Introduction of inverse dose optimization for ultrasound-based high-dose-rate boost brachytherapy: How we do it in Kiel

Introduction of inverse dose optimization for ultrasound-based high-dose-rate boost brachytherapy: How we do it in Kiel

Brachytherapy 13 (2014) 250e256 Technical Note Introduction of inverse dose optimization for ultrasound-based high-dose-rate boost brachytherapy: Ho...

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Brachytherapy 13 (2014) 250e256

Technical Note

Introduction of inverse dose optimization for ultrasound-based high-dose-rate boost brachytherapy: How we do it in Kiel Frank-Andre Siebert1,*, Sabine Wolf1, Hagen Bertermann2, Nils N€ urnberg2, Gunnar Bockelmann1, Bernhard Kimmig1 1

University Hospital of Schleswig-Holstein, Campus Kiel, Clinic of Radiotherapy, Kiel, Germany 2 Urologische Gemeinschaftspraxis, Kiel, Germany

ABSTRACT

OBJECTIVES: To describe the introduction of inverse planning optimization for a two clinical target volume (CTV) concept in the online planning technique of temporary high-dose-rate brachytherapy for prostate cancer. METHODS AND MATERIALS: Doseevolume constraints were defined delivering a prescription dose of 8.5 Gy for CTV1 (whole prostate) and 15 Gy for CTV2 (peripheral zone). A total of 38 implants of 20 patients were inversely planned using the constraints and dose indices (D90 CTV1,2; V200 CTV1,2; D2 cc rectum; D0.1 cc urethra; dose nonhomogeneity ratio; and conformal index) compared against those derived from conventional planning (CP). RESULTS: The inversely planned (IP) treatment plans showed similar target volume coverage than by CP. The value of D90 CTV1 for CP was 5.62 Gy and 5.63 Gy for IPs. For CTV2, the D90 was also similar between both methods: 11.03 Gy and 10.89 Gy, respectively. Only V200 CTV2 was found to be significantly lower for CP than for IP: 5.76% vs. 8.14% ( p!0.01). Values for D0.1 cc urethra were found to be: 9.57 Gy and 9.02 Gy, respectively. Rectal dosimetry: D2 cc Rectum was quite stable with 6.04 Gy and 6.12 Gy for CP and IP, respectively. The conformal index and dose nonhomogeneity ratio values for CTV1 and CTV2 for both planning types were very similar. CONCLUSIONS: After defining an objective second target volume CTV2 and introducing adequate IP constraints to the treatment planning system, clinically applicable treatment plans could be created by an IP approach. They feature user independency, time saving, and good preservation of the OARs. Ó 2014 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.

Keywords:

High-dose-rate brachytherapy; Inverse dose optimization; Prostate cancer

Introduction Radiotherapy is an alternative treatment option for the treatment of localized prostate cancer. Brachytherapy (BT) can be applied as temporary high dose rate (HDR) or as permanent (seeds) implantation. A common treatment option, especially in intermediate- and high- risk casesd prostate-specific antigen level higher than 10 ng/mL, Gleason sum greater than seven, T-stage minimal T2bdis the application of HDR-BT using typically an 192Ir stepping

* Corresponding author. University Hospital of Schleswig-Holstein, Campus Kiel, Clinic of Radiotherapy, Arnold-Heller-Str 3, Haus 50, 24105 Kiel, Germany. Tel.: þ49-0-431-597-3022; fax: þ49-0-431-5973110. E-mail address: [email protected] (F.-A. Siebert).

source afterloader (1e3). In our clinic, intermediate- and high-risk prostate cancers are generally treated in combination of external beam radiation therapy giving 50 Gy in a four-field box technique (15MV photons) to the pelvis, delivering only 40 Gy to the prostate by external beam radiation therapy using individual blocks sparing the prostate in the anterior and posterior fields (4). Two complementary HDR-BT fractions, each of 15 Gy, are delivered 2 weeks apart. Dose is prescribed to the periphery of the prostate glanddthe clinical target volume two (CTV2). The CTV1 is defined as the dose prescribed to the whole prostate and should be encompassed by 8.5 Gy. This treatment strategy started in 1986 using a preplanning method (4). In the present report, the recent improvement for our technique, application of inverse dose optimization for our HDR boost technique is described.

