Idealized line source configuration for permanent 125I prostate implants

Radiotherapy and Oncology 72 (2004) 213–220 www.elsevier.com/locate/radonline

Idealized line source configuration for permanent

125

I prostate implants

Ghyslain Leclerca,b,*, Marie-Claude Lavalle´ea,b, Dragan Tubica,c, Julie Me´tiviera,b, E´ric Vigneaulta, Luc Beaulieua,b a

De´partement de radio-oncologie et Centre de recherche en cance´rologie, Centre Hospitalier Universitaire de Que´bec, Pavillon Hoˆtel-Dieu, 11 Coˆte du Palais, Que´bec, QC, Canada, G1R 2J6 b De´partement de physique, ge´nie physique et optique, Universite´ Laval, Que´bec, QC, Canada, G1K 7P4 c De´partement de ge´nie e´lectrique et ge´nie informatique, Universite´ Laval, Que´bec, QC, Canada, G1K 7P4 Received 12 August 2003; received in revised form 17 March 2004; accepted 22 April 2004 Available online 19 June 2004

Abstract Background and purpose: To validate the use of idealized seed orientations in conjunction with the line source formalism for post-implant dosimetry of permanent 125I prostate implants. Patients and methods: Post-implant, a CT scan and three fluoroscopic images were obtained for 32 patients having undergone permanent implants. From these images, the seed positions and orientations ðf; uÞ were determined (1625 individual seeds). Two different dosimetric calculations were done: one using real orientations and one using idealized orientations (seeds along the axis of implantation). Dose volume histograms (DVHs) and key dosimetric parameters were compiled for the prostate, urethra, rectum, bladder and penile bulb, to evaluate the difference between the two approximations. Results: The f angle distribution ðf
¼ 1:18; sf ¼ 22:98Þ and the u angle distribution ðu
¼ 24:298; su ¼ 27:18Þ were found to be similar to the first order except for the pronounced peak of the f angle distribution. The DVHs comparison and dosimetric parameters study reveal no significant difference between the two approximations. The difference in D90 for the prostate was only 0.02% ðs ¼ 0:91%Þ: The differences were slightly higher in the case of the organs at risk, as expected from the dosimetric characteristics of the seed model used. Conclusions: The angular distributions ðf; uÞ of individual seeds were determined. The dosimetric evaluation shows that line source formalism can be used in conjunction with an idealized seed configuration presented here to report prostate and organs at risk dose coverage. q 2004 Elsevier Ireland Ltd. All rights reserved. Keywords: Prostate; Brachytherapy; Seed implants; Post-implant dosimetry; Anisotropy; Line source

1. Introduction The American Brachytherapy Society (ABS) recommends that post-implant dosimetry should be performed on all patients undergoing permanent prostate brachytherapy for optimal patient care [12]. This requires a post-implant dose calculation. The dosimetric quality of a delivered implant in permanent prostate brachytherapy is a topic of great interest in recent literature [1,3,8,11,17]. To this day, no analytical model is available to deal with dose calculations using real 3D-shaped sources. As a result, approximations must be used in order to simplify calculations and reduce the computation time. The American Association of Physicists in Medicine Radiation Therapy Task Group No. 43 (TG-43) [13] describes two of those approximations: the point source and the line source. In * Corresponding author. 0167-8140/$ - see front matter q 2004 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2004.04.001

clinical practice, most centers use the point source formalism to evaluate the dose delivered to the organ being treated, mostly because the line source formalism requires the orientation of the sources which is not easily determined. Still, considering the always growing speed of modern computers, the line source formalism is becoming one that could be used regularly. In spite of the ongoing debate as to which formalism should be used in clinic, one can widen the scope of the investigation regarding the line source approximation. Should this formalism be found to be more adequate than the point source one, its implementation in a clinical practice might still not be simple because of the needed source orientations. Previous studies [5,7,15] have addressed, within certain assumptions, the dosimetric differences for the target volume between line source and point source formalisms (seed anisotropy). The results of these studies indicate that the effects of the line source

