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Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation
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Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation Atefeh Mahmoudi , Ghazale Geraily , Tahereh Hadisi Nia , Alireza Shirazi , Milad Najafzadeh PII: DOI: Reference:
S0169-2607(19)31997-2 https://doi.org/10.1016/j.cmpb.2019.105261 COMM 105261
To appear in:
Computer Methods and Programs in Biomedicine
Received date: Revised date: Accepted date:
4 November 2019 30 November 2019 4 December 2019
Please cite this article as: Atefeh Mahmoudi , Ghazale Geraily , Tahereh Hadisi Nia , Alireza Shirazi , Milad Najafzadeh , Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation, Computer Methods and Programs in Biomedicine (2019), doi: https://doi.org/10.1016/j.cmpb.2019.105261
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Highlights
Considerable reduction in physical penumbra was achieved using the designed filters The most penumbra reduction was seen for lead filter of 4 mm collimator The curved lateral surface of the filters led to lower hot spots near the beam edge Lead filters caused lower hot spots and beam attenuation than to the tungsten filters Negligible variations were seen by increasing SDD parameter
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Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation Atefeh Mahmoudi1, Ghazale Geraily*2, Tahereh Hadisi Nia3, Alireza Shirazi4, Milad Najafzadeh5 1 MSc of Medical Physics, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran. Email: [email protected] 2 Associate Professor, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran Email: [email protected] 3 PhD Student, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran. Email: [email protected] 4 Full Professor, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran. Email: [email protected] 5 MSc of Medical Physics, Department of Radiology, Faculty of Para-Medicine, Hormozgan University of Medical Sciences, Bandar Abbas, Islamic Republic of Iran. Email: [email protected]
*Corresponding author: Ghazale Geraily, Assistant Professor, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences. Islamic Republic of Iran. Email: [email protected] Phone number: +989124308726
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Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation Atefeh Mahmoudi1, Ghazale Geraily*2, Alireza Shirazi3, Tahereh Hadisi Nia4, Milad Najafzadeh5
Abstract Background and objective: In small radiation fields used in stereotactic radiosurgery penumbra is an important portion of the field size especially when critical organs at risk are located near the treatment sites. This study was aimed to reduce penumbra width (90%-50% isodose lines) of Gamma Knife (GK) machine by investigating of source to diaphragm distance (SDD) and designing compensating filter. Methods: Compensating filters at the end of the helmet collimators with the aim of reducing penumbra as well as reducing hot spots appeared near the edge of beam were modeled using Monte Carlo simulation code. Moreover, the SDD parameter was increased as one of the effective factors on penumbra width. Results: Results showed that single beam penumbra width using optimal design of filters was decreased by 59.49%, 42.50%, 39.02% and 34.44% with attenuation of 30.53%, 13.67%, 11.43% and 9.82% for 4, 8, 14 and 18 mm field sizes, respectively. Conclusions: The designed filters lead to considerable reductions in single beams penumbra width as well as a noticeable reduction in maximum dose emerged near the beam edge due to the curved lateral surface of filters. Keywords: Gamma Knife, physical penumbra width, compensating filter, SDD
1. Introduction Stereotactic radiosurgery (SRS) is an advanced form of radiotherapy technique with high precision in which intracranial tumors and functional disorders are treated with multiple high focused non-coplanar arcs of x-ray or gamma radiation beams. Stereotactic target localization and dose delivery have caused minimum radiation dose to be imparted to adjacent normal structures [1, 2, 3]. Nowadays, SRS is performed using linac-based radiosurgery, cyberknife systems, and Gamma Knife machine. Gamma Knife is a highly accurate radiation device invented by Lars Leksell in 1968. It is internationally recognized as a feasible alternative modality to treat brain tumors either benign or malignant which are inaccessible for brain surgery [4, 5, 6]. Converged radiation beams directed
