Radiobiological dose calculation parameters for cervix cancer brachytherapy: A systematic review

Brachytherapy

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(2019)

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Review Article

Radiobiological dose calculation parameters for cervix cancer brachytherapy: A systematic review Braden Chow, Brad Warkentin, Geetha Menon* Division of Medical Physics, Department of Oncology, Cross Cancer Institute, University of Alberta, Edmonton, Alberta, Canada

ABSTRACT

The GEC-ESTRO recommendation in cervical cancer treatment planning, including external beam radiotherapy and brachytherapy boosts, is to use radiobiological dose calculations. Such calculations utilize the linear-quadratic model to estimate the effect of multiple cellular response factors and dose delivery parameters. The radiobiological parameters utilized in these calculations are literature values estimated based on clinical and experimental results. However, the impact of the uncertainties associated with these parameters is often not fully appreciated. This review includes a summary of the radiobiological dose calculation (for both high-dose-rate and pulsed-dose-rate brachytherapy boost treatments) for cervical cancer and a compilation of the reported values of the associated parameters. As discrepancies exist between conventionally recommended and published values, equivalencies between current brachytherapy boosts may be imprecise and could create underappreciated uncertainties in the radiobiological dose calculations. This review highlights these uncertainties by calculating the radiobiological dose delivered by the brachytherapy boost when assuming different radiobiological parameter values (within the range reported by previous research). Furthermore, conventional treatment planning does not consider the effects of proliferation of the tumor over the treatment time, which can significantly decrease its radiobiological dose and can introduce an additional variance of over 7 Gy10. Further investigation of uncertainties in parameter values and modifications of current dose models could improve the accuracy of radiobiological dose calculation. Ó 2019 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.

Keywords:

Brachytherapy; Cervical cancer; Radiobiological dose calculation; Linear-quadratic model; Uncertainties

Introduction According to the International Association for Cancer Registries, cervical cancer is the fourth most common cancer in women worldwide with an estimated 570,000 new cases in 2018 (1). The standard treatment for locally advanced cervical cancer is concurrent chemoradiotherapy followed by a brachytherapy (BT) boost (2). The use of BT plays a key role in tumor control. Review of the Surveillance,

Received 20 August 2018; received in revised form 22 February 2019; accepted 28 February 2019. Financial disclosure: This research has been funded by generous supporters of the Lois Hole Hospital for Women through the Women and Children’s Health Research Institute. Conflict of interest: The authors report no proprietary or commercial interest in any product mentioned or concept discussed in this article. * Corresponding author. Department of Oncology, University of Alberta, 11560-University Ave, Edmonton, Alberta T6G 1Z2, Canada. Tel.: þ1780-432-8619; fax: +1-780-432-8615. E-mail address: [email protected] (G. Menon).

Epidemiology, and End Results database for patients with cervical cancer of stage IB2 to IVA suggests that the use of BT during treatment significantly improves both causespecific survival and overall survival of patients (3). Recent paradigm shifts in cervical cancer BT have been highlighted in the ICRU 89 report and the EMBRACE study (4,5). Major changes have occurred in dose delivery technique, moving away from continuous low-dose-rate techniques (LDR; !1 Gy/h to point A) historically used for intracavitary BT in favor of high-dose-rate (HDR; O12 Gy/h) treatments and to a smaller extent pulseddose-rate (PDR; !1 Gy/pulse with one pulse delivered per hour) treatments (6,7). With comparable average dose rates, LDR and PDR treatments may have similar radiobiological outcomes (8,9). Another area of development has been in the treatment planning process of cervical cancer BT (10,11). The evolution from two-dimensional pointbased planning using X-ray radiographs to threedimensional volume-based treatment planning using MRI, which provides superior soft tissue contrast, has led to more

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effective detection of tumor extent and accurate delineation of the surrounding normal tissue including the bladder, sigmoid colon, rectum, and small bowel (5,11). An important dosimetric change in cervical cancer treatment planning has been the adoption of radiobiological dose prescription. Radiobiological dose contrasts with physical dose by incorporating the relationship between cellular response factors and dose delivery parameters to better predict treatment outcome (12,13). Clinical data suggest that these parameters play a significant role in cervical cancer patient outcomes (14e16). Therefore, incorporation of these parameters is essential for meaningful dosimetry comparisons of different BT treatments, and could prevent suboptimal treatments. The increasing reliance on radiobiological dose prescriptions demands a fuller understanding of the underlying models and the different parameters used in calculation. Variances in the assumed radiobiological values can strongly affect the calculated dose and these values are also not tailored for use for individual patients (17,18). Publications such as that of van Leeuwen et al. summarize published values of some radiobiological parameters for several tumors (19). However, they do not include a comprehensive evaluation of all radiobiological dose calculation parameters associated with cervical cancer BT. Uncertainties in radiobiological parameters and disagreement between conventional values and experimental results could impact current treatment outcomes; therefore, an attempt to identify these uncertainties is made in this article. As more centers are heading toward prescribing cervical cancer treatments in terms of radiobiological doses, we believe it would be beneficial to have a detailed review that describes the theory of radiobiological models used for dose calculation, summarizes published values of parameters used in these calculations, and highlights potential pitfalls of the current approach. The linear-quadratic model and radiobiological doses Radiobiological dose calculation in cervical cancer treatment planning is generally based on the linearquadratic (LQ) model (4,5). The LQ model was initially developed by both Chadwick and Leenhouts, as well as Kellerer and Rossi, independently (20,21). The model uses relatively few parameters and is reasonably well-validated for fraction sizes up to 10 Gy (22). This makes the model suitable for the typical dose fraction sizes used in HDR BT for cervical cancer. The LQ model assumes that the cause of radiation-induced cell death results from different types of cellular damage (20). The model correlates the surviving fraction (SF; the fraction of viable cells surviving irradiation with a range of 1 to 0) to the physical dose delivered. When a total physical dose D is delivered to cells, the SF can be expressed by (22):

 SF 5 exp  aD þ bGD2 ð1Þ where a and b are radiosensitivity parameters that relate to two different mechanisms of cell death and have units of

