Radiotherapy and Oncology xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Radiotherapy and Oncology journal homepage: www.thegreenjournal.com
Original article
Beam orientation in stereotactic radiosurgery using an artificial neural network Agnieszka Skrobala ⇑, Julian Malicki Department of Electroradiology, University of Medical Science; and Department of Medical Physics, Greater Poland Cancer Centre, Poznan, Poland
a r t i c l e
i n f o
Article history: Received 12 February 2013 Received in revised form 16 March 2014 Accepted 19 March 2014 Available online xxxx Keywords: Beam orientation Artificial neural network Stereotactic radiosurgery
a b s t r a c t Background and purpose: To investigate the feasibility of using an artificial neural network (ANN) to generate beam orientations in stereotactic radiosurgery (SRS). Material and methods: A dataset of 669 intracranial lesions was used to build, train, and validate three ANNs. In ANN1, Cartesian coordinates described the localization of the PTV and OARs. In ANN2, a genetic algorithm was used to optimize the model. In ANN3, vectors were used to define the distance between the PTV and OARs. In all ANNs, inputs consisted of the treatment plan parameters plus the patient’s particular geometric parameters; outputs were beam and table angles. The ANN- and human-generated plans were then compared using dose–volume histograms, root-mean-square (RMS) and Gamma index methods. Results: The mean volume of PTV covered by the 95% isodose was 99.2% in the MP’s plan vs. 99.3%, 98.5% and 99.2% for ANN1, ANN2, and ANN3, respectively. No significant differences were observed between the plans. ANN1 showed the best agreement (Gamma index) with the human planner. While RMS errors in the three ANN models were comparable, ANN1 showed the lowest (best) values. Conclusion: ANN models were able to determine beam orientation in SRS. ANN-generated treatment plans were comparable to human-designed plans. Ó 2014 Elsevier Ireland Ltd. All rights reserved. Radiotherapy and Oncology xxx (2014) xxx–xxx
In recent years, stereotactic radiosurgery (SRS) has become a standard treatment option for many pathologies of the central nervous system, including metastases [1–6]. The number of beams needed and their arrangement are strictly related to the prescribed dose to the PTV and the location of nearby critical organs [7,8]. When a linear accelerator is used to perform SRS, optimal treatment plans are achieved when the plan consists of several coplanar and non-coplanar beams selected by the medical physicist (MP) [9–12]. Unlike other radiotherapy procedures, SRS uses multiple narrow beams whose number and orientation vary so much that the use of a standard template is less effective than in most other radiotherapy modalities; even so, standard templates are used in certain tumor locations [12]. Given that beam configuration in SRS always requires a compromise between target coverage and OAR sparing [13–16], numerous studies have evaluated algorithms that might support automated beam orientation selection [14] for both coplanar [17–19] and non-coplanar [15,19,20] beams.
The complexity inherent to the wide array of potential beam configurations provides an opportunity to apply an artificial intelligence support system [17,21,22]. Artificial neural networks (ANN) have an important advantage over conventional modeling methods in that the neural net requires no prior knowledge of the functional relationship between the various input values, nor between input and output parameters. For this reason, ANNs have been used in many medical applications, as an adjunct to standardized treatment planning [23,24], to adjust treatment planning parameters [17,22,25], to improve the treatment process [26], and to predict treatment outcomes [27,28]. The main aim of the present study was to determine whether an ANN could help accelerate and improve the process of SRS planning. To do this, we constructed three ANN models to predict SRS beam arrangement (gantry and table orientations) using various sets of inputs.
⇑ Corresponding author. Address: Department of Medical Physics, Greater Poland Cancer Centre, Garbary 15st., 61-866 Poznan, Poland. E-mail address: [email protected] (A. Skrobala).
A total of 539 patients ranging in age from 16 to 85 years were treated with SRS for intracranial lesions at our clinic between November 2004 and November 2012 (for treatment planning
Material and methods
http://dx.doi.org/10.1016/j.radonc.2014.03.010 0167-8140/Ó 2014 Elsevier Ireland Ltd. All rights reserved.
