Correction of measured Gamma-Knife output factors for angular dependence of diode detectors and PinPoint ionization chamber

Physica Medica xxx (2014) 1e6

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Original paper

Correction of measured Gamma-Knife output factors for angular dependence of diode detectors and PinPoint ionization chamber Hrvoje Hr
sak a, *, Marija Majer b, Timor Grego a, Juraj Bibi c a, Zdravko Heinrich a a b

University Hospital Centre Zagreb, Ki
spaticeva 12, 10000 Zagreb, Croatia RuCer Bo
skovic Institute, Bijeni
cka 54, 10000 Zagreb, Croatia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 July 2014 Received in revised form 28 August 2014 Accepted 4 September 2014 Available online xxx

Dosimetry for Gamma-Knife requires detectors with high spatial resolution and minimal angular dependence of response. Angular dependence and end effect time for p-type silicon detectors (PTW Diode P and Diode E) and PTW PinPoint ionization chamber were measured with Gamma-Knife beams. Weighted angular dependence correction factors were calculated for each detector. The Gamma-Knife output factors were corrected for angular dependence and end effect time. For Gamma-Knife beams angle range of 84
e54
. Diode P shows considerable angular dependence of 9% and 8% for the 18 mm and 14, 8, 4 mm collimator, respectively. For Diode E this dependence is about 4% for all collimators. PinPoint ionization chamber shows angular dependence of less than 3% for 18, 14 and 8 mm helmet and 10% for 4 mm collimator due to volumetric averaging effect in a small photon beam. Corrected output factors for 14 mm helmet are in very good agreement (within ±0.3%) with published data and values recommended by vendor (Elekta AB, Stockholm, Sweden). For the 8 mm collimator diodes are still in good agreement with recommended values (within ±0.6%), while PinPoint gives 3% less value. For the 4 mm helmet Diodes P and E show over-response of 2.8% and 1.8%, respectively. For PinPoint chamber output factor of 4 mm collimator is 25% lower than Elekta value which is generally not consequence of angular dependence, but of volumetric averaging effect and lack of lateral electronic equilibrium. Diodes P and E represent good choice for Gamma-Knife dosimetry.

Keywords: Gamma-Knife output factor Silicon diode PinPoint ionization chamber Correction for angular dependence

© 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Introduction Gamma-Knife radiosurgery is highly precise method for treatment of small intracranial lesions with high single radiation dose [1e4]. For Leksell Gamma-Knife unit (LGK) Model C (Elekta AB, Stockholm, Sweden) radiosurgery uses 201 convergent narrow Co60 photon beams, collimated with the 18, 14, 8 and 4 mm collimator helmet. An important parameter for treatment planning in GammaKnife radiosurgery is a collimator output factor defined for each collimator helmet as a dose ratio to the 18 mm collimator. In the last two decades a number of dosimetrical methods and Monte Carlo calculations [5,6] have been introduced for determination of LGK

* Corresponding author. Department of Oncology, Radiotherapy Unit, University Hospital Centre Zagreb, Ki
spati ceva 12, HR10000 Zagreb, Croatia. Tel.: þ385 989144644, þ385 12388780; fax: þ385 12388779. E-mail addresses: [email protected], [email protected] (H. Hr
sak).

output factors. For the dosimetry different detectors have been used: small ionization chambers, semiconductor diodes, small thermoluminescent detector (TLD) rods and cubes [7e10], radiographic and radiochromic films [8,9,11e14], radiophotoluminescent detector [15], alanine pellets, liquid ionization chamber and diamond detector [8,13,16]. Output factor values based on measurements with TLDs, liquid ionization chamber and diode detectors, and also Monte Carlo simulations and analytical calculations [11,17] (0.984, 0.956 and 0.870 for 14, 8 and 4 mm collimator, respectively) are now recommended by vendor (Elekta AB, Stockholm, Sweden) and being used in most Gamma-Knife centres. As a part of quality assurance program in Gamma-Knife radiosurgery measurements of output factors should be regularly performed [18]. However, determination of output factors is a nontrivial task, especially for 4 mm collimator. It is associated with a dosimetrical problems such as loss of lateral electronic equilibrium, volumetric averaging of a measured signal and change in a dose response of detector in a presence of small photon field. For dosimetry in the above mentioned conditions detectors should

http://dx.doi.org/10.1016/j.ejmp.2014.09.002 1120-1797/© 2014 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: Hr
sak H, et al., Correction of measured Gamma-Knife output factors for angular dependence of diode detectors and PinPoint ionization chamber, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.09.002