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Gy and Gy2, respectively. The values of both a and b are dependent on the cell type (13). The loss in SF from the a component represents the formation of nonrepairable (lethal) lesions in the DNA caused by a single radiation event, whereas the b component represents lethal damage originating from the interaction of repairable (sublethal) lesions, each produced by independent radiation events (23). G represents the generalized Lea-Catcheside time factor, which quantifies the impact of dose rate and dose fractionation due to cellular repair of sublethal damage during irradiation (23). The value of G can range from 0 to 1, with a value of 1 representing the special case of a single acute fraction of radiation (23). Thus, unlike the a component, the final amount of cell damage caused by b interactions is modulated by the G factor, which is dependent on the dose delivery technique. Radiobiological dose can be formulated by using the LQ model to quantify the biological effect in a tissue. The biological effect (E ), which represents the average number of effective lesions in an irradiated cell, for a single acute fraction of dose d is related to SF as (24) E 5  lnðSFÞ 5 ad þ bd 2

ð2Þ

If subsequent fractions are added, separated far enough in time such that there is no remaining sublethal damage at the time of each new fraction, the proportion of cell kill of each new fraction is independent of the previous fractions. In this case, the overall survival is multiplicative, such that the cumulative biological effect after n fractions is
 E 5  lnðSF n Þ 5  n lnðSFÞ 5 n ad þ bd2 ð3Þ Note that the survival fraction in Equation 3 is equivalent to Equation 1 if D 5 nd and G 5 1/n. Equation 3 can then be rewritten to express the biologically effective dose (BED), described as the theoretical total dose required to cause the same amount of cell death if the dose was delivered at an infinitesimally low dose rate and in infinitesimally small fractions separated far apart in time (24,25): ! E d BED 5 5 nd 1 þ a ð4Þ a b BED has units of GyZ where Z is the a/b ratio of the tissue. As shown in Equation 4, radiobiological metrics often utilize the a/b ratio rather than a and b independently. The a/b ratio determines the sensitivity of the tissue to dose rate and fractionation: a low a/b ratio corresponds to a potential for significantly less damage when the dose rate or dose fraction size is reduced (26). To determine the biological equivalence of different prescriptions, the BED is usually converted to the equieffective dose delivered in 2 Gy fractions (EQD2), the common external beam radiotherapy (EBRT) fraction size (27,28): EQD2 5

BED 1 þ 2a b

ð5Þ

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EQD2 is also expressed as GyZ and any use of GyZ in this review will refer to EQD2. Current recommendations for curative treatment of advanced cervical cancer are to use a physical dose of 45e50 Gy delivered by EBRT in 1.8e2.0 Gy per fraction with an additional boost dose given by BT for a dose of 90e95 Gy10 to 90% of the tumor volume (D90), which is typically specified as the high-risk clinical target volume (5). Equation 4 describes a unique scenario where dose fractions are delivered quickly and are well separated (i.e., G 5 1/n), allowing for the repair of all sublethal lesions between fractions. However, this may not be true when the time between fractions decreases. If this time is shortened to the point that not all previously generated sublethal lesions are fully repaired before a new fraction is delivered, sublethal lesions created by two different fractions can interact to form lethal lesions (26). This will cause the tissue to experience increased biological effect. The rate of repair of sublethal lesions is described by the time repair constant (m), which is expressed in terms of the halftime of repair (T1/2), the time required to repair half of the sublethal damage in the tissue assuming a single exponential rate of repair (26,29): m5

lnð2Þ T12

ð6Þ

One model that can be used to quantify incomplete repair is the Thames model, which has been previously used in cervical cancer studies (30,31). It introduces the factor Hm to represent the amount of incomplete repair remaining at the start of each fraction assuming monoexponential repair (32):     2 k m  ð1  km Þ Hm 5 ð7Þ m 1k 1k where m is the number of fractions and k is a function of the repair rate that depends on the time interval between fractions (X ) (32): k 5 expðmXÞ

ð8Þ

The value of Hm is positive and approaches 0 if sufficient time is provided between fractions. The BED formula, including Hm, for an n fraction treatment delivering equal dose d per fraction, is given as (32) " # dð1 þ Hm Þ BED 5 nd 1 þ ð9Þ a b

For fractionated treatments that are sufficiently separated, allowing for complete sublethal damage repair, the value of Hm becomes approximately 0 and Equation 9 simplifies to Equation 4.

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these are based on an LQ model that incorporates only cellular repair, and ignores proliferation. Proliferation is thus considered separately. EBRT and HDR BT Radiobiological doses in EBRT and HDR BT treatments for cervical cancer are calculated using the same method as both treatments have a fractionated schedule (4). Based on the currently accepted values for T1/2 and the sufficiently separated fractionation schedules of EBRT and HDR BT, dose calculations for both treatments generally assume complete sublethal damage repair in between fractions (2). As a result, Equation 4 is commonly used in dose calculation of EBRT and HDR BT treatments for cervical cancer. PDR BT PDR BT has been introduced as an alternative to LDR BT as it attempts to mimic the latter in radiobiological outcome by keeping the same average dose rate (26). This is achieved by deploying a radioactive source for a few minutes at a time on an hourly basis (a pulse) (2). PDR afterloaders typically utilize Ir-192 sources with nominal source strengths of 2040e8160 cGy cm2/h (or U; corresponding to 0.5 to 2 Ci, respectively) for treatment, in contrast to a 40,800 U (or 10 Ci) Ir-192 source commonly used for HDR BT. The pulse interval in PDR BT is insufficient to recover all sublethal damage between pulses. For example, even if a T1/2 of 0.25 h is assumed (close to the smallest value reported in Table 1), approximately 6.25% of the sublethal damage created by one pulse would remain at the start of the next pulse. As a result, calculation of the radiobiological dose in PDR BT relies on multiple factors, including pulse time, pulse interval, dose rate, and number of pulses (4). The BED formalism for PDR BT is given by (43)   !  d 2 1  2 NY  SY BEDPDR 5Nd 1 þ a 1 mT NmT b ð10Þ where N is the number of pulses delivered in a single insertion, d is the dose delivered by each pulse, and T is the pulse delivery time. S and Y are functions as described in the following (43): S5

Nk  k  Nk2 z þ kNþ1 zN ð1  kzÞ2

ð11Þ

where k 5 exp(mX ), z 5 exp(mT ), Y 5 (1z), and X is the time without irradiation between pulses.

