Time resolved dose rate distributions in brachytherapy

Physica Medica xxx (2017) xxx–xxx

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Original paper

Time resolved dose rate distributions in brachytherapy Vasiliki Peppa ⇑, Eleftherios P. Pappas, Pantelis Karaiskos, Panagiotis Papagiannis Medical Physics Laboratory, Medical School, National and Kapodistrian University of Athens, Athens, Greece

a r t i c l e

i n f o

Article history: Received 30 December 2016 Received in Revised form 18 March 2017 Accepted 9 April 2017 Available online xxxx Keywords: Dose rate Brachytherapy Radiobiology

a b s t r a c t Purpose: To investigate the biological significance of introducing time-resolved dose rate distributions (TR-DRD) in brachytherapy. Materials and methods: The treatment plan of a head and neck patient treated with pulsed-dose-rate (PDR) brachytherapy was considered. The TR-DRD was calculated on the basis of a Monte Carlo generated single source dose rate matrix taking into account the dose rate per source dwell position. Biologically Effective Dose (BED) was obtained considering either the mean dose rate per pulse (analytical method) or the TR-DRD (numerical method). Corresponding Tumor Control Probabilities (TCP) were calculated and compared for various PDR schemes and repair half-times from the literature. The dose of the biologically equivalent high-dose-rate (HDR) treatment schedule was also evaluated. Results: The analytical method presents an overall BED underestimation (up to 2%) relative to TR-DRD results. This is associated with an analytical-based TCP underestimation which increases with dose/pulse, pulse duration and period time and decreases with total dose. The half-time of repair seems to have the largest impact on the TCP calculations, with significant differences (up to 39.1%) corresponding to the shorter repair half-times. Regarding the equivalent HDR treatment schedule, the analytical method resulted to a HDR isoeffective dose underestimation lower than 2.2% and thus does not warrant any change in the derivation of the equivalent HDR scheme. Conclusion: TR-DRD data should be taken into account for PDR biological effectiveness estimations, especially for short tissue repair half-times. This does not appear however to influence dose prescription of the equivalent HDR treatment schedule for mobile tongue carcinoma. Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

1. Introduction Base-of-tongue cancer can be effectively treated using External Beam Radiotherapy (EBRT) combined with 192Ir brachytherapy boost [1]. Pulsed-dose-rate (PDR) interstitial brachytherapy constitutes an effective treatment for patients with head and neck squamous cell carcinoma, with excellent long-term results [2–4]. Recently, published data have demonstrated that high-dose-rate (HDR) brachytherapy could also be a safe alternative for the treatment of oral cancer with excellent local control and a low incidence of side effects [5–7]. The Biologically Effective Dose (BED) is a clinical tool frequently used to assess and compare the biological effects in malignant and normal tissues, as well as to convert between different fractionation schedules [8,9]. Although local control and complications are strongly dependent on dose rate [10,11], studies published on ⇑ Corresponding author at: Medical Physics Laboratory, Medical School, National and Kapodistrian University of Athens, Mikras Asias 75, Goudi, Athens 115 27, Greece. E-mail address: [email protected] (V. Peppa).

the biological effectiveness of PDR and HDR brachytherapy [12–14], as well as on the derivation of the biologically equivalent HDR scheme [12,15] rely on time-integrated dose rate calculations ignoring the intra-fraction dose rate from each individual source dwell position. While the dose rate response of tissues to radiation is considered to be stable in HDR brachytherapy [16], the effect of varying dose rate on the treatment outcome of PDR brachytherapy should be evaluated since dose rates lower than 1 Gy/min, where the response begins to change [11,17], can be observed. Lately, the radiation therapy community has shown an interest in the assessment of the time-resolved distribution of dose rates across the patient geometry [18–22]. Podesta et al. [18] and Mackeprang et al. [19] have recently developed methods to calculate the dose rate distributions in volumetric modulated arc therapy (VMAT) plans, which could serve as input for future radiobiological studies. Andersen et al. [22] performed in vivo dosimetry in five patients undergoing PDR brachytherapy and demonstrated that time-resolved dose rate measurements revealed an increased sensitivity in detecting dose-delivery errors. This work presents a method to calculate the intra-fraction dose rate distribution in PDR brachytherapy using Monte Carlo (MC)

http://dx.doi.org/10.1016/j.ejmp.2017.04.013 1120-1797/Ó 2017 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Peppa V et al. Time resolved dose rate distributions in brachytherapy. Phys. Med. (2017), http://dx.doi.org/10.1016/j. ejmp.2017.04.013

