Effect of pressure, temperature and humidity in air on photon fluence and air kerma values at low photon energies

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1 ARTICLE IN PRESS Radiation Physics and Chemistry 68 (2003) Effect of pressure, temperature and humidity in air on photon fluence and air kerma values at low photon energies M. Assiamah, D. Mavunda, T.L. Nam, R.J. Keddy* Health Physics Service, Schonland Research Institute for Nuclear Sciences, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa Received 3 April 2003; accepted 19 May 2003 Abstract An investigation into the effect of pressure, temperature and humidity in air on photon fluence at a typical mammography, low bremsstrahlung energy (25 kvp), has been carried out. Pressure values corrected for humidity at varying temperatures were employed to determine the density of moist air. Using the corrected moist air densities, the X-ray photon fluence remaining after air attenuation has been computed assuming an X-ray focal spot-detector distance of 65 cm. Bremsstrahlung spectral distributions and the effects of pressure, temperature and humidity on the photon fluence from molybdenum and tungsten targets are illustrated. Comparative results suggest that such effects could be significant and need to be considered when calculating exposure levels from low-energy photons. The investigation showed that air kerma values from an X-ray spectrum that has significant lower-energy components is likely to be more sensitive to changes in pressure, temperature and humidity than the air kerma from an X-ray spectrum with lower-energy components less pronounced. Non-negligible air kerma values are involved. r 2003 Elsevier Ltd. All rights reserved. Keywords: X-ray photon fluence; Attenuation; Mammography; Bremsstrahlung; Air kerma 1. Introduction Mammography X-ray examinations are typically performed at a focal-spot detector distance (FSD) of cm. In the calculation of the photon fluence reaching the detector for dose or exposure measurements at mammography energies, the attenuation due to air for the specific FSD must be taken into consideration. In many such calculations, the air is normally assumed to be dry; hence it is common to find the density of dry air at sea level being applied in such computations. However, sea level atmospheric pressures do not apply with many measurements being conducted at centres at significant altitudes. Air normally contains water vapour and is classified as dry or humid based on *Corresponding author. Tel.: ; fax: address: keddy@src.wits.ac.za (R.J. Keddy). its water vapour content. The humidity is specified using partial pressures of water in the air. The relative humidity of the water content in the air is not constant, varying from a minimum of zero to a maximum of 100%, determined by the saturated vapour pressure of water at the given air temperature. The density of air is therefore affected by changes in environmental conditions, i.e. temperature, pressure and moisture or humidity. This study sets out to determine the effect of these physical properties on the photon fluence and air kerma values of mammography bremsstrahlung beams. 2. Methodology The photon fluence (photons/cm 2 ) used for this study was obtained from a computer generated X-ray spectrum code namely: molybdenum anode spectra model using interpolation polynomial (MASMIP) and X/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi: /s x(03)

