A collision prediction framework for noncoplanar radiotherapy planning and delivery

Abstract Purpose Noncoplanar radiotherapy can provide significant dosimetric benefits. However, clinical implementation of such techniques is not fully realized, partially due to the absence of a collision prediction tool integrated into the clinical workflow. In this work, the feasibility of developing a collision prediction system (CPS) suitable for integration into clinical practice has been investigated. Methods The CPS is based on a geometric model of the Linear Accelerator (Linac), and patient morphology acquired at the simulator using a combination of the planning CT scan and 3‐D vision camera (Microsoft, Kinect) data. Physical dimensions of Linac components were taken to construct a geometric model. The Linac components include the treatment couch, gantry, and imaging devices. The treatment couch coordinates were determined based on a correspondence among the CT couch top, Linac couch, and the treatment isocenter location. A collision is predicted based on dot products between vectors denoting points in Linac components and patient morphology. Collision test cases were simulated with the CPS and experimentally verified using ArcCheck and Rando phantoms to simulate a patient. Results For 111 collision test cases, the sensitivity and specificity of the CPS model were calculated to be 0.95 and 1.00, respectively. The CPS predicted collision states that left conservative margins, as designed, relative to actual collision locations. The average difference between the predicted and measured collision states was 2.3 cm for lateral couch movements. The predicted couch rotational position for a collision between the gantry and a patient analog differed from actual values on average by 3.8°. The magnitude of these differences is sufficient to account for interfractional patient positioning variations during treatment. Conclusion The feasibility of developing a CPS using geometric models and standard vector algebra has been investigated. This study outlines a framework for potential clinical implementation of a CPS for noncoplanar radiotherapy.


| INTRODUCTION
The primary objective in radiation therapy is to maximize dose to the target, while minimizing dose to surrounding healthy tissue and organs at risk. Treatment planning has evolved over the years to better achieve this objective by taking advantage of additional degrees of freedom in beam delivery. The introduction of dynamic MLC leaves allowed for not only better coverage of the target while shielding of organs at risks but also allowed modulation of beam intensity (as in IMRT). 1 Subsequently, volumetric modulated arc therapy (VMAT) introduced an additional degree of freedom by allowing the ability to deliver radiation while the gantry is rotating with variable speed and dose rate to provide a more desirable dose distribution. 2 The use of noncoplanar treatment beams could be considered the next step in this evolution of treatment techniques. Noncoplanar treatments are enabled by using various couch angles (in the range of 0°to ± 90°) in combination with a range of gantry angles.
Although treatment fields involving couch rotations are currently used in a limited capacity for cranial treatment sites, the full potential of noncoplanar radiation therapy has not been realized. A properly designed noncoplanar approach would allow an increase in the number of independent beam paths to the target, and consequently could help spread the unwanted dose spillage to a larger volume of lower dose while potentially escalating dose to the target. The feasibility of achieving a better dose distribution with optimized noncoplanar beams have been demonstrated in several studies to reduce dose to surrounding critical structures while depositing the desired dose to the target volume [3][4][5][6][7][8][9][10][11][12][13] . However, for clinicians to confidently incorporate such advanced techniques into their clinical practice, a reliable collision prediction system during the treatment planning process is essential.
Since the very early days of C-arm Linacs, patient safety as well as equipment safety has been a concern due to potential collisions of the rotating gantry with the treatment couch or patient. Traditionally, treatment planners and therapists would conduct a dry run prior to plan delivery. With increasing complexity of treatment plans the need for a collision avoidance system has become more relevant recently, especially with increased prevalence of stereotactic body radiotherapy (SBRT) and stereotactic radiosurgery (SRS) treatments.
Stereotactic treatments often involve the use of couch kicks, specialized immobilization devices, and in some cases stereotactic cones which can result in tight clearances.
Collision detection and avoidance in radiation therapy has been explored using different approaches over the last several decades. [14][15][16][17][18][19][20][21][22][23][24][25][26][27] Some of the earlier works on collision detection involved using geometric analytical models of the Linac and treatment couch but did not provide a realistic method for incorporating patient-specific models. 17,[19][20][21]23,25,26 Some other approaches focused primarily on graphical treatment simulation user interfaces involving generic patient models or partial body contours from planning CT scans. 18,22,24,27 More recent works on collision detection, however, have involved more complex approaches. Yu et al. have used a highly detailed computer-assisted design model of the linear accelerator and treatment couch while using a hand-held 3D scanner to capture patient surface anatomy. 14 Both Padilla and Cardan have used multiple Microsoft Kinect cameras to acquire patient-specific models. 15,16 Previous works on collision prediction either did not or only partially addressed all practical aspects of integrating noncoplanar radiotherapy into clinical workflow. None of the previous literature has explicitly mentioned the need for a couch coordinate prediction methodology in order for the collision prediction tool to effectively provide the treatment planner the collision-free treatment delivery space. In addition, it is not clear how some of these previously developed collision prediction tools account for interfractional changes in patient positioning on the treatment couch. Furthermore, one of the major aspects of noncoplanar delivery and workflow that has not been considered in previous works is the need for imaging to verify patient positioning after a couch rotation has been applied.
The primary goal of this work is to develop a general framework for collision prediction that addresses some of the key challenges with integrating noncoplanar radiotherapy into clinical workflow. In this work we investigate the feasibility of a specific implementation of the developed framework through the use of a single Microsoft Kinect Camera, in combination with CT scan images to model the patient set-up geometry, and geometric information of various Linac components to develop a CPS. Methods have been explored to determine the Linac couch coordinates based on the selection of a treatment isocenter. In the context of noncoplanar treatment delivery workflow, to address the need for imaging capabilities to verify patient positioning after couch has been rotated, the imaging components for both MV and kV systems have been modeled.