Please cite this article in press as: Skrobala A, Malicki J. Beam orientation in stereotactic radiosurgery using an artificial neural network. Radiother Oncol (2014), http://dx.doi.org/10.1016/j.radonc.2014.03.010
2
An artificial neural network in stereotactic radiosurgery
details and inclusion criteria see Supplementary Material). Most patients (425) had only a single lesion (425 lesions), while 98 patients had two lesions (98 2 = 196 lesions), and 16 had three lesions (16 3 = 48 lesions). Therefore, a total of 669 lesions were included in the study; of these, 617 were used to train the ANNs while the remaining 52 were used for prospective validation. The ANN models architecture is described in the Supplementary Material. A pilot study using multivariate analysis was performed to define the number and type of inputs needed. In that study, multiple linear regressions were performed to identify those parameters that provided non-relevant information. Such parameters were excluded from the model because they increased the processing time without providing any useful information. The general inputs were obtained from the treatment planning system (TPS) and included the prescribed dose value, number of PTVs treated concomitantly (maximum three), and the volumes of the PTVs (PTV, PTV1 and PTV2) and the 6 OARs. Supplementary Table 1 (see in Supplementary Material) summarizes and presents the set of 12 general inputs (with their range and median values). Input parameter #12 (Region) describes the localization of the PTV in one of the eight brain sub-volumes defined by the authors in Table 1. This was done to define PTV localization in the brain and to separate intracranial lesions by location. Two approaches to mapping patient geometric information to the corresponding set of input parameters were evaluated. Both sets of inputs were based on defining the position of the PTV and the geometric relationship between the PTV and other structures. The first approach used the Cartesian system defined by the TPS: each structure was mathematically reduced to three coordinates (x, y, z) of the middle point above structures. Supplementary Fig. 1a (in Supplementary Material) provides an example. Using this reduction scheme, each lesion could be reduced to just 27 geometric input parameters (3 for each of the 9 analyzed structures). In the second approach, patient geometric structures were defined by 8 vectors that described the distances [in cm] between the middle points of the PTV and the other structures. The (x, y, z) coordinate inputs for the PTV were retained as shown in Supplementary Fig. 1b (in Supplementary Material). The second approach reduced the number of inputs to only 11 input parameters (8 vectors + 3 coordinates [x, y, z] of the middle of the PTV). Linear accelerator-based SRS treatment plans typically have more than a dozen beams [9,10,12]. In our study, the largest number of beams was 14. For each beam, two separate nets were constructed to account for the gantry and table angles as the outputs of the neural networks. ANN design, training, testing and validation The ANNs were built with data from 617 lesions based on a back propagation algorithm with 0.01 learning coefficient. The neural network was trained for approximately 10,000 iterations until
Table 1 Eight regions of the brain (sub-volumes) defined by the authors. Patients were divided into 8 subgroups according to the PTV localization in the brain. The number of PTVs in each particular region with its anatomical localization is presented in the table. Index
Anatomical localization
Number of PTVs
R1 R2 R3 R4 R5 R6 R7 R8
Right cranial anterior Left cranial anterior Right cranial posterior Left cranial posterior Right caudal anterior Left caudal anterior Right caudal posterior Left caudal posterior
71 95 100 102 40 27 89 93
the expected decrease in performance due to overtraining was observed. The errors for the nets were 0.001. The number of epochs ranged from 1000 to 3000. The lesions were randomly stratified to either training (517 lesions) or testing (100 lesions) by a random resampling technique (cross-validation). Each input parameter was converted to numerical form (normalized according to the maximal value) and assigned a 10 digit code, which corresponded to 10 neurons. To illustrate this coding system, it is best to provide an example: for the 1st general input (i.e., the prescribed dose) doses could range from 6 to 24 Gy, thus a dose of 18 Gy was coded in binary form as 0000001000. Output parameters were represented by 73 digits, which corresponded to 73 neurons, and converted to a 72-digit number (360/ 5° = 72; 5° accuracy) plus the 37th position with 0 for presence and 1 for absence of the particular angle. For example, a 30° angle was presented as 0010000000. . .. . .0 (all digits following the third digit were ‘‘0’’, including the 37th digit). During the validation phase of the study, we used a set of clinical data (the inputs) for 40 consecutive patients (28 with one lesion and 12 with two lesions) that were unknown to the ANN models. These 52 (28 + 24 [12 2]) lesions were located in each of the eight brain regions: 11 lesions in region 1, and 8, 9, 6, 2, 3, 3, 10 lesions, respectively. The datasets for each ANN model were extracted from the TPS and converted into binary form. Because the maximum number of beams was 14 and each beam orientation was defined by both gantry and table angles, a total of 28 neural nets (14 2) were needed. The MP used ANN-generated beam orientations to prepare a total of 156 new treatment plans in the TPS. The other treatment plan parameters were the same as those used in the original treatment plans. To reduce bias, all plans were created at the same time.
