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1Division of Medical Physics and Medical Engineering and Departments of 2Radiation Physics, 3Radiology and 4Medicine, Göteborg University, Sahlgrenska University Hospital, Bruna Stråket 13, SE-413 45 Göteborg, Sweden
Correspondence: Göran Starck, Sahlgrenska University Hospital, MR Centre, Bruna Stråket 13, SE-413 45 Gothenburg, Sweden
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Abstract |
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 Top Abstract IntroductionTheoryMaterials and methodsResultsDiscussionEvaluation of CT system...ConclusionsReferences |
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Introduction |
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TopAbstractIntroductionTheoryMaterials and methodsResultsDiscussionEvaluation of CT system...ConclusionsReferences |
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Image quality can be defined in terms of image noise, which limits low contrast resolution, and spatial resolution. If spatial resolution is kept constant, the radiation dose required to obtain a CT image is inversely related to the square of the image noise. The radiation dose required for CT imaging at a fixed level of image noise is inversely related to the third power of the spatial resolution [7]. Hence, spatial resolution is the image quality parameter that has the greatest effect on the radiation dose required. Patient size is also important in relation to CT image quality. A small child or baby is usually not subjected to scans with the same set of scan parameters as an adult. As in conventional radiography, greater attenuation in larger patients means that fewer photons are available to construct the image, resulting in an increase in noise level [7]. Hence, CT scans of a slim individual may be performed at a lower dose with maintained image noise compared with a corpulent individual. A difference of 5 cm in the diameter of a tomographic section corresponds to a factor of two or more in the radiation dose required for the same image quality. Yet standardized sets of scan parameters are routinely used regardless of body size unless the patient is very large, in which case the mAs, and thereby the radiation dose, is increased. In a recent phantom simulation study, the dependence of body weight on image quality in abdominal CT was investigated. The authors indicated how scan parameters for minimum radiation dose may be selected as a function of patient weight [8]. Whilst body weight might correlate to abdominal cross-section in a large population, weight is not directly related to actual size in the individual CT examination. Scan parameter selection based on body weight would therefore lead to large variations in image quality between, for example, tall and short persons with the same weight.
Techniques exist to reduce overall mAs without degrading image quality. Since, for example, frontal projections of a patient in the supine position may require less radiation than lateral projections, the dose may be reduced using a fixed scheme of current modulation during tube rotation [9, 10]. In recent studies tube current was adapted to the attenuation of the actual projection, and dose reductions of 20–40% were reported in body sections [11–14]. However, radiation dose was not adjusted to the overall size of the tomographic section in these studies.
It is important to limit the contribution to the collective dose from CT and to avoid excess dose to the individual patient [15, 16]. Reduced radiation doses may also justify a more frequent use of CT for repeated follow-up examinations, or in research applications where there is no clinical benefit to the volunteer. One such application in which there is a very large potential for dose reduction [5] is CT determination of tissue areas and volumes [17]. To justify the use of CT procedures in large studies, they must be performed with very low radiation dose.
The aim of this study was to develop a method of determining scan parameters to obtain the same levels of image noise for patients of various sizes, thereby minimizing radiation dose. The method was then verified on 11 volunteers using an application with a high image noise level, i.e. tissue area determination.
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Theory |
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The scanning process is basically a large number of attenuation measurements arranged in projections. Each scan may be considered as a number of projections m, each sampled using parallel rays with a width equal to the sampling interval R (Figure 1
). Filtered back-projection is used to reconstruct the image. In the following derivation, a ramp filter with a cut-off frequency 1/(2R), determined by the sampling interval, is assumed resulting in a spatial resolution corresponding to a smallest detail of size R.
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where 
is the line integral of the linear attenuation coefficient µ along the ray, N is the average number of unscattered photons incident on the detector and N0 is the average number of photons emitted by the X-ray tube.
N0 can be estimated through the air kerma (kinetic energy released per unit mass). Air kerma is the sum of the initial kinetic energies of all the charged particles liberated by ionizing uncharged particles (in this case photons) in air, per unit mass of air [18]. A measurement with a thin circular cylindrical (pencil-shaped) ionization chamber positioned in the centre of rotation, perpendicular through the scan field provides the line integral of the air kerma (the kerma length product (KLPtube)) (see Figure 1
). The reading of the ionization chamber will be proportional to the density of the photon output from the X-ray tube, N0/R, in the central rays, i.e. the number of photons per unit length of projection. For a measurement performed during one scan, the reading of the ionization chamber will also be proportional to m. We thus obtain
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where CPhK is a conversion factor with the dimensions Gy m2.
