Generalized EPID calibration for in vivo transit dosimetry

Article Outline

• Abstract
• Introduction
• Material and methods
  • Linacs equipments
  • Transit dosimetry method for the isocenter dose reconstruction
    • Mid-plane dose measurements
  • The aSi EPID
    • EPID signal reproducibility and long term stability
    • EPID calibration
    • Ghosting effect
    • Transit signal field size dependence and f(TPR,d,L) empirical factors
  • Diso reconstruction
• Results
• Discussion
• Conclusions
• References
• Copyright

Abstract 

Many researchers are studying new in vivo dosimetry methods based on the use of Elelctronic portal imaging devices (EPIDs) that are simple and efficient in their daily use. However the need of time consuming implementation measurements with solid water phantoms for the in vivo dosimetry implementation can discourage someone in their use.

In this paper a procedure has been proposed to calibrate aSi EPIDs for in vivo transit dosimetry. The dosimetric equivalence of three aSi Varian EPIDs has been investigated in terms of signal reproducibility and long term stability, signal linearity with MU and dose per pulse and signal dependence on the field dimensions. The signal reproducibility was within ±0.5% (2SD), while the long term signal stability has been maintained well within ±2%. The signal linearity with the monitor units (MU) was within ±2% and within ±0.5% for the EPIDs controlled by the IAS 2, and IAS 3 respectively. In particular it was verified that the correction factor for the signal linearity with the monitor units, k_lin, is independent of the beam quality, and the dose per pulse absorbed by the EPID.

For 6, 10 and 15MV photon beams, a generalized set of correlation functions F(TPR,w,L) and empirical factors f(TPR,d,L) as a function of the Tissue Phantom Ratio (TPR), the phantom thickness, w, the square field side, L, and the distance, d, between the phantom mid-plane and the isocentre were determined to reconstruct the isocenter dose.

The tolerance levels of the present in vivo dosimetry method ranged between ±5% and ±6% depending on the tumor body location.

In conclusion, the procedure proposed, that use generalized correlation functions, reduces the effort for the in vivo dosimetry method implementation for those photon beams with TPR within ±0.3% as respect those here used.

Keywords: In vivo dosimetry, EPID calibration, Quality assurance, Radiotherapy

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Introduction 

In these last years, several groups have published experiences of in vivo transit dosimetry performed by different detectors as ionization chambers [1], [2] and electronic portal imaging devices (EPIDs) [3], [4], [5], [6], [7]. All these experiences have assessed that the transit dosimetry on the beam central axis can be a valuable tool to detect errors in the radiotherapy treatment that can be summarized in four categories [7] 1) errors occurred in the treatment planning stage, 2) errors occurred in the data transfer from treatment planning system (TPS) to the beam delivery unit, 3) errors due to the functioning of the radiotherapy equipment (including the beam calibration), 4) errors due to the patient's set-up and organ motion.

Nowadays the elective detector to perform the in vivo transit dosimetry is the EPID because it is simple to manage during the patient's treatment, and can supply bi-dimensional information. In particular the behavior of Varian aS500/1000 EPIDs (Varian Medical Systems, Palo Alto, CA) has been investigated in terms of signal linearity, signal reproducibility, ghosting effect and signal dependence on the field size [5], [8], [9]. These papers have assessed that the EPIDs are suitable for routine in vivo dosimetry verifications.

Recently the present authors have developed an in vivo dosimetry method for the 3D Conformed Radiotherapy (3D CRT) based on correlation functions obtained by the ratios between the transit signals, measured by an aSi EPID positioned behind water phantoms of different thicknesses and the phantom mid-plane doses, measured by an ion-chamber positioned along the beam central axis [5]. The method has been applied for the in vivo dosimetry of head, thorax, pelvic and breast tumors [10], [11], [12] with tolerance action levels ranging between 5% and 6% depending on the body district in which the tumor is present. However, such as for all the transit in vivo dosimetry methods [3], [4] also the procedure proposed by the present authors requires specific measurements for every beam that can discourage someone in its use. Indeed even if the recent Varian models have very similar Tissue Phantom Ratio indexes (TPR_20,10) [13] (within ±0.3%) for the same nominal megavoltage (MV), the aSi EPID sensitivity can change for different therapy units.