| MATERIALS AND METHODS
The CPS framework has been developed with the intent of making it compatible with the expected clinical workflow. A practical CPS must include the following characteristics: (a) model treatment delivery components accurately, (b) acquire patient set-up geometry during simulation, (c) predict the treatment couch coordinates based on the correspondence between the CT couch, Linac couch, and the beam isocenter selected during the plan development, (d) provide collision information for verification imaging following each couch position adjustment, and (e) account for day-to-day variation in patient set up on the treatment couch. An overview of the various elements of the CPS process flow is illustrated in the diagram in

2.A | CPS geometric model of Linac and couch
The CPS uses the coordinate system convention of the International Electrotechnique Commission (IEC), which is also used in most modern treatment planning systems. The collision model developed in this work is based on fundamental principles in geometry. Separate components of the treatment couch and linear accelerator were modeled using geometric shapes in a three-dimensional space with the origin corresponding to the Linac isocenter. The components included the gantry and collimator head, kV source head, MV and kV Imaging panels, and the treatment couch (as shown in Fig. 2, for simplicity imaging devices are not shown). The physical dimensions of the treatment couch, gantry, MV imager, kV imager, and kV source were measured in the treatment room for a Varian True Beam STX.
The treatment couch was modeled using the eight corner points of a trapezoidal prism that corresponds to the shape of the couch top.
The MV-imager, kV-source, and kV-Imager structures were each modeled using eight corner points to define a rectangular prism that encapsulates the corresponding structure. The gantry head has been modeled using four cylinders with a diameter corresponding to the appropriate part of the gantry head (Fig. 3). The lowest point of these set of cylinders corresponds to the lowest point on the collimator face. Each cylinder has been represented using three points: two points on the central axis and one point on the circumference Similarly, the following rotation matrix has been applied to all corner points used to model the couch: Note that for both equations above, the rows, columns, and coordinates correspond to the CPS coordinate system displayed in where m represents the magnitude of the shift required and D is a unit direction vector derived from a pair of points used to model the couch that correspond to the direction of the couch motion. The  The following steps were used to determine the appropriate transformation required: 1. In the raw Kinect Camera scan data, the 3-D coordinates of four distinct corners of the block were identified as references points A, B, C, and D (as shown in Fig. 4).