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configuration are not completely negligible on the postimplant dosimetry. However, the real seed orientations were not known nor used in these studies and some approximations had to be made for at least one of the angles. The investigation led here allows the individual seed orientation distribution to be determined. It also seeks to evaluate and validate an idealized source distribution for 125I prostate implants to be used in conjunction with the line source formalism. This configuration of sources will be compared to the real one through the dosimetric evaluation of the target volume and several organs at risk (OARs). Should it prove to be a good approximation, it would allow for the line source formalism presented in TG-43 to be used without having the inconvenience of finding the source orientations. The study has been broken down into two distinct parts. First, a study of the orientation of the individual sources of an implant had to be done in order to establish the difference between the idealized model and the real 3D one. To obtain the distributions, a set of automated algorithms [19,20] has been used. These algorithms can (i) localize the seeds on fluoroscopic images (or films), (ii) give the 3D positions and orientations of those seeds and (iii) match the seeds with the CT dataset, all within minutes only. The second part of the research implied a dosimetric study for the target volume and the following OARs: urethra, rectum, bladder and penile bulb. Following the localization of the sources, post-implant dosimetric calculations using the line source formalism were done on 32 clinical cases. Two different configurations of sources were studied. The first one uses an idealized situation in which the sources are all aligned along the axis of implantation. The second case uses the real 3D configuration determined by using the above mentioned reconstruction algorithms. A comparison between those situations has been done using dose volume histograms (DVHs) and relevant dosimetric quantities such as D90 and V100 :

2. Methods and materials 2.1. Considered cases The post-implant dosimetry of 32 clinical cases was studied. Each patient was implanted with loose seeds (no rapidstrand used) of the Amersham Health 6711 125I source model. The average air kerma strength of a single source was 0.53 mCi (0.67 U) with a standard deviation of 0.04 mCi (0.05 U). The planning of the implants was performed using an in-house inverse planning system (IOdose) based on simulated annealing using an ultrasound image dataset [2,14]. The prescription dose was 144 Gy as suggested in the paper by Luse et al. [9] on the implementation of TG-43 for iodine implants. Then, about 42 days after the implantation (s ¼ 5 days), a CT data set was obtained as well as three fluoroscopic images for each

case. The CT images were used to determine a target volume and allowed for the organs at risk to be contoured by an oncologist. The considered OARs are the urethra, the rectum, the bladder and the penile bulb. In each of the clinical cases, the fluoroscopic images were used to determine the relative coordinates of the sources which were used in conjunction with the CT images to determine the coordinates of the sources within the prostate. Then, a dosimetric calculation was done for two different configurations for each contoured organ: † Configuration 1: line source approximation with all sources aligned along the axis of implantation, i.e. the axis perpendicular to the ultrasound image plane. This axis is identified as the y-axis and is the infero –superior axis. The x-axis is the lateral one and the z-axis is the antero – posterior one. † Configuration 2: line source approximation with the orientations given by the reconstruction algorithms. 2.2. Particular OAR: the urethra Usually, because of patient discomfort, no catheter is inserted in the urethra when the post-implant CT exam is done making the urethra practically impossible to contour on CT images. This explains why the urethra was not contoured by an oncologist in 31 of the 32 cases. It was thus decided that a surrogate urethra was going to be used for those 31 cases, since the urethral dose is a good indicator of urinary complications [10] and its knowledge is recommended by the ABS [12]. Such a surrogate urethra was studied by Bucci et al. [4] and has proven to be a good approximation of the real urethra (20 cases in their study) given the small dosimetric differences found. An in-house algorithm generating the surrogate urethra was used. The urethra’s position and size were determined using the statistics of 105 clinical cases. For each of those cases, the urethra and the prostate were contoured on a set of ultrasound images. Then, for every slice of a particular case, the position of the center of the urethra relative to the center of the prostate’s contour ðrxz Þ was determined. This information is crucial to the model. In order to determine that quantity, the position, on the slice considered, of the geometric center of the urethra’s contour (uc) was found. Then, all that is needed is the center of the prostate’s contour (pc) which allows one to evaluate: ðrxz Þi ¼ uc 2 pc