The aim of this work has been the determination of a generalized procedure to calibrate aSi Varian EPIDs for in vivo dosimetry with 6, 10 and 15MV photon beams. In particular in this paper the calibration procedure has been applied to three EPIDs using their DICOM images obtained at a fixed Source to EPID Distance (SED). The dosimetric characteristics of the three EPIDs were evaluated in terms of signal reproducibility, signal linearity with the Monitor Unit (MU) and dose per pulse and signal dependence on the field dimensions. Therefore generalized correlation functions F(TPR,w,L), (dependent on the TPR_20,10, here named TPR, the phantom thickness, w, and the square field size, L) and empirical factors f(TPR,d,L) (that account for the different contributions of the scattered photons on the transit signal per MU, s_t, as a function of the distance, d, between the phantom mid-plane and the isocenter) were obtained averaging the data supplied by the three EPIDs.

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Material and methods 

Linacs equipments 

In this work, three Varian linacs, supplying overall six photon beams of 6MV, 10MV and 15MV, and equipped with multileaf collimators existing of 120 leaves have been used. All the measurements were performed with the MU rate used clinically equal to 400MU/min.

The x-ray beams have been calibrated in water phantom following the IAEA protocol [13] and a dose per MU equal to 1cGy/MU was imposed at the depth of maximum dose, d_max, with the Source to phantom Surface Distance (SSD) coincident with the Source to Axis Distance (SAD) equal to 100cm. The reference dose measurements were performed with a calibrated ionization chamber PTW Farmer type model TM31010 (0.6cm³) in combination with an electrometer PTW Tandem (PTW Freiburg, Germany).

The quality index of each beam was obtained as the ratio between ionizations [14] measured in the water phantom at the water depths of 20cm and 10cm respectively (here named TPR), with an uncertainty of ±0.3%. Table 1 reports the linac models, the photon beams supplied by each linac and the relative TPR values.

Table 1. Varian linac models, photon beams available and relative TPRs. For the EPID systems the image detection unit (IDU), the image acquisition unit (IAS) and arm models are also reported.

Transit dosimetry method for the isocenter dose reconstruction 

The method proposed by the present authors in a previous work [5], for the reconstruction of the in vivo dose, D_iso, at the isocenter point, is based on correlation functions defined as the ratios between the transit signals per MU, obtained by an aSi EPID positioned below a solid water phantom and the dose per MU values measured along the beam central axis at phantom mid-plane coincident with the SAD. The measurements needed to implement the method are described in detail in the previous paper [5]. In particular, Fig. 1a shows the experimental set-up used to determine the mid-plane doses per MU, D(TPR,w/2,L), and the transit signals per MU, s_t(TPR,w,L), measured at the Source to EPID Distance (SED), while Fig. 1b shows an experimental set-up used to measure the transit signals per MU s_t(TPR,w,L,d) when the phantom mid-plane was shifted of a distance, d, from the SAD. These last values were used to determine the empirical factors f(TPR,d,L) that takes into account the variations of the scattered photon contributions on the EPID due to the different phantom position as respect to the SAD.

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• Figure 1 

  Solid water-phantom set-ups used to measure the phantom mid-plane doses per MU D(TPR,w/2,L), and the EPID transit signals per MU s_t(TPR,w,L) and s_t(TPR,w,L,d). w is the phantom thickness, L is the side of the square filed and the SED is the Source to EPID Distance equal to 159cm a) Reference configuration with the phantom mid-plan at the source to axis distance SAD=100cm. The ion chamber (●) was positioned at the phantom mid-plane to determine D(TPR,w/2,L), while s_t(TPR,w,L) was measured in the point (○) b) the phantom mid-plane is at the distance, d, below the SAD. The dose, D_iso, at the isocenter point can be obtained by equation (15); c) phantom set-up used to determine D_SAD at the depth, d_max, of the maximum dose for a 10×10cm² field.

