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A parametric method for determining mammographic X-ray tube output and half value layer

Regional Medical Physics Department, Newcastle General Hospital, Westgate Road, Newcastle upon Tyne NE4 6BE, UK

	Abstract

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 
In the National Health Service Breast Screening Programme, regular assessment of the mean glandular doses received by a group of women is recognized as an important part of a quality assurance programme. The use of different tube voltages, to improve the beam penetration for thick or dense breasts, and of X-ray units with programmable exposure modes, requires a large number of measurements to ensure that all the values of tube output and half value layer required for the dose calculations are available. In this work, a computer model is used to produce data that allow the calculation of tube output and half value layer for the range of clinically encountered conditions from measurements routinely obtained during quality assurance tests. The data are given as a series of equations and parameters, enabling the calculations to be easily incorporated into a dose calculation spreadsheet. The results of an experimental verification of the model are presented, showing good agreement between the measured and predicted values of half value layer and tube output for a range of combinations of target, filter and tube voltage.

	Introduction

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 
In any radiographic procedure it is important that the radiation dose is as low as reasonably practicable while maintaining adequate image quality. This is particularly important for a screening programme where the exposed population is assumed to be asymptomatic. In mammography, the dose quantity used is the mean glandular dose (MGD), which gives a measure of the dose to the tissue most at risk from radiation induced carcinogenesis. The method employed to routinely assess the MGD involves measurements made using a 40 mm thick Perspex phantom to simulate a 45 mm thick standard breast. This technique is described in detail elsewhere [1].

In addition to these routine measurements, which are carried out as part of a quality assurance (QA) programme, it is recommended [2] that an assessment of the individual doses delivered to a group of women be made at regular intervals. Several studies of this type appear in the literature [3–5] and the methodology used is described in greater depth elsewhere [1]. An assessment of MGDs received by a group of women attending for screening is also recommended as part of the schedule for QA audit visits to breast screening centres [6].

The technique of determining doses to a sample of women involves calculation of entrance surface air kerma, and conversion of this to MGD using published conversion factors [7]. These factors are dependent on compressed breast thickness and X-ray beam quality. To calculate MGD the following quantities are required: the air kerma behind the compression plate at the tube potential and target/filter being used; and the half value layer (HVL) of the beam at the tube potential and target/filter being used with the compression plate in place.

Often it is most practical to obtain these values from a recent set of routine QA measurements performed on the unit. If all mammography examinations were performed at the same tube potential, for example 28 kV, then the process would be straightforward. However, for large or dense breasts, tube voltage is often increased to perhaps 29 kV or 30 kV to increase the mean photon energy and improve penetration. In addition, new generation machines such as the IGE DMR (GE Medical Systems, Buc, France) and Siemens Mammomat 3000 (Siemens-Elema AB, Solna, Sweden) utilize targets and filters of several materials. These units are often used in modes in which the machine automatically selects a combination of tube voltage, target and filter material to suit the imaging requirements of a particular breast (for example, 26 kV with a molybdenum filter and target (Mo/Mo) may be chosen to optimize contrast). If dose is to be calculated for a group of women for these systems, many additional measurements on various combinations of tube voltage, target and filter may need to be made by the physicist as it is not known beforehand what factors will be selected. This makes the task of conducting a dose survey more difficult, since a large combination of factors are involved. A further complication is that between the last set of QA tests (when output and HVL measurements will have been made) and completion of the dose survey, changes may have been made to the programme settings on the automatic modes of new generation units, resulting in different combinations of voltage, target and filter being used. Unless the physicist is aware of this and hence performs new measurements of output and HVL for each of the new settings, the accuracy of dose calculation will be reduced due to the use of inappropriate output and HVL data, or it will not be possible to calculate some of the doses owing to the correct data not being available.

At present, data have been published enabling the HVL at any given tube potential to be determined from measurements made at another tube potential [8, 9]. However, these measurements are displayed graphically and are, therefore, less readily incorporated into a computerized method of dose calculation. It should also be noted that these data were produced before the introduction of units with multiple targets and filters and therefore refer mainly to a single molybdenum target/filter combination (Mo/Mo). The data of Robson et al [9] specifically excluded the effect of the compression plate, as these data were calculated to enable the filter thickness to be determined from HVL measurements and the presence of a compression plate of unknown thickness and composition introduces a further uncertainty into the measurement. Typical HVL data for different targets and filters at different values of nominal tube potential, using the nominal values of filter thicknesses, are available [4, 10] but no corresponding data relating to tube output are given. The use of the data as given in these tables could result in errors in the dose calculation, as no account is taken of the differences between individual machines.