In the subsequent analysis, a homogeneous circular cylindrical object concentric with the centre of rotation was assumed. For this object the incidence of unscattered photons on the detector (KLPdet) can be calculated in terms of the air kerma length product from the measured quantity KLPtube. By combining Equations (1) and (2) we obtain
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Assuming no other sources of statistical fluctuation, the variance of the reconstructed linear attenuation coefficient is determined by Poisson statistics of N. At the centre of the homogeneous circular cylindrical object this variance is (Equation 3 [19])
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Combining Equations (1), (2) and (4) gives a relationship between the measured value of KLPtube and the standard deviation (SD) of the linear attenuation coefficient in a pixel at the centre of the object image:
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where the constant 
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This equation expresses the well-established relationship between the SD of the pixel value, i.e. image noise, spatial resolution, object attenuation and the radiation dose, here represented by KLPtube.
The variables for image noise and spatial resolution are now combined to define a CT noise figure (nf):
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The quantity nf represents the inaccuracy in the scan data before the trade-off has been made between spatial resolution and noise, in the CT image. This quantity was discussed by Joseph et al [20], who considered it a possible useful index of CT system performance. Using this definition and Equation (3), Equation (5) may be rearranged and rewritten for the ideal CT concept:
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This equation states that a decrease in photon incidence on the detector will result in increased inaccuracy in the scan data and, consequently, reduced image quality. This could be caused by reduced exposure to reduce radiation dose to the patient. It could also be the result of the high attenuation of photons in a corpulent patient (compare with Equation (3)).
The derivation above is valid only for the centre of rotation and the central region of the image and should therefore be compared with the performance of real CT systems in the corresponding region. Also, the effect of beam-shaping filters is minimal in the centre and constant through all projection angles. The derivation was made assuming attenuation measurements with parallel rays. In real CT systems, divergent rays arranged in fan beam projections are used. The theoretical analysis is, however, still valid since the value of KLPtube of the rays that pass through the centre of rotation is independent of whether the rays are arranged in fan beams or are parallel. Also, since KLPtube is measured at the centre of rotation and KLPdet is calculated at the same position (Equation (3)) they are independent of the centre-to-detector distance in fan beam projections. Furthermore, the divergent rays of fan beam projections can be re-ordered into parallel projections permitting the same filtered back-projection algorithm to be used for reconstruction [21]. This algorithm performs reconstruction giving image noise close to the theoretical lower limit [22].
Equation (7) represents an ideal CT concept, but in reality CT is more complicated. Multi-energetic photons from bremsstrahlung are used. Both primary and scattered photons impinge on the detector and only a fraction of these photons will be detected. Other sources of noise may also contribute, e.g. noise in detector electronics and limited precision in the reconstruction calculations.
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Materials and methods |
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Effective dose per tomographic section in the trunk was calculated for the reference scan parameters (120 kV, 250 mA, 1 s, 10 mm) using the CT dose index (CTDI) and the practical approach devised by Leitz et al [23]. However, instead of using CTDI100 according to Leitz et al, the CTDI stipulated by the Food and Drug Administration (FDA) of the USA (CTDIFDA), was used [24]. CTDI100 is obtained when the dose profile is integrated over a length of 100 mm, whereas CTDIFDA is obtained through integration of the dose profile over fourteen times the section thickness, in this case 140 mm. The calculated effective dose for thick slices will thus be slightly higher (25%) when CTDIFDA is used instead of CTDI100 [23]. Values of CTDIFDA were obtained from the manufacturer of the CT systems [25, 26]. The effective dose for all other sets of scan parameters was calculated by multiplying the effective dose for the reference scan parameters by the quotient of KLPtube for the actual set of scan parameters and KLPtube for the reference scan.