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have high spatial resolution, linear dose response, water equivalence and minimal angular dependence. Semiconductor diodes are often used for dosimetry in radiosurgery because of a small measuring volume (thickness of a several tens of micrometres and diameter equal or less than 1 mm) and therefore high spatial resolution. However, they show considerable angular dependence (up to 10% difference in measured signal between 0
and 90
angle of incident radiation beam). So far, there is just one published study dealing with angular dependence of detectors used for Gamma-Knife dosimetry [15]. In that work angular dependence correction was derived for a radiophotoluminescent dosimeter and a small diode detector by simulating Gamma-Knife beams with the linear accelerator-based radiosurgery collimators. In this paper, influence of angular dependence of detectors on measurement of LGK Model C output factors was investigated and the correction method for angular dependence was proposed. Comparing to the work of Araki et al. [15] where Gamma-Knife beams were not used for measurement of angular dependence, in this work correction was based on measurements with the all sizes of Gamma-Knife collimator, using two models of p-type silicon diodes (shielded and unshielded) and PinPoint ionization chamber for which angular dependence of response is generally not expected. Corrected results were compared to recommended Elekta values of output factors. Angular dependence of all three detectors was measured.

D ¼ 39 and E ¼ 35). Output factors (OF) for the Model C collimator helmets are determined according to the following formula:

OF14;8;4 mm ¼

D14;8;4 mm D18 mm

where D14;8;4 mm is measured dose for the 14, 8 or 4 mm collimator, respectively, and D18mm is measured dose for 18 mm collimator. OF for 18 mm collimator helmet is equal to 1 by definition. Dosimetry methods All measurements were performed in the commercially available spherical phantom made of tissue equivalent acrylic material (PTGR, Tübingen, Germany) with a diameter of 16 cm. This phantom is composed of two hemi-spheres with special inserts that can accommodate standard detectors for radiosurgery (Fig. 2). The phantom was mounted to the collimator helmet (Fig. 3) with a centre adjusted to the UCP. Detectors were positioned in the centre of the phantom (with the longitudinal axis along z-direction) in a way that the centre of measuring volume of diode detectors and the reference point of ionization chamber coincide with the UCP within the radius of 0.1 mm. For the determination of angular dependence, detector signal corresponding to the angle of interest ðMA;B;C;D;E Þ was measured indirectly:

MA;B;C;D;E ¼ M  M1;2;3;4;5 Materials and methods Gamma-Knife unit In the Leksell Gamma-Knife unit Model C 201 Co-60 sources are placed in five parallel rings (marked as A, B, C, D and E ring in Fig. 1) on a semi-hemispherical surface, delivering the 201 photon beams that are focused to single point of intersection, known as the unit centre point (UCP), at the source-to-focus distance of 40.3 cm. The beams are collimated with a 18, 14, 8 and 4 mm collimator helmet giving almost spherical dose distribution around UCP. The source rings are separated by an angle interval of 7.5
, starting from ring A at 84
and ending with ring E at 54
off the horizontal z-axis (Fig. 1). Each ring has fixed number of sources (A ¼ 44, B ¼ 44, C ¼ 39,

Figure 1. Collimator helmet with the ring B sources blocked, i.e. 44 beam channels are plugged. This beam arrangement corresponds to the detector signal reading M2 at the UCP.

(1)

(2)

where M is detector signal reading when all beam channels are open and M1;2;3;4;5 are readings when beam channels belonging to ring A, B, C, D and E, respectively, are blocked (plugged) (Fig. 1). For the blocking of beam channels, a 6 cm-thick tungsten alloy plugs were used (Fig. 3). In the previous study [7] radiation transmission through the plugs was measured and it was found to be

Figure 2. The spherical PMMA phantom consisting of two hemi-spheres (a) and the special inserts that can accommodate Diode detector and PinPoint ionization chamber (b).

