Health Physics Pergamon Press 1975. Vol. 28 (June), pp. 751-754. Printed in Northern Ireland

MONTE CARL0 CALCULATIONS OF SCATTERED X-RAYS FROM SNYDER PHANTOMS L ~ S Z LKOBLINGER ~

Health Physics Department, Central Research Institute for Physics, P.O. Box 49, 1525 Budapest, Hungary (Received 25 February 1974; aceeped 27 September 1974)

Abstract-Monte Carlo calculations are performed to determine the intensity of diagnostic X-rays scattered at 90' from human phantoms. The X-ray source is placed at 90 cm from the centre of the body while the phantom to detector distance is 1 m. Both the homogeneous and inhomogeneous Snyder phantoms are irradiated by an X-ray tube operated at 110 kVp with 3 mm A1 filtration. The field size is 14 in. x 17 in. (35.6 cm x 43.2 cm). The ratio of the exposures of the scattered and primary beams is about 3 x The shapes of the spectra of the primary and scattered photons are similar to each other; only the very low and high energy photons are missing from the scattered beam. The calculated results are compared with published measured data. INTRODUCTION

the Snyder phantoms. The irradiation circumstances for the two models are given in Figs. 1 and 2. The water block chest-phantom is assumed to be irradiated by a parallel beam while the Snyder phantoms are examined by photons emitted from a point source. The size of the irradiation field is 14jn. x 17 in. (35.6 cm x 43.2 cm), the phantom to detector distance is 1 m in both cases and the source to phantom distance is 90 cm in the second model. Naturally, the modelling for the Snyder phantoms is closer to the clinical METHOD conditions but the study of the water block can A computer code DISDOS (KOBLINGER,provide interesting data for a n estimation of the 1971) has been written for Monte Carlo simula- effects due to dilferences in irradiation circumtion of photon histories in the homogeneous or stances and patients' measures. A further inhomogeneous Snyder phantoms (SNYDERet advantage of the water block phantom is that al., 1969). This program can be used, after its simple geometry enables a certain analytical some modifications, for the determination of the check of the computer program. radiation scattered a t right angles from the Ideally a point detector should be considered phantom. (Hereafter scattered radiation means but as in the code DISDOS the actual surface always the radiation scattered at right angles.) crossing events are encountered, there is no The program follows the photon paths stepappropriate statistics on too small detector areas. by-step from the emission to the absorption or I n our model four detector areas are used (see escape. The energy of a photon is assumed to Figs. 1 and 2); the first is a 20 cm x 43.2 cm be totally absorbed in site of the collision if it parallelogram while the second to fourth decreases below 5 keV and in case of photo- detectors are circles having diameters of 20, 10 electric interaction. and 6.67 cm, respectively. The best approxiThe photon interaction cross-sections are mation of a point-like detector is the smallest taken from tables of HUBBELL (1969). circle but on that area the statistic is the MODELS poorest. The input spectrum of a typical diagnostic Two kinds of phantoms are considered: a simple rectangular block filled with water, and unit operated at 110 kVp with a filtration of

FORTHE protection of people working in clinical laboratories where X-ray examinations are carried out the knowledge of the intensity and the spectrum of the scattered radiation is very important. By the Monte Carlo calculations described in the present paper both the spectrum of the radiation scattered from some phantoms and the ratio of the scattered and primary intensities are determined.

7

75 1

752

CALCULATIONS OF SCATTERED X-RAYS FROM SNYDER PHANTOMS Poral lel

beam

FIG.1. Irradiation circumstances to the simple chest-phantom.

Energy,

keV

FIG.3. The spectra of the incident and scattered beams. (The curves are normalized for the same total numbers of photons.) Continuous graph: approximation of the incident spectrum. spectrum of the photons Histograms: scattered from the homogeneous Snyder phantom; - - - - spectrum of the photons scattered from the inhomogeneous Snyder phantom.

-

FIG.2. Irradiation circumstances to the Snyder phantoms.