1538-4721/$ - see front matter Ó 2014 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.brachy.2014.01.010

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Methods and materials The technique of HDR-prostate BT using preplanning is already well covered in the literature (4e6). To improve the quality of temporary HDR implantations of the prostate, our clinic introduced a real-time planning protocol in 2003 (7), which was refined and improved within the following years. The recent implant procedure used in our clinic is outlined in the following paragraphs.

Needle implantation and imaging Patient setup and general needle implantation are described in previous publications (4, 8). The needles are arranged in a U-shaped form in the periphery of the prostate without performing a preplan. According to the International Commission on Radiation Units and Measurements Report 58 (9), CTVs were defined. For our treatment strategy, the CTV is being split in two parts, namely CTV1 and CTV2. The prescribed dose of the U-shaped CTV2 is 15 Gy. Furthermore, the whole prostate gland, often denoted as CTV1, should be treated with 8.5 Gy. As an organ at risk (OAR), the urethra dose should not exceed 10 Gy per fraction. Even for intensity-modulated BT (8), the geometry of the catheters is essential. To later obtain an adequate dose distribution, the implantation needles are normally positioned in distances of about 7 mm from one needle to another in the transversal plane. Because of the shadowing effect of the implant needles, first of all the ventral needles are then placed in the prostate, followed by the dorsal ones. If the prostate gland is large enough and the urethra remains in the anterior section of the gland normally, two more implant needles are inserted in the medium part of the prostate. These needles help to cover the dose in the middle section and in the apex of the gland (Figs. 1 and 2 for illustration of the implant geometry and the definition of the CTV2). The exact depth and the curvature of the implant needles are determined by live longitudinal transrectal ultrasound (TRUS) imaging using the Vitesse v. 2.5 software (Varian Medical Systems, Inc., Palo Alto, CA). In a previous study, the accuracy (better than 1 mm) of the detection of the needle tips was investigated (10). The transversal TRUS image data of the prostate is acquired in 2.5-mm step width via a video connection into the Vitesse (Varian) software from the bladder neck to the end of the prostatic apex. Contouring of the prostate, urethra, seminal vesicles, and the visible part of the rectal wall is manually performed according to the Groupe Europeen de Curietherapie and the European Society for Therapeutic Radiology and Oncology and European Association of Urology guidelines (1). Thereafter, images and structures are exported in DICOM format into the commercial treatment planning system (TPS), BrachyVision 8.1 (Varian). Shortly after the export of the image data set, the treatment planning procedure starts.

Fig. 1. Comparison of the dose distribution of an arbitrary patient using conventional planning (CP; a) and inverse planning (IP; b). White arrows outline the major differences between those two planning types: The CP leading to more dosage to the organs at risk (1), the IP creating hot spots within the clinical target volume (2).

Inverse planning approach So far, a forward planning or conventional planning (CP) method of adjusting dwell times to optimize the dose distribution of an HDR-prostate implant has successfully been practiced (4) using distances between dwell positions of 5 mm in each catheter. Despite strong arguments suggest a mathematical approach to treatment planning, the former method of manual optimization keenly depends on the planning physicist’s experience and consumes between 10 and 15 min time. Also, the latter accepted treatment plan will surely meet the therapist’s requirements, but cannot account to be the truly optimal plan, so that there exists no better solution to escalate more dose to the target volume or less to the OAR. The mathematical approach to dose optimization defines dose constraints to all structures in advance, an optimization algorithm determines independently of the user and within short time (one minute) the best possible dwell time distribution according to those chosen boundary conditions. This change of perspective in planning organization has contributed to the term of

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applicable treatment plans meeting the clinical constraints chosen in advance. We used the following doseevolume parameters as optimization constraints for the abovementioned structures: 1. Minimal/maximal dose within a structure, 2. Percentage of the volume considered for maximum/ minimum dose (doseevolume histogram [DVH] parameters), 3. Priority of the structures, 4. Maximum of time at a single dwell position, 5. Starting time for all dwell positions, 6. Priority of homogeneity (‘‘Smooth’’).

Fig. 2. Implantation scheme for the presented high-dose-rate prostate boost brachytherapy. The CTV2 is defined as the envelope of threedimensional hulls (0.5 cm) around the applicator needles. CTV 5 clinical target volume.