ð1Þ

where ðrxz Þi is the position of the center of the urethra relative to the center of the prostate’s contour for the ith slice. The radius ðRÞ of the urethra was found as well, but it should be emphasized that this radius generally depends on the inserted catheter. Still, the radius was obtained by finding the geometric center of the urethra’s contour (on the slice considered) and evaluating the average difference

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between the points of this contour (uc) and the center that has been determined: Ri ¼ kuc 2 up k

ð2Þ

where Ri is the radius of the urethra for the ith slice of the prostate. Having these information, it is possible to generate the contour of a surrogate urethra for each slice and, by doing so, take into account the curvature of the urethra from the base (first slice) to the apex (last slice). The generated urethra is only the segment of the urethra that is inside the prostate. 2.3. Reconstruction algorithms The 3D reconstruction algorithms [19,20] used in this study extract the 3D coordinates of the implanted seed cluster from three fluoroscopic images (obtained from three different angles). These algorithms use mathematical morphology to detect the center of the seeds as well as their orientation on the image plane. This information (centers and orientation in 2D) is then used to perform 3D reconstruction by matching seed projections using simulated annealing. The algorithms output the center and orientation of the seeds in 3D space. The orientations are precise within 58 for 75% of the cases [20]. In the first case (Configuration 1) discussed in Section 2.1, the algorithms use the fluoroscopic images to reconstruct the ðx; y; zÞ coordinates of the sources centers. These are then modified to obtain the coordinates of the ends of a source of length l with its center situated at the ðx; y; zÞ point, thus: ðx; y 2 l=2; zÞ and ðx; y þ l=2; zÞ with the chosen value of 4.5 mm for l: This generates a source of length l aligned with the y-axis which is the axis of implantation. In the second case (Configuration 2), the algorithms provide the needed coordinates directly, i.e. the ðx1 ; y1 ; z1 Þ and ðx2 ; y2 ; z2 Þ coordinates of both ends of each source. A real 3D seed distribution is therefore obtained and no assumptions are made as to the angular distribution of either angle (f or u, see Fig. 1), a situation which differs from several anisotropy studies [5,7] in which assumptions had to be made for the source orientation. In fact, this information can be used to determine the angular distribution of the source orientations in an implant. 2.4. Seed orientation Once the reconstruction and the acquisition of the source coordinates had been achieved, a study of the angular distribution of the seeds was done. The total number of seeds considered in this study is 1625 (the number of seeds in the 32 clinical cases). For each of those, the angular coordinates ðf; uÞ were determined through a simple transformation from cartesian coordinates to spherical

Fig. 1. Angular coordinates definition for the angular distribution of the sources.

ones. Fig. 1 shows the definition of the coordinates as well as that of the angles for the angular distribution study. As can be seen, the f angle can be determined by:
 y2 2 y1 f ¼ atan 2 908 ð3Þ x2 2 x1 and is measured counterclockwise from the y-axis on the xy plane. As for u, it can be obtained from:
 z 2 z1 u ¼ 908 2 acos 2 ð4Þ l where l is the length of the source. It is measured counterclockwise in the zy plane between the projection of the source on the xy plane and the source itself. Both angles have been defined from 2 908 to 908. Those values cover all possible orientations considering the symmetry of the cylindrically shaped sources (model 6711). 2.5. Dose calculations The formalism used in the dose calculations is the one recommended in the TG-43 [13] of the American Association of Physicists in Medicine (AAPM). The TG-43 document [13] defines the dose rate of a line source as: _ ¼ LSk Gðr; uÞ gðrÞFðr; uÞ D Gðr0 ; u0 Þ

ð5Þ

where the coordinates are the ones recommended, hence L is the dose rate constant; Sk is the air kerma strength; Gðr; uÞ is the geometry factor; gðrÞ is the radial dose function and Fðr; uÞ is the anisotropy function. The geometry factor in (5) is defined as: Gðr; uÞ ¼