2 708 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) tungsten anode spectra model using interpolation polynomial (TASMIP) developed by Boone et al. (1997). The X-ray spectrum for a 25 kvp tube potential was generated from both the MASMIP and TASMIP models. A nominal filtration of 0.03 mm molybdenum was applied to the molybdenum target spectrum, whilst a 0.05 mm rhodium filtration was applied to the tungsten target spectrum. The spectral shaping (filters) materials applied are routinely used on clinical mammography systems. A focal spot-detector distance of 65 cm (an FSD commonly used at clinical mammography settings) was assumed for the calculation. For computational purposes the bremsstrahlung spectrum was divided into 0.5 kev energy bins. The photon fluence remaining in each bin after air attenuation was calculated by applying, to each bin, the energy-dependent Lambert Beer s law equation f ¼ f 0 expð meþ; ð1þ where f is the photon fluence (photon/cm 2 ) in each bin after attenuation by air of thickness e (g/cm 2 ) with mass attenuation coefficients m (cm 2 /g) and f 0 is the initial photon fluence before attenuation (Archer and Wagner, 1982; Attix, 1986; Wolbarst, 1993). The thickness e is given by the product of the density r in g/cm 3 and the focal spot-detector distance x in cm. The density of air used in Eq. (1) has been corrected for temperature, pressure and humidity. The corrected air densities used for this investigation are those given in the CRC Handbookof Chemistry and Physics ( ) for a temperature range of 5 35 C and corrected pressure range of mmhg. The densities for moist air at temperatures 40 C, 45 C and 50 C, not given in the reference for the specified corrected pressures, were calculated using Eq. (2) and Table II of section F of Weast et al. ( ). The density r T;P;H of moist air at absolute temperature T, barometric pressure P in mmhg, is given by r T;P;H ¼ 1: :13 T P 0:3783e 760 ; ð2þ where is the density of dry air in g/l at standard temperature and pressure (s.t.p.) i.e. 0 C/ K and 760 mmhg/101.3 kpa, respectively. The parameter e appearing in Eq. (2) is the vapour pressure of the moisture in the air in millimetres. Employing the dewpoint method and the vapour pressure of water at different dew points, the humidity H of the air has been accounted for (Marion and Hornyak, 1982). The corrected pressure values at various temperatures were then employed to determine the density of moist air for the calculated relative humidity. Relative humidities of 0 100% at intervals of 10% were used in the calculations. Using the photon fluence f iðcorrþ ; that which remains after 65 cm air attenuation, exposures X i ðeþ T;P;H in roentgen (R) at absolute temperature T, barometric pressure P and humidity H was calculated employing X i ðeþ T;P;H ¼ 1: f iðcorrþ E i ðm en rþ airi r T;P;H : ð3þ The subscript i refers to the ith photon energy interval E i (kev), m en, is the mass energy-absorption coefficient (cm 2 /g) of air at s.t.p., r and r T;P;H are the densities of air at s.t.p. and at absolute temperature T, barometric pressure P in mmhg, and relative humidity H, respectively (Cember, 1996). From the exposure X i (E) values, the air kerma K i (E) values in cgy were calculated using the exposure and air kerma relationship given by Wolbarst (Wolbarst, 1993). K i ðeþ ¼0:873X i ðeþ: The mass attenuation and mass energy-absorption coefficients data used for this study are those compiled by Hubbell and Seltzer (1996) and reworked into an extremely user-friendly windows program, WinXCom, (Gerward et al., 2001). To obtain data covering the energy of interest, a fitting algorithm was developed to obtain mass energy-absorption coefficient values with negligible deviation from the original published data (Assiamah et al., 2003). Both the mass attenuation and mass energy coefficients data were corrected to s.t.p. In analysing the results, the photon fluence data at temperature 0 C, 760 mmhg corrected pressure and 0% relative humidity was chosen as a reference data point. The results of the study are presented in tabular and graphical forms. 3. Results and discussion The effects of pressure on the photon fluence are illustrated in Figs. 1 and 2 for the molybdenum target spectrum and in Figs. 3 and 4 for the tungsten target. The temperature effects on the photon fluence are presented in Figs. 5 and 6 for the molybdenum target and in Figs. 7 and 8 for the tungsten target. The effects of humidity on the photon fluence are illustrated in Figs. 9 and 10 for the molybdenum target and in Figs. 11 and 12 for the tungsten target. A comparison of a typical photon fluence (photons/ cm 2 ) spectrum from molybdenum and tungsten targets at tube voltage of 25 kvp, 760 mmhg, 0 C and 0% relative humidity (reference spectrum) with a spectrum at the same tube voltage but corrected for air density at a pressure of 600 mmhg, temperature 35 C and 50% relative humidity are shown in Figs. 13, 14 and 15, respectively. Table 1 presents a comparison of the contributions of three arbitrary energy segments to the overall photon fluence from the reference and corrected molybdenum spectra. The comparison of the photon ð4þ

3 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 1. Deviation of the photon fluence due to pressure variation from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a molybdenum target at 25 kvp. Fig. 2. Overall deviation (%) due to pressure on the integrated photon fluence from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a molybdenum target spectrum at 25 kvp.

4 710 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 3. Deviation of the photon fluence due to pressure variation from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a tungsten target at 25 kvp. Fig. 4. Overall deviation (%) due to pressure on the integrated photon fluence from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a tungsten target spectrum at 25 kvp.

5 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 5. Deviation of the photon fluence due to temperature variation from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a molybdenum target at 25 kvp. Fig. 6. Overall deviation (%) due to temperature on the integrated photon fluence from the photon fluence calculated at 0 C, 760 mmhg at 0% relative humidity for a molybdenum target at 25 kvp.

6 712 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 7. Deviation of the photon fluence due to temperature variation from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a tungsten target spectrum at 25 kvp. Fig 8. Overall deviation (%) due to temperature on the integrated photon fluence from the photon fluence calculated at 0 C, 760 mmhg and 0% relative humidity for a tungsten target spectrum at 25 kvp.

7 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 9. Deviation of photon fluence due to a humidity variation from the photon fluence calculated at 0 C and 760 mmhg for a molybdenum target at 25 kvp. Fig. 10. Overall deviation (%) due to humidity on the integrated photon fluence from the photon fluence calculated at 0 C and 760 mmhg for a molybdenum target at 25 kvp.

