^{1}, J. H. Siewerdsen

^{2,a)}, Y. B. Cho

^{3}, D. A. Jaffray

^{4}and J. C. Irish

^{5}

### Abstract

A geometric calibration method that determines a complete description of source-detector geometry was adapted to a mobile C-arm for cone-beam computed tomography(CBCT). The non-iterative calibration algorithm calculates a unique solution for the positions of the source , detector, piercing point , and detector rotation angles based on projections of a phantom consisting of two plane-parallel circles of ball bearings encased in a cylindrical acrylic tube. The prototype C-arm system was based on a Siemens PowerMobil modified to provide flat-panel CBCT for image-guided interventions. The magnitude of geometric nonidealities in the source-detector orbit was measured, and the short-term and long-term ( months) reproducibility of the calibration was evaluated. The C-arm exhibits large geometric nonidealities due to mechanical flex, with maximum departures from the average semicircular orbit of and (for the piercing point), and and (for the source and detector), and , , and (for the detector tilt/rotation). Despite such significant departures from a semicircular orbit, these system parameters were found to be reproducible, and therefore correctable by geometric calibration. Short-term reproducibility was (subpixel) for the piercing point coordinates, for the source-detector and , for the source-detector , and for the detector angles. Long-term reproducibility was similarly high, demonstrated by image quality and spatial resolution measurements over a period of 6 months. For example, the full-width at half-maximum (FWHM) in axial images of a thin steel wire increased slightly as a function of the time between calibration and image acquisition: , 0.63, 0.66, 0.71, and at , , 1 day, 1 month, and 6 months, respectively. For ongoing clinical trials in CBCT-guided surgery at our institution, geometric calibration is conducted monthly to provide sufficient three-dimensional (3D) image quality while managing time and workflow considerations of the calibration and quality assurance process. The sensitivity of 3D image quality to each of the system parameters was investigated, as was the tolerance to systematic and random errors in the geometric parameters, showing the most sensitive parameters to be the piercing point coordinates and in-plane positions of the source and detector. Errors in the out-of-plane position of the source and detector and the detector angles were shown to have subtler effects on 3D image quality.

The C-arm prototype was developed in collaboration with Siemens Medical Systems, Special Products Division (Erlangen, Germany), with the scientific and engineering support of Dr. R. Graumann, Dr. K. Hermann, Dr. D. Ritter, and Dr. M. Mitschke. The authors express their gratitude to Dr. D. J. Moseley and Dr. S. M. Kim (University Health Network, Toronto ON) for assistance with implementing the calibration algorithm. Thanks also to S. Ansell and G. Wilson (University Health Network) for expertise with software components of the imaging system. Ongoing collaboration with surgeons and scientists in the Guided Therapeutics (GTx) Program at the University Health Network is gratefully acknowledged, including: Dr. M. Fehlings, Dr. M. Jewett, Dr. W. Kucharczyk, Dr. J. Trachtenberg, Dr. R. Weersink, and Dr. B. Wilson. The research was supported by the Princess Margaret Hospital Foundation and the National Institutes of Health Grant No. R01-CA-127444-01.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. Mobile isocentric C-arm for flat-panel cone-beam CT

II.B. Image quality evaluation

II.C. Geometric calibration

II.C.1. System geometry

II.C.2. Calibration phantom

II.C.3. Calibration algorithm

II.D. Geometric reproducibility

II.D.1. Short-term and long-term reproducibility

II.D.2. Effect of C-arm position

II.E. Calibration sensitivity and tolerance

II.E.1. Sensitivity: Parameter knockout

II.E.2. Calibration comparison: Full, single-BB, and semicircular

II.E.3. Tolerance: Systematic and random perturbations

III. RESULTS

III.A. Geometric reproducibility

III.A.1. Short-term and long-term reproducibility

III.A.2. Effect of C-arm position

III.B. Calibration sensitivity and tolerance

III.B.1. Sensitivity: Parameter knockout

III.B.2. Calibration comparison: Full, single-BB, and semicircular

III.B.3. Tolerance: Systematic and random perturbations

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- Calibration
- 107.0
- Medical imaging
- 82.0
- Image sensors
- 62.0
- Position sensitive detectors
- 45.0
- Cone beam computed tomography
- 43.0

## Figures

(a) Experimental setup for geometric calibration of the prototype C-arm. (b) Coronal, (c) sagittal, (d) axial, and (e) volumetric renderings illustrating CBCT image quality over the volumetric field of view. The anthropomorphic head phantom contains soft-tissue simulating spheres (denoted S) and a natural human skeleton, with anatomical regions of interest denoted SB (skull base), SS (sphenoid sinus), MS (maxillary sinus), C (cochlea), M (mastoid air cells), and AC (auditory canal).

