British Journal of Radiology (2006) 79, 347-352
© 2006 British Institute of Radiology
doi: 10.1259/bjr/54848398
Study of scattered radiation for in-air calibration by a multiple-distance method using ionization chambers and an HDR 192Ir brachytherapy source
N P Patel, MSc, DipRP1,
B Majumdar, MSc, PhD, PDC2 and
V Vijayan, MSc, DipRP, PhD3
1 Department of Medical Physics, Acharya Harihar Regional Cancer Centre, Cuttack-753007, India, 2 Department of Physics, Government College of Science, Raipur-492010, India , 3 Health Physics Unit, Institute of Physics, Bhubaneswar-751005, India
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Abstract
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The aim of this study is to estimate the room-scatter correction when measuring air kerma rate of an HDR 192Ir brachytherapy source by in-air calibration. The variation in scattered radiation due to the specially designed jig and from the room walls was also studied. Two therapy ion chambers of volume 0.1 cm3 and 0.6 cm3 were used in the present study. Air kerma was measured by placing the source at several distances between 10 cm and 20 cm from the chamber. The scatter radiation was determined by superimposing the theoretically derived model curve of known scatter (based on the inverse square law) over the plot of measured air kerma strength values. The scatter radiation was estimated in terms of percentage of the primary radiation at 10 cm measurement distance. The scatter estimated by the 0.6 cm3 chamber at two positions was 0.33% and 0.59%, respectively. Similarly the scatter estimated at two other positions by the 0.1 cm3 chamber was 0.58% and 1.11%. This variation in scatter with position as well as with the chamber was due to the varying scatter contribution from components of the measurement set-up. The scatter radiation becomes constant at a distance greater than 100 cm from the walls of the room. We conclude that a fixed chamber with changing source positions should be used in multiple-distance measurement of air kerma rate when using a measurement jig.
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Introduction
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Calibration of brachytherapy sources is an end-user requirement prior to clinical use. The recommended quantity for specifying a brachytherapy source is the air kerma strength (AKS) [1]. Air kerma strength is defined as the product of air kerma rate at a calibration distance, d, in free space, K(d), measured along the transverse bisector of the source, and the square of the distance, d. A source calibration accuracy of ±3% relative to existing AKS standards seems reasonable [2]. At present, high dose rate 192Ir sources are widely used for brachytherapy treatment due to their high specific activity and low effective photon energy.
Calibration of an HDR 192Ir source is performed by in-air measurement or by a solid phantom technique using a thimble chamber. An alternative method is to use a well-type chamber. An IAEA technical document has discussed several factors including measurement distance, chamber size, positioning uncertainty, charge leakage and room scatter to be considered for in-air measurement [3]. The measurement distance should be chosen such that the combined uncertainty in source calibration due to other factors can be minimized. The optimum measurement distance estimated for a Farmer-type chamber with an HDR 192Ir source is 16 cm [4]. Experimental studies have estimated the room scatter using a large volume spherical chamber (3.6 cm3) by multiple-distance measurement from 10 cm to 40 cm in a specially designed jig [5, 6]. The ESTRO guidelines recommend minimizing the positioning uncertainty and scatter contribution using a calibration jig with source positions at a distance of 10 cm from both sides of a centrally placed 0.6 cm3 Farmer-type chamber [7]. The Monte Carlo study found that the assumption of constant room scatter over the measurement distance is not valid and that in-air measurement needs correction for accurate estimation of AKS [8].
The calibration jig is designed to hold the ionization chamber and source applicator for in-air measurement. Although several factors that might affect the source calibration have been taken care of in designing the jig, the contribution of scattered radiation seems significant. The aim of the present study is to estimate the scattered radiation by a multiple-distance method using therapy level ionization chambers. The variation in scatter radiation inside the jig and from the walls of the measurement room is discussed.
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Methods and materials
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We have used a slightly different method in the present study to estimate the scattered radiation from that used by earlier experimental studies [5, 6]. In air measurement, the measured air kerma (Md) at distance d is the sum of the primary (Mp) and scatter (Ms) radiation, i.e. Md = Mp+Ms. The primary radiation (Mp) follows the inverse square law and the scatter radiation (Ms) is a constant. The product of Md and the square of the distance d is a variable quantity which is denoted by f(d) and expressed by Equation (1).
The f(d) values for different source to chamber distances were normalized with respect to the f(d) value at minimum measurement distance and plotted against d. The scatter (Ms) shown in Equation (1) is unknown but can be determined by generating an equivalent curve from theoretical calculation.
