Dosimetric characteristics of the novel 2D ionization chamber array OCTAVIUS Detector 1500 T. S. Stelljes, A. Harmeyer, J. Reuter, H. K. Looe, N. Chofor, D. Harder, and B. Poppe Citation: Medical Physics 42, 1528 (2015); doi: 10.1118/1.4914151 View online: http://dx.doi.org/10.1118/1.4914151 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/42/4?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in A 2D ion chamber array audit of wedged and asymmetric fields in an inhomogeneous lung phantom Med. Phys. 41, 101712 (2014); 10.1118/1.4896097 Technical Note: A method for improving the calibration reproducibility of an ionization chamber detector array Med. Phys. 41, 091704 (2014); 10.1118/1.4892607 The Octavius1500 2D ion chamber array and its associated phantoms: Dosimetric characterization of a new prototype Med. Phys. 41, 091708 (2014); 10.1118/1.4892178 Characterization of a novel 2D array dosimeter for patient-specific quality assurance with volumetric arc therapy Med. Phys. 40, 071731 (2013); 10.1118/1.4812415 An Active Matrix Flat Panel Dosimeter (AMFPD) for in-phantom dosimetric measurements Med. Phys. 32, 466 (2005); 10.1118/1.1855012

Dosimetric characteristics of the novel 2D ionization chamber array OCTAVIUS Detector 1500 T. S. Stelljesa) Clinic for Radiation Therapy, Pius-Hospital, Oldenburg 26121, Germany and WG Medical Radiation Physics, Carl von Ossietzky University, Oldenburg 26129, Germany

A. Harmeyer and J. Reuter WG Medical Radiation Physics, Carl von Ossietzky University, Oldenburg 26129, Germany

H. K. Looe and N. Chofor Clinic for Radiation Therapy, Pius-Hospital, Oldenburg 26121, Germany and WG Medical Radiation Physics, Carl von Ossietzky University, Oldenburg 26129, Germany

D. Harder Prof. em., Medical Physics and Biophysics, Georg August University, Göttingen 37073, Germany

B. Poppe Clinic for Radiation Therapy, Pius-Hospital, Oldenburg 26121, Germany and WG Medical Radiation Physics, Carl von Ossietzky University, Oldenburg 26129, Germany

(Received 3 August 2014; revised 21 January 2015; accepted for publication 22 January 2015; published 13 March 2015) Purpose: The dosimetric properties of the OCTAVIUS Detector 1500 (OD1500) ionization chamber array (PTW-Freiburg, Freiburg, Germany) have been investigated. A comparative study was carried out with the OCTAVIUS Detector 729 and OCTAVIUS Detector 1000 SRS arrays. Methods: The OD1500 array is an air vented ionization chamber array with 1405 detectors in a 27 × 27 cm2 measurement area arranged in a checkerboard pattern with a chamber-to-chamber distance of 10 mm in each row. A sampling step width of 5 mm can be achieved by merging two measurements shifted by 5 mm, thus fulfilling the Nyquist theorem for intensity modulated dose distributions. The stability, linearity, and dose per pulse dependence were investigated using a Semiflex 31013 chamber (PTW-Freiburg, Freiburg, Germany) as a reference detector. The effective depth of measurement was determined by measuring TPR curves with the array and a Roos chamber type 31004 (PTW-Freiburg, Freiburg, Germany). Comparative output factor measurements were performed with the array, the Semiflex 31010 ionization chamber and the Diode 60012 (both PTW-Freiburg, Freiburg, Germany). The energy dependence of the OD1500 was measured by comparing the array’s readings to those of a Semiflex 31010 ionization chamber for varying mean photon energies at the depth of measurement, applying to the Semiflex chamber readings the correction factor kNR for nonreference conditions. The Gaussian lateral dose response function of a single array detector was determined by searching the convolution kernel suitable to convert the slit beam profiles measured with a Diode 60012 into those measured with the array’s central chamber. An intensity modulated dose distribution measured with the array was verified by comparing a OD1500 measurement to TPS calculations and film measurements. Results: The stability and interchamber sensitivity variation of the OD1500 array were within ±0.2% and ±0.58%, respectively. Dose linearity was within 1% over the range from 5 to 1000 MU. The effective point of measurement of the OD1500 for dose measurements in RW3 phantoms was determined to be (8.7 ± 0.2) mm below its front surface. Output factors showed deviations below 1% for field sizes exceeding 4 × 4 cm2. The dose per pulse dependence was smaller than 0.4% for doses per pulse from 0.2 to 1 mGy. The energy dependence of the array did not exceed ±0.9%. The parameter σ of the Gaussian lateral dose response function was determined as σ6MV = (2.07 ± 0.02) mm for 6 MV and σ15MV = (2.09 ± 0.02) mm for 15 MV. An IMRT verification showed passing rates well above 90% for a local 3 mm/3% criterion. Conclusions: The OD1500 array’s dosimetric properties showed the applicability of the array for clinical dosimetry with the possibility to increase the spatial sampling frequency and the coverage of a dose distribution with the sensitive areas of ionization chambers by merging two measurements. C 2015 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4914151] Key words: OCTAVIUS Detector 1500, 2D-array, IMRT, dosimetry

