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British Journal of Radiology (2004) 77, 224-230
© 2004 British Institute of Radiology
doi: 10.1259/bjr/32409995
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Full Paper

Evaluation of the use of six diagnostic X-ray spectra computer codes

P Meyer, PhD 1 E Buffard, MS 1 L Mertz, PhD 2 C Kennel A Constantinesco, PhD 2 and P Siffert, PhD 1

1 Laboratoire PHASE/CNRS, 23 rue du Loess, BP 20, 67037 Strasbourg Cedex and 2 Laboratoire de Biophysique et Médecine Nucléaire, CHU Hautepierre, Avenue Molière, 67000 Strasbourg, France


   Abstract
Top
 Abstract
Introduction
 Materials and method
 Results
 Discussion
 Conclusion
 References
 
A knowledge of photon energy spectra emitted from X-ray tubes in radiology is crucial for many research domains in the medical field. Since spectrometry is difficult because of high photon fluence rates, a convenient solution is to use computational models. This paper describes the use of six computer codes based on semiempirical or empirical models. The use of the codes was assessed, notably by comparing theoretical half value layers and air kerma with measurements on five different X-ray tubes used in a research hospital. It was found that three out of the six computer codes give relative spectra very close to those produced by X-ray units equipped with constant potential generators: the mean difference between measured and modelled half value layer was less than 3% with a standard deviation of 3.6% whatever the tube and the applied voltage. Absolute output is less accurate: for four computer codes, the mean difference between the measured and modelled air kerma was between 18% and 36%, with a standard deviation of 9% whatever the tube (except for the single phase generator) and the applied voltage. One of the codes gives a good output and beam quality for X-ray units equipped with 100% ripple voltage generators. The use of computational codes as described in this paper provides a means of modelling relative diagnostic X-ray spectra, the usefulness of the tube output data depending on the accuracy required by the end user.


   Introduction
Top
 Abstract
 Introduction
Materials and method
 Results
 Discussion
 Conclusion
 References
 
The spectral distribution is an important property of an X-ray beam used in radiology, allowing calculation of the half value layer (HVL), air kerma, mean energy and other properties. Unfortunately, spectral measurements are difficult in the medical field since the photon fluence rates are very high [1, 2]. For this reason, the spectral characteristics of a beam emitted from an X-ray tube are usually described by the HVL at a given high voltage. However, because of its integral nature, the HVL value contains limited information.

Knowledge of spectral distribution is crucial in many research and development areas: for example in the design of X-ray detectors in radiology, to model the energy response variation of dosimeters or to compare theoretical spectra with experimental data [3–5]; in the characterization of the performance of imaging systems in order to evaluate the noise equivalent quanta [6–8]; and in radiological optimization, to improve diagnostic imaging techniques [9, 10].

Given these needs and the complexity of X-ray spectrometry, some authors have proposed semiempirical or empirical models for generating tungsten target X-ray spectra as a function of tube parameters [11–13]. Several computer codes implementing these models have then been designed [14–16].

This paper investigates the use of six different computer codes conceived to generate tungsten target X-ray spectra in the diagnostic radiology energy range. The HVL and air kerma per mAs have been measured for five X-ray tubes at several high voltage values, and have been compared with the theoretical HVL and air kerma per mAs obtained with the six computer codes. This comparison enables the assessment of the output and the beam quality accuracy of the theoretical spectra.


   Materials and method
Top
 Abstract
 Introduction
 Materials and method
Results
 Discussion
 Conclusion
 References
 
X-ray units
Five X-ray units used daily in different services of a teaching hospital have been studied in this work (Table 1Go). The spectral characteristics of the beam emitted from these tubes were measured, with the corresponding values being given in Table 2Go. Quality control measurements performed on all these facilities did not show any non-conformity according to the French Medical Physicist protocol [17]. The characteristics of each tube were used as inputs for the computer modelling codes.


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  		Table 1. Main technical characteristics of the X-ray units. The voltage ripples are theoretical and not measured values

 

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  		Table 2. High voltage, air kerma/mAs and HVL measurements performed on the five X-ray tubes; total filtration values are obtained by using the Drexler tables [Dre]

 
Tube potential-meter and ionization chamber
Measurement of the high voltage applied to the X-ray tubes was achieved with a tube potential-meter model 35080B (Keithley, USA), associated with an electrometer model 35050A (Keithley, USA). Linearity and filtration corrections were applied to the raw measurements. The calibration of this instrument is traceable to the National Institute of Standards and Technology (NIST), its accuracy being ±2%.

