First published online September 17, 2007
British Journal of Radiology (2007) 80, 835-840
© 2007 British Institute of Radiology
doi: 10.1259/bjr/41664978
Accurate geometric calibration in stepping-table digital subtraction angiography
M A Schmidt, PhD
1
S L Nayak, DCR(R)
2
A-M Belli, FRCR
2 and
A J Britten, PhD
1
Departments of 1 Medical Physics and 2 Radiology, St George's Hospital, London SW17 0QT, UK
Correspondence: Dr M A Schmidt, Department of Medical Physics, St George's Hospital, Blackshaw Road, London SW17 0QT, UK. E-mail: maria.schmidt{at}stgeorges.nhs.uk
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Abstract
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Accurate measurements of vessel dimensions are desirable in many clinical applications. This work uses the known relative motion between X-ray source and the patient in stepping-table digital subtraction angiography (DSA) to provide an accurate geometric calibration for quantitative measurements. The method results in a calibration factor that converts the size of the object measured in pixels on the image to its size in millimetres. The main sources of error relate to: (i) the assessment of relative displacement of a structure in a series of images; (ii) patient motion throughout data acquisition; and (iii) image distortion. Error was evaluated both with a test object consisting of a large grid of ball bearings (2x2 cm spaced) and, in vivo, in five renal DSA examinations performed with identical catheters of known diameter. The calibration factor was calculated with 0.1% accuracy for the test object and at least 2% accuracy in vivo, even with breath holding and pulsatile motion. This demonstrates that the calculation of the calibration factor can be very accurate, and that the method we propose is capable of the submillimetre accuracy required for clinical studies if used in conjunction with an accurate measurement of the vessel size in pixels. In conclusion, accurate geometric measurements can be performed in stepping-table DSA, without the need for external reference objects.
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Introduction
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Radiographic images are projective and are thus not suitable for precise geometric measurements because the magnification of the structures depicted is position dependent and basically unknown. Image distortion is an additional problem if images are obtained with image intensifiers (II) [1, 2]. However, accurate measurements of vessel dimensions are desirable in a number of clinical applications as they enable clinicians to tailor devices to individual interventions and to monitor the progression of vascular disease quantitatively. It has been shown that the measurement of vessel size, and not only the degree of stenosis, is relevant for the prediction of clinical outcome in coronary disease [3, 4].
Geometric measurements can be performed in radiographic images using known reference objects for comparison if the reference objects are located near the structure of interest or at least at the same distance from the detector as the structure of interest to be measured. This condition is often excessively restrictive and is only occasionally met in digital subtraction angiography (DSA), when catheters of accurately known diameters, or with reference marks of known spacing, are used to deliver the contrast agent.
Vascular structures have been rendered in three dimensions using data from multiple radiographic views and knowledge of the changes in the position of the X-ray apparatus in relation to the object of interest [5–7]. Stereotactic X-ray systems have also been used in the past to provide vessel size measurements without reference objects [8]. This technique makes use of the high resolution of DSA images and was shown to yield accurate results, with test object diameters measured with 0.1 mm accuracy [8].
Stereotactic X-ray tube systems are currently uncommon and most clinical studies requiring three-dimensional information make use of X-ray, CT and MR angiography. In terms of vessel size measurement, however, these three-dimensional techniques do not achieve a spatial and temporal resolution comparable to that of DSA.
Relative motion between the object of interest and the X-ray apparatus is a standard part of basic DSA procedures: stepping DSA for bolus chasing into the peripheral vasculature and rotational DSA for vessel assessment. In either case the apparatus motion is accurately known and repeatable. We propose to use the relative motion between X-ray source and object to provide an accurate geometric calibration to enable quantitative measurements. This work investigates using the patient translation on the couch to perform vessel size measurements in DSA images. This technique does not require any additional hardware, is widely available and is based on high-resolution images. It is therefore our objective to assess the precision and the accuracy of geometric measurements performed with stepping-table DSA.
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Methods
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The relative movement of the X-ray apparatus and object leads to a relative shift in the object position when radiographic images are compared. In stepping DSA the movement is the table translation along the superior–inferior axis. By knowing the object displacement in millimeters (d) (the table step) and by measuring the projected displacement of the object of interest in the image in pixels (D), the magnification can be calculated by triangulation (Figure 1
). It is desirable to make the measurement independent of the detector dimensions by defining a calibration factor (C), which relates directly the projected object size in pixels in the image (S) to the actual object size in millimeters (s) for each object:
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Figure 1. Diagram of the triangulation process leading to the definition of the calibration factor C as the ratio between the object displacement d(in millimeters) and the projected object displacement in the images D (in pixels). The object size (s) and the projected object size (S) are shown.
