Evaluation of a new inverse, globally convex TPS algorithm for Gamma Knife® radiosurgery within a prospective trial - advantages and disadvantages in practical application

Open AccessPublished:June 28, 2022DOI:



      A new inverse planning (IP) software based on a global convex optimization algorithm was adopted for the Gamma Knife radiosurgery (GKRS). We investigated the IP's suitability for daily clinical use and its applicability for different cerebral entities.

      Methods and Materials

      For 230 target volumes, IP was tested in a prospective trial. The computed treatment plans were compared with conventional expert pre-plans, which included forward planning by the expert and local internal optimization. Based on the same dose constraints, we used the default settings for the inverse calculation of the treatment plans. Plan quality metrics such as the Paddick conformity index (PCI) were compared for both planning techniques with additional subdivisions into the three selectable IP planning strategies and different entity groups.


      IP calculated treatment plans of the quality similar to pre-plans created by expert planners. Some plan quality metrics, especially those related to conformity and dose gradient, attained statistically significant higher scores combined with high coverage for the inversely generated plans except for the selectivity optimizing strategy. Normal Brain V12Gy or V10Gy did not show significant differences for the coverage optimizing strategies. IP demonstrated significantly shorter planning times versus manual planning as well as greater numbers of isocenters, often associated with longer treatment times. In terms of total time, these differences almost balanced out again.


      Our results suggest that IP is advantageous for complex tumors. We observed general clinical significance for conformity and superiority for the selectivity optimizing strategy. Finally, the high-quality calculation from IP enables the novices in the profession to achieve the treatment of the pre-plan quality. IP allows for optimizing the sparing of surrounding tissue and the conformity for benign tumors within a short time. Thus, IP forms a solid basis for further planning on the treatment day.

      Index of Abbreviations:

      AN (acoustic neuroma), AVM (arteriovenous malformation), BOT (beam-on time), CT (computed tomography), DVH (dose-volume histogram), EI (efficiency index), GI (gradient index), GK (Gamma Knife®), GKRS (Gamma Knife radiosurgery), IP (inverse planning (with IntuitivePlan®)), LGP (Leksell GammaPlan®), MRI (magnetic resonance imaging), OAR (organ at risk), PCI (Paddick conformity index), PD (prescription dose), PI (prescription isodose), SRS (stereotactic radiosurgery), TPS (treatment planning system), TV (target volume)
      In the early 1950s, the Swedish neurosurgeon Lars Leksell introduced stereotactic radiosurgery to treat localized narrow lesions in the brain1. Leksell used cross-firing photon beams instead of an open surgery procedure. Recently, the use of Leksell's approach, known as Gamma Knife® (GK), has considerably increased and has been applied to treat benign and malignant brain tumors, vascular malformations, and functional disorders because of its high dose gradient and high precision2–4.
      In contrast to other radiotherapies, in Gamma Knife® radiosurgery (GKRS), the standard technique for radiation treatment planning is forward planning, which includes the manual placement of isocenters. In the next step, they can be edited through the internal optimization in Leksell GammaPlan® (LGP) software, optimizing the position, weight, and collimator configuration of all the shots in the target according to an objective function. However, this inverse dose planning often finds only the local and not the global minimum of the cost function5. In addition, the time for treatment planning depends on the planner's experience. Therefore, an alternative or complement is being sought in the form of an automated inverse dose planning, particularly for complex and irregularly shaped target volumes (TVs). The software IntuitivePlan® (IP) with an inverse planning algorithm developed by a university start-up company presents such an alternative. It was CE marked for its use with Leksell Gamma Knife® in June 2019. We have been provided with this algorithm free of charge for study purposes. The software promises to find the global minimum by prescribing a dose to the target volume and specifying dose constraints for the organs at risk (OARs)5.
      The specific objective of this study was to examine the default performance of IP in comparison to the common expert planning technique in clinical routine. We conducted a prospective study with 117 cases of different cerebral diseases using both methods in each case. Further, our research aimed to verify the applicability of IP for various diseases that occurred within the scope of this study.