Please cite this article in press as: Hr
sak H, et al., Correction of measured Gamma-Knife output factors for angular dependence of diode detectors and PinPoint ionization chamber, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.09.002

H. Hr
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Figure 3. The spherical phantom mounted to the 14 mm collimator helmet and adjusted to the UCP (a) and the tungsten alloy plug next to the single beam collimator (b).

0.35% of the dose with beam channels open. Since in our experiment at the most 44 of 201 sources were plugged the transmission contribution was less than 0.1% and therefore considered as negligible. Since the measurements were performed in the period of five weeks, detectors readings were corrected for radioactive decay of Co-60 sources. The dose rate of Gamma-Knife unit ranged from 2.922 Gy/min to 2.884 Gy/min for the 18 mm collimator during period of measurement in this study. The relative response of detectors, representing angular A;B;C;D;E dependent correction factors fcorr (per source), is normalized to
the reading obtained at 84 (ring A) of the z-axis (Figs. 4 and 5): i fcorr ¼

Mi =Ni ; i ¼ A; B; C; D; E MA =44

3

Figure 4. The relative response, i.e. angular dependence of the diode detectors (Diode P and Diode E) measured with the Gamma-Knife beams and linear accelerator using a 6 MV X-ray beam with the size of 2  2 cm2. The response is normalized to the reading at the 84
and 90
for the Gamma-Knife and linear accelerator, respectively.

2  2 cm2) from Siemens ONCOR Expression linear accelerator, are compared in the same spherical phantom for all three detectors (Figs. 4 and 5). To avoid geometrical uncertainties in the measuring setup, no X-ray beams smaller than 2  2 cm2 were used. We consider this beam size as comparable to the 18 mm collimator helmet. The exposure time in our experiment is set to 2 min for all beam sizes. In the Gamma-Knife patient treatment procedure exposure time is always measured with Gamma-Knife unit timer and to avoid possible systematic errors the same timer was used instead of electrometer timer for exposure time measurements in our

(3)

where Ni is the number of sources belonging to ring i. For OF measurements, correction of readings for angular dependence was calculated as a weighted sum of angular dependent correction factors: ang:

fcorr ¼

X

Ni i fcorr 201 i¼A;B;C;D;E

(4)

where

X

Ni ¼ 201

(5)

i¼A;B;C;D;E

For the response consistency check, the relative responses of detectors measured with Gamma-Knife and 6 MV X-ray beam (size

Figure 5. The angular dependence of the PinPoint ionization chamber, measured with the Gamma-Knife and linear accelerator beams. The response is normalized to the reading at the 84
and 90
for the Gamma-Knife and linear accelerator, respectively.

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sak H, et al., Correction of measured Gamma-Knife output factors for angular dependence of diode detectors and PinPoint ionization chamber, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.09.002

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experiment. However, since collimator helmets have different sizes, a difference in actual exposure times is expected. Therefore, we have measured the end effect time ðtendeff Þ using pairs of exposures ðM2min and M1þ1min Þ [12,15]:

Results and discussion

_ ¼ 2M2min  M1þ1min M 2min tend eff ¼

(6)

M1þ1min  M2min _ M

(7)

End effect time correction for the exposure time t was derived according to formula: end eff fcorr ¼

M t ¼ Muncorr t þ tend eff

(8)

The measured output factors are corrected for the end effect time and angular dependence of detectors according to the following formula: 14;8;4 mm OF14;8;4 mm ¼ OFmeasured

ang end eff fcorr fcorr 14;8;4 mm 18 mm ang end eff fcorr 14;8;4 mm fcorr 18 mm

(9)

where ang ang fcorr 14;8;4 mm and fcorr 18 mm are correction factors for angular dependence, end eff end eff fcorr 14;8;4 mm and fcorr 18 mm are end effect time correction factors for collimator helmets, and

are measured output factors. OF14;8;4mm measured

Detectors Two models of p-type silicon diodes (shielded Diode P PTW60016 and unshielded Diode E PTW60017) and air-vented ionization chamber (PinPoint PTW31006) (PTW-Freiburg, Germany) are used for the measurements in this work in conjunction with PTW UNIDOS E electrometer (PTW-Freiburg). The PinPoint PTW31006 is predecessor of model PTW31014 which is being widely used today for dosimetry of small photon fields [19]. Details of all detectors are given in Table 1. A silicon detector will over-respond to low-energy scattered photons due to photoelectric effect in silicon sensitive volume [20]. To reduce this effect in the Diode P a disk-shaped silicon chip is surrounded by metal shielding. In unshielded Diode E which is designed for small photon and electron beams this metal shielding is replaced by a polymer plastic to diminish the unwanted backscattering of electrons from the shield [21]. Both of diodes have high spatial resolution and are suitable for dosimetry in small beams. PinPoint ionization chamber is specially designed for dosimetry in small photon beams. It has a small measuring volume surrounded by tissue equivalent wall material made of polymethyl