In the work presented here, a technique for deriving all the necessary data from those measurements routinely performed is described and a set of equations is produced that can be used to determine the output and HVL for a range of tube voltages for a given target/filter combination. The advantage of this method is that the data are derived from measurements made on a particular X-ray set rather than being based on typical values.

	Method

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 
Computer modelling
A computer model was employed to simulate the generation and filtration of X-ray spectra. To model the spectra used clinically, the effect of the compression plate must be included. This plate is made of a transparent plastic material whose composition and thickness will vary between manufacturers. Cranley [8] used equivalent thicknesses of 1 mm and 2 mm Perspex to simulate the compression plate. In the present work, this assumption was checked by measuring the HVL at a nominal tube potential of 28 kV with the compression plate in position and comparing that with the HVL measured with known thicknesses of Perspex in place of the compression plate. Measurements were made on eight compression plates from four different models of X-ray unit:Soredex Mamex dcS (Orion Corporation, Helsinki, Finland); Gendex AMI (Gendex Corporation, Franklin Park, IL); Siemens Mammomat 300 (Siemens-Elema AB, Solna, Sweden); and Siemens Mammomat 3 (Siemens AG, Erlangen, Germany).

Measurements were made using a calibrated ionization chamber, placed in the X-ray beam in such a position that its centre lay on the axis from the tube focus to a point 4 cm in from the chest wall edge of the table. To reduce the effects of scattered radiation, the beam size was limited to the size of the chamber's sensitive area by using a lead collimator placed close to the tube focus. The compression plate was positioned as far as possible from the ionization chamber.

High purity (99.99%) aluminium (Al) foils (Goodfellow Metals, Cambridge, UK) were used to perform the measurement of HVL. The foils were placed on top of the compression plate approximately halfway between the tube focus and the ionization chamber. When the HVL had been determined, the compression plate was removed and replaced by known thicknesses of Perspex positioned in the beam at the collimator. For each thickness of Perspex, the HVL was measured. For all the measurements, the HVL was determined using the semi-logarithmic interpolation method given by Wagner et al [11]. The Perspex equivalence of the compression plate was taken as being the thickness of Perspex required to give the same HVL as the compression plate.

Most of the modelling of X-ray spectra was performed using spectrum processing software supplied with IPEM Report 78 [12], which allows the generation of spectra for a variety of target and filter materials over the mammographic energy range. For a given set of input parameters, the software calculates the air kerma in µGy mAs^-1 at 75 cm and the HVL in millimetres of Al. In this work, the simulation was run using a range of tube voltages between 25 kV and 32 kV (the clinically useful range). The following Mo, Rhodium (Rh), Al target/filter combinations were studied: Mo/Mo; Mo/Rh; Mo/Al; Rh/Rh; and Rh/Al. For each combination, a range of filter thicknesses and Perspex thicknesses (to simulate the compression plate) were considered. In all cases, the spectrum included the effect of attenuation by 550 mm of air, a typical focus-to-chamber distance used in the measurement of tube output and HVL.

For tungsten targets, the software from IPEM Report 78 only allows calculation of data for 30 kV and above, which is slightly higher than that usually used with this target/filter combination in modern mammography units. An existing implementation of the algorithm of Birch and Marshall [13], which allows the generation of spectra below 30 kV, was used to provide all the data for tungsten targets. Tungsten spectra for tube potentials in the range 25–32 kV were generated and the air kerma and HVL calculated for a range of filter and Perspex thicknesses.

The calculated air kerma and HVL were recorded for each combination of filter thickness and Perspex thickness at each value of tube potential. Conventionally, the output of an X-ray tube in µGy mAs^-1 is empirically related to the measured tube voltage by a relationship of the form

where A and n are constants, with n typically taking a value between 2 and 3. For mammography units with a Mo target and filter (Mo/Mo), it is more usual for n to take a value of approximately 3 [1]. By taking the logarithm of each side, Equation (1) reduces to the linear form given in Equation (2) below. For each set of conditions, the logarithm of the air kerma at 75 cm was plotted against the logarithm of the tube voltage, and first order curves of the form given below were fitted through the data using a commercially available plotting/curve-fitting software package (FigP, Biosoft, Cambridge, UK).

