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[en] Robotic radiosurgery enables precise dose delivery throughout the body. Planning for robotic radiosurgery comprises of finding a suitable set of beams and beam weights. The problem can be addressed by generating a large set of candidate beams, and selection of beams with nonzero weight by mathematical programming. We propose to use different randomized beam generation methods depending on the type of lesion and the clinical objective. Results for three patient cases indicate that this can improve the plan quality. (orig.)

[en] Purpose: The CyberKnife delivers a large number of beams originating at different non-planar positions and with different orientation. We study how much the quality of treatment plans depends on the beams considered during plan optimization. Particularly, we evaluate a new approach to search for optimal treatment plans in parallel by running optimization steps concurrently. Methods: So far, no deterministic, complete and efficient method to select the optimal beam configuration for robotic SRS/SBRT is known. Considering a large candidate beam set increases the likelihood to achieve a good plan, but the optimization problem becomes large and impractical to solve. We have implemented an approach that parallelizes the search by solving multiple linear programming problems concurrently while iteratively resampling zero weighted beams. Each optimization problem contains the same set of constraints but different variables representing candidate beams. The search is synchronized by sharing the resulting basis variables among the parallel optimizations. We demonstrate the utility of the approach based on an actual spinal case with the objective to improve the coverage. Results: The objective function is falling and reaches a value of 5000 after 49, 31, 25 and 15 iterations for 1, 2, 4, and 8 parallel processes. This corresponds to approximately 97% coverage in 77%, 59%, and 36% of the mean number of iterations with one process for 2, 4, and 8 parallel processes, respectively. Overall, coverage increases from approximately 91.5% to approximately 98.5%. Conclusion: While on our current computer with uniform memory access the reduced number of iterations does not translate into a similar speedup, the approach illustrates how to effectively parallelize the search for the optimal beam configuration. The experimental results also indicate that for complex geometries the beam selection is critical for further plan optimization

[en] Purpose: Ultrasound presents a fast, volumetric image modality for real-time tracking of abdominal organ motion. How-ever, ultrasound transducer placement during radiation therapy is challenging. Recently, approaches using robotic arms for intra-treatment ultrasound imaging have been proposed. Good and reliable imaging requires placing the transducer close to the PTV. We studied the effect of a seven degrees of freedom robot on the fea-sible beam directions. Methods: For five CyberKnife prostate treatment plans we established viewports for the transducer, i.e., points on the patient surface with a soft tissue view towards the PTV. Choosing a feasible transducer pose and using the kinematic redundancy of the KUKA LBR iiwa robot, we considered three robot poses. Poses 1 to 3 had the elbow point anterior, superior, and inferior, respectively. For each pose and each beam starting point, the pro-jections of robot and PTV were computed. We added a 20 mm margin accounting for organ / beam motion. The number of nodes for which the PTV was partially of fully blocked were established. Moreover, the cumula-tive overlap for each of the poses and the minimum overlap over all poses were computed. Results: The fully and partially blocked nodes ranged from 12% to 20% and 13% to 27%, respectively. Typically, pose 3 caused the fewest blocked nodes. The cumulative overlap ranged from 19% to 29%. Taking the minimum overlap, i.e., considering moving the robot’s elbow while maintaining the transducer pose, the cumulative over-lap was reduced to 16% to 18% and was 3% to 6% lower than for the best individual pose. Conclusion: Our results indicate that it is possible to identify feasible ultrasound transducer poses and to use the kinematic redundancy of a 7 DOF robot to minimize the impact of the imaging subsystem on the feasible beam directions for ultrasound guided and motion compensated SBRT. Research partially funded by DFG grants ER 817/1-1 and SCHL 1844/3-1.

