Smartphone application for mechanical quality assurance of medical linear accelerators

Three motion sensors (gyroscope, accelerator and magnetic field sensor) embedded in the smartphone (device) were used to measure gantry and collimator angles. As shown in figure 2, the roll rotation axis of the device is perpendicular to the central axis (CAX) of the medical linear accelerator. Hence, the rotation angle of the smartphone refers to that of the gantry or the collimator. Combined use of three different sensors (known as the sensor fusion method) enhanced the accuracy of determining the orientation of the smartphone with respect to gravity (described in section 2.2) (Ayub et al 2012).

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An optical-image processing module using an image taken by the high-resolution camera was developed to assess jaw-positioning, crosshair-centering and SSD. A series of image processing steps was employed to determine the location of feature points such as the crosshair-center and edges of X and Y jaws (described in section 2.3).

In order to acquire exact locations of jaw openings from a light field image projected on the treatment couch, image pre-processing was needed. First, a gray-scale image was acquired by normalizing 16 bit RGB images to eliminate illumination effects; thereafter, a binary image was created by dividing pixels into ones above and below half of the maximum intensity as a threshold. Finally, the binary image was segmented with the Canny method (Bao et al 2005) to recognize the crosshair and full-width at half-maximum (FWHM) of the light field.

To measure the absolute length from an image, images of a known geometry (herein a 100 KRW coin) were taken. A circle detection module was implemented using the Hough transform method to determine the radius of the circle (Roushdy 2007). With the determined radius, we could get a calibration factor as below:

$$\begin{align}{\rm Calibration}\,{\rm factor}=~{}^{{\rm real}\,{\rm length}\,({\rm mm})}\!\!\diagup\!\!{}_{{\rm number}\,{\rm of}\,{\rm pixels}\,{\rm from}\,{\rm the}\,{\rm acquired}\,{\rm image}\,({\rm px})}.\nonumber \end{align}$$

For instance, if the real radius of the known geometry was 12 mm and the number of pixels corresponding to the radius was 50 px, then the calibration factor was determined to be 0.24 mm px^–1.

The Harris corner detection method was employed to produce second partial derivatives of image intensities. It derives Hessian matrix with second partial derivatives (Harris and Stephens 1988).

For corners, the matrix was characterized by two large eigenvalues, and thus best features from the edge image were obtained. In figure 4, the top five best features referred one to the crosshair and the rest to each jaw's position. For refining the corner locations in sub-pixel accuracy, the intensity gradient from the grayscale image was calculated near each corner. Given the fact that the dot product between two vectors perpendicular to each other is zero, several equations were made and solved using the candidate points near the detected corner by the Harris method.

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The accuracy and precision of the system for the rotation angle were evaluated by measuring various orientations of the smartphone attached to an optical rotation stage (ST1-418-B4, Sciencetown, South Korea). The roll rotation angle of the smartphone referred to the gantry rotation angle and the yaw rotation angle of the smartphone facing right, referred to as the collimator rotation angle (figure 5). The tests were performed at various angles set up with the optical rotation stage. For the roll rotation, the optical rotation stage varied from  −20° to 20° with a 1° resolution and a 0.03° precision. For the yaw rotation, we measured 0° to 270° rotations of the smartphone attached to the optical rotation stage with a 0.1° resolution and a 0.003° precision. Test sets included 10 known rotations and each of them was repeated three times. We derived MAEs and SDs for 10 test sets.

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The accuracy and precision for the optical length were evaluated by measuring the sizes of 10 test templates (5  ×  5 cm², 7  ×  7 cm², 9.5  ×  9.5 cm², 9.8  ×  9.8 cm², 10  ×  10 cm², 10.2  ×  10.2 cm², 10.5  ×  10.5 cm², 12  ×  12 cm², 15  ×  15 cm², and 20  ×  20 cm² squares) at a camera-to-template distance of 50 cm, following calibration with the known geometry of a 5 cm radius circle. Each template size was confirmed by using digital calipers with a 0.03 mm precision (Absolute 500, Mitutoyo, IL, USA). Each of the test sets was repeated three times. We derived MAEs and SDs of 10 test sets.

The roll rotation axis of the smartphone was perpendicular to the CAX of the medical linear accelerator. Hence, the rotation angle of the smartphone referred to that of the gantry. The gantry rotation was measured at gantry angles of 0°, 90°, 180° and 270°. The angles measured by the developed system were compared to values on the LINAC's digital indicator. Simultaneously, the accuracy of the developed system was confirmed by using a bubble level (manual method). Each test set was repeated twice and experiments were conducted over three or five different days. We derived the MAEs and SDs of the test sets.

As an electronic device, a LINAC can interrupt the geomagnetic signal of a compass sensor. Therefore, we used the yaw rotation of a smartphone at the gantry angle of 90°—the smartphone facing right. At this position, we could obtain the absolute yaw rotation of the smartphone with respect to gravity and this referred to the angle of the collimator. The collimator rotation was measured at the collimator angles of 0°, 90° and 270° (180° collimator rotation was not allowed). The measured angles were compared to the LINAC's digital indicator. Simultaneously, the accuracy of the developed system was confirmed by using a bubble level (manual method). Each test set was repeated twice and experiments were conducted over three or five different days. We derived MAEs and SDs of the test sets.

