately 2 Gy (1.8 Gy if source decay and repair kinetic of cells are considered). In the same year, Fowler et al (6) proposed 3 methods to estimate the radiosensitivity parameter for prostate cancer. In the first method they compared the 3-year survival data of EBRT with BT, whereas in the second method they directly analyzed the outcome data and correlated them in a maximum likelihood estimation with prescription doses. Third, they analyzed the 2-year outcome data of high-dose-rate (HDR) and HDR boost treatments. Overall, the 3 methods agreed on an a/b ratio smaller than 2 Gy. They proposed an estimation of 1.5 Gy for the a/b ratio of prostate cancer derived from their second method. Brenner et al (7) used dose-escalation trials with EBRT in combination with HDR BT. The analysis of the outcomes led the authors to obtain an a/b value of 1.2 Gy for prostate cancer. On the basis of the assumption that EBRT and BT are biologically equivalent, Wang et al (8) reanalyzed the data used by Fowler et al (6) and included the effect of cell proliferation. They concluded that a is approximately 0.15 Gy1, which is in the range reported for in vitro values and is far more plausible than Brenner’s value (4-9). They estimated that the a/b is twice the value predicted by Fowler at approximately 3 Gy (8). In a later article, Wang and Li (10) confirmed the results of their former works by analyzing the survival data of HDR BT and EBRT treatments. On the basis of the works of Wang et al (8, 11, 12), American Association of Physicists in Medicine Task Group 137 (TG137) (13) recommends an a/b of 3.0 Gy to be used for prostate cancer. Contrary to the assumption of a low a/b, some authors insist that the response of prostate cancer to radiation is similar to other tumors and that its a/b ratio is not small. By performing in vitro radiobiological clonogenic assays, Nahum et al (9) obtained a mean a/b ratio of 8.3 Gy. Proclaiming that a low a/b value may be a calculation artefact due to the presence of hypoxic clonogens in approximately 20% of the prostate cancer cases, they claimed that the interpatient and intratumor variation in radiosensitivity should be considered in calculations (14). Different works tried to find the impact of interpatient or intratumor heterogeneity on the a/b estimates (15-18). Carlone et al (15, 16) investigated the issue of intratumor heterogeneity of clonogens but concluded with large uncertainties on the value of a/b. This suggests that the difference between homogeneous and heterogeneous models is not clinically detectable (17). Because its importance was also stressed by King and Mayo (3), Lindsay et al (18) studied the sensitivity of the estimation of a/b with the heterogeneity of dose distributions in BT. For a potential doubling time (Tpot) of 45 days and a Z 0.2 Gy1, they observed an overall a/b range from 1.1 to 12.3 Gy for clinical BT cases. Overall, the heterogeneous models add more degrees of freedom and uncertainties in determining the LQ parameters. All the above-mentioned works have one thing in common; they all correlate the clinical outcomes with the dose being the prescription dose or any dose metric from EBRT or BT treatments. Whatever the dose parameter used, it needs to be estimated with good accuracy. It is well known that current clinical
International Journal of Radiation Oncology Biology Physics dosimetry algorithms in BT neglect the heterogeneities of the medium, namely the tissue heterogeneity (TH) and the interseed attenuation (ISA) in the case of permanent seed implants. The dosimetric importance of taking the heterogeneities into account for low-dose-rate BT has already been reported in several articles (19-21). Nevertheless, the radiobiological impact of those heterogeneities has not been fully explored. In this work, we investigated the impact of dose heterogeneities on the estimations of the a/b parameter for prostate cancer. Following the first calculation method proposed by Fowler et al (6), an isoeffectiveness relation is used to compare the biological effect of BT and EBRT and to extract the a/b ratio for prostate cancer. Equivalent uniform BED (EUBED) (13) is used for BT, to better quantify the effect of large dose gradients of BT in the calculations.