Methods of plans comparison Dose values and dose distribution were used to compare the ANN-generated plans to the plan prepared by the MP. Both the MP and ANN-generated plans were required to fulfill the criteria for target coverage [30]. The comparison was performed in three steps in order to choose the best ANN model. In the first comparison, the maximal doses to the OARs and maximal and minimal dose to PTV for the MP-designed plans and the three ANN-generated were compared for all lesions from the validation group. All doses were read from the respective dose–volume histograms (DVH). In the second comparison, rootmean-square (RMS) discrepancies between the MP-designed and ANN-generated plans were calculated for the number of beams (NB), maximal and minimal doses (Dmax, Dmin,) in selected OARs, volume of PTV receiving 95% of the prescribed dose (V95%), and conformity index (CI 95%). The RMS error was defined as follows: RMS = square root (sum (PMP PANN)), where parameters P were: NB, Dmax, Dmin, CI 95%, V95%. In the third comparison, we used a dedicated program (OmnioPro IMRT v.1.6; IBA Dosimetry GmbH, Germany) to apply the Gamma index method proposed by Low et al. [34]. Agreement between the MP-derived plans and those predicted by the three ANN models was checked for the areas encompassed by the 60%, 80%, 90%, 95% and 99% threshold isodose levels. The areas considered were located at the reference transversal scan (intersecting isocenter). For each isodose level, we calculated the percentage of points with a gamma index below 1 (c < 1) and the percentage of the field areas (%FA) that passed the agreement criteria (dose difference [DD] = 2%, dose to agreement [DTA] = 2 mm).
Please cite this article in press as: Skrobala A, Malicki J. Beam orientation in stereotactic radiosurgery using an artificial neural network. Radiother Oncol (2014), http://dx.doi.org/10.1016/j.radonc.2014.03.010
3
A. Skrobala, J. Malicki / Radiotherapy and Oncology xxx (2014) xxx–xxx
Results The 1st ANN model (ANN1) used 12 general parameters. In addition, the first approach (i.e., Cartesian coordinates, described above) was used to select the geometric parameters (27 inputs). As a result, the total number of inputs for ANN1 was 12 + 27 = 39, each of which was assigned a 10-digit code (neurons), thus providing a total of 390 neurons. The 2nd ANN model (ANN2) used a genetic algorithm to evaluate and optimize the ANN1 in order to reduce the number of inputs from 39 (in ANN1) to 12, with the consequent reduction in the number of neurons (12 10 = 120 neurons) [31–33,18]. After eliminating numerous parameters through this algorithm, the following inputs remained: coordinates: PTV (x coordinate), right eye (y), left and right optic nerves (y); and the following volumes: PTV1, PTV2, left and right eyes, left and right optic nerves, and the brain stem. The 3rd ANN model (ANN3) used vectors to select geometric parameters. ANN3 thus contained 12 general inputs and 11 geometric inputs, for a total of 23 inputs (23 10 = 230 neurons). In all three ANN models, there was one output with 73 neurons for the gantry and table angles, respectively. The ANN design, which included 28 separate networks consisting of single output for either table angle or gantry angle (for the maximum number of beams: 14) proved to be efficient because the appropriate modeling of the synaptic weights could be done quickly. However, because the input parameter ‘‘region’’ is divided into 8 sub-volumes, separate nets had to be built for each region and angle, for a total of 224 nets (28 8). The RMS error factors to obtain the discrepancy between the values estimated by the ANN and the real values for the 100 lesions used for testing the ANN1, ANN2, and ANN3 were, respectively, 25.0%, 23.1%, and 23.4% for the gantry angle (G), and 25.7%, 23.1%, and 19.9% for the table angle (T). The learning stage for the nets was stopped when the models were able to recognize the output for the testing set. Table 2 compares the MP-developed plans to the three ANNgenerated plans. These data include all 52 lesions passed through the three models. The RMS error discrepancy between the plans developed by the MP and the ANN models is included in the second comparison shown in Table 3. In SRS, at least 98.5% of the volume must be within the 95% isodose. For this reason, we also evaluated that parameter, without finding any significant differences. The mean volume of PTV covered by the 95% isodose was 99.2% in the MP’s plan vs. 99.3%, 98.5%, and 99.2% for ANN1, ANN2, and ANN3, respectively. Fig. 1 shows the differences in dose distributions (calculated by the Gamma index method) between the MP-designed plans and those generated by the ANNs. The data are shown for the areas located at
