setup, and real-time treatment planning/re-planning. Two approaches have been considered. The first is the tomotherapy approach [1] that uses a spiral CT type.
Cone-Beam Computed Tomography (CT) for a Megavoltage Linear Accelerator (LINAC) Using an Electronic Portal Imaging Device (EPID) and the Algebraic Reconstruction Technique (ART) K. Mueller1 , J. Chang2, *, H. Amols2 , C.C. Ling2 Abstract - This study investigates the feasibility and applicability of cone beam CT for a megavoltage therapeutic LINAC. A Rando head phantom was irradiated using the 15 MV beam of a Varian 2100C LINAC at MSKCC for gantry angles from -102° to 102° with a 2° increment. The projection image for each gantry angle was obtained using a Varian Mark II EPID. Reference images without phantom were also collected at different angles. Pixel readings of each image were converted to dose rate using the EPID calibration curve. The ray sum (sum of linear attenuation coefficients along the ray from the source to a pixel) is calculated as the negative logarithm of the ratio of dose rate of that pixel to that of the corresponding pixel in the reference image. The ray sums were then used for volumetric reconstruction using ART. ART is an iterative method that solves a system of linear equations by iteratively updating the volume to reduce the errors between the measured and calculated ray sums. Our results indicate that reasonably good tomographic images can be obtained using projections at every 8°, even after only one iteration (typically, 2-3 iterations are used.) The image quality depends on the number of projections and the number of iterations. The reconstruction can be achieved within a reasonable time (~2 hours for pure software and ~5 min with the help of graphics hardware). We thus conclude that cone beam CT for megavoltage therapeutic LINAC has a potential to obtain useful tomographic images. Key words - ART, Cone beam CT, EPID, image reconstruction, megavoltage LINAC I. INTRODUCTION Using a high-energy LINAC to obtain tomographic images is a research topic that has emerged just a few ________________________________________________________________________
years ago. The potentials of such a technology include CT simulation on a LINAC, on-line verification of patient setup, and real-time treatment planning/re-planning. Two approaches have been considered. The first is the tomotherapy approach [1] that uses a spiral CT type machine with a 6 MV x-ray source. This approach adopts a similar reconstruction method that is used for spiral CT. The second approach, suitable for a C-arm type unit, involves cone-beam CT [2, 3]. Unlike the tomotherapy approach that employs one-dimensional ring detectors and reconstructs one slice at a time, the cone beam approach collects data using two-dimensional (2D) detectors and reconstructs the entire volume simultaneously. So far, the difficulty with the cone beam approach has been that it is generally inconvenient to collect 2D radiation fluence data, and that the computation complexity is too high for realtime reconstruction. However, given recent advances in EPID technology, the collection of 2D fluence distributions has become practical. Computer technology has also improved to obtain a reconstruction in reasonable time. For example, with the help of hardware [4], a three-dimensional (3D) reconstruction can be performed within minutes for CT angiography using the ART method. In addition, the Carm technology used by many LINACs has improved significantly, and although still not perfect makes the measurements suitable for volumetric tomography. In this study, 3D reconstructions were performed using the algebraic reconstruction technique (ART) that has previously been applied to both 2D [5, 6] and 3D tomographic reconstruction [7, 8]. Compared to the more popular filtered back projection (FBP) method [3, 9], ART potentially requires less projections [10] and can also be more tolerant to insufficient or incomplete data [6]. In addition, by employing graphics hardware, the reconstruction time of ART can be comparable to that of FBP [4]. II. THEORY AND METHODS
1
State University of New York at Stony Brook, Computer Science Department, Stony Brook, NY 11794 2 Memorial Sloan–Kettering Cancer Center, Medical Physics Department, New York, NY 10021 *
Author to whom inquiries should be addressed.