A correlation function F(TPR,w,L), defined as

has been determined for each square field of side L and beam quality TPR as a function of the solid water phantom thickness w.

The empirical factor f(TPR,d,L) was defined by the ratio

as a function of w and L for distances, d, varying in the range of ±7cm. The factors f(TPR,d,L) were independent of w within ±0.5% as reported in a previous work [5], therefore their values were obtained averaging the data obtained with different phantom thickness for fixed TPR, d, L values.

In conclusion referring to Fig. 1a and b, the dose (TPR,w_iso,L) at depth w_iso could be determined by

where s_t(TPR,w,L) is the EPID transit signal and the is the ratio between the Tissue Maximum Ratios evaluated at the depths, w_iso, and w/2, respectively. The accuracy of equation (3) was estimated equal to ±4.5% also in inhomogeneous phantoms where, w, was obtained in terms of radiological thickness [1], [5].

The correlation functions F(TPR,w,L) obtained in the previous paper [5] had to be determined for every linac beam because they depend on the MU calibration, and the EPID sensitivity variations as a function of the MU rate, dose per pulse and field dimensions. The aim of this work is to define generalized correlation functions, dependent on the beam quality index TPR, that can be used for aSi Varian EPIDs with dosimetric characteristics equivalent to those of the EPIDs here used.

Mid-plane dose measurements 

The solid water phantom, used in this work, was an RMI model 457 (Gammex, RMI Middelton, WI) consisted of 30×30cm² square slabs of various thicknesses.

The phantom mid-plane doses per MU, D(TPR,w/2,L), in terms of cGy/MU, have been obtained, for open and wedged square fields equal to 4×4cm², 8×8cm², 10×10cm² 12×12cm²,16×16cm² and 20×20cm² and with three 6MV, two 10MV and one 15MV photon beams. The wedged fields were obtained with hard wedges of 15°, 30° and 45°. Phantoms of thicknesses equal to 10, 22, 30 and 42cm were irradiated delivering 100MU.

The same PTW Farmer ion-chamber connected to the Tandem electrometer, used to calibrate the linac beams, was also used to measure the phantom mid-plane dose.

A water equivalency correction factor k_WE for the phantom was determined as the ratio between the chamber reading in natural water and that in solid phantom, at the same linear depth of 10cm for the 6MV, 10MV and 15MV photon beams with a field 10×10cm² in size. So the ion-chamber reading was multiplied for the water equivalency factor, k_WE to obtain the dose to water by dose measurements performed in the phantom.

The dose per MU values, D_SAD (Fig. 1c), measured for the field 10×10cm² positioning d_max at the SAD, (assumed as reference condition for the correlation functions determination), can differ from centre to centre even if the same IAEA [13] protocol is used. To take into account this problem a factor k₀, for every beam was defined as

where D_SAD⁰=1cGy/UM. This way multiplying D(TPR,w/2,L) by k₀a set of dose per MU values D⁰(TPR,w/2,L), in terms of cGy/MU, independent of the MU calibration adopted by the centre can be obtained. In other words for every couple of (w/2,L) the dose per MU obtained by the equation (5) resulted dependent on the TPR index only.

The aSi EPID 

The Varian EPID system, described in detail elsewhere [15], [16], includes (i) an image detection unit (IDU) featuring the detector and accessory electronics; (ii) an image acquisition unit, IAS interfacing the hardware that controls and reads the IDU; (iii) a dedicated workstation (Portal Vision PC). The models, of the IDUs, IASs and arms are reported in Table 1 for the three aSi EPIDs used in this work. All the IDUs worked with matrixes of 512×384 pixels with a resolution of 0.784×0.784mm² and with a total sensitive area of about 40×30cm².