Table 3 The root-mean-square errors for selected rated parameters for the three ANNgenerated plans compared to the physicist-developed treatment plans. For each parameter, the best (lowest) RMS error rates are shown in bold. Parameter
RMS
NB Dmax body Dmax PTV Dmin PTV Dmax brain stem Dmax eye right Dmax eye left Dmax optic nerve right Dmax optic nerve left Dmax chiasm V95% 95% conformity index
ANN1
ANN2
ANN3
1.6 2.8 0.5 1.5 1.6 0.6 1.2 0.9 1.2 1.3 0.5 0.16
1.8 2.9 1.4 1.5 1.0 0.6 1.0 1.4 1.3 1.7 1.6 0.15
1.6 2.9 0.5 1.4 1.9 0.8 1.0 1.1 1.3 1.5 0.6 0.16
the reference transversal scan inside the isodose values: 60%, 80%, 90%, 95% and 99% of the prescription dose. Discussion Our study shows that ANNs are able to generate effective beam arrangements even when very basic patient information is used [17]. A simple set of inputs drawn directly from the TPS—such as dose, structure volume, and geometric parameters that define the localization of PTV and OARs—were sufficient to generate feasible beams. The models we have built prove that ANNs can use these inputs to generate output data efficiently. Moreover, ANNs can successfully solve the problem of developing appropriate algorithms capable of calculating complex beam configurations [28,29]. Generating an optimal treatment plan for SRS requires analysis of numerous different treatment parameters, including beam orientation. To solve this problem, customized beam orientations with numerous narrow beams should be applied. In addition, patient-to-patient variations in target localization and its proximity to adjacent brain structures must be taken into account. Performing the necessary steps manually through an iterative process is a time-consuming process requiring the human planner to make multiple, iterative adjustments to the main treatment variables to achieve the best dose distribution. During the testing phase of the ANNs, the RMS error factor between ANN and MP estimated values was similar in all 3 models and shows a satisfactory degree of accuracy. The validation phase showed that all three models produced satisfactory results, despite some performance differences. The mean doses in the OARs—particularly in the brain stem— were higher in the ANN-generated plans vs. the MP plan. The mean
Table 2 The maximal and minimal doses to the PTV and the maximal doses to the OARs for the MP-designed plans and the three ANN-generated plans. Parameter
Max body Min PTV Max PTV Max brain stem Max eye right Max eye left Max optic nerve right Max optic nerve left Max chiasm
MP
ANN1
ANN2
ANN3
Mean (%)
SD (%)
Mean (%)
SD (%)
Mean (%)
SD (%)
Mean (%)
SD (%)
107.4 92.6 106.5 8.8 1.2 1.0 3.2 2.0 3.9
3.0 2.4 8.6 11.4 2.5 2.4 10.9 3.2 7.1
106.9 92.8 107.4 14.0 2.6 4.1 5.2 4.5 7.6
3.2 1.3 3.2 15.3 4.0 7.4 12.8 6.8 11.5
106.9 91.3 107.3 15.7 1.5 3.3 3.7 5.1 8.6
3.2 7.1 3.2 17.5 3.6 5.5 5.7 12.3 13.1
107.5 92.4 107.9 14.6 2.7 3.2 5.5 4.8 7.8
3.3 1.4 3.3 14.8 4.7 5.5 14.2 7.7 14.8
MP indicates medical physicist. SD indicates standard deviation.
Please cite this article in press as: Skrobala A, Malicki J. Beam orientation in stereotactic radiosurgery using an artificial neural network. Radiother Oncol (2014), http://dx.doi.org/10.1016/j.radonc.2014.03.010
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An artificial neural network in stereotactic radiosurgery
Fig. 1. The percent agreement for the field areas encompassed by the 60%, 80%, 90%, 95% and 99% threshold isodose levels between the MP dose distribution and that predicted by the three ANN models.
