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Analysis of surface dose variation in CT procedures

¹Physics Department, The Royal Marsden NHS Trust, Fulham Road, London SW3 6JJ, UK and ²Departamento de Radiología, Facultad de Medicina, Universidad Complutense de Madrid, Madrid 28040, Spain

	Abstract

Top Abstract Introduction Method Results and discussion Conclusions References

 
An experimental and theoretical study has been made of the variations in air kerma–length product (AKLP) at the surface of a phantom exposed in a CT scanner, using clinical parameters. For the theoretical part, a computer simulation was developed, based on a simple analytical model, requiring information generic to the scanner model. The effects of patient size, position within the gantry plane and beam-shaping filter type were studied using three different elliptical phantoms. A dose reduction technique based on a sinusoidal tube current modulation system was also investigated. The surface AKLP was shown to be independent of phantom size (within experimental error) but decreases as the surface moves vertically away from the isocentre. The major contributor to this variation is the beam-shaping filter. A maximum difference of 19% between the values of surface AKLP was calculated for the two beam-shaping filters available. When the tube current modulation system was used, the maximum surface dose reduction was 18%. A maximum difference of 2% was found between measurements and computer simulations. It is therefore possible to predict the behaviour of AKLP using the analytical model. As the dose measured on the surface of a patient is simply related to AKLP, the model can be applied to data obtained from patient surface dose surveys and can be helpful in interpreting the sources of variation in the latter.

	Introduction

Top Abstract Introduction Method Results and discussion Conclusions References

 
CT is a high dose diagnostic technique, estimated to be responsible for 40% of the total collective dose from all diagnostic procedures in the UK [1–3]. State-of-the-art CT scanners (multislice CT scanners) now allow a wider choice of slice thickness and a decrease in exposure time. Such scanners have the potential to improve visualization of small structures and so examination frequency is expected to further increase [4]. Consequently, there is a need to evaluate patient doses and the risk associated with these procedures. It is very important that CT examination exposure parameters are optimized and patient dose is kept as low as reasonably achievable consistent with the need to obtain adequate diagnostic information. This is in accordance with a recent European Directive [5]. Therefore, measurement of patient dose forms an essential part of the CT quality assurance programme.

Patient dose can be estimated from the CT dose index (CTDI) [6], which for this purpose is defined as

where D(z) is the dose from a single slice expressed as a function of position along an axis parallel to the axis of rotation of the scanner (z-axis) and T is the nominal slice thickness. The integral is evaluated over 10 cm, which is the active length of the pencil ionization chambers used routinely for this measurement.

In practice, CTDI is evaluated free-in-air or in a standard American Association of Physicists in Medicine (AAPM) head or body phantom (cylindrical phantoms of 16 cm or 32 cm diameter, and 15 cm thickness made from polymethylmethacrylate (PMMA)) [7]. In the case of measurements in AAPM phantoms, CTDI can be averaged over the phantom radius [8]. The resulting weighted CTDI (CTDI_w) may then be combined, as follows, with the known scan parameters for a complete CT examination to produce a dose–length product (DLP), which is more representative of the total risk than the CTDI itself:

where N is the number of slices and C is the product of tube current and exposure time used for each slice.

Alternatively, CTDI may be combined with conversion factors (calculated using Monte Carlo techniques) that relate it to organ doses or effective doses for single slices. The conversion factors currently available [9, 10] are scanner-specific and require the measurement of CTDI free-in-air on the axis of the scanner, a quantity that does not account for the quality and geometry of the X-ray beam (including the effect of the bow tie filter) in a given scanner. The EU CT protocol [8] proposes a simplified approach that applies examination-specific conversion factors, for any given CT scanner, to the DLP values.

In both the above approaches, the measured dosimetric quantity is not dependent upon patient size or their position within the gantry plane. However, CT procedures and technical parameters are (or should be) tailored to individual patient sizes and clinical indications [11]. It has been recognized [12–14] that patient size needs to be taken into account when designing imaging protocols for patients undergoing CT examinations. Thus, it can be considered desirable that dose measurements for a particular examination and scanner reflect the variability that should be found in practice.