2.
All points in the raw Kinect dataset were transformed, using vector subtraction so that the new origin is located at the reference point A.
3. The angular offset between the unit vector Ux and AD was determined and the corresponding rotation matrix was subsequently applied to all raw Kinect data so that Ux and AD were aligned.

The previous step was then repeated to align vectors AC and AB
with the corresponding unit vectors Uz and Uy.

5.
Since the physical distances between the reference points are known, the appropriate scaling factor was determined and applied for each corresponding dimension of the raw Kinect data.
6. Finally, the origin was then translated from reference point A to the center of block using vector subtraction.

2.C | Treatment couch coordinate prediction
The couch coordinates are predicted using a couch coordinate prediction protocol that has been developed and implemented clinically.
This approach utilizes identical couch indexing to establish a F I G . 3. Schematic diagram of Gantry Model for CPS.
F I G . 4. Illustration of the coordinate transformation and scaling applied to raw Kinect Camera data prior to importing into CPS.
correspondence between the CT and Linac couches. Special radioopaque markers have been embedded under the CT couch top in order to mark reference positions on the CT couch. The Linac couch coordinates corresponding to these markers on the CT couch were determined ahead of time in order to establish a mapping between the two couches. Once the dosimetrist selects the treatment isocenter, the corresponding Linac couch coordinates can be calculated based on the relative position of the radio-opaque markers on the CT couch. This approach assumes that the patient will be set up on the CT and Linac couches in identical locations (both in lateral and longitude directions) on the couch top, with reference to the couch indices.
The following example illustrates the principle used to predict couch coordinates. Suppose the CT scan of a patient has been acquired. Subsequently, the treatment planner selects the treatment isocenter. In order to predict the final couch coordinates on the Linac, the coordinates of one of the radio-opaque reference markers underneath the CT couch need to be identified in the CT image sets in the treatment planning system. Suppose (X, Y, Z) denotes the location of the treatment isocenter and (X*, Y*, Z*) denotes the location of the radio-opaque reference marker (Fig. 5). Since the reference marker has been laterally centered in the treatment couch, the couch lateral value can be predicted using the following formula: Since the vertical distance from the reference marker to the top of the CT couch top has been measured and known (e.g., 4.1 cm), the couch vertical value can be predicted using the following formula: Since it has been predetermined that the radio-opaque marker corresponds to Linac couch longitude value of 140, the couch longitude value can be calculated: Note that the method for couch LNG coordinate prediction assumes that the existing clinical workflow uses a couch indexing method to develop a direct correspondence between the patient set up in the CT sim couch and the Linac couch. Furthermore, the approach described above can be refined to account for various other factors such as couch sag and differences in placement of patient immobilization accessories from CT couch to Linac couch.

2.D | Collision detection algorithm
The CPS detects potential collision scenarios by iteratively looping Subsequently if the point is found to be between those two planes, the perpendicular distance to the central axis of the cylinder is calculated. If the distance to the central axis is less than the radius of the cylinder then a collision has been detected.
In the full gantry head model consisting of four cylinders, any given test point is first tested to be in between plane 1 and plane 5 using the dot product approach (See Fig. 3)

3.A.3 | MV-imager collisions
To test the MV-imager model, a similar type of experiment was con-

3.A.4 | kV-imager and kV-source collisions
The kV-imager and kV-source models were tested using the same approach as the MV imager. The gantry was kept static at several

3.B | Evaluation of Kinect camera patient model
The Kinect camera scan data were scaled and transformed using a combination of the calibration procedure, described in section 2.B, as well as the ICP algorithm to match the Kinect scan with the planning CT body contour. This methodology minimizes the differences between the Kinect point cloud and the planning CT point cloud of the body. Since the planning CT is already an established baseline that is clinically acceptable, a reasonably strong registration between the two-point clouds should be sufficient for the CPS's purposes.
Due to inherent limitations and error in the Kinect camera's depth perception capabilities, the Kinect point cloud has some inaccuracies which have been documented in the past. 30 These inaccuracies result in an imperfect registration with the planning CT body contour, however, the discrepancy between the two-point clouds was not significant enough to effect the CPS performance.