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V. Peppa et al. / Physica Medica xxx (2017) xxx–xxx

simulation. Furthermore, a formalism including tools that are frequently used in clinical practice was developed in order to assess the effect of accounting for time-resolved dose rate distributions (TR-DRD) on biological effectiveness of PDR brachytherapy as well as on the choice of the biologically equivalent HDR treatment schedule. 2. Materials and methods 2.1. Treatment planning details and dose rate calculation The treatment plan of a clinical case of mobile tongue carcinoma was selected in this study. PDR brachytherapy was performed using 4 flexible plastic catheters and 27 dwell positions of the 192Ir microSelectron PDR source (Fig. 1) [23], with source step size of 5 mm. The planning aim dose was 15 Gy delivered with a dose rate/pulse dose of 0.5 Gy/h/24 h, following surgery as well as external beam radiotherapy delivery of 45 Gy. Two methods were developed in this work for the calculation of the dose rate. The analytical method, where the mean dose rate per pulse was considered, and the numerical method (TR-DRD), where the dose rate of each dwell position was taken into account. A reference dose rate distribution was first generated using version 6.1 of the MCNP Monte Carlo code [24]. In short, the radioactive core of the 192Ir microSelectron PDR source was centered in a 15 cm radius water sphere, mimicking TG43 conditions [25]. The 192Ir spectrum presented in the work of Glasgow and Dillman [26] was considered in this study, since this spectrum was used for the generation of the TG43 data for the microSelectron PDR source included in Treatment Planning Systems (TPSs) [23]. Dose was approximated by collision Kerma and Dw,w was calculated using the ⁄FMESH4 tally over the whole geometry (1
1
1 mm3 resolution), along with the corresponding mass energy absorption coefficients to convert MC output data from MeV/cm2 per starting particle to MeV/g. 8
108 initial photon histories were used yielding a MC Type A uncertainty of 2.5% at points most distal to the source. A separate simulation was also performed for the calculation of the source airkerma strength to convert MC results from MeV/g per starting particle to Gy/hU.

The source dwell positions, directions and corresponding dwell times were parsed from the treatment’s RT plan file using BrachyGuide, an in-house developed software for the preparation of MCNP input files from treatment plans exported in DICOM RT format [27]. The TR-DRD was calculated within the Planning Target Volume (PTV) using the MC-based reference dose rate distribution applying the appropriate translations and rotations according to each dwell position and direction of the source, respectively, using a custom routine developed in MATLAB (MathWorks, Natick, MA). This resulted to a total number of 27 dose rate distributions (equal to the number of the dwell positions used in the treatment plan) which were multiplied by the air-kerma strength included in the RT plan to convert results from Gy/hU to Gy/h. The mean dose rate was considered as the fraction of the dose distribution delivered within a pulse, per pulse duration. The dose distribution was calculated by the sum of the MC-based dose distributions of all dwell positions weighted by the corresponding source dwell times. The volume of the PTV receiving dose levels higher than 800% of the prescribed dose was excluded from the analysis of this study, since this region lies within the catheters and presents no clinical interest. The same upper dose limit is applied in TPSs employed for clinical treatment planning. In order to evaluate the impact of TR-DRD on biological effectiveness of PDR brachytherapy in head and neck patients as well as on the prediction of the isoeffective dose of a different HDR brachytherapy treatment schedule, a formalism including frequently used clinical tools that account for the effect of dose rate was developed in this work. 2.2. Formalism 2.2.1. Cell Surviving fraction, S The Linear-Quadratic (LQ) model [9] was considered to define the cell surviving fraction. According to this model, the surviving fraction S is given by:

SðDÞ ¼ exp½aD  bqðtÞD2 þ cT tot 

ð1Þ

where a and b characterize intrinsic radiosensitivity, D is the total dose, Ttot is the treatment duration, c is the effective tumor-cell repopulation rate (c ¼ lnð2Þ=T d , for tumor-cell doubling time Td). The effect of dose rate is represented in Eq. (1) by the dose rate function q(t) [16]:

Rt qðtÞ ¼

0

sðtÞhðuÞdu Rt hðuÞdu 0

ð2Þ

In this expression,

sðtÞ ¼ elt

ð3Þ

stands for the probability that a sublesion remains unrepaired t units of time after being formed, h(t)dt is the pairwise probability distribution of time intervals between pairs of sublesions and l ¼ ln 2=T 1=2 , where T1/2 is the half-time of sublethal damage repair. If I(t) is the dose rate at time t, it follows that:

Z

hðtÞ /

1

IðuÞIðu þ tÞdu

ð4Þ

0

Taking into account the dose rate of each dwell position, Eq. (2) leads to: T X eldti Ri t i Riþ1 t iþ1 dti

Fig. 1. A 3D reconstruction of the external patient contour (brown) and the Planning Target Volume (red) along with the 4 plastic catheters and the 27 source dwell positions.

qðtÞ ¼

0 T X Ri t i Riþ1 t iþ1 dt i

;

ð5Þ

0

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V. Peppa et al. / Physica Medica xxx (2017) xxx–xxx

where Ri and Ri+1 are two consecutive dose rates, ti and ti+1 their corresponding dwell times, dti the time interval between them and T the pulse duration. 2.2.2. Biologically effective dose, BED The BED was calculated for each method using Dale’s formula for PDR treatment [28]:

      SY 2 SY d cT tot þ  BED ¼ Nd 1 þ qðtÞ 1  N lT N a=b a

ð6Þ

with:

S¼

NK  K  NK 2 Z þ Z N K Nþ1 ð1  KZÞ2

pulse duration in the above equations varied from 10 to 40 min, to account for the range of the source activity used in the clinical practice of PDR brachytherapy [2]. Although GEC-ESTRO recommends a period time of 1 h, period times of 2 and 3 h have also been reported in the literature and evaluated in this work [2]. The dose protocol adopted in terms of dose/pulse and total dose followed the GEC-ESTRO recommendations, including values of 0.3–0.7 Gy and 10–24 Gy, respectively [31]. As the biological outcome of different dose rates depends on the sublethal damage repair, a wide range of repair half-times (0.3, 0.5, 1, 1.5 and 2 h) was considered in this study [31–34]. It should be noted that the conversion between the different fractionation schemes was performed by adjusting the air-kerma strength and the corresponding dwell times included in the RT plan file according to the given dose/pulse and pulse duration.

Z ¼ elT 3. Results

Y ¼1Z

3.1. Dose rate distributions

K ¼ elx x ¼ Tp  T where N is the number of pulses, Tp is the period time and x is the radiation free-interval between pulses. For the analytical method, the dose rate function was described by the expression that corresponds to a single dose of radiation delivered at constant dose rate [16]:

qðtÞanalytical ¼

  2 1  elT 1 lT lT

ð7Þ

For the numerical method, the expression of dose rate function described by Eq. (5) was considered. 2.2.3. Tumor Control Probability, TCP The Tumor Control Probability (TCP) was calculated for each method from the mean cell surviving fraction, Smean , using the Poisson hypothesis [29]:

TCP ¼ ekSmean

ð8Þ

where k is the initial number of malignant cells. The Smean was calculated for the analytical and the numerical method using the corresponding BED volume histograms, according to:

Figs. 2(a)–(d) present a colormap representation of the dose rate distribution on the central axial slice of the PTV for the analytical method as well as for three indicative dose rate distributions (corresponding to three different source dwell positions) of the numerical method, for the PDR scheme of the clinical case. Figs. 2 (e) and (f) show the percentage of the PTV volume receiving specific dose rates according to the analytical and the numerical-based results, respectively. Results in this figure demonstrate that the analytical method resulted in a mean dose rate ranging from 0.8 to almost 8 Gy/h. The numerical method, however showed that dose rates up to 20 Gy/h can be observed. Moreover, while the 97.4% of the PTV volume receives a mean dose rate up to 5 Gy/h, the corresponding fraction of the PTV for the TR-DRD is on average 54.7%. It can be also seen that according to the numerical method a fraction equal to 4.6% on average of the PTV volume located close to the source dwell positions receives dose rates ranging from 15 to 20 Gy/h. 3.2. Radiobiological evaluation for Tp = 1h Fig. 3 presents a colormap representation of the percentage BED differences between the analytical and the numerical results   BED BEDanalytical % numerical on the central axial plane of the PTV. The BED analytical