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at the tumor from 201 cobalt-60 sources deliver a single high dose to the localized target with a precision greater than 0.3 mm and sharp dose gradient while preserving nearby critical tissues intact [4, 7, 8]. Radiosurgery treatment can sometimes be challenged by the small tumor grown near the vital structures such as trigeminal neuralgia treatment. In such cases, the penumbra is a leading factor for the dose received by normal tumor-bound tissues. The penumbra is defined qualitatively as the region of high dose gradient at the edge of a beam and from a quantitative aspect as the distance between the 80%-20% or the 90%-50% isodose lines at a defined depth [9]. Thus, the penumbra must be considered especially in SRS treatments in which the prescribed radiation dose is high and subsequently, the dose delivered to the penumbra region will be high [9]. Several methods have been proposed to reduce the beam penumbra width in stereotactic radiosurgery. The source to diaphragm distance (SDD) has been evaluated in small radiosurgery fields as one of the factors affecting the geometric penumbra width. Although the penumbra width is expected to shrink by increasing the SDD, no dramatic changes have been observed because of the inappreciable contribution of the geometric penumbra to the physical penumbra [10, 11]. On the other hand, scatter photons and secondary electrons contribute to radiological penumbra. However, in radiation fields especially smaller than 2 cm, scattered photons are negligible so secondary electrons are considered as the primary cause of radiological penumbra. Under these circumstances, use of low megavoltage beams leads to diminished ranges of secondary electrons thus shrinking the beam penumbra [2, 9, 12-14]. Compensating filters which reduce penumbra through increasing primary radiation at the beam edges have been investigated in standard and radiosurgery fields as another factor for penumbra reduction. Thomas [11] and Guerrero et al. [15] studied the flattening filter effect on penumbra width in linac-based radiosurgery and Gamma Knife, respectively. Reduced penumbra and greater field homogeneity were reported using compensating filters in small circular fields. Bender et al. [16] also reduced small field penumbra by inserting needles as compensators within conical collimators. The purpose of this study was to reduce beam penumbra of Gamma Knife machine model 4C with lower hot spots emerging near the beam edge which are relatively high in conical filters used in Guerrero et al.’s work. To this aim, first different designed flattening filter shapes of various materials were modeled for 4, 8, 14, and 18 mm collimators. Then, the increase in the source to diaphragm distance (SDD) was studied using Monte Carlo simulation.
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2. Materials and methods Geometry simulations and photon transports were performed using Monte Carlo-based BEAMnrc code built on the EGSnrc. The EGSnrc is an extended version of the EGS4 code in which transport physics is substantially improved when compared with EGS4 [17]. Initial gamma rays emitted by 60Co source decays and secondary electrons are conducted to the isocentre point by passing through the Gamma Knife channel. Each beam channel consists of a fixed collimator placed in the machine body and helmet collimator which defines the final beam diameter at the focus point [5, 7, 8] (Figure 1). One of the unique features of the BEAMnrc code is availability of pre-made geometries called component module impressively improving the facility and reducing the time of geometric modeling in radiotherapy applications. Single channel geometry was modeled using FLATFILT module. The outer aperture diameter of helmet collimator (d) is 2.5, 5.0, 8.5, and 10.6 mm for 4, 8, 14, and 18 mm collimators, respectively.
Figure 1. The view of the single channel geometry
In order to simulate the source, a 1.25 MeV point source at the active center of the 60Co cylindrical source was considered [7]. The accuracy of the simulated geometry was validated through comparing the simulated profiles with film dosimetry results [18].
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2.1 Compensating filter design The shape of the compensating filter was derived from the particles planar fluence distribution generated by beamdp code. Since the collimated output particles distribution was Gaussian and non-uniform, the required filter thickness in the beam path was calculated using the Lambert’s law equation: I = I0 Where, I is the least fluence and I0 is fluence at different points with different thicknesses x of filter, whereby the overall shape of the filter was obtained. FLATFILT module was selected to mode the filter geometry. The filter placed at the end of the helmet collimator [11, 15] was composed of multiple truncated cones with various heights and radii. The coronal cross-section of the simulated filter at the outer collimator aperture and the three-dimensional shape of the modeled filter for 4-mm collimator can be observed in Figure 2.
Figure 2. Coronal view (X-Z) of the modeled filter at the end of the single channel (left), tridimensional shape of filter (right) for 4 mm collimator. The height of filter is 5 mm.
