^{1,a)}, James Bowsher

^{2}and Fang-Fang Yin

^{2}

### Abstract

In order to achieve functional and molecular imaging as patients are in position for radiation therapy, a robotic multipinhole SPECT system is being developed. Alignment of the SPECT system—to the linear accelerator (LINAC) coordinate frame and to the coordinate frames of other on-board imaging systems such as cone-beam CT (CBCT)—is essential for target localization and image reconstruction. An alignment method that utilizes line sources and one pinhole projection is proposed and investigated to achieve this goal. Potentially, this method could also be applied to the calibration of the other pinhole SPECT systems.

An alignment model consisting of multiple alignment parameters was developed which maps line sources in three-dimensional (3D) space to their two-dimensional (2D) projections on the SPECT detector. In a computer-simulation study, 3D coordinates of line-sources were defined in a reference room coordinate frame, such as the LINAC coordinate frame. Corresponding 2D line-source projections were generated by computer simulation that included SPECT blurring and noise effects. The Radon transform was utilized to detect angles (α) and offsets (ρ) of the line-source projections. Alignment parameters were then estimated by a nonlinear least squares method, based on the α and ρ values and the alignment model. Alignment performance was evaluated as a function of number of line sources, Radon transform accuracy, finite line-source width, intrinsic camera resolution, Poisson noise, and acquisition geometry. Experimental evaluations were performed using a physical line-source phantom and a pinhole-collimated gamma camera attached to a robot.

In computer-simulation studies, when there was no error in determining angles (α) and offsets (ρ) of the measured projections, six alignment parameters (three translational and three rotational) were estimated perfectly using three line sources. When angles (α) and offsets (ρ) were provided by the Radon transform, estimation accuracy was reduced. The estimation error was associated with rounding errors of Radon transform, finite line-source width, Poisson noise, number of line sources, intrinsic camera resolution, and detector acquisition geometry. Statistically, the estimation accuracy was significantly improved by using four line sources rather than three and by thinner line-source projections (obtained by better intrinsic detector resolution). With five line sources, median errors were 0.2 mm for the detector translations, 0.7 mm for the detector radius of rotation, and less than 0.5° for detector rotation, tilt, and twist. In experimental evaluations, average errors relative to a different, independent registration technique were about 1.8 mm for detector translations, 1.1 mm for the detector radius of rotation (ROR), 0.5° and 0.4° for detector rotation and tilt, respectively, and 1.2° for detector twist.

Alignment parameters can be estimated using one pinhole projection of line sources. Alignment errors are largely associated with limited accuracy of the Radon transform in determining angles (α) and offsets (ρ) of the line-source projections. This alignment method may be important for multipinhole SPECT, where relative pinhole alignment may vary during rotation. For pinhole and multipinhole SPECT imaging on-board radiation therapy machines, the method could provide alignment of SPECT coordinates with those of CBCT and the LINAC.

This work is supported by PHS/NIH/NCI Grant No. R21-CA156390-01A1. The authors would like to thank Bernie Jelinek and Richard Nappi from the Duke University physics instrument shop for constructing the line-source phantom and the connection joint between detector and the robotic arm; KUKA Robotics Corporation (Shelby Township, MI), and Digirad Corporation (Poway, CA) for their assistance with the robot and detector, respectively; and the Duke University Medical Center Radiopharmacy for providing Tc-99m radiotracer for the experiment.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. Alignment model

II.B. Estimation of alignment parameters

II.C. Angles and offsets of line-source projections

II.D. Evaluation of alignment model

II.E. Experimental evaluation of alignment method

III. RESULTS

IV. DISCUSSION

V. CONCLUSIONS

### Key Topics

- Single photon emission computed tomography
- 45.0
- Medical imaging
- 32.0
- Robotics
- 23.0
- Cone beam computed tomography
- 17.0
- Radiation therapy
- 17.0

##### A61B6/03

##### A61N5/00

##### G01N33/48

##### G01T1/164

##### G01T1/167

##### G06F19/00

##### H05H9/00

## Figures

Computer-aided design illustration of a robotic multipinhole SPECT system imaging a patient in position for radiation therapy. Also shown are a patient table and LINAC. The system involves a robotic arm (KUKA Robotics Corporation, Shelby Township, MI) which maneuvers a 49-pinhole-SPECT system about the patient. This multipinhole SPECT system would concentrate detector area on a limited region of interest, e.g., the radiation-therapy target, thereby improving SPECT sensitivity for that region of interest and potentially allowing relatively short scan times.

