Comparison of measured and calculated absorbed doses from tangential irradiation of the breast

Radiotherapyand Oncology, 7 (1986) 81-88 Elsevier

81

RTO 00235

Comparison of measured and calculated absorbed doses from tangential irradiation of the breast T o m m y Kn66s, Lars Ahlgren and Mats Nilsson Department of Radiation Physics, Maim6 Allmdnna Sjukhus, S-214 O1 Malta6, Sweden

(Received 2 April 1985, revisionreceived 17 March 1986, accepted 19 March 1986)

Key words." Breastcancer; Tangentialtreatment; Radiationtherapy; Dose planning; Phantommeasurements

Summary Calculated absorbed dose distributions from tangential irradiation of the breast have been compared with TLD measurements in a anthropomorfic body-shaped phantom which has gone through all phases of the radiation treatment planning cycle, including mapping of electron densities with a CT scanner, simulation of beam set-up and several treatments with an accelerator. The absorbed doses, measured in the breast are 2-6% lower than those calculated with the clinically used treatment planning system. The deviation is slightly higher when wedges are used. The main source for this deviation is shown to be the limitations in the lossof-scatter correction in the dose calculation algorithm used. It has also been noted that the variation of the absorbed dose in the target volume is in general smaller than predicted by the calculations.

Introduction An important step in the development of a new treatment technique in radiation therapy is the comparison between the obtained dose distribution in the patient during a sequence of treatments and the distribution calculated by the treatment planning system clinically used. With a well functioning measuring system an investigation of this kind is easily performed. It can also be used for evaluation of different dose calculation algorithms. Different irradiation geometries can be used, for instance a cubic water-equivalent phantom with slab-shaped inhomogenities [9] or a body-shaped

anthropomorfic phantom with substitutes for soft tissue, lung and bone tissues. A typical verification protocol consisting of, for example, normal and oblique incidence with and without wedges has been proposed [7]. In this work, measurements of the absorbed dose distribution in an anatomical phantom (Alderson Rando Phantom) have been performed. Using this phantom, it is possible to proceed through all stages in the dose planning process including CT scanning, simulation and several treatments with the accelerator. This procedure will also include positioning and set-up uncertainties. This investigation will present the overall differences between calculated absorbed dose distribu-

0167-8140/86/$03.50 9 1986ElsevierSciencePublishers B.V. (BiomedicalDivision)

82 tions and the distribution obtained in the patient during a treatment course, except from patient movements during simulation and treatment. Tangential treatment of breast cancer after breast-saving surgery [4,8, I 1] involves large corrections for different electron densities and large variations in the patient outline over the irradiated volume. The corrections are dependent on the treatment technique used at the specific radiation therapy centre. In this investigation, two opposing 6 MV X-ray fields, tangentially applied and with the longitudinal axis parallel to the thoracic wall, are used. Using this technique, a large portion of the beam will not enter the patient. The lack of scattering tissues and the oblique incidence will create further problems for the algorithms to calculate the absorbed dose distribution in the patient (phantom).

Materials and methods

Thermoluminescent dosimeters ( TLD ) The absorbed dose measurements were performed with hot pressed LiF chips (3 • 3 • 1 mm3), calibrated in a cubic Lucite phantom (200 • 200 • 80 mm 3) at 5 mm depth to ensure full build-up when irradiated by a 6~ The dosimeters were individually calibrated in groups of 20, and were kept in the same group to ensure as identical irradiation history as possible. The absorbed dose to the TLDs was approximately 1.5 Gy when calibration was performed. Every calibration cycle started with thermal treatment at 400~ for one hour in order to restore all electron traps in the LiF crystal. The TLDs were always heated to 400~ for 10 min prior to the exposure at measurement, thus giving the dosimeters the same initial conditions before irradiation. The fading sensitive traps were emptied at 135~ and the signal was integrated at 2650C. A calibration cycle involved three irradiations, each followed by read-out. The criteria to use the dosimeters for measurements was that the quotient of absorbed dose/signal ratio between two consequtive irradiations should

have a coefficient of variation less than 2% for the entire TLD group. For each measurement, three TLDs were randomly selected from each group as reference dosimeters. These dosimeters were irradiated under the same condition as when they were calibrated and the differences obtained were assumed to be representative for the whole group of dosimeters. If the reference TLDs differed more than 5% from their individual calibration factor, a new calibration cycle was initiated.