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Two different materials, tungsten (74W) and lead (82Pb), with linear attenuation coefficients of 1.025 and 0.6252
and densities of 19.3 and 11.34
, respectively were used as materials of
the filters. The initial studies of the designed filter with the thickness obtained from the Lambert equation showed that value of generated hot spots was very high. So, new filters were designed in which the thickness of all points was reduced to the same ratio. Accordingly, totally 56 configurations with different filter heights and two materials were modeled for collimator sizes of 4, 8, 14, and 18 mm. The flattening filters designed for all studied thicknesses and materials were made of 9, 12, 12, and 13 truncated cones for 4, 8, 14, and 18 mm field sizes, respectively. The bottom radius of the first truncated cone of filters (R 1T) was equal to the output aperture radius of helmet collimators. But for the top radius of the last truncated cone of filters (R 2T), all considered modes, according to the mentioned fluence calculation, was 0.06, 0.13, 0.21, and 0.80 mm for 4, 8, 14, and 18 mm collimators, respectively. The electron and photon transport cut-off energies were set to 0.7 and 0.01 MeV, respectively. Specifically, 6×108 initial photon trajectories were simulated for each beam diameter. DOSXYZnrc code which is a general purpose MC EGSnrc user-code for three-dimensional dosimetry was implemented in energy deposition calculations [19]. For this purpose, the voxelbased cubic phantom made of Plexiglas (PMMA) was used. The phantom was made of 0.25 mm voxel sizes for 4 and 8 collimators and 0.50 mm voxel sizes for 14 and 18 mm collimators along the X and Y axes [15]. In the present study, because of the insignificant contribution of voxel sizes along Z axis in dose calculation, the intersecting voxel with other axes was only considered small. The phase space file generated through BEAMnrc execution was used as the phase space source in DOSXYZnrc code. The number of histories assigned to obtain the statistical errors less than 1% was 6×109 and 8×109 for 0.25 and 0.50 mm voxel sizes, respectively. Then, STATDOSE program was employed to calculate the single beam profiles at the isocentre depth through reading the “.3ddose” file (output file from DOSXYZnrc) [20]. Physical penumbra width (90%-50%) was measured for different field sizes in MATLAB software. Additionally, to assess the beam attenuation due to the presence of filter, filtered and unfiltered profiles for each thickness were compared with each other. Given the similarity of X and Y profiles, only Xprofiles were evaluated. In order to verify our filter efficiency in diminishing of the hot spots appeared near the beam edge, one simple lead conical filter with a height of 8mm for 4mm collimator which produces a larger penumbra-field radius ratio compared to the other collimators was designed. .
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2.1 Increase in source-to-diaphragm distance (SDD) In order to investigate the effect of SDD parameter on the physical penumbra width of single beam, SDD was elevated in five 1-cm steps for 4, 8, 14, and 18 mm collimator sizes. Increase in SDD was performed by raising the helmet collimator height. With increase in every 1-cm step, the SDD values changed to 24.6, 25.6, 26.6, 27.6, and 28.6 cm. The method discussed for the dose and profile calculations in section 2.1 was also applied in this section.
3. Results 3.1 simulated compensating filters Physical penumbra width (90%-50%) values in the presence of the designed filters as well as beam attenuation are presented in Tables 1-4 for 4, 8, 14, and 18 mm field sizes. Use of filters led to reduced beam penumbra width. With enlargement of the filter thickness, greater penumbra reductions were achieved. This decline was small for low heights especially for 4 mm collimator. Furthermore, a greater intensity loss of filters with a higher thickness was seen, where the filter attenuation was less for the lead filter with equal heights to tungsten filters. The simulated filters for 4 mm collimator showed a different behavior than the other collimators. For this reason, filter thicknesses up to 8 mm were studied. The penumbra width (90%-50%) of 4 mm radiation field size without filter was 0.79 mm, which decreased by 11.21% and 63.06% as the tungsten filter thickness varied from 1 to 8 mm.