The measurements performed to determine the correlation functions were obtained at an SED equal to 159cm. This distance was chosen to ensure the EPID to rotate around the couch during the treatments and because this distance is common with other linacs (as those manufactured by Elekta) that use a fixed SED. This way in future could be examined the accuracy of the present method also for aSi EPID supplied by different manufacturers.

In this work the integrate image acquisition mode was used for all the EPID measurements, i.e. the imaging starts with beam-on and stops when the beam turns off. The acquisition software is the Varian Vision version 7.3.10 SP3 that stored two-dimensional grayscale images determined as the averaged over all the subframes measured during the irradiation [15]. The final image is automatically corrected for individual pixel sensitivity, dead pixels, and dark current by the acquisition software as reported by Van Esch's paper [15]. The images were exported as DICOM files to be analyzed by Spyglass Transform version 3.0 (Spyglass Inc). The pixel values, S′(x,y), localized in the (x,y) PEID position, were subtracted from offset numbers equal to 16,384 (2¹⁴) and 32,768 (2¹⁵) for the images supplied by the IAS 3 and IAS 2 respectively. Thus they were multiplied by the number of subframes to obtain integral signal values, S(x,y), proportional to the MU delivered. At the end, the EPID integral signals along the beam central axis, S, were obtained averaging the pixel values, in terms of arbitrary unit (a.u.), determined within an EPID central region of 0.4×0.4cm². Moreover the S values were corrected for daily machine monitor output variations.

EPID signal reproducibility and long term stability 

The reproducibility and long-term stability of the EPID signal per MU, s, have been investigated for each beam positioning the EPIDs at an SED=159cm. Six portal images of a field 10×10cm² (at the SAD) were acquired delivering 100MU one time a week during a period of about 6 months. For each beam the mean value, (in terms of a.u./MU) over the measurement performed during the first month was determined. The long-term reproducibility was expressed as the standard deviation of the s values as respect to the value. The EPID signal reproducibility was evaluated as the average standard deviation of the six measurements performed for each session.

EPID calibration 

A sensitivity factor k_s, in terms of cCU/a.u., for every beam, has been determined by

where was obtained for each beam during the first month of the long term stability evaluation. In other words, multiplying by k_s a signal per MU, s⁰, equal to 0.3956 cCU/MU was imposed for every EPID and x-ray beam quality in reference condition. EPID sensitivity changes greater than a tolerance level of 2.0%, have been taken into account determining new k_s factors.

Ghosting effect 

The ghosting effect of the aSi EPID may be distinguished as two separate effects both due to the trapped charge in the photodiodes [17], [18] that are the image lag and the change in sensitivity with the dose per pulse absorbed by the EPID. The Image lag is a signal delay, so charges generated during the acquisition of one image frame are read out in subsequent frame acquisitions, adding an offset to the signal in subsequent recorded frames [18]. In particular the signal delay could be explained considering that some charges produced during the irradiation are stored in shallow trapping states and then emitted after a certain time interval. Previous works have studied image lag by measuring the residual signal in the dark field, lasting in the order of minutes following beam off [17], [18]. In this work the lag effect was investigated performing measurements of integral signal, S, at SED=159cm and SED=105cm, as a function of the MUs for the six beams available using a 10×10cm² fields (at the SAD). This way the image lag was investigated for two doses per pulse values (obtained varying the SED), and for the three beam qualities delivering MU between 50 and 400MU. A correction factor k_lin for S has been defined as

where s₁₀₀ and s_N are the signals per MU obtained for 100MU and for a number N of monitor units respectively.

