ASSESMENT OF UNCERTAINTIES IN A DAILY-CHECK BEAM ANALYZER. J. Melgar, C. Martín, C. Montes, F. Sáez, E. De Sena, P. Gómez

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1 ASSESMENT OF UNCERTAINTIES IN A DAILY-CHECK BEAM ANALYZER J. Melgar, C. Martín, C. Montes, F. Sáez, E. De Sena, P. Gómez Servicio de Radiofísica y Protección Radiológica. Hospital Universitario de Salamanca. Pº San Vicente, Salamanca (Spain) Phone: mfbordes@usal.es Abstract. An evaluation of the theoretic uncertainties for the measurements of absorbed dose by the central ionization chamber of daily-check beam analyzer QC6 was made, with the aim of establishing an action level for the daily measurements of the cgy/mu factor in a Saturno-42 (GE-CGR) linac for low and high energy photons. Several factors were obtained from technical data reports of electrometer - chamber set. Other factors were evaluated from measurements. All these factors were used to estimate the type A and type B uncertainties. Uncertainties from measurements of thermometer and barometer were estimated too. Using the QC6 beam analyzer for the measurements, a relative measuring uncertainty of 1.1% was obtained, which is expressed at the level of two standard deviation (k=2). The tolerance for the cgy/mu calibration factor in a medical accelerator is established at ±2%, according to the Spanish regulations. So, the action level was set to a value of ± 3.1% to assure reasonably that the linac works properly. In addition, a reference level for the reading of the central ionization chamber of QC6 for both energies was found. This reference value was obtained with a relative standard deviation of about 0.6%. The previous action level has been applied over this reference value in order to set a tolerance range for the daily measurements. In order to verify that this tolerance range was consistent with the daily measurements in the linac, we checked that the measurements of the last year were included in the defined range. 1.Introduction In our department, we make the quality control of radiation beams from a Saturno-42 (GE-CGR) linac every day. We evaluate parameters like homogeneity, symmetry, cgy/mu factor and beam quality with the PTW-QC6 Plus beam analyzer. In this paper, we will only study the constancy of the cgy/mu factor for low and high energy photon beams (6 and 18 MV, respectively), with the aim of establishing an action level, i.e., an upper limit for the change of this factor, from the collected charge in the central ionization chamber of QC6 Plus, corrected by pressure and temperature. If the daily measure exceeds this action level, it is possible to assure that the linac does not work properly, and corrective actions should be taken to assure appropriate working of the linac. Although several authors have studied some kind of daily-check beam analyzer [1-4], only one of them estimates the associated uncertainties of these detectors. None of them sets an action level for daily measurements. 2. Description of the equipment and daily measurements According to technical data from this equipment, QC6 Plus has six ionization chambers of 0.54 cm 3 into a PMMA phantom in different geometrical positions. Five of them are placed at 5 mm depth from the surface; one of these chambers is in the centre of the phantom (D5), and the other four chambers (D1-D4) are in the two principal axis (at 8 cm from D5). The sixth chamber (D6) is in the centre of phantom at 27 mm depth from the surface. Daily positioning of equipment is done in a quick and easy way. QC6 Plus is connected to a PTW - MULTIDOS electrometer, and several PMMA sheets with different thickness (5 mm or 10 mm) are placed over QC6 Plus depending to the quality of the beam (1.5 cm for 6 MV and 3 cm for 18 MV). Also, there is a filter (PMMA or Pb) that can be placed between chambers D5 and D6, in order to evaluate the beam quality from readings of these chambers. In the case of photons, the Pb filter is used. The electrometer has a RS-232 output port, which allows to control its operation by means of a PC computer, with the QCWin application software. This application displays the measurements of 1