‘‘inverse planning’’ (IP) or ‘‘inverse dose optimization’’ in the literature (11). Before using IP routinely with a newer version of our TPS, BrachyVision 8.8 (Varian), a retrospective study of 38 implants of 20 patients took place in our clinic. For anatomy-based inverse dose optimization, two CTVs are delineated: the CTV2 (peripheral zone) is usually not clearly visible in TRUS, in particular after insertion of the implant needles. Thus, the CTV2 is objectively defined as the envelope of 0.5-cm diameter hulls around the applicator needles, completely lying within CTV1 (whole prostate gland), the second CTV (Fig. 2). For IP calculation of this study, contouring of the former plans had not been changed, and ultrasound pictures and contour margins were exported to BrachyVision 8.8 (Varian) before the calculation took place. As we considered a group of patients who had been treated throughout the year of 2011, contouring was done by several physicians working in our BT department; the 38 patients represent a good crosssection of their technique at our clinic. Nevertheless, contouring of the corresponding IP plan to its ‘‘former’’ CP plan has not changed for CTV1 and the OARs defined as urethra and ventral rectal wall. Choosing dose constraints for each structure is the most important interface between a mathematical optimal solution and its clinical practicability. It is important to point out that clinical and mathematical constraints are no 100% match, the latter defining the ‘‘working area’’ for the optimization algorithm within the planning software. These input constraints are crucial to optimize the dwell time distribution to produce

Inverse plans of the 38 implants were computed, which had originally received BT treatment in our clinic in 2010/2011 using CP. The IP results were compared against those existing CP by using D90 CTV1,2; V200 CTV1,2; D2 cc rectum; D0.1 cc urethra; dose nonhomogeneity ratio (DNR) 5 V150 value divided by V100 value, and conformal index (COIN) 5 CTVref/ OAR CTV  CTVref/Vref  PN i 5 1 (1  VOARref,i/VOAR,i)(12).Statistical significance of the differences between those planning types ( p!0.05) was analyzed by the ManneWhitney rank sum test. Starting condition for all dwell positions was 3 s using a nominal 370GBq 192Ir source. Calculation time for the IP algorithm in the TPS was 1 min, maximum dwell time of 10 s was allowed, and dwell time smooth function was set to maximum of 100%. The function ‘‘Smooth’’ intends to increase homogeneity of the whole dwell time distribution to minimize the occurrence of hot spots (high amount of dosage in small volumes) as suggested in Ref. (13). Table 1 shows our predefined IP template we used to calculate the IP plans for all our considered patients. Priority ‘‘0’’ of the rectum wall might seem surprising. But after elaborate exploration of the algorithm’s convergence behavior according to the given constraints, it had been observed to do better without prioritizing the rectum. Achieving evenly distributed dwell times is also crucial concerning the robustness of a treatment plan owing to errors that may occur in localization or positioning of dwell locations and hence spatial uncertainties in dose delivery. Therefore, homogeneity should also be considered as a major priority within the optimization process. Reasons

Table 1 Dose constraints used for inverse dose optimization Dose constraints

Min/Max

Prostate (CTV1) Min Peripheral Zone Min (CTV2) Urethra Max Rectum Max Maximal dwell time: 10 s Starting dwell time: 3 s Smooth: 100%

Percentage (%)

Dose (Gy)

Priority

95 95

8 15

250 100

5 5

8 8

90 0

CTV 5 clinical target volume.

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that lead to error in determining dwell location are diverse, they range from physical positioning error of the source itself within the system, imaging uncertainty in locating applicators, to needle displacement owing to patient movement or simply treatment time and have been subject of explicit investigation elsewhere (14, 15). Hence, to investigate the general nature and differences of robustness in CP and IP plans in our study, we looked into dose alteration, varying dwell positions of a randomly picked patient. Both CP and IP treatment plans were recalculated with their original dwell times held constant, but their dwell positions varied separately for 1 mm in any spatial direction, namely x(lateral left: þ/lateral right: ), y (anterior: þ/posterior: ), and z (cranial: þ/caudal: ), the drift of the parameters D90 CTV1,2; V100 CTV1,2; D2 cc rectum; and D1 urethra being analyzed. We considered a 1mm shift of all applicators in total. The 1mm range corresponds to the dimension of multiple positional errors or changes studied in literature, for example, being the dimension of positional uncertainty for source localization within the applicator system suggested in Ref. (16) or localization uncertainty owing to imaging modalities (17), respectively.