In the theoretical calculation, the air kerma from primary radiation Ep at minimum measurement distance was taken to be one and the inverse square law was used to calculate the air kerma at all other true measurement distances d' = d+
, where is the offset error in measuring the initial nominal distance d. The offset error is due to the offset positioning of the chamber (
) and source (
), i.e. = +. The variable quantities F(d) were determined using Equation (2):
The scatter value Es was assumed constant over the range of measurement distance. The curve of normalized F(d) values vs distance d was generated by choosing the value of Es such that:
then Ms = Es
The condition as described in Equation (3) was accomplished when the theoretical curve F(d) was fitted to the measured normalized f(d) curve. It is evident from Equation (2) that for a constant value of Es, different curves of F(d) vs distance can be generated for primary radiations Ep with different offsets . In the present study, nominal distances d for measurement of air kerma (Md) were chosen between 10 cm and 20 cm. Calculation was performed using Excel Workbook (Microsoft Corporation).
A simple mathematical formula was derived to show the relationship between the scatter levels and ratio of air kerma for constant distance at two different positions inside the room. If r is the ratio of measured air kerma from unknown to known scatter position, air kerma from primary radiation (Mp) and the scatter at two positions are (Ms) and (Ms'), respectively, we can express the unknown scatter by
The GammaMed Plus brachytherapy unit with an HDR 192Ir source supplied by MDS-Nordion Haan GmbH, Germany (at present Varian Medical Systems) was used in this experiment. Two different therapy ion chambers (volume 0.6 cm3 and 0.1 cm3) with UNIDOS dosimeter from PTW – Freiburg, Germany were used. The wall thickness and build up cap (60Co beam) of the 0.6 cm3 chamber were 0.054 g cm–2 and 0.547 g cm–2, respectively. The wall thickness of the 0.1 cm3 chamber without any build up cap was 0.12 g cm–2.
Figure 1
shows the specially designed measurement jig. The dimensions of the jig were about 30 cm x 20 cm x 27 cm and it was made up of non-scattering low Z materials of acrylic plates and wooden frames. Figure 2a shows the lateral view of the measurement set-up. The chamber holder was mechanically fixed at positions A and B in the jig whereas the applicator holder was shifted linearly along the track. A fine laser beam was projected over the jig to verify the sagittal, transverse and coronal cross-sections planes. Two parallel scale systems aligned with the help of laser beams were used to determine the measurement distance and the vertical position of the source applicator. A laser beam and magnifying glass were used to determine the offset position () of the central axis of the chamber with the scale system. Figure 2b shows the positioning of the centres of the chamber and source with respect to the measuring scale. The source applicator (inner and outer diameter of 1.35 mm and 1.65 mm, respectively) can be placed at any scale pointer with an accuracy of about ±0.01 cm.
A plan view and the dimensions of the brachytherapy treatment room used in the present study are shown in Figure 3. The wall of the treatment room is made of concrete (density 2.35 g cm–2). The figure indicates the location of measurement at the centre of the room and other locations used to study single and double wall scattering effects. The contribution to scattering from the walls at the centre of the room was assumed negligible. The locations of measurement for the wall effect study were at various distances from 12.5 cm to 125 cm from the single wall (square marks) and as well as from two walls (circle marks) as shown in the Figure 3.
First, the jig was placed at a height of 120 cm from the floor at the centre of the room. The 0.6 cm3 chamber was fixed at position A in the jig. The source applicator was placed 1 cm from the chamber. Successive measurements were taken by vertical scanning of the source to determine the reference dwell position where the chamber shows maximum response. In the vertical scanning, the source was moved to dwell positions (stepping size of 0.2 cm) along the applicator. The reference dwell position where the chamber shows maximum response lies on the transverse axis that passes through the centre of the source as well as chamber. For measurement of air kerma, the source applicator was placed at measuring distance and the source was moved to the reference dwell position. Air kerma was measured for 100 s. A similar procedure was followed for measurements at other distances. The nominal distances (d) were 10 cm, 12 cm, 14 cm, 16 cm, 18 cm, and 20 cm. At each nominal distance, five source offset positions ( = –0.4, –0.2, 0.0, +0.2, and +0.4 cm) were taken. Air kerma measurements at offsets of 10 cm distance were repeated as their readings were used for normalization. Hence 30 values of air kerma at different source to chamber distance were measured. Measured values were corrected for air attenuation and non-uniformity due to chamber size [9]. Transit time correction was not required as the dosemeter timer was used to collect the charge during an interval after the source stopped moving. The leakage current was negligible. A change in temperature and pressure was monitored and successive corrections were made. The offset of the chamber position () was determined to calculate the total offset () as shown in Figure 2b
. The scattered radiation Es was estimated as per the methodology described in the text using a computer. A similar procedure was followed to estimate the scatter for the 0.6 cm3 chamber at position B. In the case of the 0.1 cm3 chamber, a similar procedure (except the stepping distance was 0.1 cm and air kerma measurement period 200 s) was used to estimate the scatter at positions A and B.