The second type of ghosting effect is due to the change of the EPID sensitivity as a function of the dose per pulse. This last effect was investigated delivering 100 MU with a field 10×10cm² (defined at the SED) for all the six photon beams. The EPIDs were positioned at different SEDs ranging between 105cm and 159cm. Dose values were measured positioning the ion-chamber at a water equivalent depth equal to d_max and at distances from the source equal to the SEDs used for the EPID irradiations. Average dose per pulse, p, and the EPID signal per pulse, z, values were obtained dividing the dose and S values for the pulse repetition frequency equal to 240Hz and for the beam delivering time equal to 15s (for 100MU). In order quantify the EPID reading dependence on the dose per pulse, the following expression was used [19]

where β is a constant and Δ is a fitting parameter that depends on the EPID signal non linearity as a function of p. In particular Δ is greater than one when the EPID shows an over-response, and less than one if the EPID shows an under-response.

Transit signal field size dependence and f(TPR,d,L) empirical factors 

The s_t(TPR,w,L) were measured by the three EPID at an SED=159cm for open and wedged fields of sizes 4×4cm², 8×8cm², 10×10cm² 12×12cm²,16×16cm² and 20×20cm² and with the six photon beams available. The wedged fields were obtained with hard wedges of 15°, 30° and 45°. Phantoms of thicknesses equal to 0, 10, 22, 30 and 42cm were irradiated delivering 100MU.

The Farmer ion-chamber, positioned in the solid water phantom at depth d_max, and at distance from the source equal to 159cm, was irradiated (without interposed phantom) delivering 100MU for square fields of different dimensions. The s_t(TPR,w,L) values were used both to determine the correlation functions and to evaluate the dependence of the EPID signal on the field size. For this last purpose the ion-chamber and EPID data were normalized to the respective signals acquired for the field 10×10cm² to obtain the output factors. Thus the EPID normalized output factors obtained for open beams were compared with those measured by the Farmer ion-chamber.

Measurements of the s_t(TPR,w,L,d) values were carried out positioning the phantom mid-plane below and above the SAD at distances, d, up to ±7cm, as a function of w and L. These last data were used determine the f(TPR,d,L) factor defined by the equation (2).

The transit signals per MU s_t(TPR,w,L) were multiplied by, k_s,

obtaining s_t⁰(TPR,w,L) values independent of both the MU calibration and the EPID sensitivity, and dependent on the TPR index.

D_iso reconstruction 

The mid-plane doses per MU D⁰(TPR,w/2,L) and the transit signals per MU s_t⁰(TPR,w,L), were used to obtain the ratios

in terms of cCU/cGy. Of course these generalized correlation functions were independent on the MU calibrations and for a fixed couple of w and L parameters the ratios were only dependent on the TPR. In particular the F(TPR,w,L) values have been fitted by the functionwhere A(L), B(L) and C(L) are fitting parameters dependent on L, while w [cm] is taken dimensionless.

The A(L) and B(L) parameters were fitted, as a function of L, by third order polynomials, while C(L) was fitted by a linear function

where a_i, b_i and c_i (i=0, 1, 2, 3) are the coefficients of the polynomial functions.

By equation (3) the dose D_iso(TPR,w_iso,L) in cGy for a generic x-ray beam quality index TPR can be rewritten as

where s_t(TPR,w,L,d) is the transit integral signal in terms of a.u., F(TPR,w,L) is obtained by the equation (10), and f(TPR,d,L) is the factor defined by equation (2). s_t(TPR,w,L), obtained for a generic MU number, is converted by the sensitivity factor k_s in cCU is corrected by the k_lin factor that accounts for the image lag and is divided by k₀ factor that accounts for the MU calibration adopted for the specific beam.

In clinical practice, the parameters, w, w_iso, and d, present in equation (15) can be obtained following two steps i) the patient's CT scan is used to measure, along the beam central axis, the patient's geometrical thickness, t, the distance, d, and the isocenter depth, d_iso; ii) the calibrated CT numbers are used to determine the mean relative electronic density along the patient's thickness, t, and d_iso (that are generally supplied automatically by the TPS). Therefore, the water-equivalent thicknesses, w and depth w_iso can be determined as the product of t and d_iso by the respective relative mean physical densities, obtained by the linear relation between the electronic density and physical density [20]. The equivalent square field, L×L, is supplied automatically by some TPSs, otherwise it can be obtained by the Sterling approximation [21].