A complementary approach to the in-air or in-phantom measurements is the direct measurement of patient surface dose using thermoluminescent dosemeters (TLDs). We are developing such an approach [15, 16], which has the advantage of taking into account individual customized CT parameters and patient size and position. This method also has the potential to be used in routine patient surveys since it is inexpensive (the dosemeters could simply be sent to the clinic with a protocol) and may be more convenient for use in centres with a high workload as it does not require measurement of CTDI. As part of the development of this technique, it was considered important to study the variation of surface dose with patient size and gantry position. This paper reports a study of their effects for single CT slices, based on both phantom measurements and computer simulation. The influence of tube current modulation techniques, which are available on some CT scanners for saving dose, is also investigated.

	Method

Top Abstract Introduction Method Results and discussion Conclusions References

 
The variation of surface dose with patient size and position within the gantry plane, the choice of bow tie filter and the application of tube current modulation techniques have been studied with measurements and computer simulations of exposures in a GE HiSpeed CT/i scanner (GE Medical Systems, Milwaukee, WI). This is a third generation, helical CT scanner with a single-row, solid state ceramic detector array.

The scanner has two beam-shaping filters available for use in different clinical scanning protocols. The standard filter is referred to as the "small" bow tie filter whilst the other is referred to as the "large" or SmartBeam^TM, bow tie filter. These filters cause a reduction in radiation dose at the phantom or patient edges to compensate for the shorter path lengths of the fan beam through the periphery of the patient. The small bow tie filter is designed for general scanning but is most suited to small cross-sections through the patient (such as head examinations). The large bow tie filter is suited to scanning larger cross-sections through the patient and is selected for most examinations in our hospital.

The GE HiSpeed CT/i scanner also provides an optional tube current modulation system called SmartScan^TM, which allows dose reduction in projections where attenuation of the X-ray beam decreases. In this mode, tube current varies sinusoidally throughout the entire rotation of the tube, decreasing tube current (mA) for anteroposterior (AP) projections (assuming these to be the least attenuating regions) and increasing it for lateral projections (assuming these to be the most attenuating regions), up to a maximum value selected by the operator. The CT scanner calculates tube current reduction using the ratio of patient attenuations as seen by the central part of the detector array from AP and lateral views. The maximum reduction possible is 50%.

In this work, measurements and calculations were made with three different elliptical phantoms. Their dimensions are given in Table 1 and were chosen from our database, which contains measurements of 82 patients examined using standard CT procedures. Phantom A is more representative of the human dimensions encountered in the shoulders or upper thorax examinations, whereas phantoms B and C reproduce the mean size of the lower thorax and the abdomen. The phantoms used for the measurements were specially constructed from PMMA and, for computational purposes, were modelled as such.

where D_s(z) is the surface dose from a single slice expressed as a function of position along the z-axis. The integral is over the active length of the chamber. AKLP is simply the surface CTDI multiplied by the nominal slice thickness.

Measurements of the variations in surface AKLP
Every experiment was initially set up by positioning the selected phantom symmetrically in the centre of the gantry with a 10 cm long pencil ionization chamber (model No 20X5-CT with a MDH 2025 electrometer; Radcal Corporation, Monrovia, CA) on its anterior surface, positioned so that its axis was parallel to the rotation axis of the scanner. The chamber was aligned with the help of lasers. The anterior surface was chosen, as this is the part of the patient most easily accessible for dose surveys. The position of the phantom and chamber within the gantry could be verified from the CT image obtained. Therefore to evaluate the accuracy in positioning, we could make use of the grid that is overlapped onto the phantom image.

The height of the selected phantom could be adjusted by raising or lowering the couch along the vertical axis of the tomographic plane. The error in positioning of phantoms at the isocentre of the CT scanner was ±3 mm. The table has a load capacity of 180 kg, with an error of ±0.25 mm in the position along the vertical axis of the tomographic plane. For each measurement of AKLP, a single exposure consisting of three 360° rotations with no table motion was performed. This strategy was chosen to reduce any error arising from changes between exposures in the starting point of the tube and, therefore, the discontinuity in X-ray emission that occurs at this location. Results were expressed for a single 360° rotation and the coefficient of variation of AKLP from a single rotation was estimated to be ±0.4%. Positional and AKLP uncertainties were combined and the total error in AKLP was estimated to be 1%. Exposure settings were chosen to be consistent with clinical scan protocols, but for practical purposes were kept constant for all phantoms regardless of their size. Tube current was 200 mA, tube voltage 120 kVp, slice thickness 10 mm and rotation speed 360° s^-1.