The jig was placed at different locations (circle and square marks) successively as shown in Figure 3 to study the scatter effects from the walls of the room. A similar procedure was followed to estimate the scattered radiation at every location by taking 18 air kerma measurements (only for three offset positions of the source) with the 0.6 cm3 chamber placed at position A in the jig. The scatter radiation vs distance from the single and double wall was determined.
The relationship given in Equation (4) was verified experimentally. The estimated scattered radiation Ms at the centre of the room for the 0.6 cm3 chamber at position A in the jig was taken as the reference value. The estimated scattered radiation at other locations (taken as Ms') was used to calculate the ratios of air kerma r (relative ionization) for the locations to the centre of the room. To verify the accuracy of calculated relative ionization (r), the air kerma for constant source to chamber distance was measured at the centre of the room and the other locations.
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Results
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The maximum response of the 0.6 cm3 and 0.1 cm3 chambers was found at different source dwell positions 6.8 cm and 5.4 cm from the end of the source applicator, respectively. This means that the heights of the effective centres of the chambers from the base of the jig differed by 1.4 cm. Reproducibility (n = 5) of our measurement by repositioning of the source applicator was within 3%, 1%, and 0.1% at measurement distances of 1 cm, 5 cm, and 10 cm, respectively. The linearity of the dosemeter within the range of 10–200 s was 0.01% for the 0.6 cm3 chamber and 0.02% for the 0.1 cm3 chamber.
Figure 4 shows the plot of normalized f(d) values from measured air kerma (dots) and theoretically derived F(d) (lines) vs nominal distance d for different offsets () for the 0.6 cm3 chamber at position B. It shows that the plot of measured f(d) values are best fitted by the theoretical curves of corresponding offsets () with varying scatter components Es of the primary at a measurement distance of 10 cm. The mean of these scattered components Es was 0.59±0.06%. This means that the measured air kerma has a contribution from scatter (Es) of about 0.59% of the primary radiation at 10 cm distance and the scatter quantity is assumed to be constant over the range of measurement distance.
The estimated scattered radiation in terms of percentage of primary radiation at 10 cm measurement distance for both the chambers at positions A and B is shown in Table 1. These results were obtained with the jig placed at the centre of the room. The uncertainty in the positioning of chamber was about ±0.02 cm, which resulted in uncertainty of ±0.1% in the estimation of scattered radiation. The scatter measured by the 0.6 cm3 chamber at position A was 0.33% and when the chamber was moved inside the jig by 2 cm at position B, the measured scatter level increased to 0.59%. Similarly the scatter radiation measured by the 0.1 cm3 chamber at positions A and B was 0.58% and 1.11%, respectively. Even if the uncertainty in chamber position is taken into account, our results show a variation in the scattered radiation over the different measurement positions inside the jig. There is also a significant difference between the results for the 0.1 cm3 and 0.6 cm3 chamber. It should, however, be noted that the centres of the chamber volume were located at different heights. An additional chamber holder, which was very close to the chamber volume in measurement with 0.1 cm3, could have increased the scattered contribution.
Figure 5a shows the scattered radiation as a function of distance from a wall in single and double wall scattering, estimated by multiple-distance measurement using the 0.6 cm3 chamber at position A. It is observed that the scattered radiation becomes constant at about 0.33% at distances greater than about 100 cm from the walls for both single and double wall scattering. A steady increase in scattered radiation was observed below 50 cm from a single wall and 75 cm from the double wall. At 12.5 cm from the wall, scattered radiation was estimated at 2.0% and 2.7% of the primary for single and double wall, respectively.