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1. INTRODUCTION 2D detector arrays have become the standard device in many hospitals for Linac QA1–3 and verification of intensity modulated dose distributions.4–7 Typically 2D arrays are characterized by the detector type (semiconductor or ion chamber), the dimensions of the single detectors, and the arrangement as well as the number of detectors in the measurement area. Dose distributions in modern radiotherapy are often characterized by a number of changing dosimetric parameters. In a single-field dose distribution, the dose per pulse, the mean photon energy at the depth of measurement, and the dose might vary between points of measurement along the detector array. These parameters are usually only constant in the plateau region of a dose distribution. Especially for intensity modulated dose distributions, changes in these parameters regularly occur. Therefore, the ideal detector array should have a small detector volume in combination with minimal photon energy and dose per pulse dependencies. In practice, some limitations have to be considered for each detector type, and there is a need to understand the relationship between dosimetric imperfections and the detector material or technical design. For ionization chambers, the detection volume cannot be chosen below the minimum size necessary to generate a sufficient signal. Furthermore, the reading of an ion chamber is influenced by signal averaging over the sensitive volume and secondary electron transport across its wall which together result in the so called volume effect.8,9 In terms of signal theory, the volume effect can be described as a low-pass filter function, the lateral dose response function.10 Rapidly changing dose gradients, as found in typical IMRT fields, may appear flattened due to the finite volumes of ionization chambers. Diode arrays have smaller detector dimensions and therefore narrower dose response functions. However, diodes are prone to radiation damage, and their readings are influenced by changes in the dose rate and dose per pulse at the point of measurement as well as by the energy spectrum of the photon radiation.3,11 A third optionthe liquid filled ion chamber array-permits the reduction of the sensitive volume due to the much higher density of the sensitive medium compared to air. This leads to a narrower lateral dose response function in comparison to vented ion chambers, which makes liquid filled ion chambers suitable for measurements in small fields.12,13 However, their responses are also subject to influences of the dose per pulse and the mean photon energy at the effective point of measurement.12 In order to detect the smallest occurring fluence deviations, the spatial sampling frequency of a detector array has to comply with the Nyquist sampling theorem.4 But besides the resolution of the single detector and the sampling frequency, there is a third decisive characteristic of a detector array, the so called fill factor, i.e., the fraction of the total array area covered with the sensitive areas of the detectors. The significance of the fill factor was illustrated in a study of Gago-Arias et al.14 who showed that diode arrays, compared with ionization chamber arrays, are slightly less sensitive to fluence perturbations by misaligned MLC leafs. The reason is found in the higher fill factor of ionization chamber arrays. Medical Physics, Vol. 42, No. 4, April 2015

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The fill factor is determined by the FWHM of the lateral fluence response function of the single detector and by the cell area attributed to each single detector. The OCTAVIUS Detector 729 (OD729) array was designed to achieve full field coverage (fill factor 1.00) by merging 4 measurements each shifted by 5 mm. As the successor product the new OCTAVIUS Detector 1500 (OD1500) array is designed with all ion chambers arranged in a checkerboard pattern. Due to this arrangement, a fill factor of 1.00 is expected to be achievable by merging only two measurements. In this work, the dosimetric properties of the OCTAVIUS Detector 1500 array T10044 (PTW-Freiburg, Freiburg, Germany) are investigated. To provide consistency and to allow comparisons, we follow most of the methods presented in our former work on the OCTAVIUS Detector 1000 SRS (OD1000) array (PTW-Freiburg, Freiburg, Germany).12 The setup of the OD1500 array and measurement setups are described in Sec. 2. Measurements with the OD729 and OD1500 array are presented in Sec. 3. In the discussion the dosimetric properties of all three detector arrays are compared. 2. MATERIALS AND METHODS Measurements were performed with an Elekta Synergy accelerator (Elekta, Crawley, UK) equipped with an Agility MLC with 160 leaves each having a projection width of 5 mm at the isocenter, using 6 and 15 MV nominal accelerating voltages. Due to the local availability of Monte Carlo computed mean energy values (see Sec. 2.G), the energy dependence of the array response was measured with a SIEMENS Artiste accelerator (SIEMENS Healthcare, Erlangen, Germany) with a 160 MLC having a leaf width of 5 mm at the isocenter at 6 and 15 MV nominal accelerating voltages. 2.A. The OCTAVIUS Detector 1500 array