Body-shaped phantom Polystyrene slices (2 mm thick) with cavities for the dosimeters, were placed between the slices of the female Rando phantom. The cavities were of the same size as those used in the calibration phantom, giving the same irradiation geometry for calibration and measurements. The slices with the T L D chips were placed at levels corresponding to the upper axilla (18 cavities for TLDs were used) and the nipple of the breast with 26 TLDs in the thoracic wall. The breast volumes were constructed from 3 mm thick polystyrene slices to a total thickness of 30 mm and were applied to the phantom onto the surfaces used for the non-suitable breast supplied by the manufacturer. In the treated breast volume the dosimeters (94) were placed in cross-sections parallel to the main section, with a spacing of 25 mm, in order to determine if the main cross-section is representative of the dose distribution in adjacent planes. Thus, when irradiated, the phantom contains 138 dosimeters.

Dose planning and irradiation technique The patients are treated in supine position with the arms placed over their head. An overview, using the simulator is done to determine the position of the main cross-section which will be used for dose calculation, usually the cross-section through the nipple of the breast. A polyurethane foam-shell (density < 0.05 g 9 cm -3) was manufactured in order to reproduce the treatment position during the whole treatment period. CT-scanning for dose planning with the patient in the polyurethane foam-

83 shell is then carried out. The Rando-phantom has been handled using the same procedures as those for a patient. In this particular case, a set of scans, every 25th mm, was acquired, which will make dose calculation in any cross-section through the target volume possible. In patients, the target volume will include the remaining parenchyma of the breast gland, all operation scars including any drainage channels with adjacent parts of the thoracic wall. A margin of 5 mm between the target volume and the skin surface is used except in regions with scars and/or drainage where the target extends to the surface. Tissues "at risk" are the lung and the skin over the target volume. The irradiation is performed using two opposed 6 MV X-ray fields, tangentially applied and rotated

in order to follow the curvature of the thoracic wall in the treatment region, cf. Fig. 1. The treatment technique is isocentric with the isocenter placed midway between the field-entrance points. The focus-isocenter distance is 1000 mm. Absorbed dose calculations are done with the SIDOS-U2 dose planning system. The patient outline and the electron densities which are used for the dose calculations are based on CT scans. In short, the algorithm is as follows: from measured depth doses, scaled to a focus-phantom distance (SSD) equal to infinity, for quadratic field sizes between 30 x 30 mm 2 and 350 x 350 mm 2 and six profiles at different depth for each field size, the dose to a point at depth d and at a distance r from the central axis for a field size o f A, is calculated by:

D(d,r,A) = k(d, SSD) P(d~ff,A~q) O(d,r,A) W(d,r,A) Dweage

/ ( S

i I }

\

>' \-- -

x~

Fig. 1. Cross-sections through tile axillae (upper half) and the breast (lower hal 0, determined by CT on the Rando phantom with the auxiliary breast phantom applied. The " ~ " represents both the points of measurements and the points of calculation. The field sizes used are 105 x 220 mm 2 and the " O " is the isocenter point (focus-isocenter distance is equal to 1000 ram).

k(d, SSD) = inverse square law correction of the stored depth dose to the actual SSD for the ray between the point of calculation, POC, and the Xray source, k(d, SSD) = [(SSD + dm)/(SSD + d)] 2 where d~ is the depth of dose maximum, i.e. the build-up depth. P(deef,Aeq) = the depth dose, interpolated for the effective depth, deerfrom the stored depth-dose values. The field size, used, is the equivalent area, A,q for the effective field size A~fe. The effective depth dcff is determined as the water equivalent thickness of the tissues between the POC and the beam entrance, i.e. the actual depth, d is replaced by the sum of the product between the thickness of each tissue layer and its relative electron density [5]. No further correction for inhomogenities is implemented in the dose planning system. The inhomogenity correction algorithm is thus of the one-dimensional type. O(d,r,A) = the off-axis ratio, i.e, the ratio between the absorbed dose D(d,r,A) at the POC and the absorbed dose D(d,O,A) at a point at the same depth, d but on the central axis of the beam, thus

