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An open-source genetic algorithm for determining optimal seed distributions for low-dose-rate prostate brachytherapy P. McGeachy1,2,*, J. Madamesila1,2, A. Beauchamp2, R. Khan1,2,3 1

Department of Physics and Astronomy, University of Calgary, Calgary, AB, Canada 2 Department of Medical Physics, Tom Baker Cancer Center, Calgary, AB, Canada 3 Department of Oncology, University of Calgary, AB, Canada

ABSTRACT

PURPOSE: An open source optimizer that generates seed distributions for low-dose-rate prostate brachytherapy was designed, tested, and validated. METHODS: The optimizer was a simple genetic algorithm (SGA) that, given a set of prostate and urethra contours, determines the optimal seed distribution in terms of coverage of the prostate with the prescribed dose while avoiding hotspots within the urethra. The algorithm was validated in a retrospective study on 45 previously contoured low-dose-rate prostate brachytherapy patients. Dosimetric indices were evaluated to ensure solutions adhered to clinical standards. The SGA performance was further benchmarked by comparing solutions obtained from a commercial optimizer (inverse planning simulated annealing [IPSA]) with the same cohort of 45 patients. RESULTS: Clinically acceptable target coverage by the prescribed dose (V100) was obtained for both SGA and IPSA, with a mean
standard deviation of 98
2% and 99.5
0.5%, respectively. For the prostate D90, SGA and IPSA yielded 177
8 Gy and 186
7 Gy, respectively, which were both clinically acceptable. Both algorithms yielded reasonable dose to the rectum, with V100 ! 0.3 cc. A reduction in dose to the urethra was seen using SGA. SGA solutions showed a slight prostate volume dependence, with smaller prostates (!25 cc) yielding less desirable, although still clinically viable, dosimetric outcomes. SGA plans used, on average, fewer needles than IPSA (21 vs. 24, respectively), which may lead to a reduction in urinary toxicity and edema that alters postimplant dosimetry. CONCLUSIONS: An open source SGA was validated that provides a research tool for the brachytherapy community. Ó 2015 American Brachytherapy Society. Published by Elsevier Inc. All rights reserved.

Keywords:

Prostate brachytherapy; Low dose rate; Optimization; Seed distribution; Open source; Genetic algorithm

Introduction Low-dose-rate prostate brachytherapy (LDRPB) is a method of treating prostate cancer through interstitial implantation of small, radioactive seeds throughout the prostate. Numerous regimens have been carried out where LDRPB has been used as either a monotherapy or in conjunction with external beam radiotherapy (EBRT) or hormonal therapy for the treatment of various stages of prostate cancer (1e9). The American Brachytherapy Society has provided an extensive overview and consensus on Received 17 November 2014; received in revised form 16 April 2015; accepted 17 April 2015. * Corresponding author. 1331 29 Street NW, Calgary AB, Canada, T2N 4N2. Tel.: þ14035213139; fax: þ14035213327. E-mail address: [email protected] (P. McGeachy).

the prescriptive recommendations for LDRPB, from patient selection, workup, prescription dose, treatment, postimplant dosimetry, and followup (10, 11). LDRPB has shown its greatest treatment efficacy as a monotherapy for early stage, localized prostate cancer. The desired outcome for any radiation therapy treatment is achieving a conformal distribution of the prescribed dose to the target structure while minimizing the damage done to surrounding healthy structures. While LDRPB is able to provide comparable target coverage to EBRT, it has the added benefit that radiation does not traverse healthy tissue to reach the target structure, resulting in reduced dose to healthy normal tissue. This reduced damage to healthy structures facilitates the ability of LDRPB to escalate the dose to the target when compared with EBRT. However, for LDRPB, the resulting dose distribution is highly dependent on the placement of the seeds within