Results All inverse plans of this study had been calculated with the same startingdand boundary conditions and IP template. Table 2 shows the means for all patients of the DVH parameters considered, as well as COIN and DNR index. The treatment plans obtained by this IP module have proven similar in target volume coverage, and quality indices to the ones optimized by the former manual method (CP). In Fig. 1, the dose distribution of an arbitrary patient plan by CP (upper) and IP (lower) is presented. Main

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differences between the two planning types are outlined by white arrows ‘‘(1)’’ and ‘‘(2).’’ The ‘‘(1)’’ indicates a socalled ‘‘hot spot’’ that occur in some cases in IP technique, whereas CP delivers often more dosage to the OARs as it is shown close to the urethra at ‘‘(2).’’ The value of D90 CTV1 for CP was shown to be 5.62 Gy, whereas for IP it was 5.63 Gy. For the periphery of the prostate, the D90 was also similar between CP and IP: 11.03 and 10.89 Gy, respectively. Only V200 CTV2 is significantly lower for CP than for IP, 5.76% vs. 8.14%. Doses delivered to the OARs require a closer look when IP is used. Considering the total of the 38 plans used in this study, the IP technique fairly reduced (not statistically significant, p 5 0.05) the D0.1 cc urethra. Despite, after performing a sub-study of the OAR results, it could be shown that the mean of the D0.1 cc urethra has been raised owing to 4 single patients, whose IP plans had proven to be particularly poor in result owing to general IP limitations, discussed in the next section. Figure 3 shows the D0.1 cc urethra for all 38 implants considered. The D0.1 cc urethra is displayed for CP (black), IP (blue), and IP* (red), the latter representing IP without the four specific patients mentioned previously. The analysis performed without those spikes shows a statistically significant reduction of the urethral dose D*0.1 cc urethra in IP plans: 9.57 Gy for CP vs. 8.94 Gy for IP, p-value lower than 0.01. This also represented the outcome of a blinded manual evaluation of IP and CP plans in respect to target coverage and sparing of OARs, undertaken by experienced physicists and physicians at our clinic. As COIN values are not changing using either method, values of DNR (index ranges from 0 to 1.0; a low DNR value indicates a high dose homogeneity for the implant) show a mild increase for the IP technique.

Table 2 Dosimetric and quantitative parameters used for analysis Parameters

Conventional planning

Inverse planning

p-Value

D90 CTV1 (Gy) D90 CTV2 (Gy) V200 CTV1 (%) V200 CTV2 (%) DNR CTV1 DNR CTV2 COIN CTV1 COIN CTV2 D2 cc rectum (Gy) D*2 cc rectum (Gy) D0.1 cc urethra (Gy) D*0.1 cc urethra (Gy)

5.62 11.03 29.83 5.76 0.70 0.34 0.26 0.54 6.04 6.04 9.57 9.57

5.63 10.89 29.87 8.14 0.68 0.36 0.30 0.52 6.12 6.00 9.02 8.94

0.67 0.38 0.80 !0.01 0.87 !0.01 0.17 0.86 0.09 0.32 0.34 !0.01

CP 5 conventional planning; IP 5 inverse planning optimization; CTV 5 clinical target volume; DNR 5 dose nonhomogeneity ratio; COIN 5 conformity index. The means of 38 plans considered are shown. Statistically significant is the difference in V200 CTV2 and the reduction of the urethral dose of D*0.1 cc urethra.

Fig. 3. Parameter D0.1 cc urethra for the 38 implants considered. Following color code was used: CP, black; IP, blue; IP*, red. The spikes of the blue (IP) line have shown to be owing to unsatisfactory contouring in the planning process. CP 5 conventional planning; IP 5 inverse planning. (For interpretation of references to color in this figure legend, the reader is referred to the web version of this article.)

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In terms of robustness of the created plans, again the CP and the IP method have shown to be quite similar. Figures 4ae4c shows the magnitude of the mean deviation of the delivered dose in percent in every spatial direction for CP and IP planning. Figure 4d demonstrates a comparison of the dwell time distribution for CP and IP of the patient chosen. The mean deviation of the doses in x- and z-direction shows values well lower than 2%. The highest variation of the delivered dose via both planning methods is owing to uncertainty in the y-direction, which is most likely to be caused by the lack of symmetry of the applicator arrangement to the x-plane. In direct comparison of the y-uncertainty, the IP planning method shows a smaller dose variation in all considered dosimetric parameters. Apart from the similar dosimetric outcome between CP and IP, the planning time is of deep interest in clinical practice. The CP between 10 and 15 min are necessary for the planning process. In this study, we presented IP results with 1 min calculation time. Even if a manual refinement would be necessary, the IP technique is faster when using an appropriate planning template.