BED calculations relevant to cervical cancer EBRT and BT

Tumor proliferation

The BED formalisms used in cervical cancer dose prescription are summarized in the following. Conventionally,

It has been demonstrated that after irradiation, there is an onset of enhanced proliferation (cellular repopulation)

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Table 1 Recommended values for the a/b ratio and T1/2 Parameter

Conventional Other reported values recommendation (4,33) (references in brackets) Methodology of estimation

a/b ratio for tumor (Gy) 10

20.8eN (34),a

6.0e16.5 (35)

5.9e20.9 (36)

6e14 (37)

a/b ratio for late responding normal tissue (Gy)

3

4.8 (Rectum only, (38))

5.4 (Rectum only, (40)) 2.5 (13)

T1/2 for tumor (h)

T1/2 for late responding normal tissue (h)

1.5

0.0e0.64 (34)

1.5

1.9 [0.26e5.7] (35),e 0.37 [0.15e2.15] (36),e 0.32e1.11 (34) 1.5e2.5 (41)

0.20e0.40 (42)

Review of reported patient outcomes using KaplaneMeier survival curves and Cox regression analysis of 5-y followup data of patients who received LDR BT. This range of values (95% CI) was determined as most likely assuming a tumor T1/2 of 1.5 hb Calculation of survival curves of human cervical cancer lines (acquired via biopsy) at three different dose rates (0.016, 0.032, and 1.5 Gy/min) for a total physical dose up to 16 Gy. Values of a, b, and T1/2 were estimated from the survival curves.c Analysis of previously published data by Kelland and Steel (35). Maximum likelihood method was used as opposed to a best-fit from a covariance matrix as used in the original study. Values of a, b, and T1/2 were estimated.d Review of data from a variety of human tumors from different sites irradiated in situ, including sarcomas and melanomas. While citing multiple technical issues with measurement results, it was suggested that the vast majority of previous research supported that tumors have an a/b ratio above 8 Gy. Utilized the Lyman-Kutcher-Burman (LKB) model for normal tissue complication probability (NTCP) to fit data from patients in the RTOG 94-06 database with Grade 2 or higher late rectal toxicity (39). A likelihood ratio test was used to determine whether an LQ-corrected LKB model fit the data better than the LKB model based on physical dose alone. Analysis of multiple publications reporting late rectal toxicity of Grade 2 or higher. Rectal toxicity was plotted against the EQD2 for the rectum; the data was best fit when using an a/b ratio of 5.4 Gy. Review of data published from in vivo irradiation of skin, lung, spinal cord, brain, kidney, and bone marrow tissue from mice, rabbits, and humans. Two distinct groups of tissue were found with approximate a/b ratios of 10 Gy and 2.5 Gy. The latter group was later associated with late responding normal tissue. See above for methodology. The range of values (95% CI) was calculated as the most likely assuming a tumor a/b ratio of 10 Gy.b See above for methodology.c See above for methodology.d See above for methodology. This range of values (95% CI) was determined as most likely assuming a normal tissue a/b ratio of 3 Gy.b Review of reported late effects in patients receiving LDR BT. The T1/2 that caused a difference in late patient complication was estimated to be 1.5 to 2.5 h, assuming an a/b ratio in normal tissue of 2e4 Gy. Review of three studies in which LDR BT delivered with differing dose rates caused statistically equivalent late patient complication.

BT 5 brachytherapy; EQD2 5 equieffective dose delivered in 2 Gy fractions; LDR 5 low-dose-rate. a Roberts et al. report a b/a 95% confidence range of 0.018 Gy1 to 0.048 Gy1. A b/a approaching 0 would correspond to an infinitely large value for a/b. b Research methodology is the same for these reported values. c Research methodology is the same for these reported values. d Research methodology is the same for these reported values. e Reported value is a median.

in the tumor (44). This proliferation can replace cells lost to radiation and reduce the effectiveness of the radiation treatment. As Fowler notes, lack of consideration for the overall treatment time (OTT; time from the start of EBRT to the end of BT) in the base form of the LQ model is a major criticism as longer treatments may have to contend with a greater amount of proliferation (27). There is a negative correlation between the tumor control probability and OTT (4). Fowler introduced a simple modification to the

BED formula to include OTT (24). Assuming BED0 to be the dose to the tumor without consideration of proliferation, the net dose delivered (BEDE) is given by Equation 12: BEDE 5 BED0 

lnð2ÞDT aTpot

ð12Þ

where DT 5 OTTTkickoff if OTT O Tkickoff and 0 otherwise (24). DT represents the length of time over which enhanced proliferation has occurred and Tpot is the potential doubling

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time, the time required to double the number of proliferating cells in the absence of spontaneous cell loss (45). Tkickoff is the kickoff time of the tumor, the time between the start of radiation treatment and the start of increased proliferation in the tumor. Typically, cervical cancer treatments including EBRT and the BT boost can be completed within 7e8 weeks (4). It should be noted that the OTT used in Equation 12 is simply the time interval between the first and final fractions of radiation treatment. Thus, for a given OTT, any differences in how the treatments are scheduled or delivered are ignored in the calculation of the proliferation correction. In other words, a delay toward the start of treatment would be treated as equivalent to the same length of delay toward the end of treatment. Underlying this is the assumption of simple exponential repopulation dynamics (after Tkickoff) that produce the commonly reported linear reduction in radiobiological dose as a function of OTT (e.g., a given Gy per day) (13,24,46).