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the prostate. A poor seed distribution can lead to underdosage of the target structure, as well as overdosage of the surrounding healthy structures. Over the past 3 decades, an extensive amount of research has been taken up with regard to optimizing the seed arrangement that will, in turn, result in a desirable dose distribution for a given prostate patient (12e23). This breadth of research on seed placement optimization led to the commercialization of optimization algorithms that can rapidly and efficiently generate a seed distribution that provides adequate dose coverage to the target while minimizing dose to healthy structures for most organ geometries. However, there have been some limitations to its success in the clinics where the clinically implemented seed distributions are usually a combination of computergenerated seed distributions and the operator’s manual intervention. Although this commercialization has been beneficial for current clinical practice, it does not provide a sufficiently broad platform for further research and investigation that could lead to a more dosimetrically desirable outcome or reduced need for manual intervention and standardization of the procedure for generating reasonable seed distributions. Modern computer algorithms are complex and can interact in a variety of non-intuitive ways, no longer based on a set of simple instructions. Commercial clinical software is also based on copyrights, patents, and legal liability. This restricts the ability to perform quality control of software under various clinical scenarios. In certain cases, the software may not perform as intended by the designer. Recently, there has been a drive to ensure accountability and independent auditing of computer algorithms while staying within the legal jurisdictions. A real open source algorithm can open doors to scrutinize the software but also provides independent quality assurance of clinically used software. An example of the demand and need for open-source software and platforms is evident by the amount of publications that have come out due to the availability of relatively recent radiotherapy treatment planning platforms, such as Computational Environment for Radiotherapy Research (CERR) (24), 3D Slicer (25), and slicerRT (26). Therefore, to further advance optimization of radioactive seed distributions for brachytherapy, the purpose of this study was twofold: (1) To create an open source optimization algorithm that can generate a clinically acceptable seed distribution for a given set of patient contours using commonly available software tools. (2) To validate and benchmark the open-source optimization with a commercial optimizer. Both tasks were realized by performing a retrospective study on a data set of 45 previously contoured prostate patients, where solutions were generated and compared with ones obtained by a commercial optimizer. The open-source optimizer in this study was built around the genetic algorithm (27). There have been some investigations regarding permanent prostate implant optimization using a genetic algorithm as the solver (13, 15).

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These studies have focused on implementing the genetic algorithm on a simplified, ellipsoidal prostate model. Therefore, in addition to providing an open-source, research-ready optimizer, this study differs from the previous in that a relatively large set of real prostate patient files, varying in urethral complexity and prostate volume, was used to test and validate the optimizer.

Methods Simple genetic algorithm This is a stochastic algorithm that uses concepts based on principles of Darwinian Natural Selection (27). Initially, a population of 41 random seed distributions is generated. Four operators: elitism, roulette wheel selection, singlepoint crossover, and single-point mutation operators (Fig. 1) have a user-assigned probability of acting on each seed distribution to generate a new population for the next iteration. The theory suggests that the action of these operators leads to fitter individuals, which in this application are represented by radioactive seed distributions. The elitism operator ensures the optimal solution of the current iteration is not lost by allowing it to pass unaltered to the next iteration of the algorithm. Roulette wheel selection is used to determine which parent seed distributions will be used to create the new distributions for the next iteration. The probability of being selected as a parent is proportional to the individual seed distribution’s fitness score; therefore, fitter seed distributions will have a higher probability of being selected. Once the parents have been selected, the new seed distributions are generated through the action of the singlepoint crossover and mutation operators. The single-point crossover picks a crossover point between a pair of parent distributions and exchanges the portion of the distributions after this crossover point. The single-point mutation operator works by randomly selecting a point where the distribution is mutated by adding or subtracting a seed, based on the current configuration of the seeds. The user-defined objective function then calculates a fitness score for each distribution. The fitness score is a reflection of the distribution’s ability to meet the predetermined optimization criteria. For LDRPB, the desired optimization criteria are to minimize the number of needles and seeds used while covering the entire planning target volume (PTV) with a uniform prescribed dose (144 Gy) while reducing the damage to the surrounding healthy structures, such as the urethra, rectum, and bladder. For simplicity, the urethra was the only critical structure considered in the objective function when determining the optimal seed distribution. The maximum number of iterations assigned to the simple genetic algorithm (SGA) was 25,000, which was determined through trial and error. Once the algorithm reached this iteration threshold, the seed distribution with the highest fitness score was taken to be the optimal solution. The SGA algorithm was encoded and implemented in MATLAB

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Fig. 1. Representation of radioactive seed distributions before (Group A) and after (Group B) the action of the four operators (1. Elitism, 2. Roulette Wheel Selection, 3. Crossover, and 4. Mutation). The order in which the four operators act is depicted by the numbering scheme. Fitness scores for the new distributions are calculated at Step 5. The actions of the operators are depicted by the shading of the seed distributions. Elitism does not change the distribution, therefore, the shading is unchanged; crossover exchanges a portion of the two distributions, hence, the shading mixture in Group B and mutation completely alters a portion of a single distribution, which again is depicted by a completely new shading to a portion of a distribution in Group B.