2 each ionization chamber of QC6 Plus in absolute mode or relative to central chamber values. QCWin also calculates symmetry coefficients on both axis, and homogeneity coefficients on the measurement plane from the readings of the five chambers in this plane. For the purpose of this paper, we only take into account the measurements of the central chamber D5, since its reading indicates the daily constancy of cgy/mu factor. QCWin application allows to introduce the values of pressure and temperature, so readings can be corrected by these parameters in order to avoid their influence in the collected charge. Measurement of atmospheric pressure is daily made with a portable precision barometer Lufft hpa, and temperature is measured with a digital thermometer Unitest Beha Full equipment is shown in fig. 1. FIG.1. Full equipment: Lufft barometer Unitest thermometer QC6 Plus Multidos electrometer For daily measurements, QC6 Plus is positioned at 100 cm from radiation source. A field size of 20 x 20 cm 2 at the isocenter is used. PMMA sheets with 1.5 cm of thickness for 6 MV or 3 cm of thickness for 18 MV are placed over detector surface. The equipment is irradiated with 200 MU per beam. 3. Establishment of the action level Action level is defined as the interval which amplitude is equal to the amplitude of the tolerance plus the expanded uncertainty, expressed at the level of two standard deviation (k=2). This uncertainty comes from the instrumentation and the method of measurement employed [5-6]. Therefore, it is important to delimit the uncertainty related to the equipment and the method. In addition, we must establish a reference value on which the action level is applied Analysis of uncertainties in measuring instruments and procedures We can separate the uncertainties associated to each instrument, i.e., QC6 Plus - MULTIDOS set, Lufft barometer and Unitest thermometer, to obtain the uncertainties associated to the following quantities: collected charge by chamber D5 of QC6 Plus (Q), atmospheric pressure (P), and temperature (T), respectively. The purpose is to find a total expanded uncertainty of Q* (being Q corrected by pressure and temperature effects, according to eq. 1) T (º C) Q * = Q (1) P( mb) Uncertainties in beam analyzer electrometer set measurements The main sources of uncertainty associated to QC6 Plus - electrometer set and method of measurement that have been considered are those shown in table I. Furthermore, the type of uncertainty, A or B (type A: uncertainties that can be evaluated from statistical methods; type B: evaluated from other means), the relative standard uncertainty for each one of them and the way of obtaining (experimental or not) are shown in this table too. Table I. Uncertainties associated to QC6 Plus - electrometer set. 2

3 Uncertainty Type of Relative standard uncertainty uncertainty (%) Way of obtaining Reproducibility A 0.07 Experimental Accuracy B 0.29 Reference manual Long term stability per year B 0.29 Reference manual Linearity B 0.29 Reference manual Leakage current B 0.03 Experimental Charge loss B Experimental Daily positioning B 0.15 Experimental All sources of uncertainty included in the reference manual of the equipment have been taken into account. A rectangular distribution have been considered in order to calculate the relative standard uncertainty [6-7]. Obtained values for leakage current and charge loss have been entered as uncertainty values [4]. Daily positioning is related to the uncertainty of position of chamber D5 with respect to the centre of radiation field in the daily placement of QC6 Plus. The value of this uncertainty is estimated placing the detector 2 mm besides and 2 mm underneath of the reference distance from radiation source (100 cm); then, the maximum difference of the measurements is modeled as lower and upper limits of a rectangular distribution. Another type of variations like displacement of detector D5 with respect to the centre of field have not been considered, since their influence is not relevant. From the values of relative standard uncertainty in table I, the expanded uncertainty [6-7] for Q is calculated, being equal to 0.53% Uncertainties in barometer measurements The main sources of uncertainty associated to Lufft barometer that have been considered are those shown in table II. Furthermore, the type of uncertainty, A or B, the relative standard uncertainty for each one of them and the way of obtaining (experimental or not) are shown in this table too. Table II. Uncertainties associated to barometer measurements. Type of Relative standard Uncertainty Way of obtaining uncertainty uncertainty (%) Accuracy B 0.05 Reference manual From the values of relative standard uncertainty in table II, the expanded uncertainty [6-7] for P is calculated, being equal to 0.05% Uncertainties in thermometer measurements The main sources of uncertainty associated to thermometer that have been considered are those shown in table III. Table III. Uncertainties associated to thermometer measurements. Type of Relative standard Uncertainty Way of obtaining uncertainty uncertainty (%) Accuracy B 0.2 Reference manual 3