From the determined location of the feature points as described in section 2.3.3, the light field size was determined by counting the number of pixels between the crosshair and each of the jaw positions. The measured length of a light field was calculated using the calibration factor as follows:

$$\begin{align}{\rm Measured}\,{\rm length}~\left( {\rm mm} \right)={\rm Image}\,{\rm length}~\left( {\rm px} \right)\times {\rm Calibration}\,{\rm factor}\,({\rm mm}/{\rm px}).\nonumber \end{align}$$

Each jaw position was measured at an SSD of 100 cm and a field size of 10  ×  10 cm². Thereafter, we intentionally changed the field sizes asymmetrically and confirmed them by using digital calipers (0.01 mm precision) before measuring by using the developed system. Each test set was repeated twice and experiments were conducted over three or five different days. We derived MAEs and SDs of the test sets.

The developed system tracked the real-time position of a crosshair with a video mode, and thus the maximum deviation from the initial position of the crosshair (i.e. crosshair location at the collimator angle of 0°) was measured (figure 6). Each test set was repeated twice and experiments were conducted over three or five different days. We derived MAEs and SDs of the test sets.

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It was assumed that the smartphone was parallel to the image plane projected on the treatment couch and lens distortion was negligible. The pinhole camera model was defined as a one-to-one relationship between real geometry and that projected onto the image plane (figure 7).

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In order to calculate a camera-to-surface distance (CSD), a simple formula was derived as follows and all the device-related specifications were from the manufacturer of the smartphone:

$$\begin{align}{\rm CSD}=F\frac{{\rm RL}\times {\rm FL}}{{\rm IL}\times {\rm SL}}\nonumber \end{align}$$

F: focal length (mm)  =  4.13 by specification

FL: frame length (px)  =  1920 by camera setting

SL: sensor length (mm)  =  4.69 by specification

RL: real length (mm)  =  100 where SSD  =  100 cm, FS  =  10  ×  10 cm²

IL: measured length by image processing (px)

Finally, an SSD was derived from a calculated CSD by simply adding a source-to-camera distance (SCD). In this study, the SCDs were initially assumed to be 60 cm and 53 cm for the Varian LINACs and Elekta LINAC, respectively. Initial values were referenced in the Monte Carlo simulation package (provided by the manufacturer). However, to confirm the accuracy of two given parameters (SCD and focal length), nine combinations of two parameters were tested. We precisely fixed an SSD of 100 cm and a field size of 10  ×  10 cm² by using a well-calibrated front-pointer and digital calipers. Discrepancies between measured field size and actual field size (10  ×  10 cm²) were measured with nine combinations of SCD and focal length. The combination resulting in minimum discrepancy was chosen as producint true values of SCD and focal length. With these values, the SSD measured with the developed system was compared to the SSD measured with well-calibrated front-pointers for 90 cm, 100 cm and 110 cm. Ten test sets were performed for three values of SSD.

The results of the system accuracy and precision for the gantry (roll) and collimator (yaw) rotations are shown in table 1. The MAEs with an SD of rotation angle measurements were determined to be 0.05  ±  0.05° and 0.05  ±  0.05° for the roll and yaw rotations, respectively. The MAEs were 0.10° and 0.12°, respectively. Even though the motion sensor resolution specified by the manufacturer (MPU6500, Invensense Inc., CA, USA) was 0.0036°, the system precision was intentionally adjusted to the level of 0.1° due to high sensitivity to noise at high precision.

The accuracy and precision of the system for field size measurements are shown in table 1. With the camera resolution of 4128  ×  3096, the calibration factor was 0.107 mm px^–1 when the system was calibrated by using the known geometry of a 5 cm radius circle. The MAEs with an SD of field size measurements for the x and y directions were determined to be 0.24  ±  0.15 mm and 0.26  ±  0.14 mm, respectively. The total MAE with SD for various reference field sizes was 0.25  ±  0.14 mm. The maximum absolute error was 0.50 mm.

All the angles measured with the application system were consistent with those indicated by the bubble level. The system always showed better precision than the manual method. The system can also display the absolute angles of the gantry and collimator rotation with respect to gravity within 0.1° precision.

The MAE  ±  SD of measured field sizes with the system was 0.39  ±  0.36 mm. As described in 2.3.1, a binary threshold was the half of maximum intensity at the edge of the light field; thus we could eliminate the source of human error in identifying the FWHM.

The system well tracked the crosshair in real-time and the MAE of maximum measured deviations was below 1 mm (⩽5 px). With the system, one was able to relieve the effort of drawing several crosslines to measure the crosshair location offset.

Prior to SSD measurements, two parameters, focal length and SCD, were chosen to minimize the difference between measured and actual field sizes for nine combinations of two parameters listed in table 3. The optimal focal length and SCD were determined to be 4.12 mm and 600.1 mm, respectively. With these parameters, we performed SSD measurements for ODI QA for the Varian LINACs. We did the same with the Infinity LINAC. The optimal focal length and SCD for ODI QA for the Infinity LINAC were determined to be 4.12 and 530.2 mm, respectively.

The MAE  ±  SD of the measured SSD was 0.41  ±  0.32 mm over the all test sets for all LINACs. The results using the application system was also consistent with those using manual front pointers.