(a) Experimental setup for geometric calibration of the prototype C-arm. (b) Coronal, (c) sagittal, (d) axial, and (e) volumetric renderings illustrating CBCT image quality over the volumetric field of view. The anthropomorphic head phantom contains soft-tissue simulating spheres (denoted S) and a natural human skeleton, with anatomical regions of interest denoted SB (skull base), SS (sphenoid sinus), MS (maxillary sinus), C (cochlea), M (mastoid air cells), and AC (auditory canal).

(a) System geometry of the CBCT C-arm. The world coordinate system is the reference frame for object positions (e.g., source and detector) and CBCT volume reconstructions. The piercing point is the projection of the origin of the world coordinate system (i.e., the C-arm isocenter) on the detector plane . The positions of the source and detector with respect to the world coordinate system are shown. (b) Illustration of detector tilt ( and ) and rotation angles applied on the virtual detector coordinate system to produce the real detector coordinate system (not shown), which results after rotation by . (c) Example projection image of the calibration phantom, illustrating the relationship between diametrically opposed BB locations and the piercing point. The geometric system parameters are computed analytically based on two five-parameter fits to the ellipses defined by centroids of the 16 BBs as shown.

(a) System geometry of the CBCT C-arm. The world coordinate system is the reference frame for object positions (e.g., source and detector) and CBCT volume reconstructions. The piercing point is the projection of the origin of the world coordinate system (i.e., the C-arm isocenter) on the detector plane . The positions of the source and detector with respect to the world coordinate system are shown. (b) Illustration of detector tilt ( and ) and rotation angles applied on the virtual detector coordinate system to produce the real detector coordinate system (not shown), which results after rotation by . (c) Example projection image of the calibration phantom, illustrating the relationship between diametrically opposed BB locations and the piercing point. The geometric system parameters are computed analytically based on two five-parameter fits to the ellipses defined by centroids of the 16 BBs as shown.

Geometric parameters from ten repeat CBCT scans over , with one of the scans (selected arbitrarily) highlighted by the thicker black line. The system parameters computed as a function of the gantry angle include: (a) the piercing point and source-to-detector distance (SDD), (b) source position , (c) detector position , and (d) detector tilt ( and ) and rotation angles. Parameters prefixed by “” are plotted as a difference from their average value over the semicircular orbit.

Geometric parameters from ten repeat CBCT scans over , with one of the scans (selected arbitrarily) highlighted by the thicker black line. The system parameters computed as a function of the gantry angle include: (a) the piercing point and source-to-detector distance (SDD), (b) source position , (c) detector position , and (d) detector tilt ( and ) and rotation angles. Parameters prefixed by “” are plotted as a difference from their average value over the semicircular orbit.

Geometric reproducibility of the C-arm calibration over a six-month time period. (a)–(j) Axial images of a steel wire ( diameter) placed within the two-circle calibration phantom shown as a function of the time interval, , between scanning of the wire and calibration phantom. The calibration phantom was repositioned between each scan. (k) Plots of FWHM and normalized maximum signal in axial wire images as a function of (logarithmic time scale).

Geometric reproducibility of the C-arm calibration over a six-month time period. (a)–(j) Axial images of a steel wire ( diameter) placed within the two-circle calibration phantom shown as a function of the time interval, , between scanning of the wire and calibration phantom. The calibration phantom was repositioned between each scan. (k) Plots of FWHM and normalized maximum signal in axial wire images as a function of (logarithmic time scale).

Sensitivity analysis of each geometric system parameter on the spatial resolution and image quality of CBCT reconstructions. Each case shows an axial image of the anthropomorphic head phantom in the region of the skull base, with axial images of a steel wire shown as insets to demonstrate the effect on the point-spread function. (a) Image reconstructed using the complete geometric calibration. (b)–(l) Image reconstructions for which a given geometric parameter was replaced by its average value over the semicircular orbit.