      Methods and Materials
      Study assembly
      In total, over 100 planning examples with different cerebral diseases treated with GK Perfexion™ participated in the prospective clinical trial. In the final analysis, the data of a total of 117 treatment cases were evaluated. The treated entities are classified as benign, malignant, functional, and vascular (Table 1). Cerebral singular and multiple metastases were counted among malign disorders. Acoustic neuromas (ANs) and other neurinomas, pituitary adenomas, and meningiomas were classed as benign entities, whereas arteriovenous malformations (AVMs), fistulas, and cavernomas were categorized as vascular diseases and trigeminal neuralgias as functional disorders. The contouring of TVs and OARs was performed on T1- and T2-weighted 1-mm thin-layered 3D magnetic resonance imaging (MRI) images by Brainlab® Elements™ (Anatomical Mapping 1.1, SmartBrush 3.0).
      Table 1Patient demographics
      nV50% incm3PD50%in Gy
      Malign tumors1640.362520.0
      Benign tumors611.478014.0
      Vascular diseases41.365516.0
      Functional diseases10.011090.0
      Abbrevations: TV = target volume; n = number of the TVs; V50%= median target volume; PD50%= median prescription dose for forward planning.
      Table 1 Anonymized for Review.
      Forward planning with LGP
      The forward planning was performed by expert planners with long-term experience as medical physics experts and two years’ experience in GK therapy. The treatment planning system (TPS) used in this study is called Leksell GammaPlan® (version 11.3.1). With LGP's internal inverse planning feature, the plans were generally optimized. For small-sized metastasis, only manual forward planning was used, mostly with one shot.
      In general, the criteria for a good or acceptable plan are as follows: coverage of 0.95 to 1.00, selectivity of 0.7 to 1.00, gradient index below 3.0, beam-on time between 10min and 120min. These may deviate in the individual case, depending on medical reasons such as the disease and the patient's medical history. The coverage, for instance, is of primary importance for single metastases, whereas the selectivity and the irradiation time are decisive factors for ANs and multiple metastases, respectively.
      Inverse planning with IP
      The cases were replanned through the inverse planning software IntuitivePlan® (version 1.0) after the export of the patient data from LGP. According to the departmental clinical protocol, the same dose constraints as for the LGP planning were set up. The optimization strategies (“maximize coverage” with the options “favor selectivity” or “favor BOT” and “maximize selectivity”) were specifically applied for the case or entity. To compare the elementary performance of the new algorithm with the present treatment (forward) planning method, neither the default parameters for each strategy were modified nor were any other sophisticated functions used in this study, such as 3D manipulation of the isodose surfaces. For patient treatment, the resulting shot configuration of IP plans generally needs to be exported back to LGP. It is necessary to adjust the optimized prescription dose (PD) from IP to integers, which consequently affects the dose distribution and plan quality metrics, but to a slight extent. Metastases were predominantly optimized according to the two strategies focusing on coverage, whereas the strategies “maximize selectivity” and “maximize coverage, favor selectivity” were mainly applied to benign entities, vascular and functional diseases.
      Treatment plan evaluation
      Both LGP and IP plans were preliminary and were based on non-stereotactic 3D MRI images with a simulated stereotactic frame. On the treatment day, the pre-plans were finally adjusted to the entity by co-registration with stereotactic tomography (CT).
      To compare the planning results from both treatment planning methods or rather to assess the benefit for the target and healthy tissue, the following parameters were evaluated: coverage (C), selectivity (S), gradient index (GI), Paddick conformity index6(PCI), efficiency index (EI), beam-on time (BOT), planning/computational time (tplan), total set-up time (ttotal), number of shots (nshots), number of blocked sectors (nblockedsectors), prescription isodose (PI), Dmin, Dmean, Dmax, and for risk assessment for brain tissue and OAR, V12Gy, V10Gy,Dskullmean, DOARtransgression. The efficiency index proposed by Paddick7 considers the ratio of integral dose inside and outside the target:
      η50%=usefulenergytotalenergy=IntegralDoseTVIntegralDosePIV50%=DminDmaxTVdDoseDminDmaxPIV50%dDose .