Estimation of parameters used in dose calculation Calculation of the BED from Equations 9 to 12 requires use of several parameters. Parameters characterizing the dose response of irradiated tissue (tumor cells or normal tissue), such as a, b, m, Tpot, and Tkickoff, are relatively uncertain. Although there is no definitive value for any of these parameters given in literature, there are recommended values for the a/b ratio and T1/2, as they appear frequently in radiobiological dose calculation (4,33). Nonetheless, as described in the following, there remains considerable uncertainty in the values of the recommended parameters. Estimations of a and b Most research providing values for a and b was conducted with the intention of calculating the a/b ratio of the tissue. a and b are only independently required if proliferation is considered during dose calculation. Multiple groups have investigated values of a and b for cervical cancer tumors with more studies focused on a estimation. For five cervical cancer strains tested in vitro, Kelland and Steel found a median (minemax) a value of 0.33 (0.18e0.61) Gy1 and a median b value of 0.026 (0.020e0.069) Gy2 (35). Chapman and Nahum used West et al.’s experimental data on survival fractions to get an a value of 0.35  0.21 Gy1 and a b value of 0.06 Gy2 (no standard deviation provided) for cervical cancer tissue (47,48). Similarly, Roberts et al., in a clinical outcomes study, estimated the a value of cervical cancer tumors to be 0.13 (95% confidence interval [CI] of 0.06e0.20) Gy1 when assuming a T1/2 of 1.5 h (34). An explanation for the variance in reported values requires further investigation. Hall and Giaccia have stated that an a value of 0.3  0.1 Gy1 was reasonable for all tissue when used in the LQ model (49). Similar values were

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referenced by Gasinska et al., who assumed an a value of 0.2 Gy1 for radioresistant tissues and 0.3e0.4 Gy1 for radiosensitive tissue (50). The value of the a/b ratio can vary widely depending on the type of tissue (25). Late responding normal tissue is associated with an a/b ratio of 1e6 Gy and early responding normal tissue has been found to have an a/b ratio ranging from 7 to 10 Gy (4). Tumors typically have a/b ratios similar to early responding normal tissue and are often within the range of 7e20 Gy (4). As noted previously, Kelland and Steel determined the values of a and b for a series of in vitro experiments of human cervical cancer cell lines using LDR treatment to establish a median a/b ratio of 11.5 (6.0e16.5) Gy (35). Conventionally, including the ICRU 89 report, a/b ratios of 3 and 10 Gy are used for late and early responding tissue (including tumors), respectively (4,33). Estimation of the halftime of repair (T1/2) The conventional value of 1.5 h for T1/2 is recommended by GEC-ESTRO (33). According to Fowler, this has been assumed for many years ‘‘with no precise justification except its failure to contradict clinical information’’ (41). There is significant discrepancy between the experimental and recommended values for T1/2 for tumor cells. The previously mentioned study by Kelland and Steel determined a median T1/2 of 1.9 (0.26e5.7) hours (35). Based on clinical outcomes, Roberts et al. determined the highest likelihood of T1/2 for tumor cells to be 0.25 h if the conventional a/b ratio of 10 Gy was assumed, whereas a T1/2 of 1.5 h was likely only if the a/b ratio was over 50 Gy (34). The T1/2 for normal tissue is similarly contested. To explain an increase in reported complications in the vagina, urinary tract, and bowel after different LDR treatments, Fowler estimated T1/2 to likely range from 1.5 to 2.5 h in a clinical outcomes study (41). However, Roberts et al. indicated that, assuming an a/b ratio of 3 Gy, the most likely range of T1/2 values for normal tissue was 0.32e 1.11 h (34). Guerrero and Li bridged this inconsistency in results through the introduction of a sparing factor, the reduction of physical dose received in normal tissue compared with the tumor, into Fowler’s calculations (42). Based on their investigation, they estimated the halftime of repair for normal bladder and rectum tissue to be in the range of 0.20e0.40 h, assuming an a/b ratio of 3 Gy. Estimation of proliferation parameters The OTT has been correlated to treatment outcomes in several studies. Chen et al. found that prolonging HDR treatments in patients with cervical cancer with an OTT equal to or exceeding 63 days resulted in a significantly lower 5-year cause-specific survival compared with patients with an OTT shorter than 63 days (65% and 83%, respectively) (51). In addition, Gasinska et al., Song et al., Tanderup et al., and Tergas et al. found that cervical cancer

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Table 2 Reported values for proliferation Parameter

Reported values (references in brackets)

Tkickoff (d)

11e22 (57)

Tpot (d)

21e35 (50) 6.8  7.4 (50),a 5.0 (1.2e42.1) (58),b 4.4 (59),b 4.0 (60),b

a (Gy1)

0.06e0.20 (34) 0.18e0.61 (35) 0.29e0.74 (36) 0.35  0.21 (47,48)a 0.20e0.40 (49)

Estimation methodology Least c2 fit of TCP estimations to reported patient outcome was conducted while varying Tkickoff alone. All assumed parameter values required for calculating Tkickoff were adopted from literature. Values assumed. No rationale was provided for the selected range. BrdUrd labeling of biopsy samples of 229 patients with stage IB to IIIB carcinoma of the cervix treated from 1987 to 1999. BrdUrd labeling of biopsy samples of 84 patients with stage IB to IV carcinoma of the cervix from 1991 to 1996. BrdUrd labeling of biopsy samples of 138 patients with stage I to IV carcinoma of the cervix from 1991 to 1992. An interquartile range of 3.1e6.4 d was reported. BrdUrd labeling of biopsy samples of 121 patients with stage I to IV carcinoma of the cervix. An interquartile range of 3.1e6.3 d was reported. See Table 1 for methodology (same methodology as T1/2 for the tumor of 0.0e0.64 h). The range is a 95% CI.c See Table 1 for methodology.d See Table 1 for methodology.e Analysis of survival fraction of cervical cancer biopsy samples irradiated at 3.8 to 4.2 Gy/min with 2 Gy. No rationale provided.

BrdUrd 5 bromodeoxyuridine; TCP 5 tumor control probability. a Reported value is a mean. b Reported value is a median. c See b in Table 1. d See c in Table 1. e See d in Table 1.

patient outcomes improved for treatments with an OTT of less than 60, 56, 49, and 70 days, respectively (50,52e 54). ICRU 89 recommends that the OTT does not exceed 55 days (4). As shown in the subsection ‘‘Tumor Proliferation,’’ Tkickand Tpot are parameters used to incorporate proliferation off in dose calculations. To determine the influence of OTT on BED in cervical cancer, Gasinska et al. assumed a range of Tkickoff values (21, 28, and 35 days) (50). Later studies have used the lower value of 21 days, which was considered a conservative option in the calculation of radiobiological dose (50,55,56). Huang et al., based on outcomes data, estimated Tkickoff to be approximately 19 (95% CI of 11e22) days (57).