The OD1500 consists of 1405 vented ionization chambers, each having an entrance area of 4.4 × 4.4 mm2 and a height of 3 mm, resulting in an ionization volume of 0.058 cm3. This setup nearly doubles the number of measurement points covering an area of 27×27 cm2 in a single measurement, compared with the OCTAVIUS Detector 729 (PTW-Freiburg, Freiburg, Germany) which consists of 729 ionization chambers. The chambers are supplied with a voltage of 1000 V. They are arranged in rows, and the center-to-center distance between the chambers in each row is 10 mm. The distance between the rows is 5 mm. A checkerboard pattern of the chamber arrangement has been achieved by an offset of each second row of chambers, compared with its neighbour rows, of 5 mm in the row direction. Thereby, the nearest neighbour distance between chambers, measured along the diagonals, is 7.1 mm. This arrangement of the chambers results in a spatial sampling frequency of 0.1 mm−1 in each row or column and 0.14 mm−1 in the diagonal direction. By merging two measurements with the array shifted by 5 mm in lateral or longitudinal direction, the sampling frequency along each row and column can be doubled to 0.2 mm−1. The manufacturer-specified reference

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point is 7.5 mm beneath the surface and marked at the outer wall of the array. To provide comparability with other investigations of the authors, measurements were performed in identical setups (see Secs. 2.C–2.I) described in a study on the liquid filled ionization chamber array OD1000.12 Measurements carried out with the OD1500 array were also compared to results obtained with the air-filled ionization chamber array OD729, thereby providing a comparison between all three types of arrays. 2.B. Stability and linearity

To examine the stability and linearity of the OD1500 and OD729 arrays, measurements were performed in a RW3 (Polystyrene with 2% TiO2 by weight) slab phantom with 5 cm build-up and 3 cm backscatter RW3 plates with a 10 × 10 cm2 field at an SSD of 100 cm. Simultaneously, a Semiflex 31013 ionization chamber (PTW-Freiburg, Freiburg, Germany) with a build-up cap measured the dose 1 cm above the phantom to ensure that fluctuations in linearity and stability were due to the array’s response and not caused by fluctuating Linac output. 2.C. Interchamber sensitivity variation

The interchamber sensitivity variation of both arrays was measured in a RW3 slab phantom at a measurement depth of 10 cm and with 3 cm backscatter RW3 plates at 90 cm SSD. Nine different detectors, the central chamber and four chambers along each of the central axes either in target/gun or left/right direction of the array were placed in the isocenter, and the chamber signals in a 10 × 10 cm2 field with 100 MU were measured. The interchamber sensitivity variation was calculated as the ratio of the measured chamber signal and the mean signal measured by all chambers. Again, a Semiflex 31013 chamber with a build-up cap was used simultaneously to monitor the Linac output. 2.D. Effective depth of measurement

The effective depth of measurement of the OD1500 and OD729 array was measured in a TPR geometry in a RW3 slab phantom with 10 cm backscatter RW3 plates and varying thickness of build-up material as proposed by Looe et al.15 TPR curves were measured with the OD1500 array by comparison with a Roos chamber type 34001 (PTW-Freiburg, Freiburg, Germany) whose effective depth of measurement is known to lie 1.5 mm below the chamber’s front surface.15 The effective depth of measurement is determined by shifting the OD1500 TPR curve until the best agreement with the Roos chamber’s TPR curve is achieved. 2.E. Output factors

Output factors were measured at 6 and 15 MV with a Semiflex 31010 ionization chamber, a Si diode 60012 (both PTW-Freiburg, Germany), the OD1500 and the OD729 array. Medical Physics, Vol. 42, No. 4, April 2015