      The parameters Dmin, Dmean, and Dmax describe the minimum, mean, and maximum dose, respectively. PIV50%. is the absolute volume of 50% of the PI. The efficiency index for multiple targets (Gη12Gy) fixes the problem of the gradient index for nearby targets that can overlap in PIV50%7:
      Gη12Gy=n=2NIntegralDoseTVnGlobalIntegralDose12Gy .
      The efficiency indices η50% and Gη12Gy need to be extracted from the DVHs for LGP. The EI for single targets is automatically calculated by IntuitivePlan®.
      One of the most relevant late toxicities occurring after stereotactic radiosurgery (SRS) is radionecrosis, which correlates with the volume of brain irradiated with 12Gy (V12Gy) or 10Gy (V10Gy)8. Likewise, we introduced the parameter DOARtransgression, the difference between the maximum dose and dose constraint in the respective OAR (brainstem, cochlea, optic chiasma, pituitary, trigeminal nerve, vestibular apparatus, optical nerve). ttotal describes the sum of BOT and planning time. For the statistical t-tests, the times per case instead of per TV have been considered for both the plan calculation time and the total time because IP only reported the total calculation time for the cases with multiple target volumes. Since the skull contouring was not feasible with the available Brainlab® Elements™ version, the mean brain dose is represented by the parameter Dskullmean.
      Statistical analysis
      Initially, we compared the IP strategies separately with LGP. Moreover, we investigated IP in terms of its applicability to malignant and benign diseases. To determine the statistical significance between the parameters of both planning methods, we conducted two-sided paired samples t-tests9,10 with a significance level of 5% (α=0.05). The null hypothesis states that the mean values of LGP and IP do not differ (μLGP=μIP).
      With multiple testing, i.e., running various statistical tests on the same sample, the overall risk that at least one of the tests becomes falsely significant increases. To counteract alpha error accumulation, we used the conservative Bonferroni correction9, which is why the significance level was adapted to α*=α/nwith n as the number of tests (α*=0.05/20=0.0025).
      Because the sample size was too small for a statistical evaluation for both vascular and functional diseases, only the statistical calculations for the malignant and benign tumors were analyzed.
      Table 2 provides the summary statistics of the performed t-tests dependent on the IP planning strategy, including p-values for each parameter and the mean difference (per TV) between the respective IP and LGP plan. Exemplary box plots in Fig. 1 illustrate the distributions of the parameter selectivity.
      Table 2Results with IP plans for the default single run depending on the strategy
      ParameterStrategyLGP X¯±sIP Y¯±s(XY)¯±sp(α=0.05)Significance
      PI in %i)51±648±92.9±110.0003***yes
      ii)51 ± 756 ± 12-4.7±132.49*106***yes
      ii)0.996 ± 0.0080.998 ± 0.014-0.0026±0.0160.0339*yes
      ii)0.54 ± 0.210.61 ± 0.12-0.071±0.250.0002***yes
      ii)3.1 ± 0.53.1 ± 0.50.03±0.60.5472no
      ii)0.53 ± 0.210.61 ± 0.12-0.074±0.250.0001***yes
      EI in %i)40±1350±92.3±61.74*1010***yes
      ii)39 ± 1137 ± 101.5±120.3911no
      tplan per case in mini)7±74±52.3±60.0021**yes
      ii)7 ±84 ±51.8 ±120.0654no
      BOT in mini)25±1335±16-10±152.78*1017***yes
      ii)23 ±1222 ±101.8 ±120.0400*yes
      ttotal per case in mini)70±5090±70-23±504.16*105***yes
      ii)70 ±6060±604±400.4194no
      ii)4 ±510±8-6.6±75.58*1030***yes
      V12Gy in cm3i)4±103±51.1±90.0906no
      V10Gy in cm3i)5±64±60.74±40.0050**yes
      Dskullmean in Gyi)0.4±0.40.4±0.40.028±0.160.1656no
      Dmin in Gyi)17±517.7±2.7-0.6±50.0796no
      Dmean in Gyi)28±728±40.7±60.1012no
      Dmax in Gyi)37±640±9-3.3±95.57*107***yes
      DOARtransgression in Gyi)-1±6-2±51.3±2.00.0015**yes
      Abbrevations: i) "maximize coverage, favor selectivity"; ii) "maximize coverage, favor BOT"; iii) "maximize selectivity"; X¯ = mean value of the respective parameter for LGP; Y¯ = mean value for IP; s= corrected sample standard deviation.