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Results 

The s reproducibility was within 0.5% (2SD), while the, s, long-term stability was within ±1.5% (2SD) for the 6MV, 10MV and 15MV beams while a tolerance level equal to ±2.0% was assumed for the EPID sensitivity variation. This means that when the EPID sensitivities showed variations greater than ±2.0% new k_s were determined. In particular the three EPIDs were recalibrate only one time each during the six months.

Table 2 reports the k_WE, k_s and k₀ factors determined for the 6MV, 10MV and 15MV x-ray beams. The uncertainty of k_WE was of 0.4% (2SD), while the k₀ uncertainty was assumed equal to two standard deviations of the daily machine monitor output variation i.e. 1.6% (2SD).

Table 2. k_WE , k₀, k_s and Δ values determined for the of 6MV, 10MV and 15MV photon beams supplied by the three Varian linacs.

The data reported in Table 2 show that, for a given beam quality, the k_s values obtained by the images supplied by the IAS 2 EPID were about 40% higher than those obtained for the image supplied by the IAS 3 EPIDs because the image offset values were different as mentioned in Section 2.3. The k_s variations with the beam quality can be explained considering the different beam attenuations due to the copper plate positioned above the EPID sensitive matrix.

Since the correlation functions F(TPR,w,L) have been obtained delivering 100MU, the factors, k_lin, (equation 7) have been determined to correct an s_t(TPR,w,L,d) obtained with a monitor unit value different from 100MU. The k_lin values were independent of the beam quality within the experimental uncertainty of ±0.3% therefore their values were determined averaging the data obtained by EPIDs controlled by the same IAS model for the different beam qualities. Table 3 reports the k_lin values obtained with the EPIDs controlled by the IAS 2 and the IAS 3 in the range of MU between 50MU and 400MU. The k_lin values obtained at an SED=105cm were coincident with those reported in Table 3 within ±0.3%. This means that the k_lin factors were independent of the dose per pulse and can be used to correct the s_t(TPR,w,L,d) values independently of the phantom thickness. However, as reported in literature [9], the lag effect can change from EPID to EPID, therefore a k_lin factor has to be determined for each EPID.

Table 3. k_lin values, (equation (7)), for different MUs obtained with the EPIDs controlled by the IAS 2 and by the IAS 3. The k_lin values showed a standard deviation equal to ±0.003.

Table 2 also reports the Δ values obtained with the three EPIDs for all the six beams. All the Δ values can be considered coincident within the experimental uncertainty equal to ±0.005. This means that all the EPIDs showed the same sublinear trend of their signals as a function of the dose per pulse independently of the beam quality and of the IAS model. This effect is already considered in the correlation functions F(TPR,w,L), therefore it does not need to be corrected. However if one EPID should have a different signal dependence on the dose per pulse as respect to that reported here, its signals have to be corrected for their dose per pulse dependence to use the correlation functions reported in the present paper.

The normalized output factors obtained for all the beams of the same quality with and without the interposed phantom were coincident within the experimental uncertainty equal to ±0.5%. Table 4 reports the average normalized output factors obtained by the EPIDs and the ion-chamber without the interposed phantoms for the three beam qualities available.

Table 4. Average normalized output factors obtained by the EPIDs and by the ion chamber for each beam quality available.

The data point out that the trends of the EPID output factor were independent of the beam quality within the experimental uncertainty of ±0.5%. Moreover they showed greater slopes as respect to those obtained by the ion-chamber that is coherent with the energy dependence of a silicon detector as a function of the beam size and water depth as reported in literature [15], [22].

For the three beam qualities here used, the fits of the s_t⁰(TPR,w,L)/D⁰(TPR,w/2,L) ratios (equation (10)) were determined considering the average ratios of the open and wedged fields obtained by the linacs that supplied a given beam quality.