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where C is defined as:
and measured in millimetres per pixel.
The calculation of the calibration factor does not require previous knowledge of the source-to-detector distance, although this affects its value. The shift of the patient position (d) in relation to the X-ray focal spot is known with very high accuracy and therefore the main sources of error expected using this method are: (i) the error in the assessment of the relative displacement of a structure in a series of images (D); (ii) the error associated with patient motion throughout data acquisition; and (iii) the error associated with image distortion (if II are used). Our primary concern is to evaluate these error sources and determine how they affect the calculation of the calibration factor C for the measurement of vessel dimensions in DSA.
This work was undertaken in an X-ray digital subtraction angiography system (DLX; GE, Milwaukee, WI), based on a 40 cm image intensifier. Images were transferred to a PC for processing with in-house software, developed in C (Borland Software Corporation, Atlanta, GA) and IDL (IDL 6.1; RSI, Boulder, CO). In all images acquired the source-to-detector distance was kept to the range used in clinical examinations (approximately 100–120 cm), unless stated otherwise.
Assessing the relative displacement of structures in a series of images
Measuring the relative displacement of a structure in a series of images obtained with table translation can be achieved by co-registration with a chosen reference image. From the image registration methods available [9], a simple cross-correlation is expected to succeed for relatively small table steps and a fairly small change of viewpoint. This method is not expected to be suitable for very large table steps, which result in significant changes to the image as a result of parallax effects from the overlapping structures in the body.
The in-house software for registering images using cross-correlation requires the user to select a rectangular region that is subsequently magnified. Within the rectangular region the user then chooses a smaller arbitrarily shaped region of interest covering the object of interest but avoiding excessive areas of background tissue. Targeting the region of interest to a given structure of interest results in the process being more accurate and less affected by background structures. The user clicks on the subsequent images to choose an initial position and the software searches the surrounding region to find the highest correlation with the reference image. The range of the search is given by the size of the rectangular region selected by the user, i.e. the maximum horizontal and vertical shifts are given by the dimensions of the region selected initially. After locating the image shift that yields the highest cross-correlation, the software also calculates the cross-correlation associated with a shift to the eight nearest neighbours of that position, generating a 3x3 matrix of cross-correlation values. The image shift associated with the best cross-correlation value is calculated by fitting a two-dimensional second-degree polynomial to the 3x3 matrix of cross-correlation values and calculating the local maximum of this function. The projected displacement D is thus evaluated with subpixel accuracy.
The precision and accuracy of the measurement of the projected displacement D are dependent on the choice of the structure of interest and on its surroundings. For instance, the registration of single discrete objects is expected to be far more accurate than the registration of vessels or other structures, particularly if seen against a background of biological tissue. The error in the measurement of displacement was thus evaluated on a case-by-case basis, considering a series of images obtained with a given fixed table offset and taking the range of values found for the image-to-image displacement as an indication of the precision of the measurement of D. Another indication of the precision of the measurement of D is the standard deviation of values obtained when the measurement is repeated with slightly different regions of interest surrounding the object to be measured.
Correction of image distortion in image intensifier images
To perform geometric measurements without reference objects on intensified images it is necessary to first correct the pincushion image distortion. For this purpose an accurately built 2x2 cm grid of 2 mm ball bearings (in a 40 cm acrylic disk) was inserted adjacent to the image intensifier screen, replacing the scatter grid. Images were acquired and processed to detect the position of each ball bearing with subpixel accuracy. This was carried out by fitting a two-dimensional second-degree polynomial to the 5x5 image matrix surrounding the pixel of lowest intensity associated with each ball bearing. The position of the minimum calculated for the fitted polynomial is taken as the ball-bearing centre. The pincushion image distortion associated with the II was corrected by correlating two sets of points: the distorted grid points located by the software and a calculated set of points corresponding to an ideal equally spaced grid. Thin-plate splines were fitted to the data, performing elastic registration by conventional methods, discussed elsewhere [10].