The calculated values of HVL were plotted against tube voltage and the same curve-fitting program was used to fit second order curves of the form

through the data, where a, b and c are constants. In Figure 1 the logarithm of the calculated air kerma is plotted against the logarithm of the tube voltage for a selection of filter and compression plate thicknesses for the Mo/Mo target/filter combination. The solid lines show the first order curves obtained by allowing free choice of both the first order and constant terms (i.e. n and A) in Equation (2). The resulting lines have similar slope, although some variation in the value of n was found. Figure 2 shows HVL plotted against tube voltage for the same conditions as those in Figure 1. The solid lines represent second order curves based on the free choice of a, b and c in Equation (3). Once again there was some variation in the shape parameters (a and b) although the curves were of very similar shape. Similar results were obtained for the other target/filter combinations considered.

View larger version (10K): [in this window] [in a new window]   Figure 1. Plot of log10(air kerma) against log10(kV) for the molybdenum target/filter combination (Mo/Mo). The three sets of data represent the following sets of conditions: , 36.1 µm Mo, 1.75 mm Perspex; , 25 µm Mo, 1 mm Perspex; , 45 µm Mo, 3 mm Perspex. Solid lines represent the best fit allowing the free choice of both parameters in Equation (2). Dotted lines show the curve fits obtained after fixing the shape and allowing only the constant term to vary.

View larger version (14K): [in this window] [in a new window]   Figure 2. Plot of the half value layer (HVL) against tube voltage for the molybdenum target/filter combination (Mo/Mo). The three sets of data represent the following sets of conditions: , 36.1 µm Mo, 1.75 mm Perspex; , 25 µm Mo, 1 mm Perspex; , 45 µm Mo, 3 mm Perspex. Solid lines represent the best fit allowing the free choice of all parameters in Equation (3). Dotted lines show the curve fits obtained after fixing the shape and allowing only the constant term to vary.

To obtain representative values for the parameters, typical values of tube filtration and Perspex thickness need to be employed in the model. For the case of the Mo/Mo target/filter combination, the spectrum processor [12] was used to determine the Mo filter thickness from the results of HVL measurements, made at 30 kV without the compression plate, on individual mammography units. The filter thickness in the program was altered until it gave the same HVL at the measured tube voltage. Interpolation was often necessary as the software allows only integer values of tube voltage to be entered. The mean HVL was 0.336 mm Al and the mean filter thickness was calculated to be 36.1 µm Mo. An earlier national survey [14] gives a mean value of 0.337 mm Al for the HVL measured at a nominal tube voltage of 30 kV with the compression plate removed for 258 units across the Breast Screening Programme. The age of this data, before the widespread use of multiple target/filter machines, means that it will almost certainly consist only of units with Mo targets and filters. The value obtained for the units considered is in good agreement with that obtained in the national survey. For the other filter materials, the mean thickness of the nominal 25 µm Rh (Siemens Mammomat 3000 and IGE DMR) and 50 µm Rh (Siemens Mammomat 3000) filters, were found to be 29.9 µm and 58.9 µm, respectively. For the nominal 1.0 mm Al filter found on the IGE DMR unit, the mean thickness was 1.2 mm. As the 50 µm Rh filter is used with a tungsten target, it was necessary to use the existing implementation of the Birch and Marshall algorithm [13] to calculate the filter thickness to maintain consistency with the rest of the computer modelling.

The measured Perspex equivalences of the compression plates considered were found to lie between 1.1 mm and 3.0 mm Perspex with a mean thickness of 1.75 mm. This is consistent with the values assumed by Cranley [8]. To determine single values for each of the parameters n, a and b, the mean filter thicknesses and Perspex equivalence derived above were used in the model.

For the Mo/Mo target/filter combination, the theoretical points calculated using the mean filter and compression plate thickness are shown in Figures 1 and 2 by . The values of n, a and b for this set of points found using the curve-fitting program (allowing free choice of all the terms) were used to fit curves of the same shape to the other sets of data. These are shown in Figures 1 and 2 by dotted lines. Thus, in Figures 1 and 2, the equations of the dotted lines vary only in the constant term. Similar results were obtained for the other target/filter combinations.