ð u2 2 u1 Þ Lr sin u

ð6Þ

where the variables are again defined in TG-43 [13]. In this study, data for the radial dose function ðgðrÞÞ was taken from a paper by Heintz [6] and data for the

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anisotropy function ðFðr; uÞÞ was taken from another paper by Weaver [21]. All dosimetric calculations were done using the commercial software Theraplan Plus version 3.8 by MDS Nordion. The source model is, as mentioned, the Amersham Health 6711 model. The resolution of the dose grid was 2 £ 2 £ 2 mm3. The technique chosen to evaluate the quality of the implants was to compare the DVHs of the different contoured organs for the two approximations. Some key dosimetric quantities have also been considered. The symbolism used in this paper is that Dx stands for the dose received by x% of the considered volume while Vx stands for the volume that has received at least x% of the dose.

3. Results and discussion 3.1. Angular distributions Fig. 2a and b respectively, show the angular distributions obtained for the f and u angles of the source orientation study. The total number of sources, as previously mentioned, is 1625. The angular bin size was chosen to be 58. Inspection of Fig. 2a shows that the f distribution has a very narrow peak centered on the f ¼ 08 value. Approximately 30% of the sources are oriented within ^ 2.58 around the central value of the distribution. The standard deviation is 22.98. On the other hand, the u angle has no highly peaked center. The mean value of this angle is 2 4.308 and the standard deviation is 27.18. The value of 2 4.308 is interesting since there is no reason, a priori, for a preferential seed direction after the implantation. A non-zero average orientation should be the result of a non-zero needle insertion angle. Another interesting remark is the fact that even though they are graphically different (as can be seen from Fig. 2a and b), the standard deviations of the two distributions differ only by 4.28. Both these assertions are corroborated in a previous study by Taschereau et al. [18] in which the needle and seed characteristics at our institution are shown (Tables 1 and 3 of Ref. [18]). In that paper [18], it is found that the mean needle insertion angle is not zero for the u angle and that the mean displacement is not zero either. Therefore, to first order, these distributions are similar and their average is related to the average needle insertion angle. It should be noted that these results differ significantly from the distributions originally proposed by other studies [5,7]. The distributions used in these studies are usually Gaussian (or measured) for the f angle and uniform for the u angle. Therefore, the conclusions of theses studies should probably be revised to take into account the seed orientation distributions measured here.

Fig. 2. Angular distributions of the f and u angles. In (a), the f angle is depicted while in (b), it is the u angle that is depicted.

3.2. Dose volume histograms The DVHs shown in Figs. 3 and 4 are those obtained in the two different situations for each contoured volume. Fig. 3a represents the case of the prostate (PTV) while Fig. 3b shows DVHs obtained for the urethra. Fig. 4a – c depict, respectively, the cases of the rectum, bladder and penile bulb. These are the results of one clinical case, but they are a representative example of the average behavior of the other cases encountered in this study. For all other cases, the DVHs were not necessarily of the same shape, but the distance between the two different curves (real 3D and idealized) is close to zero in each and every case. Since the comparison between the idealized situation and the real situation is the aim of this particular study, those curves are good evaluation tools. They show that the difference between the two configurations of sources are very small considering that the curves are usually overlaid onto each other or, when separated, the difference

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Fig. 3. DVHs for one clinical case studied. The organs are (a) the prostate and (b) the urethra.

between them is very small. The largest differences are observed in the case of the urethra for the small volumes receiving high doses. 3.3. Dosimetric quantities: boxplots A standard boxplot (see Fig. 5) of three of the relevant dosimetric parameters ðD10 ; D90 ; V100 Þ was made to compare in a compact manner some general characteristics of all considered cases. On those graphs, the bottom and top of the box are, respectively, the first and third quartile; the line and the point inside the box give the median and the average, respectively; the whiskers represent the largest and smallest observed values that are less than 1.5 box lengths from the end of the box; the points outside of the range (whiskers) are the outliers. As can be readily seen, the two boxplots associated to a single organ for a specific dosimetric value are quite similar and therefore, the dosimetric parameters are the same as expected from the DVH study. It should be noted that even though every dosimetric parameter was not plotted, the ones shown represent the general behavior for all cases in this study. 3.4. Dosimetric quantities Six different values were extracted from every DVH: D10 ; D50 ; D90 ; V100 ; V150 and V200 : For each quantity, a study