Computer-aided design illustration of a robotic multipinhole SPECT system imaging a patient in position for radiation therapy. Also shown are a patient table and LINAC. The system involves a robotic arm (KUKA Robotics Corporation, Shelby Township, MI) which maneuvers a 49-pinhole-SPECT system about the patient. This multipinhole SPECT system would concentrate detector area on a limited region of interest, e.g., the radiation-therapy target, thereby improving SPECT sensitivity for that region of interest and potentially allowing relatively short scan times.

Pinhole projection p k of a point k. The xyz coordinates are parallel to the uvw coordinates, with the z-axis and w-axis pointing into the paper. The gray dot k represents a point. The gray dot p k on the detector represents the pinhole projection of this point. The detector translations x det and z det are the detector shifts in the x-axis and z-axis directions from the xyz origin. The pinhole translations u f and w f are relative to the detector center, which intercepts the v-axis. The detector radius of rotation y det and pinhole focal length −v f are along the v-axis direction.

Pinhole projection p k of a point k. The xyz coordinates are parallel to the uvw coordinates, with the z-axis and w-axis pointing into the paper. The gray dot k represents a point. The gray dot p k on the detector represents the pinhole projection of this point. The detector translations x det and z det are the detector shifts in the x-axis and z-axis directions from the xyz origin. The pinhole translations u f and w f are relative to the detector center, which intercepts the v-axis. The detector radius of rotation y det and pinhole focal length −v f are along the v-axis direction.

(a) The gray broad line segment is a single pinhole projection of a line source. The superimposed narrow dark gray line is the estimated ridge of the line-source projection and is computed using (15) , where (α0, ρ0) corresponds to the maximum pixel value determined from the Radon transform of the line-source projection. The offset (ρ) is the perpendicular distance from the center of the projection image to the ridge of the line-source projection. The angle (α) is between the horizontal-axis and the offset-axis. (b) Radon transform of line-source projection in (a), where (α0, ρ0) is the angle and offset corresponding to the maximum pixel value of the Radon transform and is used to draw the red line in (a).

(a) The gray broad line segment is a single pinhole projection of a line source. The superimposed narrow dark gray line is the estimated ridge of the line-source projection and is computed using (15) , where (α0, ρ0) corresponds to the maximum pixel value determined from the Radon transform of the line-source projection. The offset (ρ) is the perpendicular distance from the center of the projection image to the ridge of the line-source projection. The angle (α) is between the horizontal-axis and the offset-axis. (b) Radon transform of line-source projection in (a), where (α0, ρ0) is the angle and offset corresponding to the maximum pixel value of the Radon transform and is used to draw the red line in (a).

(a) Computer simulated line-source phantom with five line sources. (b) Projection image of the line-source phantom with pseudo random sampling from corresponding Poisson distributions.

(a) Computer simulated line-source phantom with five line sources. (b) Projection image of the line-source phantom with pseudo random sampling from corresponding Poisson distributions.

(a) Line-source phantom with Tc-99m injected in five lines. (b) Single pinhole collimated SPECT detector with line-source phantom. (c) SPECT detector attached to robotic arm imaging line-source phantom.

(a) Line-source phantom with Tc-99m injected in five lines. (b) Single pinhole collimated SPECT detector with line-source phantom. (c) SPECT detector attached to robotic arm imaging line-source phantom.

Errors in estimating six alignment parameters for Study B using three line sources, Study C using four line sources, and Study D using five line sources (from left to right). Each distribution is obtained from 400 noisy realizations. The number above each whisker is the number of outliers. The mean of each distribution is represented by an “x”. Errors in parameter estimation from noise-free projections are represented by a “+”.

Errors in estimating six alignment parameters for Study B using three line sources, Study C using four line sources, and Study D using five line sources (from left to right). Each distribution is obtained from 400 noisy realizations. The number above each whisker is the number of outliers. The mean of each distribution is represented by an “x”. Errors in parameter estimation from noise-free projections are represented by a “+”.

Box-and-whisker plots of alignment parameter error with different activity concentration of 1.85 MBq, 7.4 MBq, and 14.8 MBq per line (from left to right). Each distribution is obtained from 400 noisy realizations. The mean of each distribution is represented by an “x”. Errors in parameter estimation from noise-free projections are represented by a “+”.

Box-and-whisker plots of alignment parameter error with different activity concentration of 1.85 MBq, 7.4 MBq, and 14.8 MBq per line (from left to right). Each distribution is obtained from 400 noisy realizations. The mean of each distribution is represented by an “x”. Errors in parameter estimation from noise-free projections are represented by a “+”.

Box-and-whisker plots of alignment parameter error for seven parameters with activity concentration of 14.80 MBq per line and 3.5 mm intrinsic resolution. The number above each whisker is the number of outliers. Each distribution is obtained from 400 noisy realizations. The mean of each distribution is represented by an “x”. Errors in parameter estimation from noise-free projections are represented by a “+”.