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All detectors were placed at the point of measurement on the beam axis at a depth of 10 cm in a RW3 slab phantom with 3 cm backscatter material, with the indicated field size valid for SSD 90 cm. For field sizes from 1 × 1 cm2 to 4 × 4 cm2, the absorbed dose to water at this point was determined from the reading of the diode which had been cross-calibrated against the Semiflex 31010 in terms of absorbed dose to water at 4 × 4 cm2 field size according to DIN 6809-8.16 For larger field sizes, the absorbed dose to water at this point was directly determined from the reading of the Semiflex chamber. The output factor was defined as the quotient of the absorbed dose to water at this point and the corresponding monitor reading, normalized to the value of this quotient at 10 × 10 cm2 field size. In order to correct detector readings for the volume effect, we follow the concept of a recently introduced correction factor kV .17 In small-field dosimetry, this factor corrects for the reduction of the dosimeter reading on the central axis of a photon beam due to the volume effect. Factors kV were calculated for the OD1500 array chambers at fields sizes from 1 × 1 cm2 to 3 × 3 cm2 following Looe et al.17 Basically, kV at a point on the beam axis (x = 0) can be calculated as the ratio of the unperturbed maximum D(x = 0) of the transverse dose profile D(x) and the convolution product D(x) ∗ K(x) at x = 0, when the area-normalized convolution kernel or lateral dose response function of the detector is K(x) (see Sec. 2.H), kV (x = 0) =

D(x = 0) . [D(x) ∗ K (x)] x=0

(1)

2.F. Dose per pulse dependency

The influence of the dose per pulse at the effective depth of measurement on the OD1500 readings was investigated by embedding the array and a Semiflex 31013 detector in a RW3 slab phantom with 3 cm backscatter RW3 plates. The effective point of measurement of both detectors was placed at a depth of 10 cm. Measurements with an array chamber and with the Semiflex chamber were performed in succession at an SSD of 90 cm and with 10 × 10 cm2 field size. For all other SSDs, the collimator was readjusted so that the field size 10 × 10 cm2 at the effective point of measurement was kept constant. Each measurement was carried out in a 15 MV photon beam with 50 MU at 592 MU/min. The pulse repetition frequency was 200 Hz. By varying the SSD of the chamber setup from 60 to 140 cm, the dose per pulse was varied from 0.2 to 1 mGy. The readings of the Semiflex 31013 chamber were corrected for recombination losses following the protocol described by Bruggmoser et al.,18 as suggested in DIN 6800-2.19 The ratio of the OD1500 and the corrected Semiflex readings was calculated, and its relative values were set to unity for a dose per pulse of 0 mGy. 2.G. Sensitivity to changes in the photon spectrum at the effective point of measurement

To investigate the sensitivity of the array’s chamber readings to changes in the photon spectrum, measurements

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were carried out at a Siemens Artiste accelerator with the OD1500 and the OD729 in comparison with a Semiflex 31010 ionization chamber. The photon spectrum at the effective point of measurement was changed by varying the depth of measurement (2, 10, 15, and 20 cm) and the field size (4 × 4 cm2, 10 × 10 cm2, 20 × 20 cm2) at SSD = 100 cm. Measurements were carried out with 6 and 15 MV nominal accelerating voltages. For each setup of field size and depth, the spectral-fluence mean photon energy Em at the effective point of measurement was determined from Monte Carlo computed photon spectra. Correction factors kNR for nonreference conditions were applied to the readings of the Semiflex 31010 ionization chamber following the method proposed by Chofor et al.20,21 2.H. Detector dose response function

The approach of Looe et al.,10 already applied to the 1000 SRS array by Poppe et al.,12 was used to determine the detector dose response function of a single OD1500 ion chamber. The detector dose response function is the detectorassociated convolution kernel K(x) converting a given 1D dose profile D(x) into the 1D signal profile M(x), obtained with this detector. A 1 cm wide and 40 cm long slit beam was formed using the accelerator’s collimator system combined with tertiary lead blocks placed in the tray holder of the Elekta Synergy Linac. The array and a Si-diode PTW 60012 were embedded in RW3 plates with 10 cm backscatter material. Measurements were carried out at depths 1.5 and 2.5 cm for 6 and 15 MV, respectively. The whole setup (RW3 plates, detectors) was placed on a micrometer positioning table type M-511 with a C-863 Mercury Controller (Physik Instrumente, Karlsruhe, Germany) used to shift the array and the diode to measure signal profiles at a step width of 0.5 mm. The obtained diode signal profiles were convolved with an area-normalized 1D Gaussian function characterized by its standard deviation σ. By stepwise changing the value of σ until the best possible agreement of the convolved diode-measured signal profile with the array-measured signal profile was achieved, the width of the convolution kernel converting the former into the latter was determined. In a last step, the already known dose response function of the diode itself10 was taken into account by adding its σ value in quadrature to the one of the array chamber determined in the first step. The resulting 1D Gaussian function was regarded as the experimental approximation to the detector dose response function.