Fig. 4. DVHs for one clinical case studied. The organs are (a) the rectum, (b) the bladder and (c) the penile bulb.

of the difference between the quantity obtained from the real configuration and that obtained from the ideal configuration was used to further evaluate the plans. For the dose values ðDx Þ; the relative differences were

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used. Since the real configuration of sources is considered more accurate than the ideal one, its value was used as the normalization point in each case. Thus, the relative difference for dose values is defined as: ! Drx 2 Dix 100 ð7Þ DDx ¼ Drx where Drx ðDix Þ is the value taken from the plan which used the real (ideal) configuration of sources. The average values of those differences for each organ and each quantity are reported along with their standard deviations in Table 1. For the volumetric quantities ðVx Þ; the differences were used to characterize the plans. This was seen as representative because the relative volumes have been used in the DVHs. Thus, the differences for volumetric values are defined as: DVx ¼ Vxr 2 Vxi

ð8Þ

where the same index convention is used. Table 2 contains the average and standard deviation of the values. It should be noted again that because the volumes gathered are relative volumes (this can be observed on the DVHs of Figs. 3 and 4), the units of the differences obtained from Eq. (8) are percentages. 3.4.1. Prostate The values of Tables 1 and 2 show that for the prostate, the idealized and real configurations have the same dosimetric parameters within 2%. The differences average to very small values and the standard deviations are small as well. From this analysis, one can thus confirm the results obtained from the DVH and boxplot studies for the prostate. 3.4.2. OARs Except for the dose values (Table 1) in the penile bulb case, the dosimetric parameters of the OARs are similar between the two approximations. The differences are slightly higher than in the prostate case (ranging in value from 0.02 to 7.85%), but geometrical considerations should be taken into account to explain this fact. The position of the OAR considered relative to the prostate and axis of implantation can influence the results obtained when comparing the two source configurations. The radiation emitted by a source is most anisotropic at its tips, where the strongest underdosage is located. If all sources are aligned, Table 1 Mean values of the differences defined in Eq. (7) for the Dx

Fig. 5. Boxplots of (a) D10 ; (b) D90 ; and (c) V100 : On those graphs, the bottom and top of the box are, respectively, the first and third quartile; the line and the point inside the box give the median and the average, respectively; the whiskers represent the largest and smallest observed values that are less than 1.5 box lengths from the end of the box; the points outside of the range (whiskers) are the outliers.

Organ


10 DD (%)

sD10 (%)


50 DD (%)

sD50 (%)


90 DD (%)

sD90 (%)

Prostate Urethra Rectum Bladder Penile bulb

0.05 20.94 21.14 1.57 6.05

0.78 1.95 1.95 3.09 4.86

20.34 21.04 22.45 0.89 7.85

0.49 1.27 2.75 4.01 5.51

0.02 20.91 23.62 21.81 7.41

0.91 1.78 4.08 6.64 11.82

G. Leclerc et al. / Radiotherapy and Oncology 72 (2004) 213–220 Table 2 Mean values of the differences defined in Eq. (8) for the Vx Organ

DV
100 (%)

sV100 (%)

DV
150 (%)

sV150 (%)

DV
200 (%)

sV200 (%)