Evaluation of CT system performance
Method
The CT nf of real CT systems was determined through scans on circular cylindrical phantoms. A sufficiently large range of KLPdet must be used requiring both the object attenuation (phantom size) and KLPtube (determined by tube current and section thickness) to be varied. Firstly, KLPtube for the various sets of scan parameters was measured. KLPdet was then calculated using Equation (3) for all combinations of object attenuation and KLPtube. Images were then obtained for all combinations of object attenuation and KLPtube. The value of nf was calculated for each image according to Equation (6), using both the SD of pixel values and the spatial resolution in the central part of each image. For comparison with the experimental data, the theoretical values nfideal (Equation (7)) were calculated for the range of values of KLPdet obtained for the CT system. The absolute level of nfideal, which is not given by the relationship in Equation (7), was chosen to make the line of nfideal coincide with the plot of the best performing CT system in Figure 2a.
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). The tube voltage (120 kV) and filtration were kept constant in order to maintain the same radiation quality in all scans. Total filtration was 2.7 mm Al equivalent at 140 kV for both CTa [25] and CTb [26]. Images were reconstructed in a 512 x 512 pixel matrix (CTa and CTb) and a 256 x 256 pixel matrix (CTa) covering a 48 x 48 cm2 field of view (FOV) (CTa) and a 50 x 50 cm2 FOV (CTb). The standard reconstruction algorithm in each system was used. Image evaluation was performed on the operator consoles of the two systems.
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Evaluation
The performance of the CT systems at the centre of the scan field was evaluated as follows. In the images of the phantoms the mean and SD of CT numbers (CTN) were obtained in a central region of interest (ROI) with a diameter of one-quarter phantom diameter. The CT nf was calculated as SDw3/2 using the pixel size w and SD of pixel value as estimates for R and 
in Equation (6), and was plotted against the photon incidence on the detector, represented by KLPdet. The calculated value of KLPdet depends on the effective photon energy, through the attenuation factor e- in Equation (3), and the linear attenuation coefficient of the phantom material. Since the actual effective photon energy was unknown, calculations were performed for a range of photon energies (60–80 keV). The effective photon energy chosen for the evaluation of the performance of the CT systems was the energy at which the same values of KLPdet were obtained at the same value of the SDs for the different phantoms (70 keV, compare with Figure 2).
The performance of CTa over the full FOV was evaluated as follows. The mean and SD of CTN in a circular ROI (diameter 40 mm) were obtained at positions along the horizontal diameter in normal and high noise level images of the 30.0 cm and 48.4 cm phantoms. At positions where the SD was a maximum, which occurred 10 cm and 15 cm off-centre for the 30.0 cm and 48.4 cm diameter phantoms, respectively, the mean and SD of CTN were obtained for all sets of scan parameters (circular ROIs, diameter 75 mm). The mean and distribution of CTN were monitored during all ROI evaluations to detect abnormal images which might result when the photon incidence on the detector was very low.
The linear attenuation coefficient of water was calculated for a density of 997 kg m-3 (1 atm, 293 K) using linear interpolation between tabulated values of the mass attenuation coefficient at 60 keV and 80 keV [27]. A value 19.42 m-1 was obtained for 70 keV photons. Polyethylene plastic is available in several qualities, each of which covers a range of densities. Therefore, the linear attenuation coefficient was calculated from CTN obtained from the polyethylene phantoms used in this study, resulting in a value of 0.91 times the linear attenuation coefficient of water.
Determination of patient-specific scan parameters
Sets of patient-specific scan parameters (tube current and section thickness) for CTa for a range of patient diameters were determined as follows, based on the KLPtube and nf data from the CT system.
(1) The required accuracy in terms of spatial resolution and SD of the image was defined and the corresponding value of nf calculated according to Equation (6).
(2) The value of KLPdet that would produce the required value of nf was determined using the CT noise figure data for the CT system.
(3) Once KLPdet for the specified accuracy in the CT system was known, a set of values of KLPtube was computed (Equation (3)) for the desired set of object sizes (30 cm, 31 cm, ..., 48 cm). Attenuation in water was assumed in the calculation of the attenuation factor in Equation (3).
(4) The corresponding set of scan parameters for the CT system was determined through measurements of KLPtube. When the desired value of KLPtube could not be produced by any of the available sets of scan parameters in the CT system, the set that produced the next best value of KLPtube was used. In this way, each subject diameter in the scan parameter table will give a set of scan parameters that will produce the required accuracy or higher, while giving a minimum radiation dose.