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ratio of the area within the 50% response contour of the single detector and its cell area defined by the detector spacing. The other situation of interest in the context of ionization chamber arrays (“case B”) is that of the overlap of the 50% response contours of each single chamber with those of its neighbour chambers, in which case the fill factor is exactly unity. These definitions have been applied in evaluating the fill factors of the OD1500 and OD729 detector arrays. Case A applies to single measurements with these arrays, in which a single chamber is never lined side-by-side with another chamber. The FWHM of the 1D fluence response function K M (x) of each chamber is assessed using the convolution relationship K M (x) = K(x) ∗ K D (x), where K(x) is the Gaussian dose response function of the single detector10 and K D (x) is the dose deposition kernel. According to Djouguela et al.,22 K D (x) can be approximately described as a Lorentz function with parameter λ = 1.4 mm at 6 MV. Thus, the convolution product of a Gaussian and a Lorentz function, called the Voigt profile,23 is the function describing the 1D fluence response function. Its FWHM f V can be determined by the approximation f V ≈ 0.5346 f L + 0.2166 f L 2 + f G 2, with f L and f G being the FWHM values of the Lorentz and Gaussian functions, respectively.23 2.J. IMRT verification

The applicability of the OD1500 array for IMRT verification was investigated by measuring a three segment prostate IMRT field. The detector array was placed in a RW3 phantom with 3 cm backscatter RW3 plates with the effective point of measurement at a depth of 5 cm in the isocenter plane. Prior to the verification measurement, the array was cross-calibrated against an absolute dose measurement with a Semiflex 31013 chamber placed at the same measurement depth in a 5 × 5 cm2 field. The intensity modulated dose distribution was measured with the array’s central chamber placed at the isocenter, and the measurement was repeated after a longitudinal shift of the whole detector array by 5 mm in gun/target direction. The results of both measurements were merged by a self-written  (The MathWorks, Natick, MA) script to increase the sampling frequency. The measured and merged dose distribution was compared against treatment planning system calculations from Oncentra Masterplan ver 4.3 (Elekta, Crawley, UK) using a 2 mm dose grid to avoid aliasing effects24 and with a measurement with a Gafchromic EBT3 film25 using a local gamma index evaluation26 in the software package VeriSoft 6.0 (PTW-Freiburg, Freiburg, Germany).

2.I. Fill factor

Following Gago-Arias et al.,14 we will consider the “fill factor,” i.e., the fraction of the total area of a 2D array where detectors are able to indicate small MLC misalignments. The particular case when the area within the 50% contour of the single detector 2D fluence response function (shortly termed the “50% response contour”) does not overlap with the 50% response contours of the next-lying single detectors may be termed “case A.” In this case, the fill factor is defined as the Medical Physics, Vol. 42, No. 4, April 2015

3. RESULTS 3.A. Stability, interchamber sensitivity variation, and linearity

Without preirradiation, the signal of the OD1500’s central chamber was stable within ±0.15% for 15 consecutive measurements. Deviations in linearity from the Semiflex readings did not exceed 1% from 5 to 1000 MU. The maximum

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F. 1. Output factors measured with the OD1500, a Semiflex 31010 and a diode type 60012. All output factors are normalized to unity at a field size of 10 × 10 cm2. The lower panel shows the relative deviations of the OD1500 detector readings from the reference detectors.

deviation found was 6.27% for 1 MU at 6 MV, but this measurement point was outside of the range of use stated by the manufacturer (minimum dose of 100 mGy). This effect may be attributed to a threshold that has to be overcome for a signal to be registered. Linear fits to the OD1500 measurements from 1 to 10 and 100 to 1000 MU for 6 and 15 MV resulted in R2 values of 1. A maximum interchamber deviation of 0.58% was found measuring the dose with nine different chambers of the array at the isocenter. The OD729 was stable within 0.25% after preirradiating the array with approximately 10 Gy and 0.5% for a preirradiation with 5 Gy. Deviations in linearity were within 1% for 6 MV and 2% for 15 MV from 5 to 1000 MU. The observed maximum interchamber deviation was 0.44%. 3.B. Effective depth of measurement

The effective depth of measurement in RW3 of the available OD1500 array was determined to be (8.7±0.2) mm below the array’s surface. This corresponds to the fact that the mass per unit area of all material in front of the ionization chambers is approximately 0.8 g/cm2. The geometric reference point of the OD1500, specified by the manufacturer, is 7.5 mm below the surface and is marked on the outside of the array. For the OD729, the effective depth of measurement in RW3 was found to lie (8 ± 0.2) mm below the array’s surface. Medical Physics, Vol. 42, No. 4, April 2015