Air kerma and HVL were determined with a plane parallel chamber, model 96035B (Keithley, USA), with a 15 cm3 sensitive volume. The chamber and electrometer used with the tube potential-meter had previously been calibrated in terms of air kerma free-in-air. The calibration of this instrument is also traceable to the NIST. Calibration is performed at the Keithley equivalent of L100 (NIST defined as 100 kVp, first HVL of 2.8 mm Al, homogeneity coefficient of 59), its uncertainty being ±3%.

Computer codes
The performance of six computer codes was evaluated in this study. Their main characteristics, notably the input parameters, are summarized in Table 3Go.


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  		Table 3. Main characteristics of the computer codes used

 
xcomp5r is a DOS program developed and written in BASIC by Nowotny and Hyfer [16]. Numerical values for the differential energy intensity function and the Thomson-Whiddington constant were taken from Birch et al [11]. This program (Srs-78) calculates X-ray spectra at 1 keV intervals for tube voltages from 20 kV to 150 kV and allows the display of up to five spectra simultaneously.

Cranley et al [14] developed a program available on CD-ROM including a spectral catalogue generated by the method of Birch and Marshall [11]. This program allows the calculation of spectra from 30 kV to 150 kV at 0.5 keV intervals. Focus-to-detector distance (FDD) is 750 mm and output results for other FDD can be obtained using the inverse square law, even if not totally applicable. Indeed, deviations from this law may amount to about 5% in a clinical beam, due to the presence of extra focal radiation.

The TASMIP algorithm was conceived by Boone and Seibert to compute X-ray spectra at 1 keV intervals over a 30 kV to 140 kV range [15]. Contrary to the other codes studied, TASMIP is totally empirical and interpolates measured constant potential X-ray spectra published by Fewell et al [12]. As only the spectral distribution is available as output from the algorithm, kerma and HVL were calculated with an in-house program written in C++ language. The mass attenuation coefficients used were obtained by logarithmically interpolating the Hubbell tables [18]. The inverse square law was used to compare theoretical TASMIP values with those that were measured, since the spectra are generated at 1 m FDD.

The program Specgen (supplied by Glenn Stirling NRL, Christchurch, New Zealand) allows the calculation of X-ray spectra at 1 keV intervals over a range of 10 kV to 150 kV. Specgen allows for spectrum modelling of single phase generators, but this option was not used due to errors in the code. Specgen includes in fact two computer codes giving the user the choice between two implemented models, either Tucker et al [13] or Birch et al [11]. The names given here are based on the model by Tucker, "SpecgenT", and on the model by Birch, "SpecgenB".

Specgen replaces an older obsolete version called xraytbc (supplied by Glenn Stirling NRL, Christchurch, New Zealand), that is based upon the model of Tucker et al. Since this code has been used in the past, its properties were also evaluated, but only in qualitative terms (HVL) since it generates relative spectra in arbitrary units.

HVL measurement
HVL measurements are made following the French Medical Physicist protocol [17]. A minimum distance of 25 cm between the X-ray source and the filters on one side and between the filters and the detector on the other side is systematically applied, this being an acceptable measurement set-up [19]. A focused beam and double lead collimation are used, to avoid any scattered radiation. HVL was measured using aluminium sheets with a 99.98% minimum degree of purity.

Total filtration calculation
Total filtration is required as an input parameter for all the computer codes investigated in this paper, except TASMIP (this point is discussed later). The determination of total filtration is important since its value will influence the theoretical results.

Nagel has studied six different methods that permit measurements of total filtration without any dismantling of the X-ray assembly [20]. The most widely used, the HVL method, is based on the relationship between the measured HVL at the known voltage and total filtration, given by a so-called "quality diagram". This approach is also used in the present work.

A comparison of quality diagrams published by different authors shows large discrepancies, leading to tolerances of about ±25% for the estimation of total filtration with the HVL method [20]. However, these have a lack of theoretical HVL to total filtration data covering the full range of target angles and voltage ripples encountered in practice [21, 22].

In this work, Drexler diagrams were used which were determined for constant potential generators in a 10 kV to 150 kV voltage range and a 0.02 mm Al to 8 mm Al HVL range [23].

Evaluation of the performance of the method
The accuracy of the calculated spectra in both quantitative (tube output magnitude) and qualitative (beam quality) terms was studied.

A comparison between the air kerma per mAs measured on each tube and the theoretical air kerma per mAs obtained with a computer code allows comparison of the methods for determining outputs.