The required spatial resolution for tissue area and volume determination with CT was specified as a 48 cm FOV with a 256 x 256 pixel reconstruction matrix using the standard reconstruction algorithm (H Kvist, Personal communication), as used in previous work [17, 28] although not specified therein. An area error of less than 1% was required. This would allow for an image noise level of 30 Hounsfield units (HU) [5]. This maximal SD is required over the whole FOV, while the patient-specific scan parameters are based on the analysis of the CT nf, which is valid only for the central part of the FOV. It was also observed during the evaluation of CTa that the SD was up to 50% higher in the peripheral region of the image than at the centre for large circular phantoms (see Figure 3). To account for the increase in SD peripherally, the required SD was re-specified to 
20 HU in the central part of the FOV for patients with the largest diameter of the tomographic section >35 cm.
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) based on the size (diameter of the trunk) of the patient. The largest, i.e. horizontal, diameter of the patient, lying supine on the tabletop of the CT scanner, was determined with a slide calliper at the level of the CT scan. The scan was performed and the noise levels were subsequently evaluated in the images. Standard deviations of the CT numbers were obtained in four elliptical ROIs made as large as possible in homogeneous tissue (central in the left and right psoas muscles and peripheral in subcutaneous fat in the left and right dorsal waist areas, range 117–3965 mm2).
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Results |
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). The corresponding calculated effective doses per tomographic section in the trunk were 3–161 µSv (CTa )and 11–353 µSv (CTb) (Table 1, 2). Effective dose obtained from CTb was 13% higher than that from CTa for the same level of X-ray tube output.
Evaluation of CT system performance
The relationship between CT nf and photon incidence on the detector, in terms of KLPdet, shows that performances of CTa and CTb in the low-noise region (nf<10 HU 
) were close to those expected when noise is caused only by photon statistics (Figure 2). This noise region covers the majority of the diagnostic CT examinations performed today. Above this level, i.e. when KLPdet was further decreased, the nf of CTb increased faster and deviated markedly from that of CTa. The nf of CTa remained close to the line representing photon statistics up to a level of 110 HU . For a FOV of 48 cm this corresponds to 121 HU, 43 HU and 15 HU at resolution of 512 x 512 pixel matrix, 256 x 256 pixel matrix and 128 x 128 pixel matrix, respectively. Above this range, at the four lowest levels of KLPdet, CTa produced erroneous CTN (both mean and distribution) at the centre of the FOV.
The photon incidence on the detector, in terms of KLPdet, was 5.5 µGy cm for CTb but only 1.1 µGy cm for CTa at the specified image quality for tissue area and volume determination with CT (a CT nf of 75 HU , which is equal to a SD of 30 HU at 1.9 mm resolution) [5]. Predicted by theory (Equation (7)) however, only 0.7 µGy cm would be required to produce this image quality if the noise in CTa and CTb was caused only by photon statistics. These differences in KLPdet, which can be seen in Figure 2a as the separation of the curves at this noise figure level, indicate the large differences in effective dose that the patient would receive for tissue volume determination using CTa and CTb, and as predicted by theory.
Close inspection of Figure 2a reveals that the lines that represent the different phantoms formed two groups for each CT system. One group consists of the phantoms delivered with the CT systems, while the other represents the Philips water phantoms. The latter phantoms could not be attached to the phantom holders on the CT systems but were positioned on the tabletop. When the attenuation through the tabletop was considered by adding the effect of 1 cm water in calculating the attenuation of these phantoms, the two groups of curves merged and formed one distinct line for each CT system (Figure 2b).
Images from CTa were subsequently evaluated over the entire FOV. The SD of CTN in the images from the 30.0 cm water phantom did not increase off-centre relative to the centre. However, the SD profile in the image of the 48.4 cm polyethylene phantom (250 mAs, 10 mm) (Figure 3) had local maxima at approximately ±15 cm off-centre with 20% higher SD than at the centre. Figure 3 also shows that the noise off-centre increased more than at the centre when the value of KLPtube was decreased. At these off-centre positions, CTa produced erroneous CTN (both mean and distribution) at the six lowest levels of KLPdet. At the lowest useful level of KLPdet the maximum noise seen in the SD profile for CTa was approximately 50% higher than at the centre.