Box-and-whisker plots of alignment parameter error for seven parameters with activity concentration of 14.80 MBq per line and 3.5 mm intrinsic resolution. The number above each whisker is the number of outliers. Each distribution is obtained from 400 noisy realizations. The mean of each distribution is represented by an “x”. Errors in parameter estimation from noise-free projections are represented by a “+”.

## Tables

Simulated line source geometry used in this paper as shown in Fig. 4(a) , specified using the coefficients (a,b,c,d) of Eqs. (1) and (2) .

Simulated line source geometry used in this paper as shown in Fig. 4(a) , specified using the coefficients (a,b,c,d) of Eqs. (1) and (2) .

Four experiments designed to evaluate the proposed alignment procedure.

Four experiments designed to evaluate the proposed alignment procedure.

Four different acquisition geometries. The top first row of each acquisition geometry is the true values of alignment parameters. The true values are those used to compute the 2D line-source projections. The start points are the initial values in the iterative parameter estimation.

Four different acquisition geometries. The top first row of each acquisition geometry is the true values of alignment parameters. The true values are those used to compute the 2D line-source projections. The start points are the initial values in the iterative parameter estimation.

Physical line source geometry determined in the CT (XYZ) coordinate frame from the CT image, specified using the coefficients (a,b,c,d) of Eqs. (1) and (2) .

Physical line source geometry determined in the CT (XYZ) coordinate frame from the CT image, specified using the coefficients (a,b,c,d) of Eqs. (1) and (2) .

Three acquisition geometries for scanner-acquired projections of the physical line-source phantom. The top first row for each acquisition geometry is the true value as given by the robot tool coordinate frame. The second row gives initial values in the iterative parameter estimation.

Three acquisition geometries for scanner-acquired projections of the physical line-source phantom. The top first row for each acquisition geometry is the true value as given by the robot tool coordinate frame. The second row gives initial values in the iterative parameter estimation.

The 25% quartile (Q1), the median quartile (Q2), and the 75% quartile (Q3) values of the estimated alignment parameters of Study B, C, and D. The highest outlier values and the percent of outliers of each estimated alignment parameters of Study B, C, and D. P-values are from two-tailed Wilcoxon rank sum test with 5% significance level. Numbers in bold are p < 0.05.

The 25% quartile (Q1), the median quartile (Q2), and the 75% quartile (Q3) values of the estimated alignment parameters of Study B, C, and D. The highest outlier values and the percent of outliers of each estimated alignment parameters of Study B, C, and D. P-values are from two-tailed Wilcoxon rank sum test with 5% significance level. Numbers in bold are p < 0.05.

The 25% quartile (Q1), the median quartile (Q2), and the 75% quartile (Q3) values of the estimated alignment parameters of intrinsic detector resolution of 1.5 mm, 2.5 mm, and 3.5 mm. The highest outlier values and the percent of outliers of each estimated alignment parameters. The p-values are from a two-tailed Wilcoxon rank sum test with 5% significance level. Numbers in bold are p < 0.05.

The 25% quartile (Q1), the median quartile (Q2), and the 75% quartile (Q3) values of the estimated alignment parameters of intrinsic detector resolution of 1.5 mm, 2.5 mm, and 3.5 mm. The highest outlier values and the percent of outliers of each estimated alignment parameters. The p-values are from a two-tailed Wilcoxon rank sum test with 5% significance level. Numbers in bold are p < 0.05.

The 25% quartile (Q1), the median quartile (Q2), and the 75% quartile (Q3) values of the estimated alignment parameters of five line sources with 1.85 MBq, 7.40 MBq, and 14.80 MBq per line with 3.5 mm intrinsic resolution. The highest outlier values and the percent of outliers of each estimated alignment parameters. P-values are from two-tailed Wilcoxon rank sum test with 5% significance level. Numbers in bold are p < 0.05.

The 25% quartile (Q1), the median quartile (Q2), and the 75% quartile (Q3) values of the estimated alignment parameters of five line sources with 1.85 MBq, 7.40 MBq, and 14.80 MBq per line with 3.5 mm intrinsic resolution. The highest outlier values and the percent of outliers of each estimated alignment parameters. P-values are from two-tailed Wilcoxon rank sum test with 5% significance level. Numbers in bold are p < 0.05.

The error in alignment parameters estimated from five line-source projections with physical line-source phantom using robotic pinhole SPECT system.

The error in alignment parameters estimated from five line-source projections with physical line-source phantom using robotic pinhole SPECT system.

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