The validity of the approach was tested by using the technique to fit curves to extremes of beam quality (in terms of filter and compression plate thickness) likely to be encountered for a given target/filter combination. For the Mo/Mo data shown in Figures 1 and 2, the data shown by represent data for 1 mm thickness Perspex and 25 µm Mo, while those shown as are for 3 mm Perspex and 45 µm Mo. As can be seen from the graphs, the dotted lines are a good approximation to the solid curves, even at the extremes of the range. If all the data for each target/filter combination are considered, the maximum and mean deviations of the dotted lines from the solid lines are -6.8% and 1.1%, respectively, for the tube output. The corresponding values for the HVL are -3.3% and 0.3%.

	Experimental verification

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 
To verify the model, measurements of air kerma and HVL with the compression plate in position were required over a range of tube voltages. Measurements were made on a total of seven mammography units comprising six different models: Siemens Mammomat 2 (Siemens AG, Erlangen, Germany), 300 and 3000; IGE DMR; Lorad M-IV (Trex Medical Corporation, Danbury, CT); and Soredex Mamex dcS (Orion Corporation, Helsinki, Finland). For each unit, measurements of air kerma and HVL were made at nominal tube potentials between 25 kV and 32 kV for each target/filter combination available. For mammography units with both Mo and Rh targets, it has been assumed by Underwood et al [15] that tube voltage is the same for both targets. In the present work this approach was adopted and extended to include tungsten targets. All tube voltages were measured with a calibrated RMI 232 kVp meter (Radiation Measurements Inc, Middleton, WI) using only the Mo target. For the measurement of HVL, the experimental set-up was the same as that for the determination of the Perspex equivalence of the compression plates. For the measurement of air kerma, the position of the ionization chamber was not changed but the compression plate was brought close to the surface of the ionization chamber and the lead collimator was removed. The values of air kerma (corrected to µGy mAs^-1 at 50 cm) and HVL (mm Al) were calculated.

	Results

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 
The values for each of the parameters for the target/filter combinations considered are given inTable 1. The use of these parameters in Equations (2) and (3) to determine the tube output and HVL for a given target/filter combination is described as follows:

1. Measure the tube potential for a nominal value of 28 kV.
   
2. Measure the tube output and HVL at a nominal tube voltage of 28 kV.
   
3. Using the values found in steps (1) and (2) andthe appropriate parameters from Table 1, calculate the values of A and c from Equations (2) and (3).
   
4. With all the parameters now known, the tube output and HVL can be calculated for any other measured value of tube voltage in the range 25–32 kV for that particular unit.
   

View larger version (11K): [in this window] [in a new window]   Figure 3. (a) Predicted values of air kerma plotted against measured values for a range of tube voltages and target/filter combinations. The solid line is the line of equality, y=x. (b) Predicted values of the half value layer (HVL) plotted against measured values for a range of tube voltages and target/filter combinations. The solid line is the line of equality, y=x.

	Discussion

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

As the model relates measured tube output and HVL at a nominal 28 kV to measured tube voltage at the same setting, it is quite insensitive to the absolute accuracy of the tube voltage. If tube voltage is higher or lower than nominal, this will be reflected by the values of output and HVL calculated using the model. Uncertainties can arise, however, if tube voltages are accurate but the measuring instrument is not. If the relationship between measured tube potential and true tube potential is constant across the range, for example if measured and true tube voltages are within ±1 kV or within ±5% of each other across the whole range, the maximum errors in the calculated tube output and HVL are +2% and -1.5%, respectively. If, at a given tube voltage, the relationship is different from that at 28 kV, then the errors are slightly larger. At the tube voltage under consideration, for each 0.1 kV difference between the measured voltage and that inferred using the relationship at 28 kV, the maximum additional errors on tube output and HVL are 1.8% and 0.7%, respectively.

	Conclusions

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 
A computer simulation of X-ray production and filtration has been used to produce data that allow the user to calculate the air kerma and HVL for any value of tube voltage (in the range 25–32 kV) from a measurement of the tube output and HVL for each target/filter combination made at a single tube voltage. The advantage of this method is that by relating calculated values to measurements made on an individual machine, the data produced are specific to that machine and the use of typical values is avoided. The data have been presented in the form of general equations and parameters, enabling their straightforward inclusion in a spreadsheet or computer program used to calculate MGD to groups of women. Experimental verification of the model shows satisfactory agreement between measured and predicted values of air kerma and HVL.

Received for publication May 4, 2000. Revision received September 29, 2000. Accepted for publication December 5, 2000.

	References

Top Abstract Introduction Method Experimental verification Results Discussion Conclusions References

 

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