Resampling: An optimization method for inverse planning in robotic radiosurgery

Use of dose-area product to assess plan quality in robotic radiosurgery

PURPOSE

In robotic stereotactic radiosurgery (SRS), optimal selection of collimators from a set of fixed cones must be determined manually by trial and error. A unique and uniformly scaled metric to characterize plan quality could help identify Pareto-efficient treatment plans.

METHODS

The concept of dose-area product (DAP) was used to define a measure (DAPratio) of the targeting efficiency of a set of beams by relating the integral DAP of the beams to the mean dose achieved in the target volume. In a retrospective study of five clinical cases of brain metastases with representative target volumes (range: 0.5-5.68 ml) and 121 treatment plans with all possible collimator choices, the DAPratio was determined along with other plan metrics (conformity index CI, gradient index R50%, treatment time, total number of monitor units TotalMU, radiotoxicity index f12, and energy efficiency index η50%), and the respective Spearman's rank correlation coefficients were calculated. The ability of DAPratio to determine Pareto efficiency for collimator selection at DAPratio < 1 and DAPratio < 0.9 was tested using scatter plots.

RESULTS

The DAPratio for all plans was on average 0.95 ± 0.13 (range: 0.61-1.31). Only the variance of the DAPratio was strongly dependent on the number of collimators. For each target, there was a strong or very strong correlation of DAPratio with all other metrics of plan quality. Only for R50% and η50% was there a moderate correlation with DAPratio for the plans of all targets combined, as R50% and η50% strongly depended on target size. Optimal treatment plans with CI, R50%, f12, and η50% close to 1 were clearly associated with DAPratio < 1, and plans with DAPratio < 0.9 were even superior, but at the cost of longer treatment times and higher total monitor units.

CONCLUSIONS

The newly defined DAPratio has been demonstrated to be a metric that characterizes the target efficiency of a set of beams in robotic SRS in one single and uniformly scaled number. A DAPratio < 1 indicates Pareto efficiency. The trade-off between plan quality on the one hand and short treatment time or low total monitor units on the other hand is also represented by DAPratio.

Applying pytorch toolkit to plan optimization for circular cone based robotic radiotherapy

Background

Robotic linac is ideally suited to deliver hypo-fractionated radiotherapy due to its compact head and flexible positioning. The non-coplanar treatment space improves the delivery versatility but the complexity also leads to prolonged optimization and treatment time.

Methods

In this study, we attempted to use the deep learning (pytorch) framework for the plan optimization of circular cone based robotic radiotherapy. The optimization problem was topologized into a simple feedforward neural network, thus the treatment plan optimization was transformed into network training. With this transformation, the pytorch toolkit with high-efficiency automatic differentiation (AD) for gradient calculation was used as the optimization solver. To improve the treatment efficiency, plans with fewer nodes and beams were sought. The least absolute shrinkage and selection operator (lasso) and the group lasso were employed to address the “sparsity” issue.

Results

The AD-S (AD sparse) approach was validated on 6 brain and 6 liver cancer cases and the results were compared with the commercial MultiPlan (MLP) system. It was found that the AD-S plans achieved rapid dose fall-off and satisfactory sparing of organs at risk (OARs). Treatment efficiency was improved by the reduction in the number of nodes (28%) and beams (18%), and monitor unit (MU, 24%), respectively. The computational time was shortened to 47.3 s on average.

Conclusions

In summary, this first attempt of applying deep learning framework to the robotic radiotherapy plan optimization is promising and has the potential to be used clinically.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13014-022-02045-y.

Impact of prescription isodose level and collimator selection on dose homogeneity and plan quality in robotic radiosurgery

Purpose

In stereotactic radiosurgery (SRS), prescription isodoses and resulting dose homogeneities vary widely across different platforms and clinical entities. Our goal was to investigate the physical limitations of generating dose distributions with an intended level of homogeneity in robotic SRS.