Discussion This study showed that the usage of IP algorithms for HDR prostate boost techniques with complex CTV arrangement can yield similar and even better dosimetric results as a CP technique as shown in Table 1, especially finding a proper solution of the optimization problem-yielding opposing goals. Sparing the OAR without losing too much target coverage seems to be the most promising feature of

the IP approach, its most vulnerable phase within the contouring of the anatomic structures beforehand. The spikes of the D0.1 cc urethra for IP shown in Fig. 3 that lead to an artificial rise in the mean of the urethral dose D0.1 cc urethra have occurred in treatment plans, in which the contouring has retrospectively not proven to be completely satisfactoryda fact that is easily accounted for by the CP method in increasing or decreasing dosage to certain region of a structure by hand. A margin drawn generously or tightly will always limit an anatomy-based optimization method in producing an optimal plan, so exact contouring is even more essential to plan quality than in any manual planning method. Apart from this, reduction in dose is correlated to a decreasing risk of acute and chronic toxicity to the genitourinary and gastrointestinal tract, which generally occurs only at a low rate in our clinic (4). Regarding COIN and DNR shown in Table 1, low absolute values for CTV1  COIN (and high ones for DNR) in both planning methods are owing to the definition of the second target volume CTV2 with a higher prescription dose completely located within CTV1. Absolute values of a CTV1  COIN and DNR are therefore not applicable as parts of the CTV1 receive almost twice its prescription dose on purpose. However, the COIN of CTV2 corresponds well to COIN values shown in the literature (18, 19). Both planning techniques do not statistically differ from each other. However, IP DNR values are significantly higher ( p 5 0.01) than for CP. This is most probable owing to the hot spot problem, occurring even with the smooth function set to 100%, still remaining a field of research for algorithm programmers. The hot spots are taken care of by manual adjustment of the treatment plans in question as discussed later in this section.

Fig. 4. (aec) Magnitude of the mean deviation of dosimetric parameters considered in three spatial directions: x (lateral left: þ/lateral right: ), y (anterior: þ/posterior: ), and z (cranial: þ/caudal: ). (d): Dwell time histograms for CP and IP. CP 5 conventional planning; IP 5 inverse planning.

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It should be mentioned that the described implant technique is owing to the two CTVs concept intrinsically inhomogeneous. The COIN and DNR are used here to compare the IP and CP method, not to minimize dose homogeneity. The robustness of both methods in the considered patient has shown to be rather comparabledwith the IP doing seemingly better on the shifts in the y-direction, which might be owing to a larger amount of applicator used. The relative deviations in both the x- and the z-directions are in the range of 2%, which do fit in the statistical context of other studies for shifts in the range of above 1 mm, such as in Refs. (15, 19). Planning time can be reduced using IP technique. Even an experienced medical physicist needs longer than 1 min to create an adequate CP treatment plan. Another advantage is to have a more observer-independent planning when using IP. Furthermore, the time-saving factor is not only of logistic relevance in the clinical routine but also contributes to overall quality of the treatment. Apart from the benefit of a shortened time under anesthesia, Milickovic et al. (15) showed a negative correlation between plan quality and an increasing time gap from primary imaging to actual radiationdamong other demonstrated in statistically significant decrease of DVH parameters recommended by Groupe Europeen de Curietherapie and the European Societyfor Therapeutic Radiology and Oncology and European Association of Urology and COIN (1). The study concentrated on the influence of patient movement and anatomy changes on plan quality at different times during their HDR treatment protocol. Time period considered in Ref. (15) between needle implantation and beginning of radiation was about 50 min, which corresponds quite well to our former CP schedule. In clinical routine, the quality of a treatment plan is primarily measured by target volume coverage. To increase the latter beyond the coverage achieved by the IP planning approach in this study, it is possible to either vary priorities of the CTVs in the IP template, adjusting the boundary conditions for the optimization algorithm for each patient or, more generally applicable, by manual readjustment of the calculated dwell times by the physicist after computational optimization. Within this process, one also deals with the elimination of hot spots whenever they have appeared to be not tolerable. Different methods of optimization were investigated (20) concerning target coverage and dosage to OARs and showed for an anatomy-based IP planning approach implemented in PLATO BPS 14.2 (Nucletron, an Elekta company, Elekta AB, Stockholm, Sweden), an increase of target coverage by (53  11)% to (74  8)% by increasing urethral constraints (tuned inverse optimization) and eventually with further graphical (manual) optimization a target coverage of (90  3)% with an urethral dose now held constant. In our experience, manual readjustment done after using IP has shown not to take longer than 2 min. The number of modification used was low, but they were able to increase

