Youngbin Cho1, Douglas J. Moseley1, Jeffrey H. Siewerdsen2, and David A. Jaffray1

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Geometric calibration of a cone-beam computed tomography system and medical linear accelerator

Youngbin Cho1, Douglas J. Moseley1, Jeffrey H. Siewerdsen2, and David A. Jaffray1

1Department of Radiation Oncology, Princess Margaret Hospital, Toronto, Ontario, Canada

2Ontario Cancer Institute, Princess Margaret Hospital, Toronto, Ontario, Canada


Cone-Beam CT (CBCT) systems have been developed to provide in-situ imaging for the purpose of guiding radiation therapy. Geometric calibration involves the estimation of a set of parameters that fully describe the geometry of the system, and is essential for accurate image reconstruction and precise radiation treatment. We developed an efficient and accurate calibration method for such systems in which a kV X-ray imager is incorporated on the treatment machine. The sensitivity and accuracy of the method are proven to be excellent with an uncertainty of 0.02o and 0.1mm. The method is used to provide a complete calibration of a medical linear accelerator in this paper, including source position, portal imaging device position and tilt angles, couch motion, mechanical axis of collimator, and motion of jaw and MLC at every gantry angle. Since this method is highly automated and integrated, acceptance testing, as well as annual and daily machine QA for precision radiation therapy such as stereotatic, IMRT, CBCT on linear accelerator can be done accurately and frequently. Combining the information of the MV treatment system and kV CBCT system will greatly facilitate precise radiation therapy.


Geometric calibration, cone-beam CT, linear accelerator, image-guided radiation therapy, cross-calibration


The development of volumetric imaging systems for the purpose of guiding radiation therapy has been a major interest of research in radiation therapy1-6. Medical linear accelerators with kilo voltage (kV) CBCT system orthogonal to the Mega voltage (MV) source are currently available (See figure 1). Such systems are capable of producing images of soft tissue with excellent spatial resolution (full width at half maximum of 0.6mm)5 at acceptable imaging doses (3cGy)7. Integrating this technology with the medical linear accelerator offers a highly promising platform for high-precision, image-guided radiation therapy.

Geometric calibration is essential for accurate image reconstruction. We developed a calibration phantom and an analytic method for the estimation of the geometric parameters of the kV CBCT scanner including CBCT on medical linear accelerator, C-arm, and lab bench. The sensitivity and accuracy of the method, applied to calibration of the kV CBCT system has been shown to be excellent with an uncertainty of 0.02o and 0.1mm8.

Geometric calibration of the MV system is also important for accurate dose delivery for highly precise dose delivery technique such as IMRT, stereotactic radiosurgery and therapy. The calibration method developed for the kV CBCT system, which has been proven to be efficient and accurate, is applied to calibrating the medical linear accelerator. We used a portal imaging device to acquire images of the calibration phantom. Machine parameters include source position, portal imaging device position and tilt angles, couch motion, mechanical axis of the collimator, motion of jaw, stability of the beam position and MLC motion at every gantry angle.
Material and methods

A. CBCT geometry

To describe the geometry of the scanner, three right-handed Cartesian coordinate systems are introduced. Coordinate systems of world (w), and virtual detector (i) are shown in Figure 1. Objects, such as the calibration phantom and patient, and CT reconstruction are based on the world coordinate system. The virtual detector coordinate system describes the ideal detector, which is the same as the real detector system except that it has no tilt. The real detector coordinate system considers detector tilt and rotation from the ideal orientation. The algorithm used herein works accurately when the detector tilt is less than 45 degrees.

B. Calibration phantom

The calibration phantom consists of 24 steel ball bearings precisely located in two circular trajectories in a plastic cylinder as shown in Figure 2. In each circular pattern, twelve steel ball bearings (BBs) are spaced evenly at 30 degrees. Each ball bearing is 3mm in diameter. Precision of the ball bearing location in the phantom is important.

C. Calibration

Since the calibration is based on the location of the ball bearings in an image, portal image of the phantom should show all the ball bearings clearly. The calibration algorithm needs only one image of the phantom to determine the source position, portal imaging device position and tilt angles, and couch position with respect to the world coordinate system located at the center of the phantom. When those machine parameters are changing with gantry angle, the calibration can be repeated at every gantry angle. Calibration is done by the following procedures:

  1. Place the phantom close to machine iso-center. Although location of the phantom does not affect the calibration result, it is preferred to put the phantom close to iso-center to reduce the chance that any ball bearing is outside the field of view.

  2. Acquire a portal image of the phantom.

  3. Identify all the ball bearings in the image. This procedure was done automatically using image processing.

  4. Solve for the system geometry using the method described in the literature8. Position of BB in imaging plane is the function of geometric parameters and 3D coordinate in the world coordinate system. Since the coordinate of the BB is known and position of BB is found in step 3), geometric parameters can be determined. See the reference 8 for detail.

Results and discussion

The sensitivity of the calibration algorithm on the inaccuracy of ball bearing identification due to limitations of image quality or limited accuracy of the phantom dimension is analyzed. Table 1 shows the uncertainty of the calibration parameter due to the 0.5 pixel error. It has been shown that the pixel error of the BB position in kV image is less than 0.1 pixels for this phantom. However, the poor quality of the portal image compared to the kV diagnostic image gives poorer estimation and pixel error seems to be about 0.5 pixels on average. Effort to improve the image quality needs to be given. The current phantom consists of small size ball bearing, which was originally designed for kV CBCT calibration. Larger ball bearings and higher MU can be used to make better portal images of the phantom. Better image processing algorithm also can be helpful.