Two groups have put in considerable effort into calculating possible values of Tpot for cervical cancers (58,59). Using a cohort of 66 patients, Tsang et al. found a median Tpot of 5.0 (1.2e42.1) days using bromodeoxyuridine (BrdUrd) labeling of cervical cancer biopsies (58). Using the same method, Bolger et al. in two different studies with over 120 patients with cervical cancer in each study, determined median Tpot values of 4.4 (3.1e6.4, interquartile range) days and 4.0 (3.1e6.3, interquartile range) days, respectively (59,60). Gasinska et al. also conducted BrdUrd labeling in 229 patients and determined a mean Tpot of 6.8  7.4 days with a range of 1.4e75 days (50). A possible reason for these variances could be the large amount of interlaboratory deviation caused by systematic differences in

Table 3 Radiobiological dose to tumor calculated for an EBRT delivering 25 fractions of 1.8 Gy followed by a BT boost (either PDR1: PDR BT boost of two insertions with 37 pulses of 0.60 Gy/pulse per insertion or HDR1: HDR BT boost of five fractions of 6.6 Gy each) using different combinations of a/b ratios and T1/2 (conventionally recommended values (4) and from Roberts et al. (34)) EQD2 (Gya/b) a/b (Gy)

T1/2 (h)

Methodology

10 10 10 10 52.6 (34) 20.8 (34) Infinitely large value (34),a

1.5 0.25 (34) 0.00 (34) 0.64 (34) 1.5 1.5 1.5

Conventional Conventional Conventional Conventional Conventional Conventional Conventional

parameters a/b, most likely T1/2 a/b, lowest likely T1/2 a/b, highest likely T1/2 T1/2, most likely a/b T1/2, lowest likely a/b T1/2, highest likely a/b

PDR1

HDR1

90.4 83.5 81.3 85.6 89.6 89.9 89.4

89.9 89.9 89.9 89.9 80.6 84.3 78.0

PDR 5 pulsed-dose-rate; HDR 5 high-dose-rate; BT 5 brachytherapy; EBRT 5 external beam radiotherapy. a Roberts et al. report a b/a 95% confidence range of 0.018 Gy1 to 0.048 Gy1. A b/a approaching 0 would correspond to an infinitely large value for a/b.

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Table 4 Variation in the radiobiological dose to tumor and critical structures assuming a T1/2 of 1.5 h and different a/b ratios Dose to tumora (Gyz) BT treatment

6

10b

14

20

Dose to critical structure per pulse/fraction (% of tumor dose)c

PDR1, 37 p  0.60 Gy,  2 insertions PDR2, 58 p  0.73 Gy HDR1, 5 fr  6.6 Gy HDR2, 4 fr  7.75 Gy HDR3, 3 fr  9.5 Gy

91.0 92.0 95.8 97.2 99.1

90.4 90.4 89.9 90.1 90.6

90.2 89.6 86.9 86.6 86.3

90.0 89.0 84.5 83.7 82.8

0.34 0.40 3.41 3.93 4.71

a/b ratio (Gy)

Gy Gy Gy Gy Gy

(56%) (55%) (52%) (51%) (50%)

Dose to critical structurea (Gyz) a/b ratio (Gy) 2.5

3d

5

64.5 64.7 65.3 65.5 65.7

65.0 65.0 65.0 65.0 65.0

66.4 65.9 64.2 63.8 63.3

PDR 5 pulsed-dose-rate; HDR 5 high-dose-rate; BT 5 brachytherapy; EBRT 5 external beam radiotherapy. a Includes EBRT of 25 fractions of 1.8 Gy each. b Conventional recommendation for a/b ratio of tumor tissue. c The critical structure dose assumes: (1) the full EBRT dose was delivered to the structure (45 Gy in 25 fractions); (2) the BT brings the EQD2 to a tolerance dose of 65 Gy3. d Conventional recommendation for a/b ratio of critical structure tissue.

operator reporting patterns between laboratories during BrdUrd labeling of cervical tumor biopsies (61). Further deviation may be caused by differences in the sample population. Symonds et al. notes that Tpot may decrease with disease progression (62). Summary of conventional recommendations and other reported values Table 1 provides a summary of both the conventional recommendations of ICRU 89 and other published values for the a/b ratio and T1/2. There are no conventionally recommended values for a, Tkickoff, and Tpot. Instead of calculating the effects of proliferation, limitations are typically recommended for the maximum OTT. Table 2 provides a summary of reported values for parameters used when considering proliferation effects.

Effect of parameter uncertainties Uncertainty in conventional recommendations While conventional recommendations have been provided for the a/b ratio and T1/2, the values cited in Table 1 highlight a fair degree of uncertainty. Deviation of both parameters from conventional values (for tumor or critical structures) could result in nonequivalent radiobiological doses being delivered by the PDR and HDR BT boosts that are otherwise assumed to be dosimetrically equivalent through Equations 4 and 10. These differences in the radiobiological dose could result in differing patient outcomes depending on which BT boost was utilized. Table 3 illustrates this by presenting the radiobiological doses to the tumor when calculated using the conventional values and the different combinations of a/b and T1/2 values based on maximum likelihood calculations published by Roberts et al. (34). The calculations are carried out for an EBRT treatment delivering 25 fractions of 1.8 Gy each followed by a BT boost of (1) PDR1: 2 insertions with 37