8 714 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 11. Deviation of photon fluence due to a humidity variation from the photon fluence calculated at 0 C and 760 mmhg for a tungsten target at 25 kvp. Fig. 12. Overall deviation (%) due to humidity on the integrated photon fluence from the photon fluence calculated at 0 C, 760 mmhg at 0% relative humidity for a tungsten target at 25 kvp.

9 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 13. A comparison of the photon fluence spectrum from a molybdenum target at 25 kvp. (A) Spectrum at 760 mmhg, 0 C and 0% relative humidity. (B) Spectrum corrected for temperature (35 C), pressure (600 mmhg) and relative humidity (50%). Fig. 14. A comparison of the air kerma spectrum from a molybdenum target at 25 kvp. (A) Spectrum at 760 mmhg, 0 C and 0% relative humidity. (B) Spectrum corrected for temperature (35 C), pressure (600 mmhg) and relative humidity (50%).

10 716 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Fig. 15. A comparison of the photon fluence spectrum from a tungsten target at 25 kvp. (A) Spectrum at 760 mmhg, 0 C and 0% relative humidity. (B) Spectrum corrected for temperature (35 C), pressure (600 mmhg) and 50% relative humidity. Table 1 Comparison of contributions of three arbitrary energy segments to the overall photon fluence (photons/cm 2 ) from a molybdenum spectrum at 25 kvp, 0 C, 760 mmhg and 0% relative humidity with the molybdenum target spectrum at the same tube voltage and corrected for temperature, pressure and humidity Contribution to photon fluence by energy range 4 8 kev Contribution to photon fluence by energy range 8 15 kev Contribution to photon fluence by energy range kev Photon fluence at Total contribution 4.73E E E mmhg, 0 C, 0% RH ~ Percent contribution (%) Photon fluence at Total contribution 6.12E E E mmhg 35 C, 50% RH Percent contribution (%) % difference in photon fluence due to P, T, H Y correction The overall percentage difference in the photon fluence due to the combined effects of temperature, pressure and humidity is also shown. Overall difference in photon fluence due to P, T and H correction=3.98%. ~ RH is relative humidity. Y P, T and H are the pressure, temperature and humidity, respectively. fluence from the reference and corrected tungsten spectra are similarly shown in Table 3. A comparison of the contributions of three arbitrary energy segments to the overall air kerma values for both the reference and corrected molybdenum and tungsten spectra are presented in Tables 2 and 4. For purposes of illustrating the weights of contributions from various regions of the spectrum, three arbitrary energy segments

11 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Table 2 Comparison of contributions of three arbitrary energy segments to the overall air kerma in cgy from a molybdenum spectrum at 25 kvp, 0 C, 760 mmhg and 0% relative humidity with the molybdenum target spectrum at the same tube voltage and corrected for temperature, pressure and humidity Contribution to air kerma by energy range 4 8 kev Contribution to air kerma by energy range 8 15 kev Contribution to air kerma by energy range kev Air kerma (cgy) at Total contribution mmhg, Percent contribution (%) C, 0% RH Air kerma (cgy) at Total contribution mmhg Percent contribution (%) C, 40% RH % difference in air kerma due to P, T, H correction The overall percentage due to the combined effects of temperature, pressure and humidity is also shown. Overall difference in air kerma due to P, T and H correction=51.85%. Table 3 Comparison of contributions of three arbitrary energy segments to the overall photon fluence from tungsten spectrum at 25 kvp, 0 C, 760 mmhg and 0% relative humidity with the tungsten target spectrum at the same tube voltage and corrected for temperature, pressure and humidity Contribution to photon fluence by energy range 6 8 kev Contribution to photon fluence by energy range 8 15 kev Contribution to photon fluence by energy range kev Photon fluence at Total contribution 1.15E E E mmhg, Percent contribution (%) C, 0% RH Photon fluence at Total contribution 1.47E E E mmhg Percent contribution (%) C, 40% RH % difference in photon fluence due to P, T, H correction The overall percentage due to the combined effects of temperature, pressure and humidity is also shown. Overall difference in estimated photon fluence due to P, T and H correction=2.68%. were selected: 4 8, 8 15 and kev for the molybdenum spectrum and 6 8, 8 15 and kev for the tungsten spectrum. The overall difference in the estimated air kerma values of the entire molybdenum and tungsten spectra due to the combined effects of temperature, pressure and humidity correction is also shown in Tables 2 and Pressure As expected, the effect of pressure was more pronounced at the lower energies than at higher energies (Fig. 1). For the molybdenum spectrum, a deviation range from less than % was observed, between the energies 4 and 10 kev, for a pressure range of mmhg. For the same energy range, the deviation was 2 50% for pressure values mmhg. Above 10 kev, the deviations due to pressure effects ranged from less than 1% to 10% for the entire pressure range of mmhg. The overall effect of pressure on the integrated photon fluence is minimal with a maximum of 3% at 600 mmhg pressure and a minimum of 0.33% at 780 mmhg (Fig. 2). The low overall deviation of pressure on the photon fluence in spite of the high deviations at the lower energies is due to the fact that after filtration of the spectrum, the lower-energy