3 mm A1 is used for our calculations. Our approximation of the emission spectrum measured by WAGGENER et al. (1972) is given in Fig. 3. The Monte Carlo program chooses the energy of each photon randomly but in accordance with the emission probabilities represented by this spectrum. RESULTS

To check the scattering and path length selecting routines of the program the intensity

of the photons that reach the detector after a single collision is calculated both analytically and by the code, for the block phantom. The analytical formulation for the calculation of the single scattered radiation is given by KOBLINQER (1974). For photons that have the most probable energy of the spectrum : 46 keV, the analytically calculated ratio of the exposures of the single scattered to primary photons is 9 x The ratio calculated by the Monte Carlo program with the same input data is 8.29(f 1.17) x lo-' and 9.57(&2.07) x lo-' on the first and second detector areas, respectively. (The standard deviations are given in the parentheses. O n the

753

L. KOBLINGER

third and fourth areas the coefficients of variation are greater than 40%, so those results are statistically uncertain, and thus useless.) The results obtained analytically and by the code are in good agreement. For the two energies where the emission probability is half of that a t the peak: 31 and 6 1 keV, the analytically calculated ratios are 5 x lo-' and 10.7 x respectively. The decrease of the ratio a t low energies is stronger than the increase a t high energies, in accordance with the fact that the cross-sections (the photoelectric and thus the total) vary more a t Iow energies. Therefore it is expected that for the real input spectrum the scattered ratio will be lower than for the 46 keV photons. Really, the Monte Carlo calculation carried out with source energy sampling from the spectrum gives about 6-7 x (Table 1). The Monte Carlo calculated ratios of the exposures of all the scattered photons to the primary photons are summarized in Table 2. From among the three phantoms considered the largest scattered ratio is achieved by using the homogeneous Snyder phantom. In the inhomogeneous model the scattering is lower due to the presence of the low density lungs (0.3 g/cm3 in contrast with the average 1 g/cm3). The ratio computed for the rectangular block is lower than the ratios obtained for either

Snyder phantoms where some photons of the divergent beam (Fig. 2) enter at the edge of the phantom and these photons can reach the detector after only a short flight in the absorbing medium. This assumption is verified by the fact that the contribution of the single scattered photons (Table 1) to the total scattered intensity (Table 2) is higher for the Snyder phantoms than for the rectangular chest-phantom. Another reason for the higher scattering from the Snyder phantoms is that they scatter photons not only from the directly irradiated parts but also from other parts of the body. I n Fig. 3 the spectra of the scattered photons are presented besides the incident spectrum. The coefficients of variation are between 16-25 % for the medium energy groups (30-60 keV) and higher for the groups lying outside this range. The spectra of the scattered photons are very similar to the primary spectrum. The average energies ('Table 1) of the scattered photons in the different cases hardly differ from each other and even from the average incident energy. Naturally the very low energy photons are missing from the scattered beam as they are absorbed with high probability. Thus the average photon/cm2 to R conversion factors, which also characterize the shapes of the spectra, are significantly less (Table 2) for the scattered photons, as the conversion factor of, say, a

Tab& 1. Th ralios of fhc cxposurt of tht single scallntdphofons lo fhpn'mmj infmnfies.(Incidmf 110 kVp, 3 mm Al.) The sfandard druialions arc giwn in pumfhnes

No. I

beam:

Scattered ratio in loa, on the detector a r m No.2 No. 3 No. 4

Parallel beam, rectangular b l d

0.593 (f0.007)

0.762 (fO.165)

Statistically uncertain

Statistically uncertain

Point source, horn. Snyder phantom

I .5a (f0.14

I .36 (f0.22)

1.73 (34.47)

2.01 (f0.75)

Point source, inhom. Snyder phantom

1.21

1.43

(39.15)

(*OW

1.77 (f0.64)

-

__

Statistically uncertain

Table 2. Tk raws of tk exposurrs of rhr acatlncdphdons fo Ihcpn'mary i n l u i t j and the aunagc rncrgier and photon/cm' to R ronarrrion farfors. The rfandard dtoialionr art giuen in pmrn/hcses Scattered ratio in