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target coverage in means of V100 CTV2 by 7%, accepting an accompanying mild increase of urethral dose. This indicates promising further dosimetric improvement options via IP. Conclusion In this study, it is demonstrated that the application of IP algorithms for HDR prostate boost techniques can improve dosimetric quality in contrast to CP technique, when two CTVs are used. Treatment planning time can be reduced from 10e15 min using CP down to 1 min for IP plus sometimes additional 2 min for manual adjustments. A case study showed that plan robustness of CP and IP treatment plans are similar. However, manual inspection of the mathematically optimized IP plans cannot be abandoned, as in some cases small adjustments can improve IP quality even further, mostly in favor of CTV coverage. Acknowledgment The authors would like to thank Varian Medical Systems, Inc., for the technical support of this study. References [1] Kovacs G, P€otter R, Loch T, et al. GEC/ESTRO-EAU recommendations on temporary brachytherapy using stepping sources for localized prostate cancer. Radiother Oncol 2005;74:137e148. [2] Rodriguez RR, Nag S, Mate TP, et al. High dose rate brachytherapy for prostate cancer: Assessment of current clinical practice and the recommendations of the American Brachytherapy Society. J Brachy Int 2001;17:265e282. [3] Yamada Y, Rogers L, Demanes DJ, et al. American Brachytherapy Society consensus guidelines for high-dose-rate prostate brachytherapy. Brachytherapy 2012;11:20e32. [4] Galalae R, Kovacs G, Schultze J, et al. Long-term outcome after elective irradiation of the pelvic lymphatics and local dose escalation using high-dose-rate brachytherapy for locally advanced prostate cancer. Int J Radiat Oncol Biol Phys 2002;52:81e90. [5] Kovacs G, Galalae R, Loch T, et al. Prostate preservation by combined external beam and HDR brachytherapy in nodal negative prostate cancer. Strahlenther Onkol 1999;175(Suppl. II):87e88. [6] Aebersold DM, Isaak B, Thalmann G, et al. Applicability and dosimetric impact of ultrasound-based preplanning an high-dose-rate brachytherapy of prostate cancer. Strahlenther Onkol 2004;180:351e357. [7] Siebert FA, Kuhlmann M, Kovacs G. Enhanced quality of HDRinterstitial prostate implants due to online-planning procedure. Radiother Oncol 2006;81:S445. [8] Kovacs G, Melchert C, Sommerauer M. Intensity modulated high-doserate brachytherapy boost complementary to external beam radiation for intermediate- and high-risk localized prostate cancer patientsdHow we do it in L€ubeck/Germany. Brachytherapy 2007;6:142e148. [9] ICRU. Dose and volume specification for reporting interstitial therapy. ICRU Report 58. Bethesda, MD: International Commission on Radiation Units and Measurements; 1997. [10] Siebert FA, Hirt M, Niehoff P, et al. Imaging of implant needles for real-time HDR-brachytherapy prostate treatment using biplane ultrasound transducers. Med Phys 2009;36:3406e3412. [11] Lessard E, Pouliot J. Inverse planning anatomy-based dose optimization for HDR-brachytherapy of the prostate using fast simulated

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[16] Nath R, Anderson LL, Meli J, et al. Code of practice for brachytherapy physics: Report of the AAPM Radiation Therapy Committee Task Group No. 56. Med Phys 1997;31:1557e1598. [17] Yongbok K, Hsu I, Lessard E, et al. Dose uncertainty due to computed tomography (CT) slice thickness in CT-based high dose rate brachytherapy of the prostate cancer. Med Phys 2004; 31:2543e2548. [18] Sumida I, Shiomi H, Yoshioka V, et al. Optimization of dose distribution for HDR brachytherapy of the prostate using attractionrepulsion model. Int J Radiat Oncol Biol Phys 2006;64:643e649. [19] Fr€ohlich G, Agoston P, L€ovey J, et al. Dosimetric evaluation of highdose-rate interstitial brachytherapy boost treatments for localized prostate cancer. Strahlenther Onkol 2010;186:388e395. [20] Kolkmann-Deurloo IK, Deleye X, Jansen PP. Anatomy based inverse planning in HDR prostate brachytherapy. Radiother Oncol 2004;73:73e77.