O(d,r,A) = O(d,r,A)/O(d,O,A). W(d,r,A) = the ratio between the off-axis ratio

84 for a wedged and an open beam, i.e. W(d,r,A) =

Results and discussion

Owedge(d,r,A ) / Oope.( d,r,A ). Dwedge = correction factor for the influence on the depth dose along the central ray due to the filtration of the X-rays in the wedge. (The factor is unity when no wedge is used.) The actual field size of a beam, A is always corrected to an effective one, Aeff such that the portions of the beam that passes by the outer contour of the patient is subtracted from the real field size. This correction, using the field size, is one way to try to correct for the decrease of scatter from the areas outside the patient but inside the beam to points inside the patient. Then this effective field size is converted to its corresponding equivalent square area field size, Aeq which is equal to 4 times the area divided by the perimeter of the beam. This size is used as the depth dose value is determined. The calculations are always made in a 140 x 100 matrix giving a resolution for a typical patient size, 350 x 250 mm, of 2.5 x 2.5 ram. The maximum possible displacement of the position of the dosimeter in relation to the point of calculation is 1.75 mm. Conversion of CT numbers, N , (Hounsfield units) to electron density, Pe (number of electrons per unit volume) are performed according to the following formula [6]: For CT number, - 1 0 0 0 < N . < 150 p. = [3.31 + 3.33 10 -3 NH] 102a (electrons/cm 3) For CT number, NH > 150 Pe = [3.64 + 1.30 10 -a Nn] 1023 (electrons/cm 3) The coefficients in the equations applies only to the CT scanner, used ( S O M A T O M 2). The fields were set-up using the simulator in the same way as for patients. Eight treatments were then performed, four with open fields and four with 15~ wedges. During the treatments, an external dose-monitor was used for monitoring variation in the delivered dose. The monitor was calibrated for quadratic fields from 50 x 50 to 350 x 350 mm 2 to give 1.0 G y at the depth of dose maximum.

The results of the measurements are presented in Fig. 2 as ratios of measured to calculated absorbed dose. The mean ratio of all four treatments are; the axillary region - - 0.79 and 0.93, the thoracic wall - - 0.98 and 0.94 and for the breast volume - - 0.94 and 0.92 for open fields and fields with wedge filter, respectively. (Only three measurements where evaluable in the axillary region due to malfunction o f the dosimetry equipment.) All ratios are less (28%) than the expected value (unity). If measurements in the build-up region are excluded the ratios in the main cross-section o f the breast reduces to 0.91 and 0.89, respectively. Tissue-air ratio (TAR) calculation of the absorbed dose to a point on the central axis at a depth o f 30 mm in the main crosssection (i.e. in the centre o f the breast volume) is performed as comparison. The effective field area used is assumed to be given by the actual field length (220 mm) and a field width which is the mean distance between the patient outline and the medial boundary of the field in the main cross-section. This effective field width is found to be approximate half of the real field width (54 mm compared to 105/2

Measured abs dose/Calculated abs. dose (~

~

open fields

wedged I

~ fields

Treatment Region

3 Axillary re ion

1111111 2

3 4

Thoracic wall

1 2

3

4

Breast volume

Fig. 2. Histogram showing the ratio of the measured and the calculated mean absorbed dose in the axillae, thoracic wall and the breast volume for both the open and wedged fields.

85 mm). Thus the absorbed dose to the point is, D = Do 9 TARreduced where Do is the absorbed dose to the same point but with the phantom removed and TARreduced is given by: TARreduced =

T A R .... +

0.5 [TARlarge -

TAR .... ]

(Indices represent field sizes, i.e. 54 x 220, 0 x 0 and 105 x 220 mm z, respectively.)

This expression is evaluated with values which are linearly interpolated from the literature [3] for both 6 MV, as used in the experimental part of this investigation, and for 6~ and is compared with the dose given by a similar calculation but with a TAR-value for the "large" beamarea at the same depth. A 3% lower dose for the 6 MV case and 6% lower for 6~ is obtained. Monte Carlo calculation of central axis depth-dose curves for 6 MV

TABLE I The measured absorbed doses in five slices, separated 25 mm, through the treated breast volume, for open and wedged treatment technique, in the Rando phantom. Slice through the breast volume

Absorbed dose (Gy) Open fields

Cranial 50 m m

Mean Cranial 25 m m

Mean Main cross-section

Mean Caudal 25 m m

Mean Caudal 50 m m

Mean Whole breast volume Calculated dose Deviation

No. of dosimeters Wedged fields

0.919 0.919 O.952 0.931 0.930

0.904 0.886 O.9O8 0.919 0.904

14

0.92I 0.932 0.926 0.918 0.924

0.912 0.900 0.903 0.911 0.907

20

0.911 0.908 0.900 0.906 0.906

0.905 0.874 0,901 0.883 0.891

26

0.921 0.895 0.901 0.918 0.909

0.911 0.881 0.902 0.894 0.897

20

0.933 0.880 0.913 0.902 0.907

0.901 0.880 0.901 0.873 0.889

14

0.915 0.972 -- 5.9%

0.898 0,976 - 8.0%

94

The doses relate to 1 Gy given as mean target dose in the breast. The calculated dose is the mean value of the measurement points calculated by the dose planning system.