3.C | Evaluation of Couch coordinate prediction system
The performance of the couch coordinate prediction approach has been tested by selecting treatment plans for a wide variety of patients, and subsequently predicting the Linac couch coordinates.
The predicted couch coordinates were then compared with the actual couch coordinates that were acquired during the first fraction of treatment. Figure 13 displays the prediction errors across the 18 patients tested. The average error in couch LAT, VRT, and LNG was 0.6, 0.7 and 1.1 cm, respectively.

3.D | CPS end-to-end testing results
To evaluate the CPS as a whole, end-to-end testing was done using  Figure 14 illustrates the patient point cloud.

3.E | CPS performance metric
The overall predictive performance of the CPS was evaluated using the ROC formalism as specified earlier. The CPS prototype was tested over 111 test cases. The positive predictive value was calculated to be 0.95, while the negative predictive value was calculated to be 1. Table 3 summarizes the performance metric. In contrast to previous studies on collision detection, the CPS uses an easy to understand collision detection algorithm using the principle of dot products between vectors, and basic geometry.
Therefore, the CPS framework can be easily tailored to meet specific needs in a wide range of clinical situations. The approach used in the CPS can be used to model SRS cones, electron cones, and different types of patient accessories. Furthermore, the methods can also be applied to other radiation therapy modalities where collisions are of concern, such as in cyber knife and proton therapy.  In current clinical practice, KV or MV imaging is used to verify patient's position prior to couch rotation for noncoplanar treatments.
This approach relies on the assumption that after the couch rotation has been applied, the patient will be in the same position on the couch. For more accurate delivery, patient position should be verified after the couch rotation has been applied via imaging. Using a tool similar to the CPS described in this work, one can determine which angles are available for kV or MV imaging and subsequently plan on verifying patient positioning prior to radiation delivery at different available couch angles.
The collision prediction approach employed by Cardan involved a high-degree complexity with the use of three Kinect Cameras as well as a fast polygon interference algorithm. 15

Number of test cases
True positive 88 False positive 5 True negative 18 False negative 0 in distortions. 31 Our work demonstrates that using a single Kinect camera can be sufficient for collision prediction purposes and therefore the complexity of using multiple cameras can be avoided.

4.A | CPS performance results
The CPS has three major components: (   | 103 the geometric models of the CPS can be applied to achieve a higher level of accuracy, however, such refinements should be done with consideration of the fact that a reasonable level of conservativeness is desirable for workflow efficiency.
In normal clinical practice, the patient position on the treatment couch can vary from day to day typically on the order of 1-2 cm.
This variation in patient positioning is then reflected in a different set of treatment couch coordinates required to align the patient to treatment isocenter. This variation in day-to-day treatment couch coordinates is well documented in tolerance tables that are specific to treatment site. Most tolerances for couch position variation in all three directions were in the 1-3 cm range. 33 Therefore, an inherent Aiming for a very accurate model will run the risk of collision potential during clinically acceptable day-to-day variations in patient positioning on the couch, and subsequent couch position changes. In contrast, aiming for a model with a conservative margin will result in a loss of allowable beam approach angles available for certain couch and gantry angle combinations. To summarize, prior to clinical implementation of the CPS, the clinician must decide on a reasonable balance between accuracy and maintaining a conservative margin to account for interfractional set-up variations.

| CONCLUSION
To summarize, this work has demonstrated the feasibility of incorporating an easy to understand collision prediction framework into the modern treatment planning workflow. The methods used to model the patient, linear accelerator, treatment couch, and imaging devices can be applied to a wide range of Linac models. The output from the CPS can serve as valuable reference for treatment planners and can result in not only more efficient workflow but can also result in the development of a dosimetrically superior plan. Furthermore, the CPS can also be used postplan generation to conduct secondary collision safety checks. The framework described in this study can serve as valuable reference to clinicians who seek to apply the same principles in developing their own in-house collision prediction system.