pulses of 0.60 Gy/pulse per insertion; or (2) HDR1: 5 fractions of 6.6 Gy each. Both schedules are designed to deliver a tumor dose of approximately 90 Gy10 (combined EBRT and BT) when assuming an a/b ratio of 10 Gy and a T1/2 of 1.5 h. PDR pulse times are based on an Ir-192 source strength of 2040 U. EQD2 values calculated in Table 3 shows the variation in doses when considering different combinations of the parameter values. Larger values of a/ b result in a minimal decrease in EQD2 of about 1.0 Gy for PDR1, whereas a difference of 12.0 Gy occurs for HDR1. Conversely, lower values of T1/2 reduced the dose by over 9.0 Gy10 for PDR1, but did not have an effect on HDR1. Table 4 highlights the change in PDR and HDR treatment doses when the a/b ratio of the tumor and critical structure are varied from their conventional values of 10 and 3 Gy, respectively. The table shows the EQD2 doses when calculated with different a/b ratios (corresponding to the range given in Table 1) for four different potential BT boosts after an EBRT treatment delivering 25 fractions of 1.8 Gy each: (1) PDR1: 2 insertions with 37 pulses of 0.60 Gy/pulse per insertion; (2) PDR2: 58 pulses of 0.73 Gy/pulse; (3) HDR1: 5 fractions of 6.6 Gy each; (4) HDR2: 4 fractions of 7.75 Gy each; and (5) HDR3: 3 fractions of 9.5 Gy each. PDR treatments are commonly delivered in one or two insertions, whereas the choice of the number of HDR fractions is adopted from the American Brachytherapy Society’s consensus guidelines for locally advanced carcinoma of the cervix (63). All five treatment schedules are designed to deliver a tumor dose of approximately 90 Gy10 (combined EBRT and BT) when using conventional a/b and T1/2 values and not taking proliferation corrections into account. Without proliferation, the radiobiological doses are independent of the relative timing of the EBRT and BT. For example, if BT sequentially follows EBRT as opposed to beginning BT before EBRT completion, the combined (EBRT þ BT) dose is unchanged; this is provided the treatment fractions are separated such that no sublethal damage from a BT fraction remains at the next

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Fig. 1. Change in tumor EQD2 with T1/2 for different PDR and HDR BT regimens after EBRT (25 fr  1.8 Gy) and assuming a/b 5 10 Gy. PDR 5 pulsed-dose-rate; HDR 5 high-dose-rate; BT 5 brachytherapy; EBRT 5 external beam radiotherapy; EQD2 5 equieffective dose delivered in 2 Gy fractions.

EBRT fraction or vice versa, as would generally be the case with typical separations of at least 1 day. Relative timing is potentially important when proliferation is incorporated as it would alter the OTT (see Equation (12)). The calculations shown in Table 4 also assume that T1/2 is 1.5 h, and PDR pulse times are based on an Ir-192 source strength of 2040 U. As seen from the estimated doses in Table 4, variations in the a/b ratio have a greater effect on HDR doses than PDR doses. Consequently, as the a/b ratio deviates more from the originally assumed conventional value of 10 Gy, the difference in the total dose for the two delivery methods will also increase. For a tumor with an a/b ratio less than 10 Gy, HDR BT delivers a higher radiobiological dose than PDR BT. For example, assuming an a/b ratio of 6 Gy, the total radiobiological dose to the tumor from an HDR3 BT boost would be 7.1 Gy6 (7.7%) greater than that from a PDR2 BT boost. However, the opposite is true if the a/b ratio was 20 Gy, as a treatment with a PDR2 BT boost would deliver 6.2 Gy20 (7.0%) more than the HDR3 BT boost. Table 4 also presents an example of the variation in an assumed tolerance dose of 65 Gy3 received by a critical structure for the five different treatment schedules and two alternative assumptions for the a/b ratio with the same assumed T1/2 value of 1.5 h. Because T1/2 is not included in Equation 4 (which assumes complete repair between fractions), any variation in T1/2 does not affect fractionated HDR BT dose calculations. However, changes in T1/2 have a strong impact on the radiobiological dose calculated for PDR BT, where the treatment pulses are usually delivered hourly and there is insufficient time for complete repair of sublethal lesions (Table 3). De Leeuw et al. supports this conclusion that

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Fig. 2. Value of parameter q plotted against T1/2 for different pulse repetition times, pulse durations, and number of pulses. PDR 5 pulsed-doserate.

changes in the T1/2 had minimal effect on the calculated EQD2 for HDR BT (two insertions of two fractions each separated by 17 h) but resulted in significant variation in calculated EQD2 values for PDR BT (2 insertions of 32 pulses each) (64). A lower T1/2 would result in a smaller biological effect (tumor control or critical organ toxicity) for PDR treatments. This effect can be seen in Fig. 1, which plots radiobiological dose against T1/2 for four different BT boosts after an EBRT delivering 25 fractions of 1.8 Gy each: (1) PDR1: 2 insertions with 37 pulses of 0.60 Gy/pulse per insertion, (2) PDR2: 58 pulses of 0.73 Gy/pulse, (3) PDR3: 39 pulses of 1.0 Gy/pulse, and (4) HDR1: 5 fractions of 6.6 Gy each. The time per pulse for the PDR treatments were calculated with a 2040 U Ir-192 source. All four treatments deliver a tumor dose of approximately 90 Gy10 when assuming the conventional T1/2 of 1.5 h and an a/b ratio of 10 Gy. An increase in T1/2 will result in a higher dose being delivered by any PDR BT schedule and vice versa, while the HDR BT boost delivers the same radiobiological dose regardless of any changes to T1/2. This effect can be quite significant. For example, if the T1/2 of the tumor was 0.4 h instead of 1.5 h, consistent with one of the reported tumor values in Table 1, PDR3 would deliver approximately 9.1 Gy10 (10.1%) less dose than expected. In addition to a/b and T1/2, the BED equation for PDR (Equation 10) contains dependencies on several parameters, including pulse delivery time, pulse interval, and number of pulses. To better understand the trends in the PDR BT data seen in Fig. 1, it is useful to define a parameter q:     2 1  2 q5 NY  SY 1 ð13Þ mT NmT

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Fig. 3. Plot of combinations of T1/2 and a/b ratios that result in the same radiobiological dose for two PDR treatments (PDR1 [2 insertions with 37 pulses of 0.60 Gy/pulse per insertion] and PDR2 [58 hourly pulses of 0.73 Gy/pulse]) for four different instantaneous dose rates. The equivalency of the two treatments is assumed. PDR 5 pulsed-dose-rate.