Megavoltage beam stability is tested first. At fixed gantry angle, nine images of phantom are taken continuously. The position of the electron beam on the target was found to vary over the first nine images. Figure 3 shows the trajectory of the electrons on the target, where the Z-axis is the direction pointing out from iso-center away from gantry. Since the first couple of images and the last image are extremely poor, those images couldn’t be used. The beam position is controlled very well in the direction of cross plane (Y axis). Range of motion in Y and Z direction is about 0.3 mm and 1.5 mm, respectively.

The nominal gantry angle and measured gantry were compared. 36 portal images were taken at gantry angles spaced at 10 degrees. 10 MU are given at each gantry angle. Geometric parameters such as source position, detector position and tilt angle, and gantry angle were calculated at each angle. Figure 4 shows the nominal gantry angle reported by the linear accelerator console and measured gantry angle from the calibration. Maximum error of the gantry angle is always less than 0.1 degree as shown in Figure 4.

Figure 5 shows the MV source position and piercing point on the detector in 3 dimensional spaces. Average source to iso-center distance (SAD) is 1003.2mm and source to detector distance is 1600.4mm. The maximum deviation of the beam position from the ideal trajectory of a perfect circle is found at gantry angles of –90 degree and 90 degree. The MV source moves toward the gantry by 1.2mm and toward the couch by 1.2mm again at gantry angle of –90 and 90 degree, respectively. This movement is also found from the analysis of piercing point movement as a function of gantry angle (not shown here).

Figure 6 shows the alignment of collimator rotational axis to the MV source position. The collimator rotational axis can be found by attaching the phantom to the collimator. 36 images are taken by rotating collimator with the phantom. 10 MU is given to each image. The source position in the rotating coordinate system fixed in the phantom will stay at a point when the source is at the axis of collimator rotation. If the source is at distance from the axis of collimator rotation, the source position follows circular trajectory around the axis of collimator rotation. Thin lines with small circle represent the raw data of source positions in rotating coordinate system of the phantom. The axis of rotation can be found by averaging the source position. The average distance of the source positions from the center indicates the distance between source position and the axis of collimator rotation. Thick line represents the average motion of the source around collimator axis. It was found to be 0.9mm.

Table 1. Uncertainty in geometric parameters for different number of ball bearings and 0.5 pixel error in BB localization.

source position detector position detector angle gantry Magnification

N Ysi Zsi Ydi Zdi    angle, t Zsi/(Zsi-Zdi)

[mm] [mm] [mm] [mm] [deg] [deg] [deg] [deg] [percent]

12 1.1925 9.4450 0.7180 5.7435 0.4515 0.4430 0.0400 0.0760 0.0465

16 0.8545 7.5175 0.5155 4.5890 0.5420 0.3840 0.0485 0.3840 0.0405

20 0.7620 6.7150 0.4595 4.0990 0.4660 0.3435 0.0435 0.3385 0.0360

24 0.6955 6.1295 0.4195 3.7420 0.4425 0.3135 0.0390 0.3020 0.0330

32 0.6025 5.3085 0.3635 3.2405 0.3730 0.2715 0.0340 0.2660 0.0285

40 0.5385 4.7480 0.3250 2.8985 0.3370 0.2430 0.0315 0.2465 0.0255

60 0.4400 3.8770 0.2655 2.3665 0.3015 0.1980 0.0265 0.2110 0.0210

new method has been proposed for calibration of CBCT and medical linear accelerator. This method is robust, easy to implement and efficient. The calibration algorithm uses a linear parameter-estimation approach (fast and accurate computation) and produces a complete solution (all the calibration parameters are found) using a calibration phantom consisting of 24 steel ball bearings precisely located in two circular trajectories in a cylindrical plastic phantom.

A general and reliable method for geometric calibration of a CBCT system and medical linear accelerator is developed. Using this algorithm, characterization of kV and MV source, detectors, jaws, MLC, and couch system are possible. Once the MV system, kV system, and couch system are characterized and calibrated, precise image-guided radiation therapy is possible. Overall, a robust and convenient method has been developed and demonstrated for an accurate geometric calibration of these systems.


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  2. B.A. Groh, L. Spies, B.M. Hesse, T. Bortfeld, “Megavoltage computed tomography with an amorphous silicon detector array.” International Workshop on Electronic Portal Imaging. Phoenix, AZ, 93–94 (1998)

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  4. Y. Cho, and P. Munro, “Kilovision : Thermal modelling of a kilovoltage x-ray source integrated into a medical linear accelerator.” Med. Phys. 29, 2101-2108 (2002)

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  6. D.A. Jaffray, D. Drake, M. Moreau, et. al. “A radiographic and tomographic imaging system integrated into a medical linear accelerator for localization of bone and soft-tissue targets.” Int. J. Radiat Oncol Biol Phys., 45, 773-789 (1999)

  7. B.A. Groh, J.H. Siewerdesen, D.G. Drake, J.W. Wong, and D.A. Jaffray, “A performance comparison of flat-panel imager-based MV and KV cone-beam CT”, Med. Phys. 29, 967-975 (2002)

  8. Y. Cho, D. Moseley, J. Siewerdsen, and D.Jaffary, “Geometric calibration of a cone-beam computed tomography system” submitted to Med. Phys. for publication.

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