86 X-rays [13] shows that 8% of the dose at a depth of 4 cm is due to at least one time scattered photons for a 60 x 60 mm 2 field. This scatter fraction is increased to 17% for a field size of 200 • 200 mm 2. Our results confirm with these findings. The correction for loss o f scatter used by the treatment planning system results in a change in the dose values at 3 cm depth of less than 1% for the beam size used. Thus, a better loss-of-scatter correction in the dose planning system is desirable. Table I shows the measured absorbed dose in different slices through the breast volume. As shown in this table, the mean absorbed dose to the main cross-section, which is used for dose planning, is representative for the slices cranially and caudally to this section. The deviations from the calculated absorbed doses are overall larger when wedges are used, 6 - 8 % compared to 2 - 6 % without wedges. These findings are in agreement with other works, for example [12] in which it is reported that tangentially applied fields may give an overestimation of the dose calculation of up to 8%, but in the same work, it is also stated that the use o f wedge filters in general may underestimate the dose calculations by up to 10%, especially when the field impinges obliquely. The latter fact is not supported by this investigation. The total variance of the measurements is assumed to consist of three parameters: (a) The variance of the actual dose distribution in the phantom, a~. (b) The variance o f the reproducibility of the treatments, at2. This variance includes for example, the accuracy of the phantom positioning and the field set-up. (c) All other variances, a 2 contributing to the total variance, specially the variance of the dosimetry system including handling and calibration routines. Thus each measured value, x, in a region with a mean absorbed dose o f 2, is assumed to be the sum o f three parts as given in the following equation: x = N(X,~d) + N(0,a,) + N(0,~s)

where N(#,a) is a random value from the Gaussian distribution with a mean value of # and a variance of a 2. The mean values for the variation in treatment and for the measuring system are naturallly assumed to be zero, i.e. no systematic errors and due to their random behaviour, a Gaussian distribution can be expected. The distribution of dose values is not obviously Gaussian, but since the aim of the dose planning is to achieve as uniform dose as possible in the target volume, the distribution of dose values usually can be approximated with a Gaussian. The contribution of the latter two variances, at and as are very important to keep as small as possible and a way to estimate their contribution from the measured data to the total variance o f the measurements is the method of analysis of variance, A N O V A [2,10,14]. The results are presented in Table II. The variances as well as the mean value of the calculated dose distributions are, for comparison, shown in Table III. Only points corresponding to the measuring points are included in these values. The experimentally obtained variances (Table II) are smaller than the variances o f the calculated dose distributions (Table III) in all regions except in the axilla. These differences are mainly due to the dose calculation algorithm's rather crude way of compensating for different electron densities and oblique incidence. The reproducibility of the treatments is very high with a coefficient of variation in the order of 1%. As this investigation has been carried out with a phantom, patient variation in outline during the treatment course is not included. The measuring system shows a variance in the order of 5% which includes the whole process from calibration of the 6~ with an ionization chamber to the read-out of the T L dosimeters.

Conclusions The measured absorbed doses in the whole target volume are in general lower, 2-6%, than calculated levels and the differences are larger (up to 8%) when wedges are used as beam modifiers. The measured dose distribution also shows a smaller vari-

87 TABLE II Coefficient of variation" for the measured dose distribution, the treatment and the measuring system, together with the total. Field technique

Open

Wedge

Region

Coefficient of variation (%)

Axillab Thoracic wall Breast Axilla Thoracic wall Breast

Dose distribution

Treatment

System

Total

36.5 16.1 6.9 14.8 21.6 5.3

0.6 1.0 0.3 1.3 1.2 1.0

5.7 7.5 4.3 5.1 5.2 4.8

36.2 17.6 8.1 15.4 21.9 7.2

a The c.v. is defined as the square root of the estimated variance divided by the grand mean. b Only three treatments are included in the values for the combination open field and the axilla region due to a malfunction of the dosimetric system. The variance calculations are based on measurements from four treatments.

ation than the calculated one. The limitation of the dose calculating algorithm used is the main source for these discrepancies. Promising steps have been reported in the literature to develope more accurate methods. One of the most interesting is the method using Fourier transforms to convolute the primary absorbed dose distribution with one (or several) scattering kernel(s) [1]. The use of analysis of variance has proven to be a usable method to extract the different contributing uncertainties present in

TABLE III The mean absorbed doses in the measured regions calculated with a computerized dose planning system. Irradiation technique

Axillary region

Thoracic wall

Breast volume

Open fields Wedged fields

0.969 (16%) 0.988 (15%)

0.867 (34%) 0.901 (33%)

0.972 (9.5%) 0.976 (9.6%)

The absorbed dose is calculated in the same points as the TLDs were placed in and the mean value is determined for all the points of measurement. The absorbed doses are given per 1 Gy as mean target dose to the whole treated volume represented by the main cross-section (through the nipple of the breast). The values between parentheses are the coefficient of variation for each region.

an experimental situation, especially when determining the total variance of the measuring system and the variance of the repetition of the experiment. The latter is a very important parameter to control when results from several experiments are used.

Acknowledgements This work was supported by grants from The Allm/inna Sjukhuset In Malm6 Foundation for Cancer Research and Treatment. The technical assistance given by Miss Christel Andersson is also acknowledged.

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