(MATLAB Release 2012a, The MathWorks, Inc., Natick, Massachusetts, United States). The average runtime to generate an optimal seed distribution was 10 min, run on a dual core 2.80 GHz processor, 1.99 GB RAM HP workstation. To assess the performance of this SGA optimizer, seed distributions were generated for 45 previously contoured prostate cancer patients. For each optimal seed distribution, values obtained for certain clinically relevant pre-implant dosimetric indices (Table 1) were compared with the clinically accepted. The results from SGA were further benchmarked by comparing with seed distributions generated for the same patient cohort using the commercial inverse

Table 1 Dosimetric indices used to evaluate quality of dose distribution from a seed configuration Organ of interest

Dosimetric index

Prostate Urethra Rectum

V100,Pros, V150,Pros, V200,Pros, D90,Pros, DNRa V140,Ureth, V150,Ureth, V160,Ureth, V200,Ureth V100,Rect

Note: Indices with letter V represent relative volume of organ covered by a particular percentage of the prescribed dose (i.e., V100, Ureth is the % of the urethra covered by 100% of the prescribed dose. D90,Pros is the dose (in Gy) delivered to 90% of the prostate. V100,Rect is in units of cubic centimeters (cc). a DNR is the dose non-uniformity ratio, which is the ratio of V150,Pros to V100,Pros.

planning simulated annealing (IPSA) optimization algorithm (28). Formulation of objective function A weighted, penalty-based objective function was used to incorporate dosimetric constraints as well as seed and needle implantation constraints to find the optimal seed distribution. For any point of interest, the dose was calculated based on the one dimensional, point source approximation provided in the AAPM TG-43 report (29). The reasoning for this choice is twofold. First, the SPOT PROÔ system that was employed to calculate the final dose statistics for both IPSA and SGA used the 1D formalism; therefore, the same was used for the SGA code for consistency sake. Second, a recent study performed by Fekete et al. (30) has shown that the seed orientation does not affect main clinical dosimetric quantities of interest in a statistically significant way for the clinical target volume and urethra. For the target structure, dosimetric constraints were represented by two sets of dose points, surface and volume. These sets of points were formulated to ensure that the target is covered by the prescribed dose while attempting to decrease the level of non-uniformity of the dose throughout the prostate. For the urethra, a set of surface dose points were defined to keep the dose to this healthy structure below some clinically tolerable value. The contribution to the objective function for all dose points, regardless of

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the dose set they belonged to, has the same mathematical form. For example, the contribution to the objective function from dose point, i, of dose set x is given by
2 Wmin ðDi  Dmin Þ if Di !Dmin xDi 5 ð1Þ 2 Wmax ðDi  Dmax Þ if Di ODmax Where Wmin and Wmax are the weightings assigned for the penalty below some minimum dose limit Dmin and above some maximum dose limit Dmax, respectively. The weightings and dose limits assigned to each dose-point set are given in Table 2. These values were obtained through optimization runs on a subset of three patients until reasonable distributions were obtained. This scheme was treated as a generalized solution, which was then applied to all 45 prostate patient scans. The total contribution of dose points from dose set x was taken to be the mean of equation (1), P

i xDi

xD 5

ð2Þ

Nx

Where Nx is the total number of dose points for dose set x. The total dosimetric contribution, cd, to the objective function is then cd 5

X xD

ð3Þ

x

The needle and seed implantation constraints were designed to penalize seed distributions that did not adhere to standards at the local clinic. This feature allows for the incorporation of desired implantation criteria that has been accrued through extensive clinical experience. These constraints included penalizing the number of needles: used in a plan (Na), with only one seed (Nb), with more than five seeds (Ng), and that contained a string of three or more consecutive seeds with no spacers in between (Nd). Each of these penalties was then assigned a weighting, W, to prioritize the relative importance. The weightings for Wa, Wb, Wg, and Wd used in this study were 55, 45, 55, and 60, respectively. The contribution to the objective function for these implantation constraints, ci, then had the following form: ci 5 Wa Na þ Wb Nb þ Wg Ng þ Wd Nd