doses calculated by ANN1 were slightly lower than the doses in the two other models (Table 2). Despite these differences, it should be noted that the doses presented in Table 2 are all reasonable and might justify further use of any of the three models, particularly since no significant differences between the models were observed for the minimal and maximal dose values to the PTV. The large variation in standard deviations is due to the relatively small sample size. The very similar RMS values for all ANN models indicate that neural nets are capable of generating beam orientations and treatment plans that are comparable to those created by an MP. As the results in Table 3 show, the ANN1 had the best performance in terms of these parameters, suggesting that ANN1 is superior to ANN2 and ANN3. In ANN2, RMS values were lower than the other models in only two parameters (brain stem and left eye Dmax), although perhaps this result is not surprising given that ANN2 was based on a reduced number of inputs obtained from ANN1. Gamma Index analysis (Fig. 1) showed that the ANN1 treatment plan had the best agreement with the MP-developed plan, as evidenced by the higher %FA values for all threshold isodose levels. However, coverage differences between the 3 ANNs were small (
Contents lists available at ScienceDirect
Radiotherapy and Oncology journal homepage: www.thegreenjournal.com
Original article
Beam orientation in stereotactic radiosurgery using an artificial neural network Agnieszka Skrobala ⇑, Julian Malicki Department of Electroradiology, University of Medical Science; and Department of Medical Physics, Greater Poland Cancer Centre, Poznan, Poland
a r t i c l e
i n f o
Article history: Received 12 February 2013 Received in revised form 16 March 2014 Accepted 19 March 2014 Available online xxxx Keywords: Beam orientation Artificial neural network Stereotactic radiosurgery
a b s t r a c t Background and purpose: To investigate the feasibility of using an artificial neural network (ANN) to generate beam orientations in stereotactic radiosurgery (SRS). Material and methods: A dataset of 669 intracranial lesions was used to build, train, and validate three ANNs. In ANN1, Cartesian coordinates described the localization of the PTV and OARs. In ANN2, a genetic algorithm was used to optimize the model. In ANN3, vectors were used to define the distance between the PTV and OARs. In all ANNs, inputs consisted of the treatment plan parameters plus the patient’s particular geometric parameters; outputs were beam and table angles. The ANN- and human-generated plans were then compared using dose–volume histograms, root-mean-square (RMS) and Gamma index methods. Results: The mean volume of PTV covered by the 95% isodose was 99.2% in the MP’s plan vs. 99.3%, 98.5% and 99.2% for ANN1, ANN2, and ANN3, respectively. No significant differences were observed between the plans. ANN1 showed the best agreement (Gamma index) with the human planner. While RMS errors in the three ANN models were comparable, ANN1 showed the lowest (best) values. Conclusion: ANN models were able to determine beam orientation in SRS. ANN-generated treatment plans were comparable to human-designed plans. Ó 2014 Elsevier Ireland Ltd. All rights reserved. Radiotherapy and Oncology xxx (2014) xxx–xxx
In recent years, stereotactic radiosurgery (SRS) has become a standard treatment option for many pathologies of the central nervous system, including metastases [1–6]. The number of beams needed and their arrangement are strictly related to the prescribed dose to the PTV and the location of nearby critical organs [7,8]. When a linear accelerator is used to perform SRS, optimal treatment plans are achieved when the plan consists of several coplanar and non-coplanar beams selected by the medical physicist (MP) [9–12]. Unlike other radiotherapy procedures, SRS uses multiple narrow beams whose number and orientation vary so much that the use of a standard template is less effective than in most other radiotherapy modalities; even so, standard templates are used in certain tumor locations [12]. Given that beam configuration in SRS always requires a compromise between target coverage and OAR sparing [13–16], numerous studies have evaluated algorithms that might support automated beam orientation selection [14] for both coplanar [17–19] and non-coplanar [15,19,20] beams.
The complexity inherent to the wide array of potential beam configurations provides an opportunity to apply an artificial intelligence support system [17,21,22]. Artificial neural networks (ANN) have an important advantage over conventional modeling methods in that the neural net requires no prior knowledge of the functional relationship between the various input values, nor between input and output parameters. For this reason, ANNs have been used in many medical applications, as an adjunct to standardized treatment planning [23,24], to adjust treatment planning parameters [17,22,25], to improve the treatment process [26], and to predict treatment outcomes [27,28]. The main aim of the present study was to determine whether an ANN could help accelerate and improve the process of SRS planning. To do this, we constructed three ANN models to predict SRS beam arrangement (gantry and table orientations) using various sets of inputs.
⇑ Corresponding author. Address: Department of Medical Physics, Greater Poland Cancer Centre, Garbary 15st., 61-866 Poznan, Poland. E-mail address: [email protected] (A. Skrobala).
A total of 539 patients ranging in age from 16 to 85 years were treated with SRS for intracranial lesions at our clinic between November 2004 and November 2012 (for treatment planning
Material and methods
http://dx.doi.org/10.1016/j.radonc.2014.03.010 0167-8140/Ó 2014 Elsevier Ireland Ltd. All rights reserved.