[en] In robotic radiosurgery, it is necessary to compensate for systematic latencies arising from target tracking and mechanical constraints. This compensation is usually achieved by means of an algorithm which computes the future target position. In most scientific works on respiratory motion prediction, only one or two algorithms are evaluated on a limited amount of very short motion traces. The purpose of this work is to gain more insight into the real world capabilities of respiratory motion prediction methods by evaluating many algorithms on an unprecedented amount of data. We have evaluated six algorithms, the normalized least mean squares (nLMS), recursive least squares (RLS), multi-step linear methods (MULIN), wavelet-based multiscale autoregression (wLMS), extended Kalman filtering, and ε-support vector regression (SVRpred) methods, on an extensive database of 304 respiratory motion traces. The traces were collected during treatment with the CyberKnife (Accuray, Inc., Sunnyvale, CA, USA) and feature an average length of 71 min. Evaluation was done using a graphical prediction toolkit, which is available to the general public, as is the data we used. The experiments show that the nLMS algorithm—which is one of the algorithms currently used in the CyberKnife—is outperformed by all other methods. This is especially true in the case of the wLMS, the SVRpred, and the MULIN algorithms, which perform much better. The nLMS algorithm produces a relative root mean square (RMS) error of 75% or less (i.e., a reduction in error of 25% or more when compared to not doing prediction) in only 38% of the test cases, whereas the MULIN and SVRpred methods reach this level in more than 77%, the wLMS algorithm in more than 84% of the test cases. Our work shows that the wLMS algorithm is the most accurate algorithm and does not require parameter tuning, making it an ideal candidate for clinical implementation. Additionally, we have seen that the structure of a patient’s respiratory motion trace has strong influence on the outcome of prediction. Further work is needed to determine a priori the suitability of an individual’s respiratory behaviour to motion prediction. (paper)

[en] Achieving good conformality and a steep dose gradient around the target volume remains a key aspect of radiosurgery. Clearly, this involves a trade-off between target coverage, conformality of the dose distribution, and sparing of critical structures. Yet, image guidance and robotic beam placement have extended highly conformal dose delivery to extracranial and moving targets. Therefore, the multi-criteria nature of the optimization problem becomes even more apparent, as multiple conflicting clinical goals need to be considered coordinate to obtain an optimal treatment plan. Typically, planning for robotic radiosurgery is based on constrained optimization, namely linear programming. An extension of that approach is presented, such that each of the clinical goals can be addressed separately and in any sequential order. For a set of common clinical goals the mapping to a mathematical objective and a corresponding constraint is defined. The trade-off among the clinical goals is explored by modifying the constraints and optimizing a simple objective, while retaining feasibility of the solution. Moreover, it becomes immediately obvious whether a desired goal can be achieved and where a trade-off is possible. No importance factors or predefined prioritizations of clinical goals are necessary. The presented framework forms the basis for interactive and automated planning procedures. It is demonstrated for a sample case that the linear programming formulation is suitable to search for a clinically optimal treatment, and that the optimization steps can be performed quickly to establish that a Pareto-efficient solution has been found. Furthermore, it is demonstrated how the stepwise approach is preferable compared to modifying importance factors

[en] In extracranial robotic radiotherapy, tumour motion is compensated by tracking external and internal surrogates. To compensate system specific time delays, time series prediction of the external optical surrogates is used. We investigate whether the prediction accuracy can be increased by expanding the current clinical setup by an accelerometer, a strain belt and a flow sensor. Four previously published prediction algorithms are adapted to multivariate inputs—normalized least mean squares (nLMS), wavelet-based least mean squares (wLMS), support vector regression (SVR) and relevance vector machines (RVM)—and evaluated for three different prediction horizons. The measurement involves 18 subjects and consists of two phases, focusing on long term trends (M1) and breathing artefacts (M2). To select the most relevant and least redundant sensors, a sequential forward selection (SFS) method is proposed. Using a multivariate setting, the results show that the clinically used nLMS algorithm is susceptible to large outliers. In the case of irregular breathing (M2), the mean root mean square error (RMSE) of a univariate nLMS algorithm is 0.66 mm and can be decreased to 0.46 mm by a multivariate RVM model (best algorithm on average). To investigate the full potential of this approach, the optimal sensor combination was also estimated on the complete test set. The results indicate that a further decrease in RMSE is possible for RVM (to 0.42 mm). This motivates further research about sensor selection methods. Besides the optical surrogates, the sensors most frequently selected by the algorithms are the accelerometer and the strain belt. These sensors could be easily integrated in the current clinical setup and would allow a more precise motion compensation. (paper)