To study the influence of phantom size and phantom position within the tomographic plane on AKLP, a series of exposures was carried out with the elliptical phantoms A and B. The large bow tie filter was used for all measurements. AKLP was measured at positions along the vertical axis of the tomographic plane (y-axis). This experimental configuration is illustrated in Figure 1.

View larger version (17K): [in this window] [in a new window]   Figure 1. Configuration used to measure or calculate the air kerma–length product on the surface of an elliptical phantom (for clarity, the figure is not drawn to scale). The chamber is placed on the upper phantom surface. The horizontal and vertical axes of the tomographic plane are given by x and y, whereas z refers to the rotation axis. R is the distance between the focus and the isocentre, is the projection angle, is the angle between the chamber–focus and the focus–isocentre vectors, r is the distance between the focus and the centre of the chamber and h is distance of the ionisation chamber from the isocentre.

To study the effect of dose reduction caused by the tube current modulation system, AKLPs were also measured on the surface of the three elliptical phantoms with and without the tube current modulation feature. The maximum or prescribed mA and the average mA (Smart mA^TM) were recorded for measurements with the tube current modulation technique. For this experiment, the phantoms were set up symmetrically in the centre of the tomographic plane since the system will then carry out the reduction on the basis of difference in attenuation between the minor and major axes of the ellipses.

Calculation of the variations in surface AKLP
To understand and further investigate sources of variation in surface AKLP along the vertical axis of the tomographic plane, a computer simulation based on a straightforward model has been developed. In this model the AKLP measured with the CT chamber is calculated as an integral along a line on the surface of the patient (z-direction) parallel to the axis of rotation of the scanner. Let K_o(z,,h) X()d be the kerma at position z along this line, in the absence of the phantom and beam shaping filter, for a tube rotation through angle d from CT projection angle and at a given chamber position along the y-axis h. The function X() takes account of variation of the attenuation through the flat filter with angle of the X-ray beam ( is shown in Figure 1). The flat filter consists of inherent and additional filtration. When the radiation is normal to the filter, X() is unity. The AKLP, P, evaluated along this line with the phantom and beam-shaping filter present is given by

where L is the length of the ionization chamber, which is positioned symmetrically about z=0 and at distance h from the isocentre (Figure 1). Attenuation through the beam-shaping filter is modelled by the weighting factor w(). This factor is defined as the ratio of air kerma free-in-air at a given value of with the bow tie filter present to that with the bow tie filter removed. The exponential term in Equation (4) accounts for the attenuation through the phantom. Beam hardening is neglected and a constant linear attenuation coefficient µ is assumed. The length q(,h) is the distance the ray traverses through the phantom (z-dependence is neglected). Attenuation through the couch is not modelled. The term S(z,,h) allows for the contribution of scattered radiation to the AKLP. In practice this function was not known and it was necessary to assume that it could be replaced by some average value S for those rays making a significant contribution to the integral. The factor C() introduces sinusoidal modulation of the tube current.

The kerma function K_o(z,,h) can be rewritten to make its inverse-square law dependence explicit:

For slice widths of 10 mm or less the z² term can be neglected. The length r is the distance between the focus and the centre of the chamber (Figure 1). The function F(z,,h) can be regarded as a beam profile along the z-direction, and for the free-in-air situation will scale according to the value of rcos. Therefore,

where k is given by:

The length R is the distance between the focus and the isocentre. The assumption of free-in-air scaling of profile shape is valid provided a rectangular collimator is used to limit the extent of the beam in the z-direction. Figure 2 shows schematically how the beam profile shape scales with increasing distance from the focus. The scaling factor k is the ratio of the two distances indicated in the figure.

View larger version (12K): [in this window] [in a new window]   Figure 2. Two schematic free-in-air kerma profiles parallel to the axis of rotation of the CT scanner (z-axis), shown at distance rcos from the focus, at the isocentre. When rectangular collimation is used, the shapes of the two profiles are simply related using similar triangles once the inverse-square law dependence is explicitly stated in accordance with Equation (5). The distances rcos and R are shown in Figure 1.