No. I ~

~~

~~~~~

on detector areas

No. 3

No. 4

Average Average conversion energy factor (keV/photon) (10 -11 R.cmz/photon)

~

Parallel beam, rectangular block Point iource, horn. Snyder phantom Point source, inhom. Snyder phantom - -

No.2

2.42 ( +0.15)

3.62 ( f0.19)

3.02 (fO.22)

2.57 (3~0.26)

2.31 (f0.49)

4.12 (*0.66) 2.76 2.96 (f0.36) (f0.73) Incident beam/llO kVp; 3 m m

3.35

( f 0.3 1)

I .58

40.4

4.67

(*0.58) 4.15

49.1

4.84

3.77 (+1.33)

50.6

4.58

A1 filter/:

51.C

5.59

(Zk0.W

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CALCULATIONS OF SCATTERED X-RAYS FROM SNYDER PHANTOMS

20keV photon is nearly 5 times higher than angle (WAGGENER, 1973) and thus intercepted for a 46 keV photon. Both the average energies photons scattered from the X-ray table may be and conversion factors are calculated on the the reason for another fraction of the measured whole detector (first area). 6 6 surplus” scattering. COMPARISON WITH MEASURED RESULTS

WAGGENER et al. (1973) and TROUT and KELLEY(1972) have published scattered ratios measured for similar cases. WAGGENER et al. (1973) used the same geometry and input spectrum as we used for the calculations, the only difference is that they used a n Alderson Rando phantom. From the data published by TROUT and KELLEY (1972) the measurements carried out by the radiation of a tube operated at 100 kVp with 2.5 mm A1 (very close to our 110 kVp, 3 mm Al) can be compared to our results. The source-to-phantom and phantomto-detector distances are again identical with that used for the calculations, the field size is also 14 in. x I 7 in. but it is measured on the film surface, therefore their beam is slightly narrower. The scattering medium a t the measurements of Trout and Kelley was a tissue equivalent homogeneous elliptical cylinder torso. In both papers the measured scattered spectrum is found to be very similar to the primary spectrum with the lack of the lowest energy photons and this fact is confirmed by our calculations (Fig. 3). The scattered ratios of 4.6 x 10” measured and KELLEY (1972) are in fairly good by TROUT agreement with our 3.5-4 x lo” calculated for the homogeneous phantom (Table 2). Waggener et al. published a measured which is higher scattered ratio of 2.99 x than either the other measured or the calculated value by a factor of about 8. A part of this discrepancy can be caused by the difference between the phantoms considered but as our comparison shows, even for the extreme rectangular block chest-phantom, the choice of the phantom hardly changes the scattering more than by a factor of 2. The fact that in this experiment the detector viewed a large solid

CONCLUSIONS

O u r Monte Carlo calculations on the scattered X-rays confirmed the measurements and KELLEY(1972) and showed, by of TROUT the comparison of the ratios calculated for the homogeneous and inhomogeneous Snyder phantoms, that in chest examinations the radiation scattered from the inhomogeneous body is less than the scattering from a homogeneous phantom by about 30% due to the presence of the low density lungs. Acknowledgements-The author wishes to acknowledge (The Unithe comments of Dr. R. G. WAGGENER versity of Texas, Health Science Center at San Antonio) and the encouragement of Mr. I. FEHBR (Head of the Health Physics Department, CRIP). REFERENCES

HUBBELL J. H., 1969, Photon Cross-Sections, Attenuation Coefficients, and Energy Absorption Coefficients from 10 keV to 100 GeV. NSRDSNBS 29, Report of the National Bureau of Standards, Washington, D.C. KOBLINGER L,, 1971, Two Codes for Calculation of Dose Distribution in Human Phantoms Irradiated by External Photon Sources. KFKI-71-12, Report of the Central Research Institute for Physics, Budapest. KOBLINGER L., 1974, Photon Beam Scattering at Right Angles from Rectangular Phantoms. Analytical Approximation for Single Scattering. KFKI-74-81, Report of the Central Research Institute for Physics, Budapest. SNYDER W. S., FORDM. R., WARNER G. G. and FISHERH. L., 1969, MIRD Pamphlet No. 5, J . nucl. Med. 10, Suppl. 3, pp. 5-52. J. P., 1972, Radiology 104, TROUTE. D. and KELLEY 161. WAGGENER R. G., LEVYL. B., ROGERS L. F. and P., 1972, Radiology 105,169. ZANCA WAGGENER R. G., 1973, Private communication. WAGGENER R. G., LEVYL. B. and ZANCAP., 1973, Health Phys. 24, 59.

Monte Carlo calculations fo scattered X-rays from Snyder phantoms.

Health Physics Pergamon Press 1975. Vol. 28 (June), pp. 751-754. Printed in Northern Ireland MONTE CARL0 CALCULATIONS OF SCATTERED X-RAYS FROM SNYDER...
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