Methods and Materials We base our analysis on the methodology of Fowler et al (6). By analyzing the outcome data of BT and EBRT from different institutions, Fowler et al (6) estimated that a prescription dose of 145 Gy in 125I BT is iso-effective to an EBRT dose of 71 Gy administered in a 2-Gy-per-fraction regime. This means that for these prescription doses, both modalities are clinically equivalent. Following the LQ model, BED can be used to compare the biological effect of different treatment modalities (22). The expression relating the BED of BT with EBRT is called the biological iso-effectiveness relation. BED BT;125 I; 145 Gy Z BEDðEBRT; 71= 2 GyÞ ½1 The BED for BT is calculated as (22) Teff BED tZTeff ZD Teff RE Teff ln2 aTpot where g 1 Teff Z ln l alD0 D Teff ZD0 1 elTeff
½2
½3 ½4
2 1 1 2l D0 b 1 elTeff 1 e2lTeff RE Teff Z1 þ ml a 2l ½5 1 Teff ðmþlÞ 1e lþm a/b characterizes the intrinsic radiosensitivity of the LQ model, g is the repopulation constant of tumor cells, l is the decay constant of the implanted radionuclide (4.812 104 h1 for 125 I), m is the repair rate of tumor cells (m Z log(2)/Tr), and D0 is the total absorbed dose. In the case of EBRT, BED is calculated by (22) ( ) d T logð2Þ BEDZnd 1 þ . ½6 a Tpot a b where the second term accounts for the repopulation given that a treatment is administered over n fractions of dose d (35 fractions of 2 Gy in this case) for an overall treatment time of T Z 1.4 n (5 days per week). By solving Eq. 1, an estimation of a/b value can be found. However, a major deficiency in this way of proceeding is that the prescription dose is used to calculate the BED for BT. However,
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Volume 88 Number 2 2014 the prescription dose is just a planned dose value and does not fully represent the dose received by the prostate. Indeed, the geometry of an implant changes owing to different effects, such as edema, seed migration, or anatomic changes (13). The implant quality is usually characterized using a specific dose metric, such as the D90 (23, 24). Some investors may also use D0 Z D90 in Eqs. 3 and 4 to evaluate BED of prostate BT and to correlate it with the clinical outcome data (25-28). In an attempt to make the iso-effectiveness relation more realistic, we will replace the D0 in Eq. 3 with the postimplant D90 extracted from the postimplant dosimetry of a cohort of 287 intermediate-risk prostate cancer patients (29). This metric is first calculated using an American Association of Physicists in Medicine Task Group 43 (TG43)based calculation protocol, and an estimation of the a/b parameter is obtained from the iso-effectiveness relation. In the next step, a correction is made to this estimation by using Monte Carlo (MC) dose distributions obtained using ALGEBRA (30), a patientspecific dosimetry tool for calculating postimplant dose distributions in BT. The MC-calculated D90 metric is then used in Eq. 2 to give an estimate of a/b ratio. This way, the effects of TH and ISA can also be considered. Another deficiency of the iso-effectiveness relation in its current format (Eq. 1) stems from the fact that BED might not be appropriate for BT. Dose distributions are rather uniform in EBRT, but this is not the case for BT. As shown in the literature (31), BED does not account for the spatial heterogeneity of dose distributions because of using a single metric from a doseevolume histogram (eg, D90). Additionally, by neglecting the large dose gradients of BT, the BED over- or underestimates the biological efficiency of treatments. A more appropriate model was introduced in TG137 (13): EUBED, which generalizes the concept of BED to heterogeneous dose distributions (Eq. 7). ! X 1 a:BEDi ni e EUBEDZ ln ½7
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repair half-times of 0.25, 0.50, 1.0, and 2.0 hours are considered, to include the half-time values reported by both authors and to cover some values in between. The left and right sides of the iso-effectiveness relation are plotted in Figure 1a for different a/b values. A 95% confidence interval is also calculated for BED of EBRT and is presented in the same figure as dashed curves. The value of a/b at which the BT and EBRT curves intersect gives an estimate of prostate cancer radiosensitivity. It can be seen that the 2 curves intersect at a/b values between 1.6 and 2.3 Gy, with a best estimate of 1.9 Gy for Tr Z 0.25 hours, chosen for direct comparison with Wang et al (8). This range of a/b is in broad agreement with the results of Fowler et al (6) and Brenner and Hall (2). Wang et al (8) criticized the results of Fowler et al (6) for not taking into account the effect of clonogen repopulation on BED for both BT and EBRT. The clonogenic repopulation can be taken into account for the calculation of BED through Eqs. 2-4. The potential doubling time Tpot of 42 days is used in our analysis as per TG137 (13) recommendations. It can be seen in Figure 1b that for Tr Z 0.25 hours both curves intersect at a/b Z 3.1 Gy,
i
Here, ni is the fractional volume that receives BEDi. The EUBED is able to consider the effect of dose heterogeneity for calculating the biological efficiency of a BT plan. In the final part of this work, EUBED replaces BED of BT in the iso-effectiveness relation (Eq. 8). This way, a new estimation of the a/b value is made that corrects for the effect of spatial dose heterogeneity. By estimating the average EUBED from MC dose distributions, the medium heterogeneities, namely the ISA and the TH effects, can also be taken into account. BEDðEBRT; 2Gy 35ÞZEUBEDðBTÞ ½8 Unlike BT, the use of BED for EBRT in Eq. 8 is still a valid approximation because the dose distributions are much more uniform in EBRT that in BT (10). Furthermore, EUBED reduces simply to BED for uniform dose distributions.