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Lastly, the fitness, f, of an individual seed distribution is obtained by taking the inverse of the objective function. Therefore, by minimizing the objective function, we are in turn maximizing the fitness to find the optimal seed distribution (Fig. 2). f5

1 c

ð6Þ

Additionally, a hard constraint was also set in place to ensure that no distribution exceeded one hundred seeds, to account for the maximum number of loose seeds typically shipped in a remote afterloader cartridge. Algorithm implementation and testing The validity of the open-source optimizer that we created was tested by generating distributions of Iodine-125 seeds with an air-kerma strength of 0.555 U for contours of 45 previously treated prostate cancer patients. The process map for the implementation of the open-source optimization algorithm for a set of patient contours is shown in Fig. 3. For a given patient, Cartesian coordinates for contours of the prostate, urethra, and rectum (if it was previously contoured) from transverse ultrasound images were imported into MATLAB. As needles are required to deliver the seeds into the prostate, the first step was to determine the acceptable needle positions for a given target geometry. A rectangular grid with 5 mm spacing for needle positioning points was implemented to mimic the clinical template used for needle insertion. This rectangular grid is registered to the clinical template used for insertion of the needles of a clinical implant. In the context of this work, the grid spacing and registration were

ð4Þ

The overall objective function, c, is therefore the combination of the dosimetric and implant penalties c 5 cd þ ci

ð5Þ

Table 2 Weightings and limits for dosimetric constraints for each dose point set (equation (1)) Dose set, x

Wmin

Dmin (Gy)

Wmax

Dmax (Gy)

Prostate volume Prostate surface Urethra surface

1.0 1.0 1.0

144 144 144

0.1 1.0 0.5

274 216 173

Fig. 2. Maximum seed distribution fitness score (Equation 6) as a function of SGA generation (iteration) number. SGA 5 simple genetic algorithm.

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Fig. 3. Order of processes involved in generating and analyzing an optimal seed distribution from SGA for a set of patient contours. These operations were performed for each of the 45 patients. SGA 5 simple genetic algorithm.

not altered. Using this grid, points that fell within the prostate contour with the largest diameter were kept. From this set, points that fell within 1 cm of any of the urethra contours were removed. This was used to reduce the possibility of urethral piercing due to urethral curvature through the prostate during needle insertion. This final set of points was then taken to be the possible needle positions. The possible seed positions would then follow from these needle positions. After determining all possible seed positions for a given patient, the MATLAB encoded SGA could be employed to determine the optimal seed configuration (as described in the previous two subsections). After obtaining the solution using SGA, a map of each transverse slice with the contours of interest and optimal seed positions was obtained from MATLAB. These maps were then used to manually enter the optimal seed configuration into the Sonographic Planning of Oncology Treatment Professional software, SPOT PROÔ (Elekta/Nucletron, Veenendaal, The Netherlands), where the resulting dosee volume histograms (DVHs) were calculated, using the 1D dose formalism from TG-43. Values for the relevant preimplant dosimetric indices (Table 1) could then be obtained

and compared with clinically acceptable values. Further benchmarking of SGAwas done by comparing solutions with ones obtained with a commercial solver, the IPSA algorithm, which is implemented in the SPOT PROÔ program. For the same cohort of 45 patients, optimal seed configurations were generated with IPSA using similar constraints as depicted in Table 2. Furthermore, IPSA was restricted to a maximum of one hundred seeds, minimum of two seeds per needle and a maximum of four consecutive seeds in a single needle. The penalty per needle was set at 1500 and the maximum number of needles per implant was set to 30. The dose objective for the rectum was removed for IPSA to mimic what was implemented in SGA. By placing similar constraints on both algorithms (SGA and IPSA), this allowed for a more direct comparison between the solutions obtained by each algorithm. These weightings and constraints may not be optimal for IPSA for a broad group of patients in the present study. The reader can therefore refer to reference (14) for class solution settings for IPSA. The mean and standard deviation were calculated for the dosimetric indices obtained from SGA and IPSA solutions. The number of needles and seeds used by each solver were also investigated.