The lowest levels of the calculated photon incidence on the detector, in terms of KLPdet, of CTa were 1.1 µGy cm and 0.67 µGy cm, for reliable CTN of the 48.4 cm phantom and the 30.0 cm phantom, respectively. At these levels, reliable CTN were obtained over the entire phantom and the SD was approximately 40 HU or less (256 x 256 pixel matrix) over the full 48 cm FOV.
Verification of patient-specific scan parameters
The CT imaging resulted in image noise levels within the specified noise limit of 30 HU in all volunteers. SDs in the volunteers' images (Figure 4, 5) were on average 21 HU (range 14–30 HU) for volunteers with trunk diameters of 31–34 cm and 12 HU (range 7–18 HU) for volunteers with trunk diameters in the range 36–47 cm. The effective dose to the volunteers was reduced to 1–2% (diameter 31–34 cm) and 5–45% (diameter 36–47 cm) of the effective dose they would have received with clinical scan parameters (250 mA, 1 s, 10 mm) (Table 3).
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Discussion |
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TopAbstractIntroductionTheoryMaterials and methodsResultsDiscussionEvaluation of CT system...ConclusionsReferences |
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Evaluation of CT system performance |
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TopAbstractIntroductionTheoryMaterials and methodsResultsDiscussionEvaluation of CT system...ConclusionsReferences |
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A high-performance scanner (CTa) was compared with an economy scanner (CTb) supplied by the same manufacturer. The two CT systems had several similarities including the same total filtration, tube voltage and solid state detectors. As expected and close to theory, both CT scanners showed similar performance in the low noise range where the majority of diagnostic images are obtained (Figure 2). However, the CT nf of the two systems differed markedly at decreased levels of photon incidence on the detector, with CTa performing much better than CTb (Figure 2). In addition, the effective dose to the patient at the same level of photon incidence on the detector was slightly higher with CTb than with CTa. Imaging at lower spatial resolution or higher image noise could be performed with CTa with much lower radiation exposure than with CTb and with the same image quality. CTa is therefore more suitable than CTb for low radiation dose applications, with a CT nf greater than 10 HU . Investigation of the technical reasons for this difference is outside the scope of this paper. These results show, however, that the performance of the CT system can seriously degrade the possibilities for dose reduction. Consequently, assessment of the performance of the CT system at low radiation dose levels is necessary to make best use of the dose reductions possible in various CT applications.
Although CTa was the most suitable system for low radiation dose applications, this system is not optimized for low dose operation. Selectable tube currents are limited to a minimum of 40 mA, which is at least one order of magnitude too high. It was therefore also necessary to vary section thickness to obtain the very low doses in this work. This restricts the use of CTa in low radiation dose applications.
The noise of CTa was higher peripherally than centrally in images of larger objects and the noise also increased more in the peripheral parts than in the centre for decreased photon incidence on the detector (Figure 3). One possible explanation for this is that the beam-shaping filter after the X-ray tube was not optimized for such large objects. The use of filters individually optimized for various object sizes would reduce the peripheral noise for large objects and permit a further dose reduction without increasing the overall image noise [29]. There may also be other technical reasons, e.g. simplified design of the detector array or detector electronics, for the peripheral parts of the projections.
No attempt was made to measure the photon incidence on the detector, as this would have had to deal not only with the quantity of interest, the unscattered photons, but also with the presence of scattered photons. It would have also been necessary to interfere with the scanning process and inhibit the rotation of the tube and detector assembly. Instead, the photon incidence on the detector, in terms of KLPdet, was calculated from the measured value of KLPtube taking the attenuation in the phantom into account. This calculation required knowledge of the attenuation coefficients of the phantom materials and a suitable choice of effective photon energy. The effective photon energy was found to be a fairly insensitive parameter in the comparison of the CT systems. The nf data for CTa and CTb formed two somewhat broad but characteristic lines (Figure 2) that, over a large range of photon energies (60–80 keV), consistently showed that CTa performed much better than CTb at low radiation dose levels. However, the best fit of the noise data to the characteristic line was achieved, for each of the two CT systems, when KLPdet was calculated for 70±5 keV. At this photon energy the calculated attenuation in the largest phantom (48.4 cm) was 5180 (range 4040.4–6630.4). The uncertainty in the attenuation value of the phantom contributes the main error in the calculation of KLPdet. It should be noted, however, that this error comes in systematically, affecting the evaluation of both CT systems in the same way, and hence does not favour either of the CT systems in the comparison.