Figure 1 illustrates the notations used in this study. CAX is the central axis. SAD is the source to isocenter distance and SDD is the source to detector (EPID) distance. FS is the field size at SAD and FS' is the field
FS ′ = FS × ( SDD / SAD ) . θ is the cone beam angle, and is equal to 2 tan −1[ FS /( 2 × SAD )] or 2 tan −1[ F S′ /( 2 × SDD )] . The cone beam rotates in the transverse plane around the phantom and is assumed to cover the whole phantom from any irradiation angle. The detector (EPID in Figure 1) records the 2D radiation fluence attenuated by the phantom as well as the reference fluence without phantom. The negative logarithm of the ratio of the attenuated fluence to that of the reference fluence, the ray sum, is equal to the sum of the linear attenuation coefficients along the ray from source to detector. For a series of irradiations with different beam angles and pixel positions, the reconstruction problem can be described as a system of linear equations, size at SDD.
Source θ
SAD SDD
Isocenter
Phantom
CAX
EPID FS'
N
s i = ∑ wij µ j ,
(1)
Figure 1. Notations used in this study.
j=1
where si is the ray sum for the ith ray, µj is attenuation coefficient of voxel j, wij is the weight factor that represent the contribution of voxel j to ray sum si , and N is the total number of voxels.
0° y Source
This very large system of Eq. (1) can be solved via an iterative method [6], e.g., ART [5-8], the conjugate gradient method [11], or projection onto convex sets [12]. An iterative method updates µ (k ) , the µ’s estimate at the
Phantom
j
k iteration, to reduce the errors, e (k ) = si − ∑ wij µ (jk ) , i j =1 that is, the difference of the measured and the calculated ray sums. We have adopted ART for the reconstruction. Starting from an initial guess of µ = µ ( 0) , ART j
∑
N
l =1
w2il ,
Couch
102°
EPID
j
µ (j k +1) = µ (jk ) + λ wij ei(k )
-102°
j
sequentially updates µ (k ) during the kth iteration as (2)
where λ is the relaxation factor. λ is typically chosen in interval (0.0,1.0], but is usually much smaller than 1.0 to dampen correction overshoot. The order of the sequential updates of attenuation coefficients in Eq. (2) should use ray projections that are as orthogonal as possible [7]. The above procedure repeats until it converges (i.e., e( k ) ≈ e( k −1) , or a specified number of iterations.) i
x
N
th
i
Typically, two to three iterations are needed to reconstruct a volume within a reasonable margin of error [8]. III. EXPERIMENT Experiments were performed to test the cone-beam tomographic reconstruction. We used the 15 MV x-ray beam of a Varian 2100C LINAC at MSKCC as the source, and as the detector we used the Varian Mark II EPID [13] at SDD = 150 cm. Because the detector occupies a 32×32 cm region, the irradiation field size is 21.3×21.3 cm at
±180° Figure 2. Irradiation of the phantom in the central transverse plane. The gantry (source) rotates clockwise every 2° from -102° to 102°, which corresponds to 204/2 + 1 = 103 stops. For each stop, a 256×256 projection image with a pixel size of 1.27 mm is taken using the EPID.
SAD, which corresponds to a cone beam angle of 12.16°. The phantom is a Rando head phantom positioned at SAD. The irradiation field did not cover the whole phantom, as a small portion (~1 cm) of the top and the bottom of the phantom, respectively, were not in the field. Figure 2 illustrates the arrangement to acquire the projections from different angles. We acquired 103 EPID projection images of 256×256 pixels. The pixel size was 1.27mm. An image was acquired at every 2° from -102° (or 258°) to 102° in the transverse plane (z = 0). Reference images were also taken at gantry angles 0º, 90º, and -90º, without the phantom in the ray path. Each image was converted to a dose rate map using the EPID calibration curve that is
obtained using the iterative EPID calibration procedure [14] developed for our EPID QA system [15]. The ray sum for each pixel is calculated as − ln( D& D& 0 ) , where D& is the dose rate to that pixel, and D& 0 is the dose rate to the same pixel of the reference image. Reconstruction was performed on the calculated ray sums using ART. Different iteration numbers (1 to 3) and different projection numbers (23, 46, and all) were used to determine their effects on the reconstruction.