Some remaining image distortion could be associated with errors in the location of each ball bearing, or with terms that were poorly approximated by splines. The level of remaining image distortion in the corrected images was assessed by imaging the ball-bearing grid placed on the patient couch and reducing the source-to-detector distance. The resulting images were analysed after correction of image distortion. In this experimental set-up the positions of the ball bearings no longer coincide with the grid positions used by the software that performs the correction of image distortion. Therefore, the distance between each ball-bearing position and its position in an ideal undistorted grid allows evaluation of the quality of the distortion correction process. Images were also obtained with a test object containing straight lines (SFS TO.M1; Leeds Test Objects Ltd, Boroughbridge, UK) to provide a visual assessment of the quality of the distortion correction. All images were corrected with this software before further analysis.
Test object validation and error assessment
For validation of the technique and error estimation, the ball-bearing grid was placed on the patient couch and eight images were acquired with a 2.5 cm table step. The image distortion was corrected before any image analysis. A 2x3 group of ball bearings was taken as an object of interest. A marker was placed beside the central row to facilitate localization, and the projected displacement of this object was measured in the series of images. The error in the measurement of displacement was estimated from the range of values obtained. The known size of the grid was also calculated.
In vivo validation and error assessment
Patients undergoing DSA of the renal arteries were recruited for this study, with approval from the local authority ethics committee. All procedures were performed with an identical 4F pigtail catheter, whose dimensions were known beforehand with sufficient precision: 1.37±0.03 mm external diameter (AngioDynamics Inc., Queensbury, NY). It is known that during contrast agent injection the catheter tip moves within the vessel and, afterwards, the catheter tip can no longer be visualized within a contrast-filled vessel. For this reason the validation required the acquisition of additional images before contrast agent injection. These were obtained within a breath hold, with stepping-table motion of 2 cm in between them. These were the first images acquired and the standard examination with contrast agent injection proceeded after this.
After correction of the image distortion the catheter tip was located in each image and, using these data in conjunction with the known table step, the calibration factor C was calculated for each patient. The catheter tip thickness was measured and compared with the known actual value provided by the manufacturer. For this purpose the projected width of the catheter tip in pixels was estimated as the full width at half maximum (FWHM) of a single line profile, orthogonal to the catheter.
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Results
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Correction of intensified image distortion
The software for correction of image distortion removed the pincushion distortion and restored the known geometry of the ball-bearing grid. It also restored the straight lines to the test object SFS TO.M1 (Figure 2). In images of the ball-bearing grid placed on the patient couch, the largest displacement from a true grid position found after distortion correction was 0.5 pixel (corresponding to 0.36 mm). The average displacement from a true grid position is 0.25 pixel (0.18 mm). The size of the ball-bearing grid measured in both directions is 37.3±0.2 pixels and 37.6±0.5 pixels and, therefore, the error expected to be associated with residual distortion of the images does not exceed 1%. The accuracy of the distortion correction software was considered sufficient for the purposes of this study.
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Figure 2. Images of the grid of ball bearings(top) and test object SFS TO.M1 (bottom) placed on the patient couch. Correction of the pincushion image distortion associated with image intensifiers restores the known geometry of both test objects. Residual distortion is seen only at the outer edges.
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Test object validation
From eight images acquired with a 2.5 cm table step, seven different measurements of object shift D in the images were obtained. The average D value measured was 52.42±0.01 pixels (average±standard deviation). Values ranged from 52.40 to 52.44 pixels, and the uncertainty in the measurement of D was estimated as less than 0.04 pixels, the full range of values. The calibration factor C calculated for this object with a table step of 2.5 cm is 0.477±0.002 mm pixel–1, and the measurement of the known 20 mm grid size is 19.9±0.1 mm.
In vivo validation
Contrast is poor in radiographic images of the catheter tip, as they were obtained before the catheter was used to deliver contrast agent (Figure 3). Vessels are not visualized in these images and the catheter is seen against many background structures.
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Figure 3. Central part of three images acquired within the same breath hold, prior to contrast agent injection, with a 2 cm table step. The black arrow points to the tip of the pigtail catheter and the white line indicates the position of the image profile used to estimate the projected catheter diameter by calculating the FWHM. Parallax changes surrounding the catheter tip position are noticeable in the background.
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In the five patient examinations considered, the catheter position in the first image was taken as a reference and the displacement was calculated for the two following images. Each measurement was repeated five times, with slightly different regions of interest surrounding the catheter. Typical regions of interest used for registration are shown in Figure 4. Table 1 displays the standard deviation of the measurements of displacement calculated between different repetitions of the same measurement and between different steps. The relative uncertainty in the measurement of D (
D/D) is given in the last column, taking the worst value found for standard deviation.