3.C. Output factors

The output factors measured with the OD1500 array (see Fig. 1) showed deviations from Semiflex 31010 measurements of less than 0.75% for field sizes ranging from 5 × 5 cm2 to 27 × 27 cm2. For a 3 × 3 cm2 field, the deviations from the Diode 60012 output factors were −1.1% for 15 MV and −1.8% for 6 MV, and for a 2 × 2 cm2 field they amounted to −3.8% and −2.8% at 6 and 15 MV, respectively. For the smallest field size of 1 × 1 cm2, the deviations of the OD1500 output factors from the diode were −14.9% for 15 MV and −16.3% for 6 MV. Output factors for the OD729 array showed relative deviations of less than 1% for most of the field sizes compared to the OD1500 array. Maximum deviations from the OD1500 output factors were found to be approximately −3% for a 2 × 2 cm2 field at 6 and 15 MV, respectively. Correction factors kV (x = 0) calculated for the OD1500 at 6 and 15 MV, according to Eq. (1), are shown in Table I. This result elucidates that it is advisable to apply correction factor kV whenever the field size does not exceed 3 × 3 cm2. 3.D. Dose per pulse dependency

In the measurement range from 0.2 to 1 mGy per pulse, the array showed a maximum deviation from the recombinationcorrected Semiflex dose values of 0.4% (see Fig. 2, left

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T I. Correction factors kV calculated from the ratio of the unperturbed measured dose profile approximated with diode measurements, and the convolution product of this profile with the lateral dose response function determined in Sec. 3.F.

6 MV 15 MV

1 × 1 cm2

2 × 2 cm2

3 × 3 cm2

1.156 1.160

1.009 1.009

1.003 1.003

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be σ6MV = (2.05 ± 0.02) mm and σ15MV = (2.07 ± 0.02) mm for 6 and 15 MV, respectively. Taking into account the σvalue of the Diode 60012, σ = (0.3 ± 0.02) mm,10 the final σ values of an OD1500 single chamber were calculated, by addition in quadrature, as σ6MV = (2.07 ± 0.03) mm and σ15MV = (2.09 ± 0.03) mm. 3.G. Fill factor

panel). The OD729 array showed an increased dose per pulse dependency with a drop in collection efficiency of 1.3% over the dose per pulse measurement range (see Fig. 2, right panel). The curves of Fig. 2 may be used for an empirical correction of the signal loss due to the dose per pulse effect. 3.E. Sensitivity to changes in the photon spectrum at the effective depth of measurement

When the results of comparisons between the central chamber of the array and the Semiflex chamber at various depths and field sizes are plotted against the mean photon energy Em at the point of measurement, the OD1500 detector array showed deviations which did not exceed ±0.9% when setting the response to unity for a 10 × 10 cm2 field in a depth of 10 cm at 6 and 15 MV. A slight increase in the arrays’ response by about 1% can generally be found for increasing field size, e.g., for lower mean photon energies at the effective depth of measurement of the array (see Fig. 3). For the OD729, the observed energy dependence is still smaller with a maximum variation by 0.7%. 3.F. Detector dose response function

Figure 4 shows the signal profiles obtained with the 1 cm wide slit beam, measured with the Si diode 60012 and with the OD1500, compared with the convolution product of the diode profile with a 1D Gaussian convolution kernel chosen as the lateral response function of an OD1500 single chamber. The σ-values of the lateral dose response function for the OD1500 array in relation to the diode were determined to

Using the relationship K M (x) = K(x) ∗ K D (x) with the values σ = 2.08 mm for the Gaussian K(x) and λ = 1.4 mm for the Lorentzian K D (x), the FWHM of K M (x) has been calculated as 6.56 mm. Due to the checkerboard design of the OD1500 array, a single measurement with the OD1500 array is a realization of case A (no overlap of the 50% response contours between adjacent chambers). From FWHM2 = 43.0 mm2 and the cell area of 2 × 25 mm2 = 50 mm2 attributed to each single detector, the fill factor is calculated as c = 0.86 for a single measurement with the OD 1500 array. In the case of two merged OD1500 measurements, the 50% response contours of the adjacent chambers overlap, so that the fill factor is 1.00. 3.H. IMRT verification

Figure 5 shows the process of merging two OD1500 measured dose profiles. The merged OD1500 profiles showed a high level of agreement with profiles measured with a Gafchromic EBT3 film and with calculations making use of the treatment planning system Oncentra Masterplan version 4.3. Passing rates were above the 90% threshold for a 3 mm/3% and 2 mm/2% local gamma-index criterion when the OD1500 measurement was compared with a TPS calculation and a film measurement. For a 1 mm/1% local criterion, the passing rates were 87.4% in comparison with the TPS and 71.3% in comparison with an EBT3 film measurement. Since the TPS calculation and the film measurement represent dose distributions undisturbed by spatial detector resolution, a better agreement with the array measurements is to be expected when considering the low pass filtering effect of the

F. 2. Dose per pulse response of the OD1500 and OD729 array relative to a Semiflex 31013 measurement which was corrected for recombination losses. Medical Physics, Vol. 42, No. 4, April 2015

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F. 3. Energy dependence of the response of the OD1500 and OD729 central chamber relative to a Semiflex 31010 whose reading was corrected for nonreference conditions.

single chambers. Therefore, by convolving the film measured dose profiles with the lateral dose response function of the OD1500 array, increased passing rates of 98.3% for a 2 mm/2% criterion and 86.7% for a 1 mm/1% gamma index criterion were obtained. Convolving the TPS calculated dose distribution with the lateral dose response function of the OD1500 array even yielded a passing rate of 91.6% for a 1 mm/1% local gamma index criterion (Table II).

