Prediction of conical collimator collision for stereotactic radiosurgery

Abstract The purpose of this study is to predict the collision clearance distance of stereotactic cones with treatment setup devices in cone‐based stereotactic radiosurgery (SRS). The BrainLAB radiosurgery system with a Frameless Radiosurgery Positioning Array and dedicated couch top was targeted in this study. The positioning array and couch top were scanned with CT simulators, and their outer contours of were detected. The minimum clearance distance was estimated by calculating the Euclidian distances between the surface of the SRS cones and the nearest surface of the outer contours. The coordinate transformation of the outer contour was performed by incorporating the Beam's Eye View at a planned arc range and couch angle. From the minimum clearance distance, the collision‐free gantry ranges for each couch angle were sequentially determined. An in‐house software was developed to calculate the clearance distance between the cone surface and the outer contours, and thus determine the occurrence of a collision. The software was extensively tested for various combinations of couch and arc angles at multiple isocenter locations for two combinations of cone‐couch systems. A total of 50 arcs were used to validate the calculation accuracies of the software for each system. The calculated minimum distances and collision‐free angles from the software were verified by physical measurements. The calculated minimum distances were found to agree with the measurements to within 0.3 ± 0.9 mm. The collision‐free arc angles from the software also agreed with the measurements to within 1.1 ± 1.1° with a 5‐mm safety margin for 20 arcs. In conclusion, the in‐house software was able to calculate the minimum clearance distance with <1.0 mm accuracy and to determine the collision‐free arc range for the cone‐based BrainLab SRS system.

to treat small intracranial targets such as small benign or metastatic tumors, or functional diseases like trigeminal neuralgia. [2][3][4] The most advantageous characteristic of cone-based SRS system is a sharp dose fall-off by minimizing lateral scattering owing to its physically long and narrow design. [5][6][7] However, due to the protruding cone design, the gantry clearance space is quite smaller than that of a general MLC-based treatment system. Consequently, there are higher chances of collision between the cone and the patient and/or setup devices in cone-based treatments. However, it is quite challenging to find the collision-free gantry/couch angle combination manually due to the nature of complex three-dimensional (3D) geometries of patients with gantry and couch motions in the 3D coordinate system.
There were many previous studies on the prediction of collision among gantry, couch and patients in various systems to avoid any harm to the patient and prevent replanning. Humm et al. proposed an analytic approach and developed a software to detect the collision of gantry/couch and gantry/patient by modeling a couch surface and patient geometry mathematically. 8,9 Hua et al. also developed a mathematical collision prediction model for BrainLAB micro MLC and BRW SRS system by approximating the micro MLC rotation space as a circle and the couch as a rectangle. 10  Nederland) treatment planning system (TPS) using a two-dimensional (2D) collision map. 11 Tsiakalos et al developed an OpenGL-based room's eye view simulation solution to detect a collision by graphical modeling of the LINAC. 12 18 Similarly, a virtual simulator was developed for the detection of collision among the proton beam nozzle, patient, and couch. 19 While most of the existing collision detection method requires 3D modeling, CAD technique, or an external camera, this study introduced the mathematical operation of the contours instead of such complex techniques for the practical implementation in a clinic.
The necessity of collision prevention is more emphasized for the cone-based SRS since it introduces a protruding conical collimator which consequently leads to tighter gantry clearance margin. Multileaf-collimator-based treatment has relatively less chance of interference because there is more clearance to the gantry head. This study is aimed at developing a robust collision detection algorithm and software for cone-based SRS, which can assist the treatment planner to test any gantry and couch angle combination and to find collision-free arc range at the time of treatment planning.

2.C | Beam's eye view transformation
Beam's eye view (BEV) was employed to define the search area of the minimum distance between the SRS position array surface and the cone surface for an arbitrary gantry-couch combination. Beam's eye view is a very useful tool to visualize the patient anatomy and to design the beam aperture in the computerized treatment planning. [20][21][22] Most of the BEV application is limited to the 2D plane, that is, collimator X and Y axis, but depth information along the collimator Z axis can provide useful information on the distance from the target to an object. In general, BEV of an object is created through the successive coordinate transformations from the patient coordinate system to the collimator coordinate system as shown in