12 718 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) Table 4 Comparison of contributions of three arbitrary energy segments to the overall air kerma from a tungsten spectrum at 25 kvp, 0 C, 760 mmhg and 0% relative humidity with the tungsten target spectrum at the same tube voltage and corrected for temperature, pressure and humidity Contribution to air kerma (cgy) by energy range 6 8 kev Contribution to air kerma (cgy) by energy range 8 15 kev Contribution to air kerma (cgy) by energy range kev Air kerma (cgy) at Total contribution 1.32E mmhg, Percent contribution (%) C, 0% RH Air kerma (cgy) at Total contribution 2.42E mmhg Percent contribution (%) C, 40% RH % difference in air kerma due to P, T, H correction The overall percentage due to the combined effects of temperature, pressure and humidity is also shown. Overall difference in estimated air kerma (cgy) due to P, T and H correction=49.2%. component is removed hence its contribution towards the entire spectrum is reduced. The deviation pattern is similar for both molybdenum and tungsten targets (Figs. 3 and 4). The figures involved are however different. The effects on the tungsten target spectrum being lower than that from the molybdenum. The difference in the pressure effect on the molybdenum and tungsten targets is as a result of the molybdenum X-ray spectrum having many more lower-energy components when compared to the X-ray spectrum from tungsten Temperature The temperature effect on the photon fluence increases with increasing temperature. Below 10 kev, and for temperature range of 5 25 C, a deviation of 1 70% was calculated for the molybdenum target (Fig. 5). For the same energies, the deviation was about 5 120% at temperatures C. At temperatures above 40 C, deviations of 5% to more than 150% were observed for the same energy range. At energies greater than 10 kev, the deviations were much lower and ranged from less than 1 10% for the entire temperature range, 5 50 C. The overall temperature effect on the photon fluence from a molybdenum target yielded a deviation of % (Fig. 6). The patterns of the temperature effect on both the molybdenum and tungsten targets were similar (Figs. 7 and 8). The temperature effect was however lower for the tungsten target than for the molybdenum target. This may be attributed to the proportionally larger contribution from the low-energy components that are present in the molybdenum spectrum when compared to tungsten X-ray spectrum Humidity The humidity effects on the photon fluence for the molybdenum and tungsten targets were very low compared to the pressure and temperature effects. The deviations due to humidity effects on the entire energy spectrum of both the molybdenum and tungsten targets were less than 5% (Figs. 9 and 11) for the full relative humidity range, 0 100%, at all temperatures considered Pressure, temperature and humidity The photon fluence comparison (Table 1) showed that the effect of the pressure, temperature and humidity correction on the three arbitrary energy ranges chosen for the molybdenum target varied with the effect being highest (29.5%) in the lower energy range; 6.6% and 2.7% for the energy ranges 8 15 and kev, respectively. The overall difference in photon fluence of the molybdenum spectrum due to the correction for P, T and H was 4%. The overall difference was low in view of the fact that the contribution to the lower-energy segment of the spectrum from molybdenum is reduced due to filtration. The photon fluence comparison for the tungsten spectrum (Table 3) followed a similar pattern to the molybdenum spectrum with the overall difference even smaller. The results from the air kerma calculations of the molybdenum spectra (Table 2) indicate that at the energy range 4 8 kev, the combined effects of pressure, temperature and humidity is significant. The contribution of air kerma for this energy range to the air kerma of the entire spectrum is however negligible. The contribution to the calculated air kerma in the energy range 8 15 kev was 52% for the molybdenum spectrum