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Table 3 Comparison of mean values for dosimetric evaluation criteria from 45 patients for both SGA and IPSA generated seed distributions Evaluation metric

SGA (m
s)

V100,prostate V150,prostate V200,prostate D90,prostate DNR V140,urethra V150,urethra V160,urethra V100,rectum (cc)

98 65 30 177 0.66 2 0.3 0.06 0.05












2 4 4 8 0.04 2 0.5 0.1 0.06

(Max, Min)

IPSA (m
s)

(99.9, 91.9) (75, 54) (41, 24) (191, 151) (0.75, 0.57) (7, 0) (2, 0) (0.6, 0) (0.2, 0)

99.5 71 41 186 0.72 7 3 1 0.2












0.5 6 7 7 0.07 14 8 7 0.3

(Max, Min)

p score

(99.9, 97.5) (89, 62) (63, 32) (212, 177) (89, 62) (58, 0) (32, 0) (9, 0) (1, 0)

!! 0.05 !! 0.05 !! 0.05 !! 0.05 !! 0.05 0.006 0.04 0.2 !! 0.05

SGA 5 simple genetic algorithm; IPSA 5 inverse planning simulated annealing; DNR 5 Dose non-uniformity ratio. Note: The results are presented as the mean (m)
standard deviation (s).

Results and discussion For all comparisons in Tables 3e5, the data for a particular dosimetric index are presented as the (mean
standard deviation) for a given group of patients. Using the statistics toolbox in MATLAB, the p-values from the two-tail paired student t test were calculated to determine the statistical significance in the comparisons between SGA and IPSA dosimetric indices. Table 3 provides a comparison of the SGA optimization with IPSA for the 45 patient cases. IPSA yielded a higher

coverage of the prostate with the prescribed dose (p !! 0.05); however, the coverage provided by SGA was also clinically acceptable. Relative to IPSA, SGA reduced hot spots in the target as shown by the reductions in the average V150,prostate and V200,prostate of 6 and 11% (p !! 0.05 for both), respectively. This led to SGA producing, on average, more uniform dose distributions as represented by a lower dose non-uniformity ratio index (p !! 0.05). In interstitial brachytherapy, uniform coverage of the clinical target volume with the prescription dose has historically been

Table 4 Comparison of average values for dosimetric evaluation criteria for different prostate volume categories (small, medium, and large) Evaluation metric

SGA (m
s)

Small prostate volume (!25 cc) V100,prostate 97
2 V150,prostate 64
6 32
5 V200,prostate D90,prostate 170
9 DNR 0.65
0.06 V140,urethra 2
2 0.17
0.03 V150,urethra V160,urethra 0 V100,rectum (cc) 0.07
0.06 Intermediate prostate volume (25e40 cc) V100,prostate 99
1 V150,prostate 66
4 V200,prostate 29
2 181
6 D90,prostate DNR 0.66
0.04 V140,urethra 2
2 V150,urethra 0.4
0.6 0.1
0.2 V160,urethra V100,rectum (cc) 0.02
0.02 Large prostate volume (O40 cc) V100,prostate 98
2 V150,prostate 64
4 V200,prostate 29
3 D90,prostate 178
8 DNR 0.65
0.04 V140,urethra 0.5
0.6 V150,urethra 9e-2
1e-1 V160,urethra 2e-2
4e-2 0.05
0.07 V100,rectum (cc)

(Max, Min)

IPSA (m
s)

(99.3, 93.4) (72, 54) (41, 24) (183, 157) (0.75, 0.57) (7, 0) (0.9, 0) (0, 0) (0.2, 0)

99.1 76 47 194 0.76 16 8 0.6 0.4












(99.9, 95.2) (75, 60) (33, 24) (192, 164) (0.75, 0.61) (6, 0) (2, 0) (0.6, 0) (0.05, 0)

99.6 72 40 187 0.72 7 2 0.4 0.1

(99.8, 92) (71, 59) (36, 24) (185, 151) (0.72, 0.60) (2, 0) (0.4, 0) (0.1, 0) (0.2, 0)

99.7 68 37 183 0.69 2 0.2 4e-2 0.3

(Max, Min)

p score

0.7 6 8 8 0.07 20 12 1.0 0.4

(99.9, 97.5) (87, 65) (63, 36) (200, 182) (0.89, 0.65) (55, 0) (32, 0) (3, 0) (1, 0)