Table 1 Detectors used for measurements. Detector

Characteristics of active volume

Shielding

Diameter (mm) Length (mm) Volume (mm3) Diode P PTW60016 1.1 Diode E PTW60017 1.1 PinPoint PTW31006 2

methacrylate (PMMA) (0.56 mm) and graphite (0.15 mm). Since the measuring volume is approximately spherical a flat angular dependence of response is expected.

0.03 0.03 5

0.03 0.03 15

Shielded Unshielded e

The end effect times for each collimator helmet are given in Table 2. Table 3 shows output factors measured and corrected for angular dependence and the end effect time for each collimator helmet. The correction was calculated according to Eq. (9). Correction for angular dependence of detectors The angular dependent correction factors (Eq. (3)) were determined for Diodes P and E (Fig. 4) and PinPoint ionization chamber (Fig. 5). The difference in the relative response of Diode P for the angles 84
e54
is approximately 9% for 18, 14 and 8 mm collimator and 8% for 4 mm collimator which is slightly higher in comparison to published results [15] obtained with another type of silicon diode (Hi-pSi stereotactic field detector e SFD, Scanditronix Medical, Uppsala, Sweden). For the Diode E this difference is about 4% for all collimators, which is close to the results obtained by Araki et al. [15] for 4 mm helmet. Compared to Diode E, Diode P shows stronger angular dependence which may be explained by the increase of electron backscattering from the metal shield of active volume [21] as the angle of incident photon beam decreases, i.e. more photons are entering silicon chip perpendicularly. The difference in relative response of PinPoint ionization chamber is less than 3% for 18, 14 and 8 mm collimator (Fig. 5). For 4 mm collimator this difference is 10% which is considerably high and should be considered as a consequence of dosimetrical conditions in narrow Gamma-Knife beams, where it might be related to the change in volumetric averaging effect since for 4 mm collimator only part of the active volume (Table 1) is within the beam and the size of that part is changing as the angle of incident beam is being changed. Also, possible geometrical uncertainties in positioning of ionization chamber in a very small dose distribution may contribute to the change of detector signal. As an independent check of angular dependence measurements for Gamma-Knife, relative response of detectors was measured also with the 6 MV X-ray beam with the size of 2  2 cm2 and compared to the values obtained with 18 mm collimator (Figs. 4 and 5). Good agreement of relative responses was found for the Diodes P and E and a slight disagreement was found for the PinPoint ionization chamber. End effect time The end effect time was measured with the Diode E and PinPoint ionization chamber for the 2 min exposure time. Measured times (Table 2) are several times smaller in comparison to published data for Gamma-Knife Model B which are ranged from 0.066 min to 0.050 min for 18 mm collimator to 0.049 min and 0.029 min for 4 mm collimator [12,15]. Published values are obtained with the Xray film, semiconductor diode and ionization chamber. The end effect time depends on the size of the collimator and the speed of the treatment couch entering and leaving treatment position in Gamma-Knife unit. The speed of treatment couch for Model C is 2.6 cm/s. Since the collimator sizes are the same for Model B and Model C, we consider the speed of couch as a major cause of this difference. Unfortunately, there are no available data for speed of couch for Model B and therefore full comparison with Model C is not possible. As an independent check of our measurements for the 18 mm collimator helmet we roughly estimate the end effect time as the couch travelling time needed for the distance between 5%

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Table 2 The end effect times measured with Diode E detector and PinPoint ionization chamber. The electrometer readings correspond to the 2 min exposure time. Collimator helmet (mm)

18 14 8 4 a b

PinPointa

Diode E Electrometer reading M2 min (nC)

Electrometer reading M1þ1 min (nC)