Please cite this article in press as: Skrobala A, Malicki J. Beam orientation in stereotactic radiosurgery using an artificial neural network. Radiother Oncol (2014), http://dx.doi.org/10.1016/j.radonc.2014.03.010
2
An artificial neural network in stereotactic radiosurgery
details and inclusion criteria see Supplementary Material). Most patients (425) had only a single lesion (425 lesions), while 98 patients had two lesions (98 2 = 196 lesions), and 16 had three lesions (16 3 = 48 lesions). Therefore, a total of 669 lesions were included in the study; of these, 617 were used to train the ANNs while the remaining 52 were used for prospective validation. The ANN models architecture is described in the Supplementary Material. A pilot study using multivariate analysis was performed to define the number and type of inputs needed. In that study, multiple linear regressions were performed to identify those parameters that provided non-relevant information. Such parameters were excluded from the model because they increased the processing time without providing any useful information. The general inputs were obtained from the treatment planning system (TPS) and included the prescribed dose value, number of PTVs treated concomitantly (maximum three), and the volumes of the PTVs (PTV, PTV1 and PTV2) and the 6 OARs. Supplementary Table 1 (see in Supplementary Material) summarizes and presents the set of 12 general inputs (with their range and median values). Input parameter #12 (Region) describes the localization of the PTV in one of the eight brain sub-volumes defined by the authors in Table 1. This was done to define PTV localization in the brain and to separate intracranial lesions by location. Two approaches to mapping patient geometric information to the corresponding set of input parameters were evaluated. Both sets of inputs were based on defining the position of the PTV and the geometric relationship between the PTV and other structures. The first approach used the Cartesian system defined by the TPS: each structure was mathematically reduced to three coordinates (x, y, z) of the middle point above structures. Supplementary Fig. 1a (in Supplementary Material) provides an example. Using this reduction scheme, each lesion could be reduced to just 27 geometric input parameters (3 for each of the 9 analyzed structures). In the second approach, patient geometric structures were defined by 8 vectors that described the distances [in cm] between the middle points of the PTV and the other structures. The (x, y, z) coordinate inputs for the PTV were retained as shown in Supplementary Fig. 1b (in Supplementary Material). The second approach reduced the number of inputs to only 11 input parameters (8 vectors + 3 coordinates [x, y, z] of the middle of the PTV). Linear accelerator-based SRS treatment plans typically have more than a dozen beams [9,10,12]. In our study, the largest number of beams was 14. For each beam, two separate nets were constructed to account for the gantry and table angles as the outputs of the neural networks. ANN design, training, testing and validation The ANNs were built with data from 617 lesions based on a back propagation algorithm with 0.01 learning coefficient. The neural network was trained for approximately 10,000 iterations until
Table 1 Eight regions of the brain (sub-volumes) defined by the authors. Patients were divided into 8 subgroups according to the PTV localization in the brain. The number of PTVs in each particular region with its anatomical localization is presented in the table. Index
Anatomical localization
Number of PTVs
R1 R2 R3 R4 R5 R6 R7 R8
Right cranial anterior Left cranial anterior Right cranial posterior Left cranial posterior Right caudal anterior Left caudal anterior Right caudal posterior Left caudal posterior
71 95 100 102 40 27 89 93
the expected decrease in performance due to overtraining was observed. The errors for the nets were 0.001. The number of epochs ranged from 1000 to 3000. The lesions were randomly stratified to either training (517 lesions) or testing (100 lesions) by a random resampling technique (cross-validation). Each input parameter was converted to numerical form (normalized according to the maximal value) and assigned a 10 digit code, which corresponded to 10 neurons. To illustrate this coding system, it is best to provide an example: for the 1st general input (i.e., the prescribed dose) doses could range from 6 to 24 Gy, thus a dose of 18 Gy was coded in binary form as 0000001000. Output parameters were represented by 73 digits, which corresponded to 73 neurons, and converted to a 72-digit number (360/ 5° = 72; 5° accuracy) plus the 37th position with 0 for presence and 1 for absence of the particular angle. For example, a 30° angle was presented as 0010000000. . .. . .0 (all digits following the third digit were ‘‘0’’, including the 37th digit). During the validation phase of the study, we used a set of clinical data (the inputs) for 40 consecutive patients (28 with one lesion and 12 with two lesions) that were unknown to the ANN models. These 52 (28 + 24 [12 2]) lesions were located in each of the eight brain regions: 11 lesions in region 1, and 8, 9, 6, 2, 3, 3, 10 lesions, respectively. The datasets for each ANN model were extracted from the TPS and converted into binary form. Because the maximum number of beams was 14 and each beam orientation was defined by both gantry and table angles, a total of 28 neural nets (14 2) were needed. The MP used ANN-generated beam orientations to prepare a total of 156 new treatment plans in the TPS. The other treatment plan parameters were the same as those used in the original treatment plans. To reduce bias, all plans were created at the same time.