Fig. 2 shows the s_t⁰(TPR,w,L)/D⁰(TPR,w/2,L) ratios and the relative fits, obtained for the 15MV photon beam, as a function of the phantom thickness, w. For each square field and beam quality the fits, obtained as a function of the water equivalent thickness, w, were able to reproduce the experimental data within ±2.0% (2SD). In particular a maximum deviation equal to +3%, was observed between the ratios obtained for the 4×4cm² open and wedged (45° wedge) field with the 6MV quality and the 42cm phantom thickness.

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• Figure 2 

  s_t⁰(TPR,w,L)/D⁰(TPR,w,L) average values and the fits (continuous lines) obtained for the 4×4 (♢), 8×8 (□), 10×10 (▵), 12×12 (×), 16×16 (+), and 20×20cm² (○) open and wedged fields as a function of the phantom thickness, w, for the 15MV photon beam.

The coefficients a_i, b_i and c_i (i=0, 1, 2, 3) of the polynomial functions are reported in Table 5 for the three photon beams. This fitting procedure used 10 parameters, and the function F(TPR,w,L) reproduced the experimental data within ±3.0% (2SD). In particular the statistic significances of the fits performed for the A, B and C parameters were within 0.01 for A and B and within 0.05 for C for all the beam qualities.

Table 5. Coefficients a_i, b_i and c_i (coefficient index i=0, 1, 2, 3) of the fits performed for the A(L), B(L) and C(L) parameters with the three photon beam qualities.

Even if the slopes of the f(TPR,d,L) factors showed an increase as a function of the wedge thickness within 0.5% (i.e. of the same order of the measurement reproducibility) we have chosen to used an average trend for the open and wedge fields of same side L.

Fig. 3 shows the f(TPR,d,L) factors obtained for the 15MV for different field dimensions and the relative linear fits as a function of the distance, d, determined by the equation

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• Figure 3 

  f(TPR,d,L) average factors obtained for 4×4(♢), 8×8(□) 10×10 (▵), 12×12 (×), 16×16 (+), and 20×20cm² (○) square fields and relative fits (continuous lines), determined averaging the data obtained with the open and wedged 15MV beams.

For the three beam qualities the coefficient f₀(TPR, L) were fitted as a function of L by linear trends by the equation

The coefficients of the linear fits as a function of, L, are reported in Table 6 for the three beam qualities. The statistic significances of the fits performed for the coefficients f₀(TPR, L) were within 0.01 for all the beam qualities.

Table 6. Coefficients m and q of the linear fits obtained for the coefficients f₀(TPR,L) as a function of L, for the three photon beam qualities.

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Discussion 

In some countries, the in vivo dosimetry is required for all patients treated with external beams [23] and many researchers are studying new methods based on the use of EPIDs that are easy and efficient in their daily use and sufficiently accurate for the purpose they are serving [10], [24]. However the need of time consuming measurements to implement the in vivo dosimetry methods discourages someone in their use.

In this work a calibration procedure for aSi EPIDs manufacturer by Varian has been proposed for transit dosimetry. The dosimetric characteristics of three aSi Varian EPIDs, has been investigated in terms of signal reproducibility and long term stability, signal linearity with MU and dose per pulse and signal dependence on the field dimensions with the aim of defining generalized correlation functions for Varian aSi EPIDs.

For the EPIDs here tested the signal per MU reproducibility was within ±0.5% (2SD), while the long term signal stability could be maintained well within ±2% determining a new k_s factor when this level was overcame. Between 50MU and 400MU, the signal per MU, of the EPID controlled by the IAS 2, showed a linearity within ±2% while the EPIDs controlled by the IAS 3 showed signal per MU linearity within ±0.5% in agreement with the data reported in literature [9]. In particular it was verified that k_lin is independent of the beam quality, and the dose per pulse absorbed by the EPID. However the paper of Kavuma et al. [9] points out that different EPIDs of the same model can show different signal trends as a function of the MU. Thus it is suggested to verify the signal linearity of each EPID in order to evaluate its k_lin correction factors.