Methods

Treatment plans for non-isocentric irradiation of 4 spherical phantom targets (volume 0.27–7.70 ml) and 4 clinical targets (volume 0.50–5.70 ml) were calculated using Sequential (phantom) or VOLO^TM (clinical) optimizers (Accuray, Sunnyvale, CA, USA). Dose conformity, volume of 12 Gy isodose (V12Gy) as a measure for dose gradient, and treatment time were recorded for different prescribed isodose levels (PILs) and collimator settings. In addition, isocentric irradiation of phantom targets was examined, with dose homogeneity modified by using different collimator sizes.

Results

Dose conformity was generally high (nCI ≤ 1.25) and varied little with PIL. For all targets and collimator sets, V12Gy was highest for PIL ≥ 80% and lowest for PIL ≤ 65%. The impact of PIL on V12Gy was highest for isocentric irradiation and lowest for clinical targets (VOLO^TM optimization). The variability of V12Gy as a function of collimator selection was significantly higher than that of PIL. V12Gy and treatment time were negatively correlated. Plans utilizing a single collimator with a diameter in the range of 70–80% of the target diameter were fastest, but showed the strongest dependence on PIL.

Conclusion

Inhomogeneous dose distributions with PIL ≤ 70% can be used to minimize dose to normal tissue. PIL ≥ 90% is associated with a marked and significant increase in off-target dose exposure. Careful selection of collimators during planning is even more important.

Supplementary Information

The online version of this article (10.1007/s00066-021-01872-4) contains supplementary material, which is available to authorized users.

Clinical impact of the VOLO optimizer on treatment plan quality and clinical treatment efficiency for CyberKnife

With the recent CyberKnife treatment planning system (TPS) upgrade from Precision 1.0 to Precision 2.0, the new VOLO optimizer was released for plan optimization. The VOLO optimizer sought to overcome some of the limitations seen with the Sequential optimizer from previous TPS versions. The purpose of this study was to investigate the clinical impact of the VOLO optimizer on treatment plan quality and clinical treatment efficiency as compared to the Sequential optimizer. Treatment plan quality was evaluated in four categories of patients: Brain Simple (BS), Brain Complex (BC), Spine Complex (SC), and Prostate (PC). A total of 60 treatment plans were compared using both the Sequential and VOLO optimizers with Iris and MLC collimation with the same clinical constraints. Metrics evaluated included estimated treatment time, monitor units (MUs) delivered, conformity index (CI), and gradient index (GI). Furthermore, the clinical impact of the VOLO optimizer was evaluated through statistical analysis of the patient population treated during the 4 months before (n = 297) and 4 months after (n = 285) VOLO introduction. Significant MU and time reductions were observed for all four categories planned. MU reduction ranged from −14% (BS Iris) to −52% (BC MLC), and time reduction ranged from −11% (BS Iris) to −22% (BC MLC). The statistical analysis of patient population before and after VOLO introduction for patients using 6D Skull tracking with fixed cone, 6D Skull tracking with Iris, and Xsight Spine tracking with Iris were −4.6%, −22.2%, and −17.8% for treatment time reduction, −1.1%, −22.0%, and −28.4% for beam reduction and −3.2%, −21.8%, and −28.1% for MU reduction, respectively. The VOLO optimizer maintains or improves the plan quality while decreases the plan complexity and improves treatment efficiency. We anticipate an increase in patient throughput with the introduction of the VOLO optimizer.

A convex optimization approach to radiation treatment planning with dose constraints

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.