4. DISCUSSION The OD1500 array’s dosimetric characteristics make it well suited for daily clinical use. Stability and interchamber sensitivity variation are well below 0.2% and 0.7%, respectively. The linearity of the array is excellent, as deviations are below 1% from 5 to 1000 MU. Dose linearity in general is within 1% for the vendor specified dose range for all three arrays including

F. 4. Determination of the OD1500 dose response function. A 1 cm wide slit beam was scanned with the Si diode PTW 60012 (x) and with a single chamber of the OD1500 (o). The full line shows the convolution product of the diode-measured signal profile and a normalized 1D Gaussian kernel, the dose response function of the array chamber (see text). Medical Physics, Vol. 42, No. 4, April 2015

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F. 5. By merging two measurement files (one shifted by 5 mm) a full field coverage can be achieved with the OD1500 array. The resulting dose profile was compared to an EBT3 film measurement and TPS calculations.

the OD1000. The used OD729 in general shows comparable characteristics but needs more preirradiation before stability similar to the OD1500 and OD1000 is achieved. The effective depth of measurement is determined to be (8.7 + 0.2) mm below the array’s surface which is within the accuracy needed for the clinical use of arrays in verification measurements and constancy checks. The effective depth of measurement of the OD729 was determined in the same setup to be (8 ± 0.2) mm below the array’s surface, thus meeting the value published by Looe et al.15 The effective depth value of the 1000 SRS array determined in a previous work is 9.5 mm.12 Thus, the rotation axes of the OCTAVIUS 4D phantom coincides with the effective depth of measurement of the three detector arrays within a tolerance of 1.5 mm.6 At small field sizes, the output factors measured with the array show the expected deviations from those measured with the Semiflex chamber and Si diode due to the volume effect of the OD1500 array’s ionization chambers. For field sizes above 4 × 4 cm2, the deviations were below 1%. Deviations in output factor can be corrected by applying a correction factor kV . While the OD1500 and the OD729 array’s output factors are very similar, Poppe et al. have shown that the Octavius 1000 SRS array is a well suited array for small field dosimetry with output factors exhibiting maximum deviations from diode readings for fields ranging from 1 × 1 cm2 to 4 × 4 cm2 of 2.6% and from Semiflex 31010 readings for larger field sizes up to 27 × 27 cm2 of 2.6% for 6 MV and 1.8% for 15 MV.12 The standard deviation of the Gaussian lateral dose response function of the array was obtained as σ6MV = (2.07 ± 0.03) mm and σ15MV = (2.09 ± 0.03) mm. These values are T II. Gamma index passing rates of a merged OD1500 measurement against TPS calculations, an EBT3 film measurement and the same film measurement and TPS calculation convolved with the lateral dose response function of the OD1500 array. Reference data Local 3D gamma criterion