End effect timeb tend eff (min)

Electrometer reading M2 min (nC)

Electrometer reading M1þ1 min (nC)

End effect time tend eff (min)

50.60 49.57 48.00 45.84

50.86 49.78 48.14 45.92

0.010 0.009 0.006 0.004

1.986 1.944 1.860 1.316

1.993 1.951 1.866 1.318

0.007 0.007 0.006 0.003

Corrected for air density. The end effect time measured with Diode P gives practically the same result as Diode E.

and 100% isodose of dose distribution (calculated with the GammaKnife treatment planning system) in the z-direction, i.e. travelling direction of treatment couch. This assessment gives value of 0.015 min which is in good agreement with the value of 0.010 min measured with Diode E detector. Measurements with PinPoint ionization chamber gave smaller end effect times (Table 2) due to a partially exposed measuring volume when chamber was entering/ leaving the treatment position. The end effect correction of 4 mm collimator output factor has the largest value (1.003 for diodes and 1.002 for PinPoint chamber) and correction of 8 and 14 mm collimator output factors was slightly lower (Table 3). These values are smaller than end effect correction factors published for GammaKnife Model B by Araki et al. [15] (1.008 and 1.006 for 4 mm and 8 mm collimator, respectively and 1.000 for 14 mm collimator output factor). Corrected output factors In Table 4 corrected output factors are compared to recommended Elekta values for Gamma-Knife Model C and published data for silicon diodes and PinPoint ionization chambers. For the 14 mm collimator corrected output factors are within ±0.3% of Elekta value and published data and the angular dependence

Table 3 The output factors measured with diode detectors and PinPoint ionization chamber and corrected for angular dependence and the end effect time. Collimator Detector Measured Correction OFb helmet for angular (mm) dependence ! ang fcorr 18 mm ang fcorr 14;8;4 mm

Correction Corrected for end OF ± 1 SDc a effect time 0 1 end

eff

@fcorrend14;8;4 eff fcorr

18

mm

1.000 1.000 1.000

1.000 1.000 1.000

1.000 ± 0.006 1.000 ± 0.006 1.000 ± 0.005

14

Diode P 0.982 Diode E 0.981 PinPoint 0.980

1.000 0.999 1.002

1.001 1.001 1.000

0.983 ± 0.009 0.981 ± 0.009 0.982 ± 0.007

8

Diode P 0.951 Diode E 0.947 PinPoint 0.934

1.001 1.002 0.996

1.002 1.002 1.000

0.954 ± 0.009 0.950 ± 0.009 0.931 ± 0.007

4

Diode P 0.887 Diode E 0.890 PinPoint 0.669

1.004 0.992 0.968

1.003 1.003 1.002

0.894 ± 0.008 0.886 ± 0.008 0.649 ± 0.005

The end effect correction factors were calculated for the exposure time of 2 min. OF for 18 mm collimator helmet is 1.000 by definition. Uncertainties are expressed in the terms of one standard deviation of mean value. c

Collimator Helmet (mm)

Reference

Method

OF ± 1 SD

14

e e e e [13] [15] [13]

Diode P Diode E PinPoint chamber Elekta Diode SFD Diode SFD PinPoint chamber

0.983 0.981 0.982 0.984 0.983 0.981 0.982

e e e e [13] [15] [13]

Diode P Diode E PinPoint chamber Elekta Diode SFD Diode SFD PinPoint chamber

0.954 0.950 0.931 0.956 0.955 0.949 0.928

e e e e [13] [15] [13]

Diode P Diode E PinPoint chamber Elekta Diode SFD Diode SFD PinPoint chamber

0.894 0.886 0.649 0.870 0.887 0.867 0.663

mm

Diode P 1.000 Diode E 1.000 PinPoint 1.000

a

Table 4 Corrected output factors compared to recommended Elekta values for Gamma-Knife Model C and published data for silicon diodes and PinPoint ionization chamber.