Results and Discussion Methodology validation To verify the validity of the calculations, we first reproduce the previous values of a/b predicted by Fowler et al (6) and by Wang et al (8). Fowler et al (6) reported the first estimate of the repair halftime for sublethal damage in human prostate tumors, Tr Z 1.9 hours. A separate analysis by Wang et al (8), also derived from clinical outcomes data, resulted in a much lower value of 16 minutes for repair half-time. For the purposes of this work, 4 sublethal damage
Fig. 1. Both sides of Eq. 1 are plotted for varying a/b values without (a) and with cell repopulation (b). The biologically effective dose (brachytherapy, BT) is calculated with 4 Tr values, ranging from 15 minutes to 2 hours. EBRT Z external beam radiation therapy.
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with a range of 2.8-3.6 Gy, in agreement with the results of Wang et al (8).
New a/b calculation The first step in this study is to use the postimplant D90 in Eq. 2 to estimate BED for BT and to use it in the iso-effectiveness equation (Eq. 1). Unfortunately, no detailed dosimetry data are available for the patient cohorts considered by Fowler et al (6). To overcome this data shortage, we use a set of 287 clinical cases of intermediate-risk prostate cancer patients treated with 125I BT as a monotherapy, for which dosimetry data were available (29). This method enables an estimate of the typical postimplant D90 for prostate patients. Dosimetry based on TG43 was performed, and a mean D90 metric was determined to be 170 Gy for this cohort (V100 Z 96%). The equivalence between BT and EBRT can now be reconsidered using the mean D90 metric. It can be seen from Figure 2 that if Tr Z 0.25 hours, BT and EBRT will be isoeffective for a/b Z 2.0 Gy and if Tr Z 2 hours, a/b Z 1.5 Gy. It is worth mentioning that because there is a direct relationship between BED for BT and D90 (D0 in Eq. 2), if D90 increases (decreases), BED for BT will also increase (decrease). This will cause the intersection between BT and EBRT curves to occur sooner, and a/b becomes smaller. The TG43-based dosimetry algorithm neglects the effect of TH and ISA on dose distributions. It was shown that the dosimetric accuracy can be greatly enhanced by using MC dose calculation techniques that consider the TH and ISA effects on the energy fluence of photon beams. In the studied cohort, the average MC D90 is evaluated to be 157 Gy, which is approximately 13 Gy lower than the estimated value from TG43. The analysis was repeated using this value for D90 and is plotted in Figure 3. By comparing Figure 2 with Figure 3, it is possible to determine the impact of TH and ISA on the estimates of a/b. It can be seen that the combined effects of TH and ISA increase a/b from 2.0 Gy to 2.54 Gy for Tr Z 0.25 hours, and if Tr Z 2 hours, a/b rises from 1.5 to 2.0 Gy. We can conclude that a/b rises by approximately 30% as an effect of considering TH and ISA in models.
Fig. 2. Iso-effective curves for external beam radiation therapy (EBRT) and brachytherapy (BT) using the average D90 dose metric calculated using the American Association of Physicists in Medicine Task Group 43 formalism. The biologically effective dose (BT) is calculated with 4 Tr, ranging from 0.25 hours to 2 hours.