TPS

TPS convolved

EBT3

EBT3 convolved

3 mm/3% 2 mm/2% 1 mm/1%

99.6 96.2 87.4

100 97.9 91.6

96.9 90.09 71.3

99.8 98.3 86.7

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slightly smaller compared to those of the OD729 array which were determined by Looe et al. as σ6MV = (2.27 ± 0.03) mm and σ15MV = (2.37 ± 0.03) mm.10 The slightly narrower dose response function of the OD1500 array is owed to the smaller entrance area of its ionization chambers of 4.4 × 4.4 cm2 compared to 5 × 5 cm2 for the OD729 array. The 1000 SRS array’s response function width was reported to be σ6MV = (0.72 ± 0.03) mm and σ15MV = (0.74 ± 0.03) mm by Poppe et al., which is attributed to the much smaller single detector entrance area of 2.3 × 2.3 mm2.12 The fill factor of the OD1500 array, which characterizes its sensitivity to misaligned MLC leaves, was determined as 0.86 with a single OD1500 measurement and 1.00 with two merged OD1500 measurements. For a single measurement with the OD729 array, a fill factor of 0.5 has been obtained, which meets the value published by Gago-Arias et al.,14 whereas fill factor 1.00 is achieved merging four measurements by which a geometry with adjacent chambers is simulated. The dose per pulse dependence of the OD1500 array is minimal and below 0.4% in the range from 0.2 to 1 mGy per pulse. A correction regarding the dose per pulse at the effective depth of measurement of the array does not appear as necessary based on these findings. Interestingly, the OD729’s dependence on the dose per pulse at the effective depth of measurement is 1.3% for the same dose per pulse measurement range. This somewhat larger value is owed to the larger distance between the electrodes of the OD729 (5 mm) compared to the OD1500 array (3 mm) and can be explained by Boag’s theory of ion recombination, according to which signal losses are increasing with increasing distance between the collecting electrodes.27 As expected, for the liquid filled ion chamber array 1000 SRS Poppe et al. found much higher saturation losses of 3.5% over the measurement range.12 This is a result of the higher recombination rates of the positive and negative ions, whose mobility at the higher mass density of the sensitive medium of a liquid filled ion chamber is much lower compared with air vented ion chambers. The energy dependence of the response of the OD1500 array is smaller than for the 1000 SRS array (±2.6%) observed by Poppe et al.12 For the OD729, the energy dependence is slightly smaller but in the same order of magnitude as for the OD1500. This smaller energy dependence can be explained by the circumstance that the air-vented arrays have graphite

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chamber electrodes whereas the liquid-filled arrays have metal electrodes.12 The OD1500 array’s 1405 ion chambers are arranged in a checkerboard pattern on a measurement area of 27 × 27 cm2 with a sampling frequency of 0.1 mm−1 along each row. The higher detector density of the OD1500 compared to the OD729 array yields nearly twice the number of measurement points for a single array measurement. By merging two measurements shifted by 5 mm, the spatial sampling frequency along each row and column can be doubled to 0.2 mm−1. The OD729 array has a sampling frequency of 0.1 mm−1 along each row with 729 ion chambers arranged in a 27 × 27 cm2 grid pattern. In order to double the sampling frequency along each row and column to 0.2 mm−1, four measurements have to be merged. The sampling frequency in the inner 5 × 5 cm2 area and along the central axis of the 1000 SRS array is 0.4 mm−1. The rest of the 11 × 11 cm2 measurement area comprises a sampling frequency of 0.2 mm−1. The array consists of 977 liquid filled ion chambers. Poppe et al. showed that, in order to achieve a reconstruction of the measured dose distribution for the chambers of a 2D-Array, the Nyquist frequency, i.e., half the sampling frequency, should be around 0.1 mm−1. The 1000 SRS array has the highest sampling frequency of the arrays under investigation, meeting the Nyquist-Shannon sampling theorem, but this high resolution is limited to an area of 11 ×11 cm2, which makes the 1000 SRS only usable for the verification of small treatment volumes. By merging two OD1500 measurements, a sampling frequency of 0.2 mm−1 is achieved, thus fulfilling the sampling theorem over the full sensitive area of the OD1500 of 27 × 27 cm2. In daily clinical routine, the merging of two measurements may not be needed necessarily to verify treatment plans and conduct QA measurements. However, the method described above offers the possibility to reconstruct from the sampled dose data the complete underlying 2D dose distribution, which may be necessary in special situations such as the detailed analysis of deviations detected in plan verifications or the introduction of new plan standards. An IMRT verification carried out with the OD1500 array shows a high level of agreement to an EBT3 film measurement as well as to treatment planning system calculations similar to the 1000 SRS array.12 Convolving the signal profiles obtained with the film measurement and TPS calculations with the lateral dose response function of the OD1500 increased the passing rate by artificially broadening the lateral response function of the film measurement and the treatment planning system beam profile data to achieve a better agreement with the array measurement.

5. CONCLUSIONS The first measurements with the OD1500 array show the applicability of the array for clinical dosimetry and pretreatment plan verification with a doubled detector density compared to the OD729 array. While the energy and dose per pulse dependencies are within ±1%, it is advisable to apply correction factor kV to correct the volume effect for field sizes not exceeding 3 × 3 cm2. Achieving a uniform Medical Physics, Vol. 42, No. 4, April 2015

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sampling width of 5 mm in all directions and covering the entire measurement area of 27×27 cm2 with ion chambers by merging two measurements is a welcome addition for dose patterns to be measured with a high level of spatial resolution and increased error detection capability. ACKNOWLEDGMENT The authors would like to thank PTW-Freiburg for providing the OCTAVIUS Detector 1500 array for the present work. Dr. Henrik Schachner (Weilheim, Germany) kindly suggested the use of the Voigt function.23 a)Author

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