[en] Robotic radiosurgery using more than one circular collimator can improve treatment plan quality and reduce total monitor units (MU). The rationale for an iris collimator that allows the field size to be varied during treatment delivery is to enable the benefits of multiple-field-size treatments to be realized with no increase in treatment time due to collimator exchange or multiple traversals of the robotic manipulator by allowing each beam to be delivered with any desired field size during a single traversal. This paper describes the Iris(TM) variable aperture collimator (Accuray Incorporated, Sunnyvale, CA, USA), which incorporates 12 tungsten-copper alloy segments in two banks of six. The banks are rotated by 30 deg. with respect to each other, which limits the radiation leakage between the collimator segments and produces a 12-sided polygonal treatment beam. The beam is approximately circular, with a root-mean-square (rms) deviation in the 50% dose radius of <0.8% (corresponding to <0.25 mm at the 60 mm field size) and an rms variation in the 20-80% penumbra width of about 0.1 mm at the 5 mm field size increasing to about 0.5 mm at 60 mm. The maximum measured collimator leakage dose rate was 0.07%. A commissioning method is described by which the average dose profile can be obtained from four profile measurements at each depth based on the periodicity of the isodose line variations with azimuthal angle. The penumbra of averaged profiles increased with field size and was typically 0.2-0.6 mm larger than that of an equivalent fixed circular collimator. The aperture reproducibility is ≤0.1 mm at the lower bank, diverging to ≤0.2 mm at a nominal treatment distance of 800 mm from the beam focus. Output factors (OFs) and tissue-phantom-ratio data are identical to those used for fixed collimators, except the OFs for the two smallest field sizes (5 and 7.5 mm) are considerably lower for the Iris Collimator. If average collimator profiles are used, the assumption of circular symmetry results in dose calculation errors that are <1 mm or <1% for single beams across the full range of field sizes; errors for multiple non-coplanar beam treatment plans are expected to be smaller. Treatment plans were generated for 19 cases using the Iris Collimator (12 field sizes) and also using one and three fixed collimators. The results of the treatment planning study demonstrate that the use of multiple field sizes achieves multiple plan quality improvements, including reduction of total MU, increase of target volume coverage and improvements in conformality and homogeneity compared with using a single field size for a large proportion of the cases studied. The Iris Collimator offers the potential to greatly increase the clinical application of multiple field sizes for robotic radiosurgery.

[en] Organ motion can have a severe impact on the dose delivered by radiation therapy, and different procedures have been developed to address its effects. Conventional techniques include breath hold methods and gating. A different approach is the compensation for target motion by moving the treatment beams synchronously. Practical results have been reported for robot based radiosurgery, where a linear accelerator mounted on a robotic arm delivers the dose. However, not all organs move in the same way, which results in a relative motion of the beams with respect to the body and the tissues in the proximity of the tumor. This relative motion can severely effect the dose delivered to critical structures. We propose a method to incorporate motion in the treatment planning for robotic radiosurgery to avoid potential overdosing of organs surrounding the target. The method takes into account the motion of all considered volumes, which is discretized for dose calculations. Similarly, the beam motion is taken into account and the aggregated dose coefficient over all discrete steps is used for planning. We simulated the treatment of a moving target with three different planning methods. First, we computed beam weights based on a 3D planning situation and simulated treatment with organ motion and the beams moving synchronously to the target. Second, beam weights were computed by the 4D planning method incorporating the organ and beam motion and treatment was simulated for beams moving synchronously to the target. Third, the beam weights were determined by the 4D planning method with the beams fixed during planning and simulation. For comparison we also give results for the 3D treatment plan if there was no organ motion and when the plan is delivered by fixed beams in the presence of organ motion. The results indicate that the new 4D method is preferable and can further improve the overall conformality of motion compensated robotic radiosurgery