Clinical usefulness of MLCs in robotic radiosurgery systems for prostate SBRT

Stereotactic body radiation therapy (SBRT) using recently introduced multileaf collimators (MLC) is preferred over circular collimators in the treatment of localized prostate cancer. The objective of this study was to assess the clinical usefulness of MLCs in prostate SBRT by comparing the effectiveness of treatment plans using fixed collimators, variable collimators, and MLCs and by ensuring delivery quality assurance (DQA) for each. For each patient who underwent conventional radiation therapy for localized prostate cancer, mock SBRT plans were created using a fixed collimator, a variable collimator, and an MLC. The total MUs, treatment times, and dose-volume histograms of the planning target volumes and organs at risk for each treatment plan were compared. For DQA, a phantom with a radiochromic film or an ionization chamber was irradiated in each plan. We performed gamma-index analysis to evaluate the consistency between the measured and calculated doses. The MLC-based plans had an ~27% lower average total MU than the plans involving other collimators. Moreover, the average estimated treatment time for the MLC plan was 31% and 20% shorter than that for the fixed and variable collimator plans respectively. The gamma-index passing rate in the DQA using film measurements was slightly lower for the MLC than for the other collimators. The DQA results acquired using the ionization chamber showed that the discrepancies between the measured and calculated doses were within 3% in all cases. The results reinforce the usefulness of MLCs in robotic radiosurgery for prostrate SBRT treatment planning; most notably, the total MU and treatment time were both reduced compared to the cases using other types of collimators. Moreover, although the DQA results based on film dosimetry yielded a slightly lower gamma-index passing rate for the MLC than for the other collimators, the MLC accuracy was determined to be sufficient for clinical use.

Inverse treatment planning for spinal robotic radiosurgery: an international multi-institutional benchmark trial

Stereotactic radiosurgery (SRS) is the accurate, conformal delivery of high‐dose radiation to well‐defined targets while minimizing normal structure doses via steep dose gradients. While inverse treatment planning (ITP) with computerized optimization algorithms are routine, many aspects of the planning process remain user‐dependent. We performed an international, multi‐institutional benchmark trial to study planning variability and to analyze preferable ITP practice for spinal robotic radiosurgery. 10 SRS treatment plans were generated for a complex‐shaped spinal metastasis with 21 Gy in 3 fractions and tight constraints for spinal cord (V14Gy<2 cc, V18Gy<0.1 cc) and target (coverage >95%). The resulting plans were rated on a scale from 1 to 4 (excellent‐poor) in five categories (constraint compliance, optimization goals, low‐dose regions, ITP complexity, and clinical acceptability) by a blinded review panel. Additionally, the plans were mathematically rated based on plan indices (critical structure and target doses, conformity, monitor units, normal tissue complication probability, and treatment time) and compared to the human rankings. The treatment plans and the reviewers' rankings varied substantially among the participating centers. The average mean overall rank was 2.4 (1.2‐4.0) and 8/10 plans were rated excellent in at least one category by at least one reviewer. The mathematical rankings agreed with the mean overall human rankings in 9/10 cases pointing toward the possibility for sole mathematical plan quality comparison. The final rankings revealed that a plan with a well‐balanced trade‐off among all planning objectives was preferred for treatment by most participants, reviewers, and the mathematical ranking system. Furthermore, this plan was generated with simple planning techniques. Our multi‐institutional planning study found wide variability in ITP approaches for spinal robotic radiosurgery. The participants', reviewers', and mathematical match on preferable treatment plans and ITP techniques indicate that agreement on treatment planning and plan quality can be reached for spinal robotic radiosurgery.

PACS number(s): 87.55.de

A method to improve dose gradient for robotic radiosurgery

For targets with substantial volume, collimators of relatively large size are usually selected to minimize the treatment time in robotic radiosurgery. Their large penumbrae may adversely affect the dose gradient around the target. In this study, we implement and evaluate an inner‐shell planning method to increase the dose gradient and reduce dose to normal tissues. Ten patients previously treated with CyberKnife M6 system were randomly selected with the only criterion being that PTV be larger than 2 cm3. A new plan was generated for each patient in which the PTV was split into two regions: a 5 mm inner shell and a core, and a 7.5 mm Iris collimator was exclusively applied to the shell, with other appropriate collimators applied to the core depending on its size. The optimization objective, functions, and constraints were the same as in the corresponding clinical plan. The results were analyzed for V12 Gy, V9 Gy, V5 Gy, and gradient index (GI). Volume reduction was found for the inner‐shell method at all studied dose levels as compared to the clinical plans. The absolute dose‐volume reduction ranged from 0.05 cm3 to 18.5 cm3 with a mean of 5.6 cm3 for 12 Gy, from 0.2 cm3 to 38.1 cm3 with a mean of 9.8 cm3 for 9 Gy, and from 1.5 cm3 to 115.7 cm3 with a mean of 24.8 cm3 for 5 Gy, respectively. The GI reduction ranged from 3.2% to 23.6%, with a mean of 12.6%. Paired t‐test for GI has a p‐value of 0.0014. The range for treatment time increase is from ‐3 min to 20 min, with a mean of 7.0 min. We conclude that irradiating the PTV periphery exclusively with the 7.5 mm Iris collimator, rather than applying mixed collimators to the whole PTV, can substantially improve the dose gradient, while maintaining good coverage, conformity, and reasonable treatment time.