0.01 !! 0.05 !! 0.05 !! 0.05 0.002 0.04 0.07 0.15 0.03












0.3 6 6 8 0.06 14 7 2.0 0.1

(99.9, 98.8) (88, 64) (55, 33) (212, 179) (0.89, 0.64) (58, 0) (32, 0) (8.9, 0) (0.3, 0)

0.01 !! 0.05 !! 0.05 0.008 0.001 0.1 0.3 0.4 0.08












0.3 5 4 5 0.05 4 0.4 0.1 0.4

(99.9, 98.8) (79, 62) (43, 32) (195, 177) (0.79, 0.62) (14, 0) (2, 0) (0.4, 0) (1.1, 0.02)

0.005 0.005 !! 0.05 0.1 0.01 0.2 0.5 0.6 0.05

SGA 5 simple genetic algorithm; IPSA 5 inverse planning simulated annealing; DNR 5 Dose non-unfiormity ratio. Note: The number of patients in each group were 10 small, 20 medium, and 15 large. The results are presented as the mean (m)
standard deviation (s).

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Table 5 Average number of needles and seeds used for optimized SGA and IPSA solution for the different prostate volume categories (small, medium, and large) and for all patients (all) Seeds (m
s)

Needles (m
s)

Prostate size

Small

Medium

Large

All

Small

Medium

Large

All

SGA IPSA p Score

49
3 60
5 !! 0.05

62
6 73
7 !! 0.05

74
4 87
4 !! 0.05

63
11 75
12 !! 0.05

18
2 21
2 !! 0.05

20
2 24
2 !! 0.05

23
2 26
2 !! 0.05

21
3 24
3 !! 0.05

SGA 5 simple genetic algorithm; IPSA 5 inverse planning simulated annealing. The results are presented as the mean (m)
standard deviation (s).

postulated to be ideal, so that the closer the DNR value is to zero, the better the quality of the implant (31, 32). However, whether the observed improvement in DNR for SGA can be related to clinical outcome warrants further investigations. According to American Brachytherapy Society, although there is currently not a good understanding of the effects of dose homogeneity, efforts should be made to limit the volume of high dose regions (33). The improved uniformity can be observed from the more pronounced drop-off in the PTV DVH curve for SGA relative to IPSA (Fig. 4). It can be also seen from this DVH that for this particular patient, the urethra dose between SGA and IPSA were quite similar with IPSA showing a slight improvement in this case, while the SGA provided an improvement in the dose to the rectum. For pre-implant D90, prostate, SGA and IPSA both yielded clinically acceptable values of 177
8 Gy and 186
7 Gy, respectively. D90 is one of the most important preplan parameters related to success of the implant, with preference for post-implant D90 O 140 Gy to achieve optimal results. In terms of preplan dosimetry, this translates to a desired D90 between 170 and 180 Gy; however, it has been reported that D90 can go up to 200e205 Gy without incurring any increased toxicity while maintaining the beneficial level of biochemical control (34). Therefore, D90 from both SGA and IPSA

fall within this range. An example of the spatial dose distribution for three transverse slices from one of the patients is given in Fig. 5 for both SGA and IPSA solutions. Contours for the rectum, urethra, and PTV structures are displayed along with the 144, 215, and 288 Gy isodose curves. One can see a reduction in the V200,Prostate curve indicative of SGA’s ability to reduce the hotspots in PTV. The common ‘‘horse shoe-shaped’’ V150, Prostate that arises from restricting the placement of seeds anterior to the urethra can also be noted in the figure. The mean values of the four dose metrics investigated for the urethra from SGA and IPSA solutions were well within the clinically acceptable range (35). Values of V200, Urethra were omitted due to both SGA and IPSA yielding 0% for all patients. For all urethra dose metrics, SGA solutions provided, on average, a greater reduction in dose to the urethra than IPSA. The most notable difference was in V140, Urethra where SGA yielded a mean value of 2% in comparison to the 7% obtained by IPSA ( p 5 0.006). Although the objective function for SGA and IPSA did not explicitly penalize solutions for an overdosage to the rectum, the resulting dose to the rectum from solutions for both algorithms remained clinically acceptable, meaning that V100, rectum remained below 0.3 cc. It is worth noting that V100, Rectum for the IPSA solutions was much closer to this upper bound yielding a

Fig. 4. DVHs for SGA solution (solid curves) and IPSA solution (dashed curves) obtained for a patient with 36.2 cc prostate volume. Notice that the SGA target DVH falls off more rapidly than that of the IPSA solution beyond the prescribed dose (144 Gy), demonstrating the reduction of hot spots for SGA vs. IPSA. DVH 5 doseevolume histogram; SGA 5 simple genetic algorithm; IPSA 5 inverse planning simulated annealing.