Substituting Z=kz gives:

Provided the limits of integration are sufficiently far from the edge of the in-air beam profile (which is always the case), P becomes

where Equation (7) has been used to substitute for k and the constant f is given by

It will be seen that in this approximation, AKLP has an inverse distance dependence. In addition, it is not necessary to know S or f to compare calculations and experiments since only relative values are needed.

Finally, the factor C() in Equation (4) is given by the following expression [17]:

where mA_min is the minimum tube current selected by the system and mA_max is the maximum tube current prescribed by the user of the CT scanner. In the case of no tube current modulation, minimum and maximum tube current are equal and C() is then unity. The average tube current (mA_mean) is:

Since the value of the mean tube current is provided by the system, mA_min can be calculated using this equation.

Equation (10) has been evaluated numerically for various configurations. The product of X() and w() was determined experimentally for the two bow tie filters available in the HiSpeed CT/i scanner. For this experiment the tube was stationary and AKLP free-in-air was recorded with the large and small bow tie filter for a series of positions, regularly spaced in intervals of 1 cm, along an axis normal to the central beam and containing the isocentre. The experimental set-up was based on that used by Jansen et al for the same purpose [18]. For the calculation of the product of X() and w(), account was taken of the variation of the focus-to-chamber distance.

Equation (4) was formulated on the assumption that spectral variations can be accounted for by the choice of a suitable value of the linear attenuation coefficient µ. The value used for the majority of calculations (0.21 cm^-1 for PMMA) was determined on the basis of previous work [17, 19] and was chosen to represent a typical 120 kVp spectrum. However, to investigate the sensitivity of the results to the value of the attenuation coefficient, some calculations were repeated with values of 0.154 cm^-1 and 0.314 cm^-1, as an error in the choice of the attenuation coefficient of 30% or greater was deemed to be very unlikely.

To validate the model, the variation of AKLP with position was calculated for phantoms A and B and the results were compared with the corresponding measurements. The validated model was then used to further investigate sources of variation in the surface AKLP, including the presence or absence of the bow tie filter, the dependence on size (for all phantoms) and the effect of the GE HiSpeed CT/i dose reduction technique.

	Results and discussion

Top Abstract Introduction Method Results and discussion Conclusions References

 
Measurements of the variations in surface AKLP
Figure 3 shows the variation of AKLP with offset from the isocentre of the centre of phantoms A and B. It might be expected that differences between the two sets of results could be attributed to the effect of phantom size. However, a different conclusion can be drawn from Figure 4, where AKLP is plotted against chamber position along the y-axis of the scanner. Thus, Figure 4 shows that AKLP for both phantoms varies in the same way. Indeed, results for the two phantoms fall on the same curve. For three pairs of results, phantoms were positioned so that the chamber ended up at almost the same point on the y-axis (within 0.15 cm). In these cases the difference between AKLP values is within 2%. Consequently, AKLP depends upon chamber position and not phantom size. These data also indicate that AKLP decreases with increasing distance from the isocentre.

View larger version (11K): [in this window] [in a new window]   Figure 3. Surface air kerma–length product (AKLP) as a function of the offset of the phantom centre along the vertical y-axis of the tomographic plane. , measurements with phantom A; •, measurements with phantom B.

View larger version (10K): [in this window] [in a new window]   Figure 4. Normalized surface air kerma–length product (AKLP) as a function of the chamber position along the y-axis. Results are normalized to the maximum surface AKLP measured for phantom A at the point closest to the isocentre (the latter being the origin). , measurements with phantom A; •, measurements with phantom B.

View larger version (10K): [in this window] [in a new window]   Figure 5. Normalized air kerma–length product (AKLP) on the surface of phantom A as a function of the chamber position along the y-axis. Results are normalized to the value measured at the isocentre (origin of the coordinate system). , measurements with the large bow tie filter; •, measurements without the bow tie filter.

View larger version (13K): [in this window] [in a new window]   Figure 6. Normalized air kerma–length product (AKLP) on the surface of elliptical phantoms A, B and C. ,measurements with the tube current modulation technique; •, measurements without the tube current modulation technique.