13 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) corrected for air density and 50% for the reference molybdenum spectrum. For the same energy range, the contribution to the calculated air kerma was 26% and 25% respectively, for the corrected and reference tungsten spectra (Table 4). The overall percentage difference in the estimated air kerma value due to the pressure, temperature and humidity correction at this energy range was 55% and 53%, respectively, for the molybdenum and tungsten spectra (Tables 2 and 4). For the energy range kev, the contribution to the estimated air kerma was 53% and 54%, respectively, for the corrected and reference molybdenum spectra; 79% and 80%, respectively, for the corrected and reference tungsten spectra. The overall difference in the estimated air kerma at this energy range, due to pressure, temperature and humidity correction was 48% for both the molybdenum and tungsten spectra. The overall difference in the estimated air kerma of the entire spectrum due to the combined effects of pressure, temperature and humidity was 52% and 49%, respectively, for the molybdenum and tungsten spectra at 0 C, 760 mmhg and 0% relative humidity shown in Figs. 14 and 16 (Tables 2 and 4), respectively. For the molybdenum spectrum, the air kerma difference contrasts significantly with the 45% overall difference obtained routinely by correcting for pressure and temperature only (Table 5). 4. Conclusion The investigation has shown that the effect of pressure on photon fluence of an X-ray spectrum from both molybdenum and tungsten targets are significant at Fig. 16. A comparison of the air kerma spectrum from a tungsten target at 25 kvp. (A) Spectrum at 760 mmhg, 0 C and 0% relative humidity. (B) Spectrum corrected for temperature (35 C), pressure (600 mmhg) and 50% relative humidity. Table 5 Comparison of change in the air kerma values obtained using normal temperature and pressure correction with values obtained from the correction procedure outlined in this study X-ray target material Predicted air kerma change (%) Expected air kerma change after normal P, T correction (%) Predicted Expected (%) Mo W

14 720 ARTICLE IN PRESS M. Assiamah et al. / Radiation Physics and Chemistry 68 (2003) photon energies less than 10 kev. Lower-pressure values showed higher deviations on the photon fluence at this energy range than higher-pressure values. Notwithstanding this observation, the contribution of the lowerenergy segment to the entire spectrum is reduced after filtration; hence, the overall deviation due to pressure of the integrated photon fluence was found to be small. It has also been established from this study that the temperature effect on photon fluence for both target materials are significant at the lower-energy segment of the X-ray spectrum. The temperature effect on the tungsten spectrum is however less than for the molybdenum target. The moisture content of the air has been found not to have any appreciable effect on photon fluence at any energy segment of the spectrum unlike temperature and pressure. The study has established that for high-altitude areas where air pressures are low, there could be a 4% difference in photon fluence when temperatures are high. It has also been established that for the same atmospheric conditions (low pressures and high temperatures) there could be a 50% overall difference in estimated air kerma values in mammography or low bremsstrahlung energy beam measurements unless the air density is corrected for pressure and temperature. The results presented suggest that unless air density is corrected for atmospheric conditions at the time of measurements, the overall difference in the estimated air kerma could be large. In the case of an X-ray spectrum with a high proportion of low-energy contributions, unless the effect of temperature, pressure and humidity on the photon flux is considered over the entire energy range, errors in kerma values significantly larger than values obtained after normal routine temperature and pressure corrections could result. This can partly be attributed, to changes in the photon fluence spectrum resulting from changes in atmospheric conditions and partly due to the influence of the energy and the linear energy-absorption product term ðe i Þðm en rþ; shown in Eq. (3). Acknowledgements The authors wish to express their gratitude to Dr. J. M. Boone, Dr. T. R. Fewell and Dr. R. J. Jennings who made available their molybdenum and tungsten anode spectral models used for this study. References Archer, B.R., Wagner, L.K., Med. Phys. 9, Assiamah, M., Mavunda, D., Nam, T.L., Keddy, R.J., Radiat. Phys. Chem. 67, 1 6. Attix, F.H., Introduction of Radiological Physics and Radiation Dosimetry. Wiley-Interscience, New York, pp Boone, J.M., Fewell, T.R., Jennings, R.J., Med. Phys. 24, Cember, H., Introduction to Health Physics (3rd Edition), McGraw-Hill, New York, pp Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., Rad. Phys. Chem. 60, Hubbell, J.H., Seltzer, S.M., Tables of X-ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 kev to 20 MeV for Elements Z=1 to 92 and 48 Additional Substances of Dosimetric Interest. National Institute of Standards and Technology, US Department of Commerce, Gaithersburg, MD Marion, J.B., Hornyak, W.F., Physics for Science and Engineering, Part 1. Saunders College Publishing, New York, pp Weast, R.C., Astle, M.J., Beyer, W.H. (Eds.), CRC Handbookof Chemistry and Physics, CRC Press, Boca Raton, FL, pp. F-9, F-10. Wolbarst, A.B., Physics of Radiology, International Edition. Appleton and Lange, Connecticut, USA, pp. 96,