The HVL measured on each tube and the theoretical HVL obtained with a computer code were compared in order to assess the beam quality.


   Results
Top
 Abstract
 Introduction
 Materials and method
 Results
Discussion
 Conclusion
 References
 
The comparison of air kerma per mAs is given in Table 4Go. For instance, air kerma values obtained with the Srs-78 computer code are on average 1.29 times the values measured on tube number 3, with a standard deviation of 4.43% in the 50–150 kV high voltage range.


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  		Table 4. Ratios between theoretical and measured air kerma/mAs. The values represent the air kerma obtained with the stated computer code divided by that measured on the X-ray tube. All the codes, except TASMIP, were not designed for 100% ripple voltage (tube 1)

 
The comparison of beam quality is given in Table 5GoGo. The HVL calculated for the 60 kV spectrum generated with SpecgenB is for example equal to that measured using tube 2.


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  		Table 5. Ratios between theoretical and measured half value layer (HVL). The values represent the HVL obtained with the stated computer code divided by that measured on the X-ray unit

 

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  		Table 5. Continued

 

   Discussion
Top
 Abstract
 Introduction
 Materials and method
 Results
 Discussion
Conclusion
 References
 
Beam intensity
Four of the five X-ray tubes are driven by high-frequency generators. Tube 1 is the only one associated with a single phase generator, assuming a 100% voltage ripple (we were not able to determine if it is half-wave or full-wave rectified). TASMIP is the only algorithm that allows this waveform to be taken into account. It results in similar measured and calculated air kerma values: the average ratio is 0.98 in a 50 kV to 130 kV range (Table 4Go), whereas the average ratios are between 3.45 and 4 for the four other computer codes that were not designed for 100% voltage ripple. TASMIP seems therefore to be the only computer code to generate X-ray spectra with a single phase X-ray generator, even if there is a high standard deviation (22%) over the kV range, so that the user should be aware of the applied kV.

Focusing on the four other X-ray units (numbers 2, 3, 4 and 5), an overestimation of the air kerma with the computational codes is observed, except for TASMIP. Indeed, the air kerma is overestimated by a mean factor of between 1.10 and 1.56 when using the four other codes. The kerma underestimation observed with the TASMIP computer code is significant, the amount being strongly a function of the applied kV (standard deviation of about 15%).

The tube output of the mobile unit (5) is better evaluated with the TASMIP code (mean ratio=0.84) but this estimation is also highly dependent on the applied voltage (standard deviation=18%). On the other hand, the air kerma calculated with the four other programs is less accurate (mean ratio comprised between 1.34 and 1.46), but with less dependence upon the applied kV (standard deviation between 5.4% and 8.6%).

Considering the systematic overestimation of the air kerma calculated with all the computer codes except TASMIP, the ionization chamber was first suspected of underestimating the kerma. This size of measurement deviation in general may not be so surprising since Green showed in 1999 that 25% of instruments used in routine use in the UK may require some adjustments before they can truly be said to be performing as the manufacturer intended [24]. An evaluation of the ionization chamber was carried out by comparing its performance with that of a Barracuda solid state detector (RTI Electronics, Sweden). The calibration of this instrument is traceable to RTI Electronics (70 kV, HVL 2.60 Al mm beam quality). The comparison did not show any significant discrepancy between the kerma measured with the ionization chamber and with the solid state detector. Therefore, it was concluded that the observed difference between the measured kerma and that resulting from use of the computer codes is not the result of chamber drift.

Before evaluating all the tube parameters, quality control measurements had not shown any non-conformity. Current reproducibility and linearity had been assessed, but unfortunately tube current accuracy had not. A tube current drift could then be a partial explanation of the kerma overestimation, particularly with unit 5, since the kerma overestimation for this unit was higher than that for units 2, 3 and 4.

A further source of uncertainty is given by tube ageing, which affects the emitted spectrum by anode roughening and by deposition of anode or cathode material on the tube window [20]. Anode roughening also acts like reducing anode angle [20]. Beyond a certain degree of anode surface roughness and tungsten deposit on the tube window, additional roughening results in total absorption of radiation, the kerma losses resulting from this effect being 10% or more [20]. Consequently, the input parameters used to generate the theoretical X-ray spectra would no longer correspond to the real parameters.