2.E | Verification of the proposed method
The proposed method was verified by measuring physical distances between the cone and the FRPA or couch at an arbitrary isocenter with multiple couch angle, arc range combinations. As aforementioned, two test systems were employed in this study -(a) BrainLAB  Table 1 were made for each system using the Eclipse v13.6 in BSW and v15.6 in UPMC Hillman Cancer Center; total of 100 arcs, or 50 arcs for each system were verified. These plans were imported in the Brainlab ExacTrac (v 6.6.0) system. Initial couch positions of each isocenter were aligned using an automatic positioning function of ExacTrac software by detecting IR markers of FRPA. Physical measurement of the clearance distance was performed with a ruler at the minimum clearance gantry angle predicted by the software. The minimum clearance angle and distance were updated if a shorter distance was found. In the meantime, the accuracy of collision-free arc range was also verified for 20 arcs equivalent to 40 potential F I G . 3. Coordinate transformation from the patient coordinate system to the collimator coordinate system. (a) Translation to the isocenter in the patient support coordinate system, (b) Rotation of the patient support coordinate system around y axis by −θ S back to the machine fixed coordinate, (c) Rotation of the machine fixed coordinate system by θ G to the gantry coordinate system, (d) Exchange of coordinate convention to the collimator coordinate system. F I G . 4. Determination of a clearance distance from the Beam's eye view coordinate of the outer contour (a) Arbitrary point within the cone radius + detection margin will be of potential collision, (b) Clearance distance is the short distance between the cone and the points found in (a) shown as shaded volume.
collisional gantry angles at five isocenters with a 5 mm safety margin using the Varian PPC system (Table 2). These arcs are designed to collide with a couch top or FRPA in the middle of the arc. Actual gantry angles at which the distances between the cone and a couch top or FRPA become 5 mm first and last were recorded in the measurement using a custom gauge.

| RESULTS
The average deviation between the measured clearance distance and the prediction was 0.1 AE 1.0 mm for the BrainLAB ExacTrac couch system and 0.6 AE 0.7 mm for the Varian PPC system. The positive deviation means the measured distance is longer than the prediction.
Only 16 out of 50 in the BrainLab Couch system and two out of 50 in the Varian Couch system showed negative deviation. The average deviation for each isocenter ranged between −0.3-0.7 mm and 0.0-0.9 mm as shown in Table 3. The minimum and maximum deviation of each system was −1 mm/+2 mm and −2 mm/+2 mm, respectively. The predicted gantry angles of minimum clearance distance were also matched in the measurement. The average deviation between the predicted collision-free gantry angle and the measured gantry angle with a 5-mm interval was 1.1 AE 1.1°as shown in

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The average deviation between the measurement and the prediction was <1 mm for both BrainLAB ExacTrac and Varian PPC systems. Though the maximal and minimal deviation in both systems were quite similar, the average deviation was a little bit higher in Varian and more negative deviation was shown in the BrainLAB system. It seems it was caused by the inter-observer variations at two different institutions, which could be improved by acquiring more independent measurement samples. The prediction accuracy is quite comparable with the previous studies using Kinect camera or CAD software. The accuracy inherits from the mathematical operation of BEV applied to the fixed CT coordinates of the outer contour. In T A B L E 1 Isocenter, couch angle, and arc ranges of test treatment plans used for the verification of clearance distance. Eclipse isocenter coordinate is based on Varian IEC convention.  The limitation of this study is the exclusion of potential transla- cases out of 40 in the collision-free gantry angle measurement also supported it. The maximum deviation was found to be 4.3°which amounts to a 5-6-cm overestimation due to the HU threshold described above and a finite CT slice thickness etc. However, considering the uncertainty in the edge of the setup device or couch, it will be acceptable to have a conservative prediction as long as it is more than the safety margin.
This study aimed specifically for cone-based SRS using the Brain-  26 It is based on the image registration of the built-in fiducial markers in the TPS to that of the patient CT image using the QFix TM mask system. Similarly, the proposed method has a potential application to conventional external beam radiation therapy as well by combining an indexed couch position, isocenter location, patient body contour and preprocessed patient setup device into the known treatment machine geometry. Extension to proton beam therapy is also easily achievable with the measured geometry of the proton beam nozzle.

| CONCLUSION
The proposed method was able to calculate the minimum clearance distance between the cone surface and the collisional object with <1 mm accuracy for cone-based SRS. Collision-free arc range also could be found accurately with a preset margin. It can be useful to provide prior information on the arrangement of collision-free couch and arc angle to the radiation treatment planners at the time of planning.

CONFLI CT OF INTEREST
No conflict of interest. T A B L E 3 Deviation between the measured clearance distance and predicted distance. Positive value means a measured distance is longer than the prediction.