such that Equation 10 can be expressed as BEDPDR 5  dq Nd 1 þ a=b , a form more directly comparable with the BED expression used for HDR (Equation 4 or 9). Larger q values represent more radiobiological dose being delivered per unit of physical dose. Figure 2 plots q against T1/2 for six different PDR BT boosts: (1) PDR1: 58 hourly pulses, (2) PDR2: 73 hourly pulses, (3) PDR3: 40 hourly pulses, (4) PDR4: 58 bihourly pulses (one pulse every 2 h), (5) PDR5: 58 semihourly pulses (one pulse every 30 min), and (6) PDR6: 58 hourly pulses with a lower dose rate. All six treatments are assumed to deliver 0.73 Gy/ pulse. PDR1 to PDR5 have an assumed time per pulse of 10 min, whereas PDR6 has an assumed time per pulse of 30 min. Compared with PDR1, PDR2 and PDR3 reflect changes in the value of q due to the number of pulses, whereas PDR4 and PDR5 demonstrate changes in q due to the time between pulses. As illustrated, by comparing PDR1 and PDR6, q is dependent on the duration of each pulse (which is a function of the dose per pulse and instantaneous dose rate), although the dependence only becomes appreciable for values of T1/2 small enough to approach the pulse duration. The repetition time (i.e., hourly, semihourly, or bihourly pulses) and the halftime of repair both strongly affect q. However, because pulses are conventionally delivered hourly, the most relevant dependence affecting q is T1/ 2. For example, when assuming an a/b ratio of 10 Gy and T1/2 of 1.5 h, the value of q for PDR1 is 4.22, resulting in a tumor dose of 46.2 Gy10 from BT (and a total dose of 90.4 Gy10 if an EBRT of 25 fractions of 1.8 Gy each is included). However, a T1/2 of 0.4 h would result in a q value of 1.33 and would significantly decrease the BT tumor dose

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(38.7 Gy10, for a total dose of 83.0 Gy10 including EBRT). In comparison, an increase in pulse duration (PDR6) changes the q value from 4.22 to 4.19, assuming a T1/2 of 1.5 h. This would only result in a small decrease in dose delivered of 0.1 Gy10. When considering parameter ranges, it is important to recognize that multiple combinations of a/b ratios and T1/2 may satisfy a given radiobiological equivalency. Consider two PDR treatments: (1) PDR1: 2 insertions with 37 pulses of 0.60 Gy/pulse per insertion and (2) PDR2: 58 pulses of 0.73 Gy/pulse. If PDR1 and PDR2 were found to be radiobiologically equivalent, the a/b ratio and T1/2 of the tissue cannot be determined from this result alone; one of the two parameters must be assumed. Figure 3 plots combinations of T1/2 and a/b ratios that result in the two PDR treatments (PDR1 and PDR2) having the same radiobiological dose (according to Equation 10) for four different Ir-192 source air-kerma strengths (and hence pulse times and dose rates): (1) Sk1: 1020 U, (2) Sk2: 2040 U, (3) Sk3: 4080 U, and (4) Sk4: 8160 U. Sk1 corresponds to a 2040 U source that has decayed by one half-life. Instead of providing a single solution, the equivalence suggests an infinite number of solutions for different combinations of the a/b ratio and T1/2 values. This correlation introduces another aspect of uncertainty into the published values of the a/b ratio and T1/2: a priori assumptions of a/b will influence the calculated T1/2 and vice versa. It is important to note that the correlations shown in Fig. 3 are derived from an assumed hypothetical equivalency between two clinically used PDR schedules; because this radiobiological equivalency may not necessarily actually exist, the specific equivalent combinations of a/b and T1/2 shown in Fig. 3 may not be correct. A similar correlation between extracted values of the a/b ratio and T1/2 was demonstrated by Roberts et al. (34). Their analysis actually excludes a T1/2 of 1.5 h from its 95% confidence interval when assuming an a/b ratio of 10 Gy, one of the combinations illustrated in Fig. 3.

Uncertainty in proliferation parameters Conventional treatment recommendations, which suggest a maximum OTT based on outcomes data, do not fully consider the radiobiological impact of proliferation. Currently, no correction is implemented for treatments that deliver the same radiobiological dose (before proliferation is considered) but have different OTTs. Treatments considered equivalent could therefore potentially correspond to different radiobiological doses and different outcomes. In the retroEMBRACE study, a loss of 1e3% in local control/week was reported for prolonged OTT (53). ICRU 89 recommends that the OTT be within 55 days, which is made possible by the following: using a simultaneously integrated nodal boost (when necessary) within the EBRT course; reducing treatment interruptions; and planning ahead the timing of the BT (4,5). An even shorter time frame is often possibledfor example, an EBRT followed

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Fig. 4. EQD2, considering proliferation, after a 90 Gy10 prescription for (a) different potential doubling times (Tpot) and a values and (b) different kickoff times (Tkickoff). DD represents the difference in dose between treatments of overall treatment times 40 days and 55 days. EQD2 5 equieffective dose delivered in 2 Gy fractions.

by a single insertion PDR boost could be completed within 40 days if there are no treatment interruptions. The difference in radiobiological dose due to increased tumor proliferation over an additional 15 days in the 55 day treatment can be calculated using Equation 12. Let DBED 5 BED1  BED2

ð14Þ

where DBED represents the difference in radiobiological dose after proliferation is considered, and BED1 and BED2 represent the radiobiological dose delivered with an OTT of T1 and T2, respectively. Assuming that all parameters (a, Tpot, Tkickoff, and BED0) except OTT are the same and the OTT values for both cases are longer than Tkickoff (DT 5 OTTTkickoff), then 
lnð2Þ OTT2  Tkickoff DBED 5 Tpot a 
lnð2Þ OTT1  Tkickoff ð15Þ  Tpot a DBED 5

lnð2ÞOTTdiff Tpot a

ð16Þ

where OTTdiff is the difference between the two OTTs (OTT1 and OTT2). For example, assuming Tpot 5 4.5 days and a 5 0.3 Gy1, a treatment lasting for 55 days will deliver 6.4 Gy10 less than if it had an OTT of 40 days (Tdiff 5 15 days). As suggested by Equation 16, smaller values of Tpot and a for tumor will increase DBED, resulting in a larger variation in tumor dose due to differences in OTT. Figure 4a highlights this effect where the radiobiological dose from a 90 Gy10 prescription (after consideration of proliferation) is plotted against OTT for four combinations of Tpot and a with an assumed Tkickoff of 21 days.