      EI includes η50% and Gη12Gy.
      * p<0.05; ** p<0.01; *** p<0.001.
      Marked in red are those rows that have a p-value just below α=0.05 but above α*. Values for DOARtransgression should be interpreted with caution because OARs did not exist for every case (e.g., metastases). For the strategies i), ii) and iii) 28, 7, and 87 OARs are counted, respectively. Notice the different sample sizes for each strategy and every parameter.
      Figure 1
      Figure 1Box plots for parameter selectivity dependent on the IP strategy including all cases. i) "maximize coverage, favor selectivity", ii) "maximize coverage, favor BOT", iii) "maximize selectivity".
      Figure 1 Anonymized for Review.
      On average, we found significantly higher selectivity and PCI values for all available IP planning strategies with high significance (<0.001). These parameters improved remarkably for the selectivity strategies with a lower variance, as can be seen from the box plots in Fig. 1. This is additionally visualized in Fig. 2 in which the inversely optimized isodose is closer to the tumor outline than for the conventional planning method.
      Figure 2
      Figure 2Horizontal T2-weighted MRIs demonstrating the comparison between the IP and LGP plan for a representative AN case adjacent to the brainstem. Left: LGP plan with C=0.99and S=0.84. Right: IP plan with C=0.98 and S=0.94. The red-black shaded area represents the intersection of the TV (red) and the 12-Gy prescription isodose (yellow). Abbreviation: PIV = prescription isodose volume.
      Figure 2 Anonymized for Review.
      The mean IP coverage values were barely distinguishable from the LGP coverage values, only inferior for the strategy prioritizing selectivity. The same applied to the mean GI values and their variance within the interquartile range, except for the strategy “maximize coverage, favor selectivity”. These results were reflected in an overall improved EI, or for the “maximum coverage, favor BOT” strategy in an equal EI. Although there was a significantly lower tplan per case for the strategies which prioritized selectivity, IP was slightly inferior to LGP in terms of BOT. These differences almost balanced out again in terms of ttotal. Furthermore, the isocenter number increased for all IP strategies. It should be noted that the optimized PI was either significantly below or above the manual adjusted, experience- and knowledge-based PI, independently of the IP strategy. The surrounding tissue, whose protection is characterized by V12Gy or V10Gy11,12, was exposed to approximately the same dose for both planning methods with similar variance, except for the strategy “maximize selectivity”.
      In contrast, the inverse planning yielded a high GI for the trigeminal neuralgia compared to LGP. Three more cases with trigeminal neuralgia were not included in the statistical testing, because they were not exportable from IP due to their high gradient index (>20) or their unsafe declared coverage. For all cases, the calculated PI was much higher than the PI set by the expert planner.
      Table 2 Anonymized for Review.
      We additionally tested the performance of the inverse optimization for benign and malignant diseases separately (see Fig. 3, Table B1, B2 and Fig. A2). Fig. 4 specifically shows the selectivity distribution for micrometastases with a volume <1cm3.
      Figure 3
      Figure 3Comparison of benign and malignant entities regarding selectivity. Top: box plots for benign entities depending on the strategy i)/ii)/iii) (same notation as in ). Bottom: box plots for malignant entities.
      Figure 4
      Figure 4Results for micrometastases regarding selectivity. Box plots for micrometastases (with 1mm safety margin) depending on the strategy i) and ii) (same notation as in ).
      Figure 3 Anonymized for Review.
      Figure 4 Anonymized for Review.