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Figure 5. (a) Estimated scattered radiation as a function of distance from the wall in double and single wall scattering by multiple-distance measurement using the 0.6 cm3 chamber at position A inside the jig. (b) Deviation in measured relative ionization from the calculated value as a function of distance from wall for both the chambers (DW, double wall; SW, single wall). The measurement distances were 12 cm, 16 cm, and 18 cm. The calculated relative ionizations were determined from estimated scattered radiations using the 0.6 cm3 chamber.
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The deviation in measured relative ionization from calculated relative ionization as a function of the distance from a single and double wall for the 0.1 cm3 and 0.6 cm3 chamber is shown in Figure 5b. The calculated relative ionizations were determined from the estimated scattered radiation at different locations using the 0.6 cm3 chamber as shown in Figure 5a. Results show that calculated relative ionization is in good agreement with measured relative ionization with most of the deviations within ±0.5% for both the chambers.
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Discussion
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The chamber used in the present study was fixed and the source applicator was moved to different positions. The accuracy of positioning of the source applicator was about ±0.01 cm. Displacement of the source inside the applicator was crucial in the measurement as it has a smaller diameter (0.9 mm) than the inner diameter of the applicator. Displacement of the source was not observed during reproducibility measurements at any reference position when performed by repositioning the applicator. However, when the applicator was moved to another position, the source was displaced laterally due to movement of the source guide tube. The maximum error in setup distance may increase by up to ±0.032 cm as a result of the combined effects of source displacement and applicator positioning. In order to minimize the uncertainty in the estimation of the scattered radiation due to positioning error, we have considered five offset positions of the source. The mean of scattered values from five offsets was calculated. The standard deviations in the measured f values (after correction of scatter) were found to be well within 0.2% and 0.3% for the 0.6 cm3 and 0.1 cm3 chamber, respectively.
Measurements were also compared with the three-equation solution technique described earlier by other authors [5, 6]. It was observed that the shape of the curve derived from Equation (3) contains a unique pair of scatter (Es) and offset () values. The solution technique was found to be very sensitive to measurement error. For example, a deviation of ±0.2% in air kerma values from primary radiation (without any scatter contribution) at five distances gives the scatter value from –0.8% to 0.65% using the solution technique. However, in the present analysis, the estimated scattered radiation was found to be well within ±0.1%. IAEA guidelines recommend that offset values determined from the solution of the three equations should not vary by more than ±0.1 cm [3]. This limit can be retained only if the deviation in measured f values (after correction of scatter) is about ±0.03%. Therefore, in the solution technique, separations between measurement distances must be very precise. In the present method, variation in separation is managed by curve fitting but it is essential to know the measurement distance for accurate estimation of scatter radiation.
The air kerma at any point is the sum of primary and scatter radiation. If the multiple-distance method is used then constancy of scatter over the measurement distance is essential for its precise estimation. Our results show that in addition to the constant scatter contribution from the room, the components of the jig also contribute significantly to scatter, which varies from position to position inside the jig. A large difference in scatter values between positions A and B shows a high gradient scatter field over the inner to outer area of the jig. The curves in Figure 4 show that the measured f(d) values of each offset were in "best fit" with the theoretical curve F(d), if the scatter gradient over the central area of the jig is assumed to be low. This means the variation in scatter contribution to the chamber from multiple source positions is negligible. Therefore, a measurement set-up with a fixed chamber position should be chosen to minimize the variation in scatter inside the jig for the multiple-distance method.
The optimum distance for a Farmer-type chamber to give minimum combined uncertainty effect from several factors was found at 16 cm [4]. IAEA recommends measurement at multiple distances between 10 cm and 40 cm [3]. In general, the calibration jig is required for the multiple-distance measurement, thus requiring estimation of scattered radiation for the local conditions. In case of the Farmer-type chamber, the measurement distances should be selected around the optimum distance of 16 cm and a separation of 2 cm between distances is sufficient to give satisfactory results for the multiple-distance method. If a larger range of measurement distances is used, the variation in scatter from the jig could enhance the uncertainty in estimation of scatter radiation as well as air kerma rate.
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Conclusion
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This study suggests that a fixed chamber with changing source positions should be used in multiple-distance measurement of air kerma rate when using a measurement jig. The source should be placed at different positions over a short-range around the optimum measurement distance of 16 cm for the Farmer-type ionization chamber. Scattered radiation estimated from above method remains unchanged for the reproducible measurement set-up, which makes the procedure of frequent source calibration very simple.
Received for publication December 7, 2004.
Revision received September 28, 2005.
Accepted for publication October 3, 2005.
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References
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Abstract
Introduction
