British Journal of Radiology 75 (2002),266-270 © 2002 The British Institute of Radiology
Assessment of distortion in a three-dimensional rotational angiography system
R R Bridcut, BSc, MSc
1
R J Winder, BSc, MSc
1
A Workman, BSc, MSc
2 and
P Flynn, MRCP, FRCR
3
1 Northern Ireland Regional Medical Physics Agency, Royal Victoria Hospital, Grosvenor Road, Belfast BT12 6BA, 2 Northern Ireland Regional Medical Physics Agency, Forster Green Hospital, 110 Saintfield Road, Belfast BT8 4HD and 3 Department of Neuroradiology, Royal Group of Hospitals, Grosvenor Road, Belfast BT12 6BA, UK
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Abstract
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The purpose of this project was to determine the degree of geometrical distortion in a three-dimensional (3D) image volume generated by a digital fluorography system with rotational image acquisition capabilities. 3D imaging is a valuable adjunct in neuroangiography for visualization and measurement of cerebral aneurysms and for determination of the optimum projection for intervention. To enable spatially accurate 3D reconstruction the system must correct for geometrical distortion in the image intensifier television system as well as for deviations in gantry motion. 3D volumes were reconstructed from 100 X-ray projections acquired over a 180° arc over a period of 8 s. A phantom was constructed to assess geometrical distortion in the three dimensions. The phantom consisted of 1 mm diameter ball bearings embedded in Perspex in a cubic lattice configuration. The ball bearings were placed at 20 mm intervals over a 140 mm cubic volume. Distortion was assessed by taking measurements between points of known separation and using a differential distortion measurement. The maximum error in the 3D location of objects was found to be 1.4 mm, while the differential distortion was found to range from -1.0% to +2.3%. The 3D images were found to have negligible visual distortion, enabling subjective assessments to be made with confidence to aid intervention.
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Introduction
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Three-dimensional rotational angiography (3DRA) acquires a series of projection X-ray images by rotating an X-ray tube and image intensifier on a C-arm around the patient. The 3D image volume is reconstructed using a "back projection" technique similar to that in CT to produce a 3D data set [1] that can be viewed from any angle.
3DRA has been found to improve the morphological depiction of cerebral aneurysms, complementing standard digital subtraction angiography [2, 3]. Figure 1a
shows a two-dimensional (2D) image of an anterior communicating aneurysm at its optimal viewing projection. The corresponding 3D volume rendered image viewed from a similar projection (Figure 1b) enables the surrounding vessel morphology to be visualized more clearly, including the anatomy at the aneurysm neck. The interventional procedure was carried out avoiding occlusion of the vessel arising from the aneurysm neck.
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Figure 1. Improved morphological depiction of an aneurysm (arrow) of the anterior communicating artery and associated blood vessels by two-dimensional visualization (a) compared with three-dimensional visualization (b).
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3DRA also allows determination of the optimal working projection for interventional neuroradiology procedures [3]. Measurements of aneurysm dimensions on 3D images have been shown to correlate with the appropriate coil diameter for embolisation procedures [4]. 3DRA may be used in the future for aneurysm and arteriovenous malformation (AVM) volume estimation prior to liquid embolisation and surgical planning. In all quantitative measurements however, there is a potential for geometric distortion and this should be quantified in order to estimate the measurement accuracy.
Two potential sources of geometric distortion that may impact on the spatial accuracy of the 3D reconstruction have been identified: (i) image intensifier television (TV) system distortion; and (ii) gantry "wobble" during image acquisition.
Gantry "wobble" was visualized as a vertical displacement between successive 2D projection images and prompted this investigation.
A calibration procedure is carried out by the manufacturer, and this is automatically applied to all images prior to 3D reconstruction, correcting for gantry wobble and geometrical distortion in the image intensifier TV system. A 30 mm3 Perspex cube containing three orthogonal metal rods of 2 mm diameter is routinely imaged and used to provide a visual check of the system calibration in the centre of the field of view (FOV). This report describes a quantitative assessment of distortion in a 3D volume data set over distances ranging from 20 mm to 208 mm.
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Materials and methods
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A Philips Integris BV5000 rotational angiography system (Philips Medical Systems, Best, The Netherlands) was assessed. Projection images were transferred to a Silicon Graphics Octane® workstation (Silicon Graphics Inc., Mountain Hill, CA) for 3D reconstruction.
2D assessment of image distortion
Image intensifier distortion was assessed by imaging a wire grid test object (Leeds, TO.M1) at each available field size. A standard differential distortion assessment was carried out [5]. Diagonal distances on the image of the grid test object were measured, where D(x) is the measured diagonal dimension of a square of actual side x cm. Relative distortion was calculated between concentric squares of dimensions x and y cm from
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Gantry wobble
Whilst viewing a cine replay of the 100 projected images, a displacement of successive images relative to each other was noted. This was due to gantry "wobble" along the axis of rotation. To investigate the extent of this "wobble", a narrow metal rod 0.8 mm in diameter was positioned on the patient table close to the centre of rotation and the centre of the FOV and was imaged using a 3D rotational acquisition. The vertical coordinate of the end point of the rod was recorded for each image and was used to measure the relative displacement of the point during a run.
Phantom design
A phantom was designed to contain a 3D lattice of equally-spaced ball bearings with a nominal diameter of 1 mm. These were embedded at a depth of 1.14 mm in polycarbonate sheets at 20 mm intervals in a 7x7 array. Seven sheets were constructed at 20 mm intervals in a water-filled Perspex cube to form a cubic 3D lattice. The components were engineered to an accuracy of ±0.02 mm. The phantom side dimension of 140 mm was chosen to assess distortion across the reconstructed 3D FOV. It was also representative of a typical anatomical volume, with a 17 cm image intensifier FOV being used to image the neurovasculature. Ball bearings separated by 20 mm allowed measurements between multiple positions in three dimensions and also provided a visual distortion assessment. The remainder of the cube was filled with water to approximate patient attenuation and to prevent saturation of the image intensifier TV system. The phantom is shown in Figure 2.