      The results of our prospective trial with over 100 cases demonstrated that the inverse planning software IntuitivePlan® calculated comparable high-quality irradiation plans competing with the conventional forward planning. Significantly higher conformity values, shorter planning time, and better OAR sparing characterized the inverse calculated plans. The study demonstrated that the resulting IP plans with their quality metrics were highly dependent on the chosen strategy.
      Compared to forward planning, the strategy “maximize selectivity” provided a significant improvement in conformity and a dose reduction in the brain as well as the respective OAR under reduced planning time. However, the dose gradients stayed the same and the BOT changed slightly. Even though the coverage was significantly lower for IP plans, this strategy was superior to the other two strategies used because the surrounding tissue and the OAR were exposed to a lower dose. Hence, we recommend “maximize selectivity” for benign cases due to their irregular shape that requires much experience and planning time. The "maximize coverage, favor selectivity" strategy obtained results similar to those of the selectivity-only optimizing strategy. Besides, the same TV coverage as for LGP and a steeper dose fall-off outside the TV were achieved compared to LGP. Substantiated by significantly higher nshots, the BOT, however, was much longer, which is known to reduce the biologically effective dose13 when treating malignant tumors.
      To improve the coverage for the final plan, either the IP preset for the minimum selectivity could be changed before computing or the PI could be adapted after the optimization and the back-import into LGP. In most cases, we finally adapted the PI to achieve an even higher plan quality than the first-run IP pre-plans with the default optimization settings. Alternatively, the dosimetrist could manually adjust the isocenter configuration and the PI in the graphical user interface of IP.
      A striking and contrasting result was the large difference in nblockedsectors. In general, manual planning includes more blocked sectors to spare radiosensitive tissue. Nevertheless, as the IP results reveal, there is no loss in the OAR protection without any blocked sectors.
      The PI differed significantly for all strategies, which consequently influenced Dmax in the TV. Significantly higher isodoses simultaneously reduced the maximum doses (see strategy “maximum selectivity”). In GKRS, the PI for manual forward planning is usually the 50% isodose because this is where the steepest dose gradients can be expected14. The effect of a higher or lower Dmax on the treatment outcome could not be confirmed so far so that a change of this is quite legitimate15,16.
      Upon closer examination of the benign diseases, IP was only better than LGP in GI and barely better in tplanand DOARtransgression. With respect to coverage, conformity, and sparing of surrounding tissue, IP was as good as LGP. The PI, by contrast, was comparatively higher for the same PD so that the Dmax in the target was lower. As a consequence, the reduced Dmax could decline the desired ablative effect of single-time irradiation of benign tumors. The dose-volume data of normal brain, a good predictor of radionecrosis, was approximately the same for both planning methods, but with higher brain protection for the “maximum selectivity” strategy. Further reduction would still be desirable. According to Blonigen et al8, the risk to develop radionecrosis would be already 34% for measured values of 6.414.5cm3 and 4.810.8cm3 in the V10Gy and V12Gy distribution, respectively.
      The so-called “one-shot plans”, which were created manually for multiple metastases and micrometastases, did show advantages compared to IP plans. Although the target conformity was much higher for IP plans optimized with “maximum coverage, favor selectivity” than that for LGP, the most important goal for these malignant cases is the TV coverage, followed by a short BOT for patients with a poor state of health. Since the strategy “maximum coverage, favor selectivity” primarily focuses on conformity, the BOT is considerably increased. For multiple metastases, the strategy “maximize coverage, favor BOT” seems to be most suitable but often not preferable to the standard manual method in which a single isocenter with the smallest possible collimator is used. For micrometastases, the surrounding brain tissue receives little dose, even with high coverage. Thus, a lower selectivity of manual single-shot plans would be less clinically relevant. More selective plans, generated by IP as default, would lead to an increase in BOT due to higher nshots.