2.3. Evaluation of the results

BED was calculated assuming a/b = 10.5 Gy, a = 0.22 Gy1, k = 200, Td = 4.5 d [7]. A reference PDR scheme was considered with 15 Gy total dose, 0.7 Gy pulse dose and 30 min pulse duration, since this treatment schedule was found to augment the differences between the two methods. The half-time of repair was considered equal to 1 h. It can be observed that the analytical method presents an overall BED underestimation relative to TR-DRD results by up to 2%, which is more pronounced as one moves towards the source dwell positions, where high dose rates are present. These results are in accordance with findings presented in Fig. 2, implying that as the time-resolved dose rates of each PTV voxel depart from the mean dose rate, the resultant constant dose rate function considered for the analytical calculations (Eq. (7)) presents an underestimation relative to the TR-DRD based dose rate function (Eq. (5)). Comparisons of the numerical and analytical results in terms of   TCP TCP analytical percentage TCP differences % numerical can be seen in TCP

In order to evaluate the difference in biological effectiveness between the two methods, several PDR schemes for mobile tongue carcinoma from the literature were considered [31]. In specific, the

Figs. 4(a)–(c). The differences are presented as a function of dose per pulse (Fig. 4(a)), total dose (Fig. 4(b)) and pulse duration (Fig. 4(c)) for all the considered half-times of repair. The comparisons are presented for indicative constant parameters selected

Smean ¼

X vi i

v0

aBEDi

ð9Þ

e

Here, vo is the PTV volume and responding to bin BEDi.

vi is the subvolume of PTV cor-

2.2.4. Isoeffective dose of a HDR brachytherapy treatment schedule   ; Dnumerical The HDR isoeffective dose for each method Danalytical HDR HDR was estimated considering that the cell surviving fraction of the HDR treatment, SHDR ; is equal to the mean surviving fraction of the PDR treatment, SPDR mean , [30] described as: 2 SHDR ¼ eðaDHDR bqHDR ðDHDR Þ þcTtot Þ ¼ SPDR mean

qHDR ¼ 1

ð10Þ

analytical

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Fig. 2. (a) A colormap representation of the spatial distribution of the mean dose rate on the central axial slice of the PTV. Corresponding indicative dose rate results of the TRDRD are presented for the (b) 1st, (c) 11th and (d) 22nd dwell position. Relative histograms of the dose rate calculated over the PTV are also depicted for (e) the analytical and (f) the numerical method. For the numerical method, a histogram was calculated for each dwell position and the fractions of the PTV receiving given dose rates were encoded as color.

on the basis of the reference PDR scheme. The analytical results exhibit a general TCP underestimation, which increases with dose per pulse and pulse duration, reaching up to 10.8%, and decreases with total dose. The analytical-based TCP underestimation becomes significant, by up to 39.1%, as the T 1=2 shortens (Fig. 4 (b)), yet it is not considerable for values of T 1=2 that are greater than 1 h, regardless of the PDR schedule assumed. Figs. 4(d)–(f) show the corresponding comparisons between the analytical and the numerical method in terms of the HDR isoeffective dose   analytical Dnumerical DHDR % HDR analytical . The percentage HDR isoeffective dose differDHDR

ences present the same pattern with the respective TCP differences in Figs. 4(a)–(c). It should be mentioned however that the magnitude of the HDR isoeffective dose underestimation by the analytical method is smaller, reaching up to 1.2%.

3.3. Radiobiological evaluation for various Tp Figs. 5(a) and (b) present the comparisons between the analytical and the numerical method in terms of the percentage TCP and corresponding HDR isoeffective dose differences as a function of

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2.2%, respectively, for the shortest half-time of repair. In line with the results presented in Fig. 4, the TCP and respective HDR isoeffective dose differences become significant for the half-times of repair that are shorter than, or equal to, 1 h.