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Figure 2. Phantom constructed to assess three-dimensional (3D) geometrical distortion. 1 mm ball bearings are positioned in a 3D lattice configuration, supported by polycarbonate sheets in a water-filled Perspex cube.
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3D assessment of image distortion
100 X-ray projection images of the phantom were acquired over a 180° rotation over an 8 s period at a 17 cm image intensifier FOV, which is the most common clinical protocol. Images were transferred to a dedicated Silicon Graphics workstation for reconstruction.
The 3D image volume was thresholded to remove voxels representing Perspex and water. A volume rendered visualization was used to display the ball bearings (Figure 3). The workstation software was used to measure distances between bearings. Using a mouse, a measurement plane was defined and distances between the centres of ball bearings intersecting the plane were measured.
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Figure 3. Visualization of the reconstructed three-dimensional image volume, thresholded to remove Perspex and water, displaying only ball bearings.
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Measured inter-bearing distances were compared with actual distances. A differential distortion assessment using the image intensifier distortion assessment methodology described above was also carried out in multiple planes.
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Results
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2D distortion
A visual assessment of the image intensifier 2D images of the Leeds grid test object showed minor S-shaped distortion at larger field sizes, with slight barrelling visible at smaller field sizes (Figure 4). The differential distortion measurement ranged from -2.1% to +2.6%. The maximum measured distortion on the 17 cm FOV image was 2.1%.
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Figure 4. Image intensifier two-dimensional image of the Leeds TO.M1 wire grid test object acquired at a nominal 17 cm field of view.
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Gantry wobble
Figure 5 shows a graph of the relative vertical displacement of a single point close to the centre of the FOV in the 100 projection images. The first image acted as a reference (zero displacement). From the graph it can be seen that the maximum displacement of 3.2 mm occurred at image number 100. The overall trend of the graph indicates a drift in gantry alignment, whilst a "wobble" was seen beginning at image 38. The maximum displacement between successive images was 1.3 mm.
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Figure 5. Graph showing the relative displacement of a point in space close to the centre of the field of view for 100 projection images, illustrating gantry wobble.
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3D distortion
Distortion was not noticeable in a visual assessment of the reconstructed 3D image volume. From multiple inter-bearing measurements ranging from 20 mm to 208 mm, the difference between measured and actual distances ranged from -1.1 mm to 1.4 mm, with no dependence on direction. Differential distortion measurements in multiple planes ranged from -1.0% to +2.3%.
The error in the measurement was estimated to be ±0.8 mm. This was calculated from a quadrature combination of ball bearing positioning errors in phantom construction (±0.02 mm), distance of the measurement point from the centre of the ball bearing (±0.57 mm) and the accuracy of the mouse position (±0.5 mm).
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Discussion
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The degree of image distortion in the 2D X-ray projections was investigated initially. The image intensifier distortion of -2.1% to +2.6% was found to be acceptable, within the normal range of ±10% [5]. With the object positioned close to the centre of rotation, the position of a point in space close to the centre of rotation was found to alter by 3.2 mm owing to gantry movement. Points further from the centre of the FOV and the centre of rotation of the C-arm would be displaced further. The manufacturer is aware of this gantry movement and has found that most systems have a smooth gantry movement with less vibration in the middle of the run [Personal communication, C Kruijer, Philips Medical Systems, Best, The Netherlands].
The ability of the manufacturer's calibration procedure to correct for these distortions in the reconstructed 3D image was then investigated. The difference between actual and measured ball bearing separations was found to range from -1.1 mm to +1.4 mm, while the differential distortion measurement in multiple planes ranged from -1.0% to +2.3%. Over the ranges measured, we estimate that distortions of ±2 mm should not affect clinical judgement. The measurements confirm adequate correction for the potential sources of distortion and allow the radiologist to proceed with confidence.
While the phantom measurements have shown geometrical distortion to be insignificant over dimensions ranging from 20 mm to 208 mm, it is recognized that distortion over smaller dimensions is possible. This may be significant when measuring small distances on the reconstructed volume, such as aneurysm dimensions to estimate the appropriate size of embolising coil, in particular when the majority of intracranial aneurysms measure less than 20 mm and usually less than 10 mm. Distortion over small dimensions could be assessed by measuring 3D reconstructions of small objects of known diameter.
The small degree of distortion measured gives us more confidence in the use of 3DRA in future applications, such as image guided surgery or radiotherapy planning. Another future application is to estimate the volume of an aneurysm or AVM prior to liquid embolisation with a histoacrylic glue or OnyxTM. Errors in volume estimations may be more significant, with errors scaling in proportion to the radius cubed.
When measuring vessel distances or volumes, the choice of threshold value would introduce another uncertainty. Software to quantify the threshold level and so ensuring consistency was not available on the workstation. Over small dimensions, threshold errors may be more significant than geometrical distortion errors.
The phantom that was developed could also be imaged periodically and used to monitor distortion of the 3DRA system over a longer time period. Some deterioration may occur owing to mechanical wear on the rotating C-arm. The initial assessment described here found distortion to be insignificant for the current clinical application.
Received for publication July 19, 2001.
Revision received December 7, 2001.
Accepted for publication December 11, 2001.
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References
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Abstract
Introduction