      Previous work by Régis17 and Paddick18 focused primarily on ANs and AVMs that require maximum selectivity. In our trial, however, the small sample size of AVMs hampered meaningful conclusions. In contrast to these previous studies 17,18, the IP strategy was not the same for all cases and varied depending on the entity. The significantly higher nshots of IP plans, which is contrary to usual expert planning, is in line with Paddick and Régis17,18. Yet, we could not verify the strong influence of nshots on the BOT. The non-superiority of the GI (except for the strategy “maximize coverage, favor selectivity”) is also consistent with former studies. Our study does not (entirely) confirm previous results regarding selectivity and PCI, because these studies achieved higher conformity values for their manual plans than our manual pre-plans (S=0.910±0.074, PCI=0.898±0.076 in Régis’ study; S=0.856, PCI=0.824 in Paddick's study). Paddick et al. assumed a positive correlation between BOT and PCI18. We proved that these parameters correlate depending on the planning method (rPearson=0.098, rPearson=0.32, rPearson=0.03 for “maximize coverage, favor selectivity”, “maximize coverage, favor BOT”, “maximize selectivity”). ANs represent one of the most challenging indications in SRS, even though the GK was originally developed for such purposes in 196919,20. Our study included 21 AN cases for which 20 IP plans were preferred with the strategy “maximize selectivity” due to comparatively higher selectivity (IP: 0.89±0.06 vs. LGP: 0.74±0.14) despite lower coverage (IP: 0.96±0.04vs. LGP: 0.987±0.007). Both previous studies did not verify the superiority of IP in OAR and brain sparing. Especially for the strategy “maximize selectivity”, our findings contrast with these results. The underlying reason is that in both studies17,18, no pre-plans but highly optimized forward plans were used for the comparison with IP.
      The planner's assessment and experience considerably influence the resulting plans, especially for GK centers with less experienced in stereotaxis personnel. Moreover, further improvements in the clinically acceptable LGP pre-plans (e.g., higher conformity) were certainly possible but had to be weighed against the planning time. As noted, the compared plans were preliminary. Staffed with more dosimetrists and equipped with a stereotactic planning MRI allowing for planning directly on stereotactic MRI images, many GK facilities routinely do not use pre-planning. Our methodology is therefore more suitable for smaller institutions. If pre-planning, the planner can spend more time on a specific case, compare different plan versions, and then select the optimal plan, which removes the time pressure on the treatment day as the patient is waiting with the frame attached. For teams with medium experience in stereotaxis, such an algorithm provides a plan alternative or basis.
      Unlike non-stereotactic TPSs, TPS in GKRS did not include a global algorithm. IP was the first available third-party algorithm for GK. A comparable algorithm Leksell Gamma Knife® Lightning was offered only later by the GK manufacturer. According to our information, there is no direct relation between the two algorithms21. The algorithm used here is freely available now and it has been and is still used in other, non-medical areas (e.g., in the planning of power supply networks) and for scientific purposes. Although the implementation in a GK-plan-compatible software is longer available for purchase, its fundamental aspects of the general usage of an optimization algorithm can nevertheless be transferred. First, inverse planning can save much time in planning and make full use of the GK device. Second, if one has the possibility to select different objectives/strategies, several optimized plans can be compared more easily to find the most suitable plan for the respective disease, its stage, and localization. Further possibilities for manual post-plan adaptation or for modification of default optimization settings, as provided by IP, allow for taking the anamnesis into account.
      The inverse planning algorithm achieved clinically acceptable pre-plans for all planning strategies within a reasonable time and with at least equal or superior quality compared to LGP. Therefore, the algorithm proves beneficial in clinical routine, especially for smaller GK facilities with less experienced planners. Our findings suggest that inverse planning is generally appropriate for complex-shaped tumors and that forward planning, by contrast, is suitable for trigeminal neuralgia or micrometastases.
      Conflict of Interest Statement for All Authors:
      Conflict of Interest: None
      Funding Statement:
      Funding: None.
      Data Availability Statement for this Work:
      Research data are stored in an institutional repository and will be shared upon request to the corresponding author.
      Supplementary Materials
      Further box plots of the parameters investigated as well as the analysis of benign and malign tumors can be found in the online version
      Declaration of interests
      ☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
      ☒ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
      Jan Bostroem reports equipment, drugs, or supplies was provided by Intuitive Therapeutics.
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      Appendix. Supplementary materials