Verification of patient-specific scan parameters
The results of measurements on volunteers verified that patient-specific scan parameters (Table 3), selected based on the largest diameter of the cross-section of the patient, could be used clinically for radiation exposure control. Large dose reductions were achieved while the image noise levels remained within the specified limit of 30 HU.
Image noise level was estimated as the SD in pixel values in ROIs in "homogeneous tissue". Hence, tissue texture and image artefacts could have contributed to the observed SD. This may have caused an overestimation, but not an underestimation, of the image noise. Still, the observed SDs in the images of the volunteers did not exceed the specified maximum noise level of 30 HU, which validates the use of the greater diameter for the selection of patient-specific scan parameters. This result, which is in agreement with the work of Kalender et al [11, 13] and Gies et al [14], indicates that noise level in CT images of non-circular objects is essentially determined by the greatest attenuation through the cross-section.
The main aim of limiting the image noise to 30 HU was achieved by manual selection of patient-specific scan parameters from Table 3. There were, however, large variations in observed SDs. Particularly in images of large volunteers, the SDs were below 20 HU. Hence, the observed increase in SD peripherally for large circular phantoms, which was also expected in large patients, did not occur in the images of non-circular, large cross-sections (Figure 3). This indicates that a further reduction in dose could be achieved while still maintaining an image noise level of 30 HU for large patients.
Radiation dose could be even further reduced by the application of techniques which adapt the X-ray tube current to the non-circular shape of the tomographic section [9–14]. These techniques reduce the dose without a corresponding increase in image noise by modulating the selected tube current. The dose reduction achieved in this way (typically 20–40%, [11]) would be independent of the large dose reductions achieved in this work. Both methods should be combined to minimize the radiation dose to the patient.
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Conclusions |
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TopAbstractIntroductionTheoryMaterials and methodsResultsDiscussionEvaluation of CT system...ConclusionsReferences |
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Plotting the CT nf vs KLPdet is a simple yet efficient means of evaluating the noise as a function of radiation dose in a CT system. It allows the comparison of CT systems on an equal basis when combined with the relation between KLPtube and effective dose. All measurements can be performed using a few circular cylindrical water phantoms, a pencil-shaped ionization chamber and the standard image evaluation capabilities of the application software of the CT system.
Patient-specific scan parameters for a CT system in various applications can be obtained via measurements on circular cylindrical water phantoms. The largest diameter of the patient in the scanning region can be used to select patient-specific scan parameters.
Dose reductions achieved in this study using patient-specific scan parameters illustrate the considerable differences in radiation dose required in CT imaging when the patients vary in size from slim to corpulent. The selection of scan parameters for each individual patient would allow a reduction in radiation dose in most CT applications. However, such a method of manual exposure control is cumbersome. The general use of exposure control in CT imaging requires this facility to be incorporated into the scanning system. This is both technically possible and reasonable, and is necessary in the evolution of the CT technique.
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Acknowledgments |
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Received for publication January 21, 2000. Accepted for publication August 17, 2001.
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C J Koller, J P Eatough, and A Bettridge Variations in radiation dose between the same model of multislice CT scanner at different hospitals Br. J. Radiol., November 1, 2003; 76(911): 798 - 802. [Abstract] [Full Text] [PDF]
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M. K. Kalra, C. Wittram, M. M. Maher, A. Sharma, G. B. Avinash, K. Karau, T. L. Toth, E. Halpern, S. Saini, and J.-A. Shepard Can Noise Reduction Filters Improve Low-Radiation-Dose Chest CT Images? Pilot Study Radiology, July 1, 2003; 228(1): 257 - 264. [Abstract] [Full Text] [PDF]
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) (30 HU in the centre) are shown. Standard deviations (SD) were obtained from circular regions ofinterest (40 mmdiameter) and the plotted profiles were normalized to unity at the centre of the phantom. Error bars represent the maximum and minimum values of six measurements.