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Fig. 5. Isodose distributions for three transverse slices from a patient for IPSA (left column) and SGA (right column) solutions. Isodose levels are shown for 144, 216, and 288 Gy. IPSA 5 inverse planning simulated annealing; SGA 5 simple genetic algorithm.

mean value of 0.2 cc while SGA solutions were significantly lower (p !! 0.05), with a mean value of 0.05 cc. To further evaluate the performance of SGA, the solutions for the 45 patients were categorized in terms of prostate volume (small, medium, and large), and the mean and standard deviations of the aforementioned dosimetric parameters were recalculated for the three volume classifications (Table 4). Small prostates were defined to be anything less than 25 cc, medium prostates were between 25 and 40 cc, and large prostates were volumes greater than 40 cc. This analysis allowed for the determination of any prostate-volume dependence on the quality of the solution obtained from SGA. Ideally, no dependence on prostate volume is desired to consistently produce high-quality seed

distributions and remove the need for manual intervention in the seed distribution. It was observed that SGA had slightly inferior, although clinically acceptable, solutions for the small prostate group, yielding a V100,prostate and D90,prostate of 97% and 170 Gy, respectively. This was most likely due to the restrictions placed on the minimum number of seeds per needle and maximum number of consecutive seeds per needle constraints that were imposed in the objective function. The needle placement was restricted to at least 1.0 cm beyond urethra contours in present study, whereas most systems use a more relaxed constraint of 0.5 cm. The other major factor is restriction on the placement of seeds/needles anterior to the urethra in SGA, which further limits the possible

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needle locations and has bearings on dose distribution. These effects are exacerbated by the small prostate volume. The user has the flexibility to relax any of the aforementioned constraints due to the open source nature of SGA. SGA yielded the best results for the medium sized prostate group with a V100,prostate and D90,prostate of 99% and 177 Gy, respectively. SGA values for the large prostate volume were clinically acceptable, although slightly lower than those obtained with IPSA (V100,prostate of 98% for SGA and 99.7% for IPSA). This may be attributed to the reduction in average number of needles and seeds used for the SGA implant when compared with IPSA (Table 5), both of which may have benefits in terms of toxicity that are further discussed below. The dose to the urethra and rectum were similar for all three volume categories and were well below the acceptable doseevolume thresholds for each organ (34, 35). All values for the prostate, urethra, and rectum were within the clinically acceptable tolerances. The solutions from IPSA appeared to be independent of the prostate volume, as similar values for the majority of dosimetric parameters were obtained for all three volume categories. The DNR index was fairly consistent for all three-volume categories for the SGA solutions. Whereas for IPSA, the small prostate category created the largest dose nonuniformity (with a mean of 0.76), whereas the IPSA DNR was fairly comparable with that of SGA for the large prostate volumes. The SGA excelled relative to IPSA in minimizing the number of needles used for the implant (Table 5). For the 45 seed distributions, the mean
standard deviation for the number of needles was 21
3 for SGA compared with IPSA’s 24
3 (p !! 0.05). This difference between algorithms, in part, can be attributed to the fact that SGA penalizes needles with more than three consecutive seeds, whereas IPSA implements a maximum number of consecutive seeds as a hard constraint. The weighting of the associated penalty and the maximum number of consecutive seeds per needle is user specified in SGA. The needles with large numbers of seeds have been hard constrained to two in SGA. This average reduction in needles for SGA is a desirable outcome as the insertion of needles into the prostate results in edema of the gland. Not only is this uncomfortable for the patient but it also alters the seed distribution as the prostate swells and then returns to its natural state. This will affect the resulting dose distribution leading to potentially suboptimal post-implant dosimetry, higher toxicity rates, and decrease in probability of tumor control (36, 37). There has been mention that edema can lead to a variation in up to 15% in the postimplant dosimetry. Furthermore, work by Keyes et al. (38) has shown that worse acute toxicity (Radiation Therapy Oncology Group Grade 2 or higher) is seen more frequently in patients that have a greater number of needles; however, this is not the sole factor that leads to worse acute toxicity. A study by Ohashi et al. (39) demonstrated that number of seeds and, more strongly, needles are