View larger version (12K): [in this window] [in a new window]   Figure 7. Normalized air kerma–length product (AKLP) calculated on the surface of phantom B as a function of the chamber position along the y-axis. For each filter, results are normalized to the maximum AKLP. , calculations with large bow tie filter; , calculations with the small bow tie filter.

Application to patient dose surveys
The extension of the above results to patient measurements with TLDs is straightforward. In clinical procedures, the practical dosimetric quantity to be measured is the surface multiple scan average dose (MSAD) [6]. Surface MSAD is related to AKLP as follows:

where I is the interval between slices. As this is a simple linear relationship, the results worked out in this paper are equally applicable to surface MSAD measured on patients, as long as sufficient slices are taken [6]; this should not pose a problem if the measurement site is chosen carefully.

The experiments and calculations above indicate that surface MSAD will depend on the offset of the dosemeter from the isocentre (as determined by patient dimensions and positioning), as well as any tailoring of the technical parameters to the size of that patient. The simple model developed in this work can be readily used to derive a normalized function of surface MSAD with offset from the isocentre. The only data required are the focus-to-isocentre distance and the X-ray attenuation distal from the central beam axis caused by the flat and beam-shaping filters. These features are generic to a scanner model and do not need to be measured directly on every scanner. If the offset of the dosemeter from the isocentre is obtained at the time of the survey, e.g. from the clinical images, then variation in surface MSAD owing to offset of the dosemeter from the isocentre can be corrected for, thus leaving a distribution that reflects variations in scanning practices rather than patient positioning.

	Conclusions

Top Abstract Introduction Method Results and discussion Conclusions References

 
In this study, measurements and simple model-based calculations of the variations in surface AKLPs were made for different elliptical phantoms, beam-shaping filters and a dose reduction technique. The maximum difference between calculations and measurements was 2%. The diversity of experiments simulated proves the versatility of our simple model. Limitations in the model were also investigated. A 30% change in the value of the linear attenuation coefficient caused a 5% variation in surface AKLP. Therefore, AKLP is determined mainly by the primary radiation arriving at the phantom surface and the contribution of scattered radiation.

For a given chamber position, surface AKLP is essentially independent of phantom size for the phantoms investigated. Surface AKLP decreases as the surface moves away from the isocentre along the vertical axis of the tomographic plane. The decrease is owing to the effect of the beam-shaping filter and, for the large filter for the GE CT/i HiSpeed scanner, amounts to 19% at 12 cm from the isocentre. When a dose reduction technique based on a sinusoidal modulation of tube current was applied, the maximum dose saving measured on the surface of the elliptical phantoms was 18%. AKLP is simply related to surface CTDI, hence conclusions about the behaviour of the former apply equally to the latter.

The simple model has not only enhanced our understanding of the factors that determine surface AKLP or CTDI, but we believe that its predictions can be simply extended to patient dose measurements. AKLP is linearly related to surface MSAD (measurable with TLDs), hence the above conclusions about the behaviour of AKLP will be equally valid for MSAD. It is envisaged that the model can be easily implemented for any CT scanner, requiring only information generic to the scanner model. TLD data from a patient surface dose survey can then be interpreted; variations arising from changes in practice, as opposed to variations in patient size and position, can be isolated.

	Acknowledgments

 
P Avilés Lucas has been funded by a EU Marie Curie grant (Proposal number ERB4001GT), which is gratefully acknowledged. We thank the Medical Physics Group (Complutense University of Madrid) and the Medical Physics Service at the Clínico Hospital of Madrid for discussions and Prof. José Manuel Calleja Pardo (Autonomous University of Madrid) for his support of the project. We are indebted to Mr Bruce Bembrick for construction of the elliptical phantoms.

Received for publication October 2, 2000. Revision received April 30, 2001. Accepted for publication June 14, 2001.

	References

Top Abstract Introduction Method Results and discussion Conclusions References

 

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This Article Abstract Figures Only Full Text (PDF) Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Avilés Lucas, P Articles by Vañó Carruana, E Search for Related Content PubMed PubMed Citation Articles by Avilés Lucas, P Articles by Vañó Carruana, E