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Figure 4. Two examples of the registration process by cross-correlation in different subjects. The leftmost columns of both (a) and (b) show the image chosen as a reference (bottom) and the selected region of interest used for calculation (top), excluding most of the background area. The other two columns show the initial position that the user provided by clicking on the subsequent images (bottom row) and the result of the registration process (top row).
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Table 1. In vivo assessment of the relative error in the measurement of the projected object displacement D in individual patient studies
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The error in the measurement of displacement therefore has two independent components: (i) the limitations of the software in locating the catheter and performing image registration; and (ii) the physiological motion of the catheter between frames, related to either pulsatile blood flow in the aorta or poor breath holding. The first is better evaluated as the standard deviation on repeated measurements and the second as the standard deviation of measurements on consecutive steps. Table 1
indicates that the second type of error source predominates, even when dealing with an object of poor contrast (the catheter).
Taking the worst values to evaluate the accuracy of the measurement of the object displacement D in the images, the relative uncertainty in the measurement of D is still in the order of 2%. Therefore, the uncertainty in the calculation of the calibration factor C is also in the order of 2%.
From the values of D in Table 1 the calibration factor was calculated for each patient and the size of the catheter calculated. The average result (1.5±0.3 mm) is in agreement with the known size of the catheter (1.37±0.03 mm). Most of the error arises from the measurement of the size of the catheter (0.5 pixel accuracy) and not from the calibration factor C.
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Discussion
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The relative uncertainty in the measurement of vessel size using the translation of the table is given by the sum in quadrature of the relative uncertainty in the measurement of the vessel size in the images S and the relative uncertainty in the measurement of the displacement D.
For table steps of the order of 2 cm, the relative uncertainty of the measurement of D was shown to be in the order of 0.1% for the ball-bearing grid and in the order of 2% for the measurement of the catheter tip. The registration of contrast-filled vessels in radiographic images is expected to be more accurate than the catheter images because of better image contrast, but perhaps not as accurate as the registration of discrete objects such as ball bearings.
The uncertainty in the measurement of displacement D is not in principle dependent on the displacement itself and, thus, the relative uncertainty in the measurement of D can be reduced by increasing the table step. The limit will be given by the size of the detector and by the detrimental effects of parallax, which may reduce the accuracy of the registration process. In DSA, however, image subtraction removes the background information, increasing the accuracy in the measurement of D.
A number of techniques have been proposed to measure the vessel size S [11–13]. In Hoffmann et al [13], the authors review and compare measurements using densitometric techniques, derivative-based techniques and model-based techniques and find that they reach submillimetre accuracy on known cylindrical test objects. However, the measurement of vessel diameters in vivo is considerably less accurate as they often differ significantly from a cylindrical shape. Measuring S with accuracy in the order of 0.5 pixels in vivo remains considerably challenging, particularly in smaller vessels. This challenge is common to all vessel measurement techniques, using reference objects, stereotactic X-ray systems or the technique that we propose.
Considering the technique based on couch translation investigated in this study, our data indicate that the uncertainty in the measurement of the vessel size (S) will dominate and that the uncertainty in the measurement of the object displacement in the images (D) is considerably smaller, even for abdominal examinations requiring breath holding. This shows that the calculation of the calibration factor C can be very accurate and that the technique we propose to perform geometric measurements on radiographic images is capable of the submillimetre accuracy required for clinical studies if used in conjunction with an accurate measurement of the vessel size S. In the catheter images presented, the difficulty in measuring S is the result of the catheter's poor contrast against background structures. This restriction does not apply to DSA images of contrast-filled vessels.
The image distortion associated with image intensifiers is no longer an intrinsic part of the DSA examination as many systems are now based on digital detectors that produce high-resolution undistorted images. DSA examinations can be adapted to exploit the use of apparatus motion to enable the calculation of an accurate calibration factor, providing quantitative measurements of vessel sizes. The additional image processing is relatively simple, and the technique we propose requires only very minor changes to routine clinical procedures. The use of translational couch motion does not require any correction for the gantry sag associated with rotational detector motion. Other types of apparatus motion can also be considered.
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Conclusions
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Geometric calibration factors with an accuracy better than 2% can be achieved in stepping-table DSA without the need for either external reference objects or the need to insert a reference catheter close to the measurement site. These findings are valuable for interventional radiology procedures that require accurate vessel size measurements.
Received for publication December 6, 2006.
Revision received February 20, 2007.
Accepted for publication March 9, 2007.
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Abstract
Introduction