4 From the values of relative standard uncertainty in table III, the expanded uncertainty [6-7] for T is calculated, being equal to 0.2%. The calculated values for uncertainties associated to the measurements of pressure and temperature are in agreement with the values estimated by other authors [6]. Resolution has not been taken into account as a source of uncertainty in none of these instruments, since we consider that manufacturer has included this parameter into the accuracy of the equipment in the reference manual Total combined uncertainty and expanded uncertainty. From combined uncertainties for parameters Q, P and T, the total combined uncertainty for parameter Q* is obtained, being equal to 0.57%. Therefore, the value of expanded uncertainty is 1.14%, which is expressed at the level of two standard deviation (k=2) Tolerance for cgy/mu factor The tolerance for the cgy/mu calibration factor in a medical accelerator is established at ± 2% according to the Spanish regulations [5] Reference value Date Table IV. Measurements to obtain a reference value. X 6 MV D5 values cgy/mu factor (f) D5 Values corrected for f=1 X 18 MV D5 values cgy/mu factor (f) D5 Values corrected for f= ,000 1,892 1,892 1,008 1,920 1, ,009 1,907 1,890 1,015 1,925 1, ,992 1,904 1,919 1,000 1,886 1, ,997 1,893 1,899 1,005 1,907 1, ,005 1,912 1,902 1,010 1,923 1, ,004 1,888 1,880 1,011 1,907 1, ,998 1,891 1,895 1,003 1,908 1, ,003 1,881 1,875 1,009 1,908 1, ,995 1,882 1,891 1,002 1,902 1, ,995 1,867 1,876 1,001 1,892 1, ,994 1,888 1,899 1,003 1,907 1, ,004 1,895 1,887 1,002 1,885 1, ,007 1,889 1,876 1,003 1,877 1, ,002 1,889 1,885 1,002 1,880 1, ,003 1,901 1,895 0,997 1,888 1, ,002 1,889 1,885 0,996 1,876 1, ,000 1,902 1,902 0,997 1,882 1,888 Average: 1,891 Average: 1,891 S.D.: 0,011 S.D.: 0,010 A reference value for the reading of the central chamber D5 of QC6 Plus for low and high energy photons (6 MV and 18 MV, respectively) was obtained. For this purpose, measurements of the 4

5 cgy/mu factor with an ionization chamber PTW (type Farmer) of 0.6 cm 3 were made, inserting the chamber into a water equivalent material. A relative standard deviation of about 0.6% was obtained. It is important to emphasize that this kind of measurement is made in our linac every Monday. In Table IV, values of cgy/mu factor measured at different days are shown. These values were obtained with an ionization chamber. These measurements are compared with those of QC6 measured the same day. The average value of the readings of the ionization chamber are corrected relative to f= This is taken as a reference value. 4. Results and conclusions From the calculated expanded uncertainty and the established tolerance, we can determine that the action level is ± 3.1%. Applying the action level to the reference value, a tolerance range for daily measurements of cgy/mu factor with QC6 Plus was established. To verify that the tolerance range is coherent with experimental values, measurements made over the last year were analyzed. All the measurements were within the interval. Measured values were out of action level only once. Corrective actions were taken, measuring the cgy/mu factor with a Farmer type ionization chamber for each beam quality and adjusting the gain of the monitor chambers. In Fig. 2, values of the readings of D5 on 2003 for both qualities are shown. Action levels and reference values are displayed in dashed lines. FIG.2. QC6 measurements on 2003 References 1. Lutz, W.R., Maddox, B.J., Kase, K.R., Daily check instrument for photon and electron beam quality assurance of medical linacs. Med. Phys., 12 (4); 462-5, (1985) 5

6 2. Muñoz, C., López, A., Gesto, C., Fernández, P., Arregui, G., Solana, V., Determinación de los rangos de variación aceptables de las medidas con el detector Hermes. Libro de Comunicaciones del VIII Congreso Nacional de la Sociedad Española de Protección Radiológica. Maspalomas, (2000) 3. Carmona, V., Lliso, F., Bea, J., Morata, B., Baños, M., Pérez-Calatayud, J., Experiencia con un nuevo analizador rápido del haz. Protocolo de controles asociado. Libro de Comunicaciones del XI Congreso Nacional de Física Médica. Valencia, (1997) 4. De Sena, E., Béjar, M.J., Cutanda, F., Martín J., Gómez, P.L., Herrera, M., Matilla, A., Puesta a punto de un equipo multidetector con cámaras de ionización para la verificación diaria de haces de radiación. Libro de Comunicaciones del XII Congreso de Física Médica. Santander, (1999) 5. Real Decreto 1566/1998, de 17 de Julio, por el que se establecen los criterios de calidad en radioterapia. B.O.E. nº 206 de 28 de Agosto; , (1998) 6. Curso de Metrología y calibración en radiaciones ionizantes y en el área de la Radiofísica Hospitalaria. Organizado por la SEFM. (2002). 7. Granados, C.E., Andreo, P., Brosed, A., Lizuain, M.C., Sáez, C., Gultresa, J., Incertidumbres y tolerancias de la dosimetría en radioterapia. Curso SEFM organizado en el Hospital Central de Asturias, (1997) 6