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predictive factors for catheterization due to acute urinary retention after Iodine-125 prostate brachytherapy. The study mentions that patients with implants consisting of more than 24 needles have approximately four-times higher risk of catheterization than implants with the number of needles less than or equal to 24. Although the average number of needles for both SGA and IPSA is below 25 needles, 14 of the IPSA distributions required more than 24 needles in comparison with only 2 for the SGA distributions. One must also consider the edema that is not only due to the number of needles but the multiple insertions of a single needle for correct positioning during the implant phase. This was not considered here as we are only considering the pre-implant seed distribution generated by SGA. SGA also provided a significant reduction (p !! 0.05) in the number of seeds required in a distribution. This may lead to more favorable outcomes in terms of reduced acute urinary toxicity. This may also provide an economic benefit for a center that is treating a large number of patients if clinically equivalent distributions can be generated using less seeds. Although this study has shown tradeoffs between SGA and IPSA algorithms in terms of potential dosimetric and implant benefits, that was not the main intent of this study. Through this work we have provided an open-source SGA platform to further research and development in brachytherapy that, in its current state, produces clinically acceptable solutions that compare favorably to solutions obtained from an established commercial solver, IPSA. Open source tools such as the SGA and others can provide necessary armamentarium to clinicians and researchers working in developing countries with limited resources. However, this would require careful validation in a particular clinic by qualified medical physicist and the physician. As previously mentioned, CERR (24) has been one of the main platforms for promoting open collaboration and research in the field of medical physics. With the aim of this study to provide a validated open-source optimizer to the medical physics research community, CERR seems like an excellent platform to interface our open-source SGA. Therefore, we have done preliminary ground work for the inclusion of SGA optimizer into CERR. Furthermore, to help ease into the use of the optimizer, a simple MATLAB-based GUI (Fig. 6) along with a small userguide has been created. The code will be available for free download from CERR in the near future or by contacting the corresponding author directly. In this work, we have used the SPOT ProÔ environment for contouring, DVH calculation and comparison purposes. From the open-source optimizer provided by this study, the next logical step would be to further build on this optimizer in hopes of creating a completely open-source platform for LDRPB treatment planning by creating the dose-statistics analysis tools specifically for evaluating seed distributions in CERR. This open-source platform will facilitate continuing research focused on

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Fig. 6. Screen-shot of MATLAB-based GUI created for the SGA optimizer. GUI 5 graphical user interface; SGA 5 simple genetic algorithm.

improving LDRPB and allow the extension into HDR brachytherapy and permanent LDR breast brachytherapy optimization. Through this work, we have provided an open infrastructure on which further brachytherapy work can be built for these applications. There has also been a wealth of research in terms of different optimization algorithms that have been applied to the LDRPB optimal seed distribution problem, and we also believe a platform in CERR that allows one to implement various optimization algorithms would be a useful tool to further research and innovation in brachytherapy.

Conclusion In this article, we have successfully designed and implemented an open-source genetic algorithm that determines a clinically acceptable seed distribution in terms of dose to the prostate and urethra for LDRPB treatment. Although the rectum was not included in the dose objective, the dose to the rectum calculated from the SGA solutions was still clinically acceptable and superior to an available clinical solver (IPSA). It was shown that, relative to IPSA, SGA produced comparable coverage to the target structure while providing improved sparing of the urethra and rectum under similar dosimetric and implant constraints. SGA, on average, produced seed distributions that required fewer seeds and needles, increased number of seeds per needle, and increased number of spacers between the seeds. This is favorable for reduction of the needle trauma and the amount of edema in the prostate. Having successfully validated, benchmarked, and commenced the process of integrating our SGA into CERR, this open source optimizer allows the optimization community concerned with brachytherapy a tool that provides the user full access to the

source code in hopes of further advancing research and collaboration in the field of brachytherapy optimization.

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