confirm that the contrast is sufficient for cone beam reconstruction. As the machine is running at a repetition rate of 240 MU/min and the EPID takes ~0.5 s to stabilize, the dose delivered during one image acquisition is 240×0.5/60 = 2 cGy at d max. This corresponds to 206 cGy, 92 cGy or 46 cGy for a reconstruction using all, 46, or 23
IV. RESULTS Figure 3 shows two projection images for gantry angles 0° and 90°, respectively. Figure 4 shows a volume rendering of the reconstructed phantom's face and skull (all 103 projection and one ART iteration were used). Figure 5 shows the reconstruction results (one ART iteration with all projections) for (A) a transverse cut at about 1/4 of the phantom height above the mid-plane, (B) the transverse slice at the mid-plane, (C) a transverse cut about 1/4 below the mid-plane, and (D) the center coronal slice. Figure 6 shows the low transverse slice of Figure 5A for (A) 103 projections, one iteration, (B) 46 projections, one iteration, and (C) 23 projections, three iterations.
(A) High
(B) Center
V. DISCUSSION AND CONCLUSIONS It is observed, in Figure 3, that the projection images for a 15 MV source contain enough contrast to distinguish bone, soft tissue, and air. Results from Figures 4-6 further
(C) Low
(D) Coronal
Figure 5. Cone beam reconstruction for (A) a high transverse slice, (B) the center transverse slice, (C) a low transverse slice, and (D) the center coronal slice, reconstructed using all (103) projections and one ART iteration.
(A) 0°
(B) 90°
Figure 3. Projection images for gantry angle (A) 0° and (B) 90°, obtained from the experiment in Figure 2 with a 15 MV cone beam source. Images are enhanced for display purposes. (A) 103 proj, 1 iter.
(A) Face
(B) Skull
Figure 4. Volume rendered face and skull, reconstructed from via cone beam CT using all (103) projections and one ART iteration.
(B) 46 proj, 1 iter.
(C) 23 proj., 3 iter. Figure 6. Cone beam reconstruction of the low transverse slice of Figure 4C for (A) 103 projections, one iteration, (B) 46 projections, one iteration, and (C) 23 projections, three iterations.
projections, respectively. These doses are on the order of therapeutic doses, but too high for simulation or setup verification purpose, which usually requires a dose less than 10 cGy. The dose can be significantly reduced if a lower repetition rate (e.g., 80 MU/min) or a faster and more sensitive detector (e.g., amorphous silicon imager) is used. Gating the LINAC beam to the EPID acquisition and readout cycle can also be implemented to reduce patient dose. The results from Figures 5 and 6 indicate that reasonably good tomographic images can be obtained from cone beam CT using a megavoltage therapeutic source. A comparison of Figures 6A-6C indicates that more iteration (Figure 6C) reduce the ring effect, while more projections (Figure 6A) reduce blurring. The quality of the reconstructed images is a function of the number of projections and the number of iterations. In general, better quality requires a higher number of projections and more iteration. However, this also leads to a longer reconstruction time, as this is linearly proportional both to the number of projections and the number of iterations. The optimal number of projections and number of iterations depend on the required image quality and the available time for reconstruction. This study proves that in principle cone beam CT can be achieved for a megavoltage LINAC. Note, however, that this study has been done in a very ideal situation. More studies are required for a practical implementation of this technology. Future work includes reconstruction using insufficient data (e.g., limited gantry angle), incomplete data (e.g., cone beam not covering the whole target), presence of interference (e.g., metal part of treatment couch). Improvements can also be achieved by pulse gating and EPID synchronization, hardware for fast reconstruction, corrections for source and EPID positioning errors (i.e., gantry sag and EPID sag), and scattering correction for more accurate weight function. 1.
2. 3. 4.
5.
6.
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