Consider a BT treatment that is prolonged by 15 days. For larger values of Tpot and a (such as 5.0 days and 0.5 Gy1, respectively), there would be a loss of 3.5 Gy10; however, for smaller Tpot and a values (such as 4.0 days and 0.2 Gy1, respectively), the dose loss of 10.8 Gy10 would potentially be much more concerning. It is worth noting that, much like how multiple combinations of the a/b ratio and T1/2 can correspond to a radiobiological equivalency, multiple combinations of Tpot and a can predict equal amounts of proliferation-based radiobiological dose reduction. Recent recommendations by Tanderup et al. suggest that the commonly cited values for Tpot and a may not accurately estimate the effects of proliferation (53). They found that an increase of 1-week to a 7-week OTT was comparable with a tumor dose de-escalation of 5 Gy10. An example of a combination of Tpot and a values that mathematically replicate this rate of dose loss is 4.0 days and 0.2 Gy1, which represents the lower end of values reported in Table 2. In comparison, because more commonly cited values of Tpot and a for the tumor are 4.5 days and 0.3 Gy1, current dose calculations incorporating proliferation may still underestimate its effect. Tkickoff variance is not expected to affect the calculated proliferation dose loss between two treatments because the shortest OTTs currently considered are longer than the maximum value of Tkickoff given in Table 2. In this case, Equation 16 is sufficient to describe differences in radiobiological dose delivered by different OTTs. This can be seen in Fig. 4b, where the radiobiological dose from a 90 Gy10 prescription (after proliferation is considered) is plotted against OTT for three values of Tkickoff. The Tpot is assumed to be 4.5 days and a is 0.3 Gy1. The difference in dose of 6.5 Gy10 between treatments delivered over 40 days and

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55 days (DD) is not impacted by the value of Tkickoff.. Similar results were found by Gasinska et al. They estimated that the amount of radiobiological dose lost daily due to proliferation was the same regardless of the assumed kickoff time (varied from 21, 28, and 35 days) (50). Further considerations Although the LQ model has been used to describe the effects of radiation damage, many suggestions have been provided to further improve the accuracy of radiobiological dose modeling. Some proposed modifications are highlighted in the following. Biexponential repair kinetics The repair rate of sublethal damage in the LQ model is assumed to be monoexponential (a single rate of repair). However, the possibility of biexponential repair has previously been raised due to growing evidence of a second repair process in animal studies (26,65). Biexponential repair models would provide an explanation for the repair of sublethal damage decreasing in mice and rat tissue as time after irradiation increases (66,67). Utilization of a biexponential repair model has been limited in human studies. Reoxygenation Studies have shown that patients with lower initial hemoglobin in cervical tumors have decreased survival rates (68). Despite the recognition of the effects of hypoxia in treatment outcome, no clinically implemented dose model considers hypoxia or reoxygenation (69). LQ model predictions may improve if reoxygenation is factored into dose calculation as the oxygen enhancement ratio for LDR BT (and likely PDR BT) is lower than HDR BT (70). This difference in oxygen enhancement may be caused by the extended recovery period in HDR BT; the separation of fractions allows for greater reoxygenation of the hypoxic regions than is possible using LDR or PDR. Alternative models to LQ Although the LQ model is commonly used for radiobiological dose calculation, more complex cell survival models have been proposed, including the repair-misrepair model, the lethal-potential lethal model, the two-lesion kinetics model, and the linear-quadratic-linear model (71e74). Although these more complex models typically reduce to an LQ form under certain limiting conditions, their predictions often deviate from those of the LQ model at higher doses per fraction, where their accuracy has been contested (75,76). At higher doses, nontargeted mechanisms not considered by the LQ model, such as vasculaturemediated and immunological effects, may contribute to tumor killing (77). Phenomenological models such as the universal survival curve model have also been developed

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to better describe the shape of the high-dose region of the cell survival relationship (78). However, Brenner has also suggested that the LQ model has been ‘‘reasonably well validated’’ for doses up to 10 Gy per fraction and is ‘‘reasonable for use up to about 18 Gy’’ (22). As typical EBRT and BT fractions (such as the examples in ICRU 89) do not reach these high doses per fraction, it is unclear whether the more complex models will provide further improvements to the calculated radiobiological dose for cervical cancer treatment.

Conclusion The use of radiobiological dose is recommended to compare treatments and outcomes from different treatment techniques used in cervical cancer BT. However, possible variance in parameter values used in dose calculation and the inconsistent consideration of proliferation introduces significant additional uncertainty into dose calculation. Variance in the a/b ratio and T1/2, within the range of values reported in literature, can introduce over 10% variance in the calculated radiobiological tumor dose for PDR treatments, whereas changes in the a/b ratio can result in over 13% variance in HDR treatments (with T1/2 not having any significant effect). Similarly, extension of OTT can introduce a variance of over 5 Gy10 due to differences in reported values of a and Tpot. This highlights the need for further efforts to establish more definitive parameter values. Improved radiobiological parameters, potentially combined with refinements to current radiobiological dose models, could increase the accuracy of treatment planning and consequently lead to better outcomes for patients with cervical cancer.

Acknowledgments None. References [1] Bray F, Ferlay J, Soerjomataram I, et al. Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA Cancer J Clin 2018;68:394e 424. [2] Banerjee R, Kamrava M. Brachytherapy in the treatment of cervical cancer: a review. Int J Womens Health 2014;6:555e564. [3] Han K, Milosevic M, Fyles A, et al. Trends in the utilization of brachytherapy in cervical cancer in the United States. Int J Radiat Oncol Biol Phys 2013;87:111e119. [4] International commission on radiation units & measurements. Report 89: Prescribing, recording, and reporting brachytherapy for cancer of the cervix. J ICRU 2013;13:1e258. [5] P€otter R, Tanderup K, Kirisits C, et al. The EMBRACE II study: The outcome and prospect of two decades of evolution within the GEC-ESTRO GYN working group and the EMBRACE studies. Clin Transl Radiat Oncol 2018;9:48e60. [6] Patankar S, Tergas A, Burke W, et al. High- versus low-dose rate brachytherapy for locally advanced cervical cancer. Gynecol Oncol 2015;136:534e541.

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