Prostate Urethra Rectum Bladder Penile bulb

20.04 20.58 20.11 0.02 0.11

0.37 1.57 0.14 0.19 0.47

20.26 21.85 20.02 0.02 0.01

0.44 2.24 0.09 0.08 0.08

20.02 20.77 20.01 0.02 0.02

0.4 1.8 0.03 0.08 0.13

the organs located outside the cluster on the end of the seeds (which is approximately the case for the bladder and the penile bulb) should be underdosed compared to the situation with the real source configuration. The fact that most of the mean differences in dosimetric parameters are positive for the bladder and penile bulb shows this. When the rectum and urethra are considered, the difference will be reversed because in the real configuration, the tips of some sources will point towards the rectum/urethra making the dose lower in this configuration. The fact that the averages in differences for the dose parameters are negative both for the rectum and the urethra confirms the geometrical arguments again. The effects are less pronounced in the urethra case (e.g. ðDD90 Þurethra ¼ 20:91; ðDD90 Þrectum ¼ 23:62Þ because it is located within the seed cluster and only the seeds closest to the urethra will have the strong anisotropy effect. Because of the rather high standard deviations (e.g. 11.82 for the D90 of the penile bulb), one could argue that the geometric arguments might not be corroborated by the data. The mean could be close to zero and the distribution, symmetric around zero. This would make the sign of the average (þ , 2 ) meaningless. The symmetry was thus tested by verifying the distributions of the differences and determining if these distributions were symmetrical around zero. The results of this study show that the distributions were asymmetrical and had a tendency towards the positive (negative) values for the bladder and penile bulb (urethra and rectum). In short, the results of the parameter study for the OARs seem to indicate that even in their case, the differences are small between the two approximations. This makes it possible to report dose to the OARs using the ideal approximation.

4. Conclusion The study has revealed a highly peaked distribution in the f angle and a wider one for the u distribution. These distributions are different from the ones usually considered when using the line source formalism. These differences between the usual distributions considered and the ones found here suggest that the weighted anisotropy function

219

Fw ðr; uÞ proposed by Corbett et al. [5] should be revised. This function was obtained using a measured distribution for one of the parameters and a uniform one for the other which is clearly not the case from this study. It should be noted though that the results obtained in the above mentioned study are not completely dissimilar from the ones obtained in the present study, suggesting that the modification should result in minor changes. This study also shows, through the comparison of 32 clinical cases, that an idealized line source configuration can be used in conjunction with the line source formalism from the AAPM TG-43 in post-implant analysis without altering the quality of the dose calculations to the prostate. It should be noted that although the seeds studied here were loose seeds, the results should apply just as well to Rapidstand as these seeds, because they are attached in a strand, should have even less difference between the real and idealized configurations. The OARs appear to be more sensitive to the configuration because of their location relative to the source cluster. The dosimetric study indicates that the ideal configuration is a valid one. The absence of a difference between the two configurations studied allows the line source formalism, with the idealized situation, to be used with no more information than is required for the point source formalism. This study says nothing about whether or not the line source formalism should be implemented, i.e. it does not validate the line source formalism. It only illustrates the fact that should this formalism be implemented, as is recommended in the revised version of the AAPM Task Group No. 43 [16], the ideal situation described in this article (sources aligned on the implantation axis) would be a valid approximation of the real 3D configuration of sources for reporting prostate dose coverage. Acknowledgements This research was funded in part by the National Cancer Institute of Canada (NCIC) with funds from the Canadian Cancer Society (CCS) and by Amersham Health. References [1] Al-Qaisieh B, Ash D, Bottomley DM, Carey BM. Impact of prostate volume evaluation by different observers on CT-based post-implant dosimetry. Radiother Oncol 2002;62:267– 73. [2] Beaulieu L, Aubin S, Taschereau R, Pouliot J, Vigneault E. Dosimetric impact of the variation of the prostate volume and shape between pretreatment planning and treatment procedure. Int J Radiat Oncol Biol Phys 2002;53:215 –21. [3] Beaulieu L, Archambault L, Aubin S, Oral E, Taschereau R, Pouliot J. The robustness of dose distributions to displacement and migration of 125 I permanent seed implants over a wide range of seed number, activity, and designs. Int J Radiat Oncol Biol Phys 2004;58: 1298– 308. [4] Bucci J, Spadinger I, Hilts M, et al. Urethral and periurethral dosimetry in prostate brachytherapy: is there a convenient surrogate? Int J Radiat Oncol Biol Phys 2002;54:1235–42.

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