A

18

b

correction of all three detectors is very small (Table 3). For the 8 mm collimator Diode P gives practically the same value as Elekta's recommendation and Diode E value is within ±0.6% of published data for diodes and Elekta value. The PinPoint output factor value is 2.7% smaller than recommended and similar to the value measured by Mack et al. [13]. This discrepancy is probably caused by the lateral electronic disequilibrium [22]. For the 8 mm collimator angular dependence correction is 1.001, 1.002 and 0.996 for Diodes P, E and Pinpoint detector, respectively (Table 3). Output factor determined with the Diode P shows 2.8% larger value than Elekta value for 4 mm collimator. Diode E value is 1.8% larger than recommended and is practically same as value measured by Mack et al. [13]. Several authors reported over-response of shielded and unshielded silicon detectors in small photon fields [20,21,23]. It was proposed that formalism for reference dosimetry of small and nonstandard fields should be applied for correction of output factors in that case [19,24e26]. However, this includes determination of field-dependent and detector-dependent correction factors which is beyond the scope of this work. Angular dependence correction for the 4 mm collimator is 1.004, 0.992 and 0.968 for Diodes P, E and Pinpoint chamber, respectively (Table 3). For the 4 mm collimator PinPoint chamber gives 25% smaller value of output factor than Elekta's recommendation and that is similar to the published value which is 24% smaller. This considerable signal

8

4

± 0.009 ± 0.009 ± 0.007 ± 0.001 ± 0.006 ± 0.001 ± 0.009 ± 0.009 ± 0.007 ± 0.002 ± 0.005 ± 0.002 ± 0.008 ± 0.008 ± 0.005 ± 0.007 ± 0.005 ± 0.006

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loss is a consequence of the volumetric averaging effect and lack of lateral electronic equilibrium in narrow Gamma-Knife beams and is generally not related to the angular dependence of the PinPoint chamber. Conclusions Shielded Diode P PTW60016 and unshielded Diode E PTW60017 represent good choice for the Gamma-Knife dosimetry because of high spatial resolution and good signal response. However, they are originally designed for dosimetry with their longitudinal axis parallel to the central axis of entering photon or electron beam and they show considerable angular dependence of measured signal, particularly Diode P. Therefore, angular dependence correction should be applied when silicon diodes are used in Gamma-Knife dosimetry. For 14 and 8 mm collimator helmet output factors diodes show good agreement with recommended Elekta values. For the 4 mm collimator there is clearly over-response of the diodes and an additional field-specific correction should be applied. The PinPoint ionization chamber PTW31006 gives good results for 14 mm collimator. For the 8 and 4 mm collimator the measured signal is significantly smaller because of the lack of lateral electronic equilibrium and volumetric averaging effect and the PinPoint chamber should be avoided in clinical measurements of output factors for the 8 and 4 mm collimator. Conflict of interest statement The authors declare that there is no conflict of interest. References [1] Verhey LJ, Smith V, Serago CF. Comparison of radiosurgery treatment modalities based on physical dose distributions. Int J Radiat Oncol Biol Phys 1998;40(2):497e505. [2] Nakamura JL, Verhey LJ, Smith V, Petti PL, Lamborn KR, Larson DA, et al. Dose conformity of Gamma-Knife radiosurgery and risk factors for complications. Int J Radiat Oncol Biol Phys 2001;51(5):1313e9. [3] Semwal MK, Sukhvir Singh, Sarin A, Bhatnagar S, Pathak HC. Comparative clinical dosimetry with X-knife and gamma knife. Phys Med 2012;28:269e72. [4] Gevaert T, Leviver M, Lacornerie T, Verellen D, Engels B, Reynaert N, et al. Dosimetric comparison of different treatment modalities for stereotactic radiosurgery of arteriovenous malformations and acoustic neuromas. Radiother Oncol 2013;106:192e7. [5] Cheung JYC, Yu KN, Ho RTK, Yu CP. Monte Carlo calculated output factors of a Leksell Gamma Knife unit. Phys Med Biol 1999;44:N247e9. [6] Battistoni G, Cappucci F, Bertolino N, Brambilla MG, Mainardi HS, Torresin A. FLUKA Monte Carlo simulation for the Leksell Gamma Knife Perfexion radiosurgery system: homogeneous media. Phys Med 2013;29(6):656e61.

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Please cite this article in press as: Hr
sak H, et al., Correction of measured Gamma-Knife output factors for angular dependence of diode detectors and PinPoint ionization chamber, Physica Medica (2014), http://dx.doi.org/10.1016/j.ejmp.2014.09.002