Methods of plans comparison Dose values and dose distribution were used to compare the ANN-generated plans to the plan prepared by the MP. Both the MP and ANN-generated plans were required to fulfill the criteria for target coverage [30]. The comparison was performed in three steps in order to choose the best ANN model. In the first comparison, the maximal doses to the OARs and maximal and minimal dose to PTV for the MP-designed plans and the three ANN-generated were compared for all lesions from the validation group. All doses were read from the respective dose–volume histograms (DVH). In the second comparison, rootmean-square (RMS) discrepancies between the MP-designed and ANN-generated plans were calculated for the number of beams (NB), maximal and minimal doses (Dmax, Dmin,) in selected OARs, volume of PTV receiving 95% of the prescribed dose (V95%), and conformity index (CI 95%). The RMS error was defined as follows: RMS = square root (sum (PMP PANN)), where parameters P were: NB, Dmax, Dmin, CI 95%, V95%. In the third comparison, we used a dedicated program (OmnioPro IMRT v.1.6; IBA Dosimetry GmbH, Germany) to apply the Gamma index method proposed by Low et al. [34]. Agreement between the MP-derived plans and those predicted by the three ANN models was checked for the areas encompassed by the 60%, 80%, 90%, 95% and 99% threshold isodose levels. The areas considered were located at the reference transversal scan (intersecting isocenter). For each isodose level, we calculated the percentage of points with a gamma index below 1 (c < 1) and the percentage of the field areas (%FA) that passed the agreement criteria (dose difference [DD] = 2%, dose to agreement [DTA] = 2 mm).
Please cite this article in press as: Skrobala A, Malicki J. Beam orientation in stereotactic radiosurgery using an artificial neural network. Radiother Oncol (2014), http://dx.doi.org/10.1016/j.radonc.2014.03.010
3
A. Skrobala, J. Malicki / Radiotherapy and Oncology xxx (2014) xxx–xxx
Results The 1st ANN model (ANN1) used 12 general parameters. In addition, the first approach (i.e., Cartesian coordinates, described above) was used to select the geometric parameters (27 inputs). As a result, the total number of inputs for ANN1 was 12 + 27 = 39, each of which was assigned a 10-digit code (neurons), thus providing a total of 390 neurons. The 2nd ANN model (ANN2) used a genetic algorithm to evaluate and optimize the ANN1 in order to reduce the number of inputs from 39 (in ANN1) to 12, with the consequent reduction in the number of neurons (12 10 = 120 neurons) [31–33,18]. After eliminating numerous parameters through this algorithm, the following inputs remained: coordinates: PTV (x coordinate), right eye (y), left and right optic nerves (y); and the following volumes: PTV1, PTV2, left and right eyes, left and right optic nerves, and the brain stem. The 3rd ANN model (ANN3) used vectors to select geometric parameters. ANN3 thus contained 12 general inputs and 11 geometric inputs, for a total of 23 inputs (23 10 = 230 neurons). In all three ANN models, there was one output with 73 neurons for the gantry and table angles, respectively. The ANN design, which included 28 separate networks consisting of single output for either table angle or gantry angle (for the maximum number of beams: 14) proved to be efficient because the appropriate modeling of the synaptic weights could be done quickly. However, because the input parameter ‘‘region’’ is divided into 8 sub-volumes, separate nets had to be built for each region and angle, for a total of 224 nets (28 8). The RMS error factors to obtain the discrepancy between the values estimated by the ANN and the real values for the 100 lesions used for testing the ANN1, ANN2, and ANN3 were, respectively, 25.0%, 23.1%, and 23.4% for the gantry angle (G), and 25.7%, 23.1%, and 19.9% for the table angle (T). The learning stage for the nets was stopped when the models were able to recognize the output for the testing set. Table 2 compares the MP-developed plans to the three ANNgenerated plans. These data include all 52 lesions passed through the three models. The RMS error discrepancy between the plans developed by the MP and the ANN models is included in the second comparison shown in Table 3. In SRS, at least 98.5% of the volume must be within the 95% isodose. For this reason, we also evaluated that parameter, without finding any significant differences. The mean volume of PTV covered by the 95% isodose was 99.2% in the MP’s plan vs. 99.3%, 98.5%, and 99.2% for ANN1, ANN2, and ANN3, respectively. Fig. 1 shows the differences in dose distributions (calculated by the Gamma index method) between the MP-designed plans and those generated by the ANNs. The data are shown for the areas located at