Total filtration calculation involves a number of uncertainties. Considering that the HVL method only provides a rough estimate for filtration with errors of typically ±25%, 0.6 mm filtration could be added to the total filtration values (for a total filtration of 3 Al mm). If this were the case, the calculated kerma would be lowered in such a manner that it fits better to the measured kerma. For example, taking 4.1 Al mm total filtration at 77 kV for tube 2 results in a ratio of 0.97 between the kerma calculated with xcomp5r and the measured kerma, instead of 1.14 with the measured 3.5 Al mm total filtration. However, the calculated HVL would no longer be close to the measured one and still for the previous example, the calculated/measured ratio would change from 1.00 to 1.08. Considering the good agreement between the calculated and the measured HVL (see Beam quality), it seems that the difference between the calculated and the measured air kerma per mAs is not due to the total filtration uncertainty.

To obtain the beam intensity data, the authors of the computer codes normalized them to the air kerma output of calibrated facilities, which are also prone to the same problems (at least with surface roughness). Considering all these uncertainties, the kerma outputs obtained following our procedure should be treated with care. Nevertheless, the differences we have observed between measured and theoretical air kerma are relatively small. The results are summarized in Table 6Go. Indeed, the mean ratio calculated with the data obtained on all the X-ray units at all applied kV was found to be between 1.18 and 1.35, depending on the code (except TASMIP), with a standard deviation of about 9%.


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  		Table 6. Summary of the results. The mean ratio and standard deviation (SD) for the output comparison does not include the data obtained on X-ray tube 1, except for the TASMIP code. The mean ratio and SD for the beam quality comparison includes all the ratios obtained with all the X-ray units

 
Beam quality
There is good agreement between calculated and measured HVL. The estimation of HVL corresponds closely to the measured one whatever the kind of X-ray unit, conventional, mobile or single phase. Standard deviations are small, implying that HVL can be reasonably accurately obtained at all kV settings. Nevertheless, these first observations should be qualified.

It can be observed in Table 5GoGo that TASMIP systematically overestimates the HVL for all the X-ray tubes (mean ratio between 1.12 and 1.29), except for tube 1. It can also be observed that xraytbc and SpecgenT, the two programs based on the Tucker model [Tuc], underestimate the HVL (mean ratio between 0.88 and 0.93, and 0.92 and 0.97, respectively). Furthermore, the standard deviation of the HVL obtained with SpecgenT over the whole kV range is larger than the standard deviation of the other codes. Note that the best results were obtained using the codes based upon the model by Birch (Srs-78 and SpecgenB).

General aspects
It should first be clarified that xraytbc is obsolete, its evaluation being given only for information. SpecgenT, which replaces xraytbc, is the code that gives the best intensity results and the worst HVL data (Table 6Go).

The relatively poor performance of the TASMIP code compared with other codes may be explained by the fact that this code is the only one that requires additional instead of total filtration. Additional filtration was converted to total filtration by adding inherent filtration. However this method does not give satisfactory results for X-ray units with high frequency voltage generators. Nevertheless, TASMIP is the only code allowing the choice of exact voltage ripple value in a 30 kV to 150 kV range, giving air kerma and HVL in good agreement with the measurements on the 100% voltage ripple X-ray unit (number 1).


   Conclusion
Top
 Abstract
 Introduction
 Materials and method
 Results
 Discussion
 Conclusion
References
 
The results of this study indicate that the xcomp5r, Srs-78 and SpecgenB codes can be taken as useful and reliable tools to compute relative diagnostic spectra with a high accuracy: the mean difference between the measured and the theoretical HVL is less than 3% with a standard deviation of 3.6%, determined on five different X-ray tubes over their full kV range. The beam intensity data should be treated with greater caution: because of all the uncertainties involved, the smallest mean difference between modelled and measured air kerma is 18%, obtained with the SpecgenT code. Furthermore, standard deviations show that the accuracy of the air kerma calculation depends on the X-ray unit and the applied kV. The TASMIP code can be used as a good alternative to compute spectra obtained with X-ray tubes associated with single phase generators. Successful use of computer codes as described in this paper to model absolute diagnostic X-ray spectra will depend on the accuracy required by the end-user.


   Acknowledgments
 
R Nowotny, G Sterling and J M Boone are acknowledged for their comments about their computer codes. Additional thanks are due to Vlad Svrcek and Malgo Malgorzata for their useful comments on the draft manuscript.


   Footnotes
 
This work was supported in part by the European Commission EC Contract # G6RD-CT-2000-00384. Back

Received for publication November 14, 2002. Revision received September 3, 2003. Accepted for publication September 30, 2003.


   References
Top
 Abstract
 Introduction
 Materials and method
 Results
 Discussion
 Conclusion
 References
 

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