PACS number: 87.55.de

Multicriteria optimization of the spatial dose distribution

PURPOSE

Treatment planning for radiation therapy involves trade-offs with respect to different clinical goals. Typically, the dose distribution is evaluated based on few statistics and dose-volume histograms. Particularly for stereotactic treatments, the spatial dose distribution represents further criteria, e.g., when considering the gradient between subregions of volumes of interest. The authors have studied how to consider the spatial dose distribution using a multicriteria optimization approach.

METHODS

The authors have extended a stepwise multicriteria optimization approach to include criteria with respect to the local dose distribution. Based on a three-dimensional visualization of the dose the authors use a software tool allowing interaction with the dose distribution to map objectives with respect to its shape to a constrained optimization problem. Similarly, conflicting criteria are highlighted and the planner decides if and where to relax the shape of the dose distribution.

RESULTS

To demonstrate the potential of spatial multicriteria optimization, the tool was applied to a prostate and meningioma case. For the prostate case, local sparing of the rectal wall and shaping of a boost volume are achieved through local relaxations and while maintaining the remaining dose distribution. For the meningioma, target coverage is improved by compromising low dose conformality toward noncritical structures. A comparison of dose-volume histograms illustrates the importance of spatial information for achieving the trade-offs.

CONCLUSIONS

The results show that it is possible to consider the location of conflicting criteria during treatment planning. Particularly, it is possible to conserve already achieved goals with respect to the dose distribution, to visualize potential trade-offs, and to relax constraints locally. Hence, the proposed approach facilitates a systematic exploration of the optimal shape of the dose distribution.

Improved efficiency of multi-criteria IMPT treatment planning using iterative resampling of randomly placed pencil beams

This study investigates whether 'pencil beam resampling', i.e. iterative selection and weight optimization of randomly placed pencil beams (PBs), reduces optimization time and improves plan quality for multi-criteria optimization in intensity-modulated proton therapy, compared with traditional modes in which PBs are distributed over a regular grid. Resampling consisted of repeatedly performing: (1) random selection of candidate PBs from a very fine grid, (2) inverse multi-criteria optimization, and (3) exclusion of low-weight PBs. The newly selected candidate PBs were added to the PBs in the existing solution, causing the solution to improve with each iteration. Resampling and traditional regular grid planning were implemented into our in-house developed multi-criteria treatment planning system 'Erasmus iCycle'. The system optimizes objectives successively according to their priorities as defined in the so-called 'wish-list'. For five head-and-neck cancer patients and two PB widths (3 and 6 mm sigma at 230 MeV), treatment plans were generated using: (1) resampling, (2) anisotropic regular grids and (3) isotropic regular grids, while using varying sample sizes (resampling) or grid spacings (regular grid). We assessed differences in optimization time (for comparable plan quality) and in plan quality parameters (for comparable optimization time). Resampling reduced optimization time by a factor of 2.8 and 5.6 on average (7.8 and 17.0 at maximum) compared with the use of anisotropic and isotropic grids, respectively. Doses to organs-at-risk were generally reduced when using resampling, with median dose reductions ranging from 0.0 to 3.0 Gy (maximum: 14.3 Gy, relative: 0%-42%) compared with anisotropic grids and from -0.3 to 2.6 Gy (maximum: 11.4 Gy, relative: -4%-19%) compared with isotropic grids. Resampling was especially effective when using thin PBs (3 mm sigma). Resampling plans contained on average fewer PBs, energy layers and protons than anisotropic grid plans and more energy layers and protons than isotropic grid plans. In conclusion, resampling resulted in improved plan quality and in considerable optimization time reduction compared with traditional regular grid planning.