Sensitivity analysis of each geometric system parameter on the spatial resolution and image quality of CBCT reconstructions. Each case shows an axial image of the anthropomorphic head phantom in the region of the skull base, with axial images of a steel wire shown as insets to demonstrate the effect on the point-spread function. (a) Image reconstructed using the complete geometric calibration. (b)–(l) Image reconstructions for which a given geometric parameter was replaced by its average value over the semicircular orbit.

Comparison of three geometric calibration methods. (a) The full geometric calibration method, which accounts for nonidealities in the positions of the source and detector and the tilt and rotation angles of the detector. (b) A “single-BB” calibration method simulated by correcting only the detector offsets of the piercing point. (c) Calibration assuming a semicircular orbit. The inset images are axial slices of a wire, and the full images are axial views of the temporal bone region within an anthropomorphic head phantom.

Comparison of three geometric calibration methods. (a) The full geometric calibration method, which accounts for nonidealities in the positions of the source and detector and the tilt and rotation angles of the detector. (b) A “single-BB” calibration method simulated by correcting only the detector offsets of the piercing point. (c) Calibration assuming a semicircular orbit. The inset images are axial slices of a wire, and the full images are axial views of the temporal bone region within an anthropomorphic head phantom.

Tolerance to (a–e) systematic and (f–j) random errors in the source position, . Plots of as a function of gantry angle are shown for (a) systematic offsets of and (f) zero-mean gaussian perturbations with variance . Images in (b)–(e) and (g)–(j) are axial reconstructions of a steel wire (inset) and a head phantom in the region of the skull base, with the position of the cochlea (C) marked by the arrow.

Tolerance to (a–e) systematic and (f–j) random errors in the source position, . Plots of as a function of gantry angle are shown for (a) systematic offsets of and (f) zero-mean gaussian perturbations with variance . Images in (b)–(e) and (g)–(j) are axial reconstructions of a steel wire (inset) and a head phantom in the region of the skull base, with the position of the cochlea (C) marked by the arrow.

Tolerance to (a–e) systematic and (f–j) random errors in the detector offset, . Plots of as a function of gantry angle are shown for (a) systematic offsets of (i.e., 0, 1, 2, and 4 pixels) and (f) zero-mean gaussian perturbations with variance . Corresponding axial wire profiles and head phantom images are shown in (b)–(e) and (g)–(j), with the posterior aspects of the skull base (SB) and maxillary sinus (MS) circled.

Tolerance to (a–e) systematic and (f–j) random errors in the detector offset, . Plots of as a function of gantry angle are shown for (a) systematic offsets of (i.e., 0, 1, 2, and 4 pixels) and (f) zero-mean gaussian perturbations with variance . Corresponding axial wire profiles and head phantom images are shown in (b)–(e) and (g)–(j), with the posterior aspects of the skull base (SB) and maxillary sinus (MS) circled.

Tolerance to (a–e) systematic and (f–j) random errors in the detector rotation, . Plots of as a function of gantry angle are shown for (a) systematic offsets of and (f) zero-mean gaussian perturbations with variance . Corresponding axial wire profiles and head phantom images are shown in (b)–(e) and (g)–(j).

Tolerance to (a–e) systematic and (f–j) random errors in the detector rotation, . Plots of as a function of gantry angle are shown for (a) systematic offsets of and (f) zero-mean gaussian perturbations with variance . Corresponding axial wire profiles and head phantom images are shown in (b)–(e) and (g)–(j).

## Tables

Glossary of geometric parameters computed by the calibration algorithm, along with results summarizing the magnitude of geometric nonideality on the CBCT C-arm and the reproducibility of geometric parameters. Geometric nonideality is reported as the maximum deviation from the average semicircular orbit over the gantry motion. Geometric reproducibility is computed as the average of the angle-dependent standard deviations evaluated for ten calibrations of the C-arm.

Glossary of geometric parameters computed by the calibration algorithm, along with results summarizing the magnitude of geometric nonideality on the CBCT C-arm and the reproducibility of geometric parameters. Geometric nonideality is reported as the maximum deviation from the average semicircular orbit over the gantry motion. Geometric reproducibility is computed as the average of the angle-dependent standard deviations evaluated for ten calibrations of the C-arm.

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