Table 3 The root-mean-square errors for selected rated parameters for the three ANNgenerated plans compared to the physicist-developed treatment plans. For each parameter, the best (lowest) RMS error rates are shown in bold. Parameter
RMS
NB Dmax body Dmax PTV Dmin PTV Dmax brain stem Dmax eye right Dmax eye left Dmax optic nerve right Dmax optic nerve left Dmax chiasm V95% 95% conformity index
ANN1
ANN2
ANN3
1.6 2.8 0.5 1.5 1.6 0.6 1.2 0.9 1.2 1.3 0.5 0.16
1.8 2.9 1.4 1.5 1.0 0.6 1.0 1.4 1.3 1.7 1.6 0.15
1.6 2.9 0.5 1.4 1.9 0.8 1.0 1.1 1.3 1.5 0.6 0.16
the reference transversal scan inside the isodose values: 60%, 80%, 90%, 95% and 99% of the prescription dose. Discussion Our study shows that ANNs are able to generate effective beam arrangements even when very basic patient information is used [17]. A simple set of inputs drawn directly from the TPS—such as dose, structure volume, and geometric parameters that define the localization of PTV and OARs—were sufficient to generate feasible beams. The models we have built prove that ANNs can use these inputs to generate output data efficiently. Moreover, ANNs can successfully solve the problem of developing appropriate algorithms capable of calculating complex beam configurations [28,29]. Generating an optimal treatment plan for SRS requires analysis of numerous different treatment parameters, including beam orientation. To solve this problem, customized beam orientations with numerous narrow beams should be applied. In addition, patient-to-patient variations in target localization and its proximity to adjacent brain structures must be taken into account. Performing the necessary steps manually through an iterative process is a time-consuming process requiring the human planner to make multiple, iterative adjustments to the main treatment variables to achieve the best dose distribution. During the testing phase of the ANNs, the RMS error factor between ANN and MP estimated values was similar in all 3 models and shows a satisfactory degree of accuracy. The validation phase showed that all three models produced satisfactory results, despite some performance differences. The mean doses in the OARs—particularly in the brain stem— were higher in the ANN-generated plans vs. the MP plan. The mean
Table 2 The maximal and minimal doses to the PTV and the maximal doses to the OARs for the MP-designed plans and the three ANN-generated plans. Parameter
Max body Min PTV Max PTV Max brain stem Max eye right Max eye left Max optic nerve right Max optic nerve left Max chiasm
MP
ANN1
ANN2
ANN3
Mean (%)
SD (%)
Mean (%)
SD (%)
Mean (%)
SD (%)
Mean (%)
SD (%)
107.4 92.6 106.5 8.8 1.2 1.0 3.2 2.0 3.9
3.0 2.4 8.6 11.4 2.5 2.4 10.9 3.2 7.1
106.9 92.8 107.4 14.0 2.6 4.1 5.2 4.5 7.6
3.2 1.3 3.2 15.3 4.0 7.4 12.8 6.8 11.5
106.9 91.3 107.3 15.7 1.5 3.3 3.7 5.1 8.6
3.2 7.1 3.2 17.5 3.6 5.5 5.7 12.3 13.1
107.5 92.4 107.9 14.6 2.7 3.2 5.5 4.8 7.8
3.3 1.4 3.3 14.8 4.7 5.5 14.2 7.7 14.8
MP indicates medical physicist. SD indicates standard deviation.
Please cite this article in press as: Skrobala A, Malicki J. Beam orientation in stereotactic radiosurgery using an artificial neural network. Radiother Oncol (2014), http://dx.doi.org/10.1016/j.radonc.2014.03.010
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An artificial neural network in stereotactic radiosurgery
Fig. 1. The percent agreement for the field areas encompassed by the 60%, 80%, 90%, 95% and 99% threshold isodose levels between the MP dose distribution and that predicted by the three ANN models.
doses calculated by ANN1 were slightly lower than the doses in the two other models (Table 2). Despite these differences, it should be noted that the doses presented in Table 2 are all reasonable and might justify further use of any of the three models, particularly since no significant differences between the models were observed for the minimal and maximal dose values to the PTV. The large variation in standard deviations is due to the relatively small sample size. The very similar RMS values for all ANN models indicate that neural nets are capable of generating beam orientations and treatment plans that are comparable to those created by an MP. As the results in Table 3 show, the ANN1 had the best performance in terms of these parameters, suggesting that ANN1 is superior to ANN2 and ANN3. In ANN2, RMS values were lower than the other models in only two parameters (brain stem and left eye Dmax), although perhaps this result is not surprising given that ANN2 was based on a reduced number of inputs obtained from ANN1. Gamma Index analysis (Fig. 1) showed that the ANN1 treatment plan had the best agreement with the MP-developed plan, as evidenced by the higher %FA values for all threshold isodose levels. However, coverage differences between the 3 ANNs were small (