Fig. 3. Iso-effective curves for external beam radiation therapy (EBRT) and brachytherapy (BT) using the average D90 from Monte Carlo calculations. The biologically effective dose (BT) is calculated with 4 Tr, ranging from 0.25 hours to 2 hours. To consider the effect of dose heterogeneity in BT, we use the new iso-effectiveness relation (Eq. 8). To obtain an estimation of the average EUBED over a typical cohort of BT 125I, the same cohort of patients is again used here. Dose distributions are generated in full geometry MC (TH and ISA), and the dose scoring is to water. For now, a is set to 0.15 Gy1 in conformity with the TG137 (13) recommendations. The main interest of this work is to study the effect of the heterogeneity of dose distributions on the estimation of a/b. It is critical to have a good estimation of a to determine a/b. It is nevertheless reasonable to fix a to reduce the degrees of freedom of the formalism and to isolate the effect of heterogeneities (medium and dose distribution) on a/ b ratio. A sensitivity analysis between the value of a and the evaluation of a/b is going to be performed at the end of this section. For now we take a Z 0.15 Gy1 as determined by Wang et al (8) to observe how consideration of the heterogeneities changes the a/b ratio for the specific a used. It can be seen from
Fig. 4. Iso-effectiveness relation between external beam radiation therapy (EBRT) using biologically effective dose and brachytherapy (BT) using equivalent uniform biologically effective dose as showed in Eq. 8.
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Figure 4 that the equivalence between BED for EBRT and EUBED for BT occurs at a/b Z 6.2 Gy. The estimation of a/b can change depending on the Tr chosen, but the variation is small. In the case of the last calculation with EUBED, it can go from 5.8 to 6.2 Gy when Tr is considered to be 2 or 0.25 hours. The impact is similar when BED is used. In vitro experiments confirm that Tr for prostate cancer may be smaller than 26 minutes (32).
This required us to use a different cohort of 287 BT patients to provide a descriptor of the average implant quality instead of the same patient cohorts reported by Fowler et al (6). To some extent, the results of this study are also limited to the number of patients studied. Larger cohorts from various centers may lead to more accurate representation of the average implant quality and lower the uncertainties of the estimation for the a/b value.
Dependence to the choice of a
Conclusion
Note that to calculate EUBED, a was fixed to 0.15 Gy1 (similar to what was used by Wang et al [8]). As a first approach, this was a reasonable approximation because our initial goal was to illustrate by how much the estimation of a/b is affected when the dose heterogeneity is considered in the calculations. It is nevertheless important to perform a sensitivity analysis of a/b versus the choice of a. In other words, we need to determine the sensitivity of our model to the choice of initial constants such as a. In vitro studies of the intrinsic radiosensitivity of human prostate tumors have reported that a values range between 0.062 Gy1 and 0.487 Gy1 (33, 34). For that reason, the average EUBED is recalculated with a Z {0.03, 0.05, 0.075, 0.1, 0.15, 0.2} Gy1, and the analysis is repeated with Tr set to 15 minutes. Figure 5 illustrates the variation of a/b with a for BED- and EUBED-based calculations. The calculations of a/b versus a behave very differently when BED or EUBED is used. When using BED, small values of a lead to large a/b, whereas for large a, a/b tends to become smaller, which is also trivially derived from Eq. 6. When EUBED-based calculations are used, the monotonously decreasing function is not apparent anymore; a/b Z 2.8 Gy when a Z 0.03 Gy1, and it increases with increasing a until attaining 7.9 Gy for a Z 0.2 Gy1.
This study concludes that depending on the dose calculation method used in BT, the estimation of a/b for prostate cancer is subject to variations. Keeping in mind that the study does not pretend to set a definitive value for a/b, the a/b predicted here is larger than the current recommendations of the TG137 (13) (if Tr Z 0.25 hours) but still smaller than typical tumors. Provided the a/b ratio for prostate cancer is not above that for late rectal damage (approximately 3 Gy), hypofractionation will be safe and will diminish the total required dose, rendering the EBRT costeffective and convenient for patients. The results of this study emphasize the importance of using accurate dose calculation algorithms in BT to account for the heterogeneities.
Limitation Analysis As mentioned before, detailed dosimetry data for the patient cohorts presented in the study of Fowler et al (6) are not available.
Fig. 5. Variation of a/b with a using biologically effective dose and equivalent uniform biologically effective dose for evaluating the biological effectiveness of brachytherapy.
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