All the EPIDs showed the same sublinear trend as a function of the dose per pulse independently of the beam quality. In particular an average Δ values equal to 0.974 was estimated considering the six beams used at an MU rate equal to 400MU/min. This behavior could be explained considering the saturation effect on the 65^th frame as described by Van Esch et al. [15].

At the end all the three EPIDs showed the same signal dependence on the field dimensions, within ±0.5% (2SD) for all the beam qualities tested. As reported in literature [15], the observed differences between the normalized output factor obtained by the EPID and the ion-chamber are due to the enhanced sensitivity of the phosphor scintillator to the low energy components in the incident radiation spectrum. Therefore the field dimension dependence of the EPID signal without interposed phantom can be considered an index to assess the signal energy dependence of the aSi EPIDs.

A generalized set of correlation functions F(TPR,w,L) and empirical factors f(TPR,d,L) was obtained for the three linacs equipped with EPIDs of equivalent dosimetric characteristics. In particular equation (5) supplies D°(TPR,w/2,L) values independent of the MU calibration performed in the centre and the s_t°(TPR,w,L) values defined by equation (9) are independent of both the EPID sensitivity and the MU calibration of the beams. This way the fits of the F(TPR,w,L) functions and of the f(TPR,d,L) factors, here reported can be used to perform in vivo dosimetry for beams with TPR equal to 0.666, 0.735 and 0.764 or however within ±0.3% of these values that represent a range of the TPR variation for the modern Varian linacs [6].

The uncertainty of equation (15) can be estimated taking into account the following uncertainties in terms of 2 SD:

Propagating these uncertainties in quadrature, an uncertainty of ±4.8% (2SD) was obtained. Because of the results of the proposed in vivo dosimetry method are reported generally in terms of ratio between the in vivo reconstructed dose, D_iso, and the predicted dose, D_iso,TPS computed by a treatment planning system (TPS) [5], [6] the TPS calculation uncertainty has to be accounted for the tolerance level determination. The uncertainty in terms of (2SD) for the D_iso,TPS can be assumed equal to ±2% in homogeneous tissue regions and ±4% in inhomogeneous tissue regions [25] and propagating in quadrature these last uncertainties, tolerance levels of ±5% and ±6% can be estimated for the ratios between D_iso and D_iso,TPS, in presence of homogenous and inhomogeneous tissues respectively. These tolerance levels are in agreement with those obtained in previous works [5], [6] for the in vivo dosimetry implementation. This result can be explained considering that the uncertainty associated to the factors k₀, k_s and k_lin were implicitly considered in the tolerance levels adopted in previous papers. These tolerance/action levels seem to be more restrictive than the ones reported by ESTRO [26] for the practical method that uses diodes. Indeed, for the same treatments the tolerance/action levels for the only entrance doses have been fixed in that report in ±5% and ±8% for the pelvic and thorax tumors respectively.

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Conclusions 

Actually the linacs manufactured by Varian supply a range of TPR values within ±1% for a common nominal MV. This means that the use of the coefficients reported in Table 5 for beams with TPRs that differ by the TPR here examined more than ±0.3% could introduce uncertainty greater than those estimated in this paper. Adopting the EPID calibration and the dose normalization procedures here proposed, the authors have in progress measurements on other beams supplied by linacs of different manufacturers. This way fits of s₀(TPR,w,L) and D₀(TPR,w/2,L), as a function of the three parameters TPR, w, L, could be the solution for a generalized in vivo dosimetric procedure based on a direct selection of the F(TPR,w,L) for every beam of quality TPR supplied by the linacs. This procedure could reduce the effort for the method implementation at the determination of the factors k₀, k_s and k_lin and at the evaluation of the EPID normalized output factor as a function of the field dimension.

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