4. Discussion

Fig. 3. A colormap representation of the spatial distribution ofthe percentage BED  BED BEDanalytical differences between the analytical and the numerical method % numerical BEDanalytical on the central axial slice of the PTV calculated for the reference PDR scheme and for T 1=2 ¼ 1h.

period time for all the considered T 1=2 . The PDR scheme involved a total dose of 15 Gy and a pulse duration of 30 min, while a constant mean dose rate equal to 0.5 Gy/h was assumed for all the considered Tp, using pulse sizes of 0.5, 1 and 1.5 Gy for the period times of 1, 2 and 3 h, respectively [35]. It can be seen that the TCP and corresponding HDR isoeffective dose differences increase considerably with period time, ranging from 8.1 to 22.8% and from 0.6 to

Analytical (mean values) and numerical (TR-DRD) calculations of the dose rate distribution within the PTV were performed in this work for a head and neck patient treated with PDR brachytherapy. Comparisons between the two methods showed that the analytical method presents a dose rate underestimation relative to TR-DRD results for each dwell position of the source, which is more evident as the source moves towards the central region of the PTV due to the small number of PTV voxels receiving dose rates lower than 2 Gy/h. These findings reveal that the presence of high dose rates close to the source dwell positions observed in the TR-DRD are compensated when the mean dose rate is considered. Since the PTV volume excluded from the comparison through the use of an upper dose limit of 800% in this work is smaller than the fraction of the PTV volume occupied by the catheters (1.03% versus 3.2%), it might be argued that differences between the two methods are overestimated. Excluding points within the catheters however was found to result in an increase of difference in terms of TCP for the reference PDR scheme by only 0.07%. Results of this work show that total dose and period time have a larger impact on BED and TCP differences between the two methods relative to pulse size and duration for the range of dose rates

    analytical Dnumerical DHDR TCP TCP analytical Fig. 4. Comparisons of the numerical and analytical results in terms of percentage local (a)–(c) TCP % numerical and (b)–(d) HDR isoeffective dose % HDR analytical TCP analytical

DHDR

differences. Results are presented in respect with dose per pulse, total dose and pulse duration for all the considered half-times of repair and for period time of 1 h.

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    Dnumerical Danalytical TCP TCP analytical HDR Fig. 5. Comparisons of the numerical and analytical results in terms of percentage local (a) TCP % numerical and (b) HDR isoeffective dose % HDR analytical TCP analytical DHDR differences. Results are presented in respect with period time for all the considered half-times of repair.

found in PDR treatment. Still, in line with the published data [33], the most dominant modeling parameter seems to be the half-time of repair. Findings in this study imply that the two methods are biologically equivalent for the tissues with longer half-times of repair, yet the analytical method significantly underestimates the TCP in the presence of shorter half-times of repair. This reveals that the instantaneous increased dose rates observed in the numerical method are associated with lower probabilities of repair relative to analytical results for the tissues with shorter half-times of repair. The analytical method can therefore be considered a safe side approach that is more accurate as the half-time of repair increases. It should be mentioned however that the reduction of the uncertainty associated with the T 1=2 [36] is highly desired in order to properly weight the biological effectiveness of the analytical against the numerical method in PDR brachytherapy. A corresponding pattern was found for the derivation of the equivalent HDR treatment scheme, yet the analytical-based TCP underestimation is not associated with significant HDR isoeffective dose differences between the two methods and does not warrant any change in the derivation of the equivalent HDR schemes. 5. Conclusion A method incorporating the effect of the varying dose rate on treatment outcome was developed and implemented in this work. Results of this method were compared with corresponding analytical calculations in terms of radiobiological parameters for a clinical case of mobile tongue carcinoma treated with PDR brachytherapy. A general TCP underestimation was observed for the analytical method since mean dose rate does not accurately account for the high dose rates close to the catheters and the consequent lower probability of repair, especially for tissues with shorter half-times of repair. The corresponding differences of the HDR isoeffective dose, however, were not significant enough to alter the derivation of the equivalent HDR treatment schedule. The method presented in this study could be applied for any type of dose rate pattern in order to evaluate the impact of TR-DRD on other treatment modalities and especially on combined radiation treatments. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Please cite this article in press as: Peppa V et al. Time resolved dose rate distributions in brachytherapy. Phys. Med. (2017), http://dx.doi.org/10.1016/j. ejmp.2017.04.013