9 Table 1. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 4 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5 6 7 8
Penumbra Penumbra width (mm) reduction (%) 0.79 0.70 0.68 0.64 0.53 0.46 0.35 0.32 0.31 0.29
12.86 13.92 19.00 32.91 41.77 55.70 59.49 60.76 63.29
Lead Beam attenuation (%)
Penumbra width (mm)
7.46 10.94 14.37 20.73 26.42 31.81 36.76 41.33 45.54
0.79 0.72 0.72 0.71 0.62 0.57 0.49 0.43 0.36 0.32
Beam Penumbra reduction (%) attenuation (%) 8.86 8.86 10.13 21.52 27.85 37.97 44.57 54.43 59.49
4.42 6.67 8.78 12.86 16.84 20.45 23.81 27.29 30.53
Table 2. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 8 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5
Penumbra Penumbra width (mm) reduction (%) 0.80 0.58 0.48 0.42 0.34 0.26 0.21
27.50 40.00 47.50 57.50 67.50 73.75
Lead Beam attenuation (%)
Penumbra width (mm)
7.55 11.22 14.54 21.00 26.86 32.13
0.80 0.69 0.59 0.56 0.46 0.38 0.33
Penumbra Beam reduction (%) attenuation (%) 13.75 26.25 30.00 42.50 52.50 58.75
4.93 7.04 9.25 13.67 17.78 21.51
10 Table 3. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 14 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5
Penumbra Penumbra width (mm) reduction (%) 0.82 0.61 0.50 0.47 0.45 0.43 0.42
25.61 39.02 42.68 45.12 47.56 49.78
Lead Beam attenuation (%)
Penumbra width (mm)
7.78 11.43 14.79 21.27 27.16 32.75
0.82 0.69 0.60 0.55 0.47 0.46 0.45
Penumbra Beam reduction (%) attenuation (%) 15.86 26.83 32.93 42.68 43.90 45.12
4.78 7.16 9.43 13.91 17.87 21.85
Table 4. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 18 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5
Penumbra Penumbra width (mm) reduction (%) 0.90 0.62 0.59 0.57 0.51 0.45 0.38
31.11 34.44 36.67 43.33 50.00 57.78
Lead Beam attenuation (%)
Penumbra width (mm)
8.18 11.78 15.34 22.10 28.42 33.97
0.90 0.77 0.63 0.59 0.59 0.55 0.51
Penumbra Beam reduction (%) attenuation (%) 14.44 30.00 34.44 34.44 38.89 43.33
5.07 7.63 9.82 14.35 18.56 22.74
Figures 3 and 4 display the half-beam profiles calculated at the isocentre depth for collimator sizes of 4, 8, 14, and 18 mm with and without the flattening filters made of tungsten and lead materials, clearly representing the effect of filter on the beam profiles. All profiles were normalized to the central axis dose. As shown on the figures, as the filter thickness grows, the internal useful area of the beam becomes flattened further. The filter usage caused appearance of hot spots near the beam edge and horn-shaped profiles. These spots grew by increasing the filter
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height. The filters made of lead produced lower hot spots than the tungsten filters at the profile edges (Figure 4).
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Figure 3. Half-beam profiles calculated along X axis at isocentre depth in Plexiglas cubic phantom in the presence of tungsten filters for collimator sizes of a) 4mm (h=1-3mm), b) 4mm (h=4-8mm), c) 8mm (h=1-2mm), d) 8mm (h=35mm), e) 14 mm (h=1-2mm), f) 14 mm (h=3-5mm) and g) 18 mm (h=1-2mm), h) 18 mm (h=3,4mm)
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Figure 4. Half-beam profiles calculated along X axis at isocentre depth in Plexiglas cubic phantom in the presence of lead filters for collimator sizes of a) 4mm (h=1-3mm), b) 4mm (h=4-8mm), c) 8mm (h=1-2mm), d) 8mm (h=35mm), e) 14 mm (h=1-2mm), f) 14 mm (h=3-5mm) and g) 18 mm (h=1-2mm), h) 18 mm (h=3-5mm)
The percentages of beam attenuation in different thicknesses of tungsten and lead filters for four collimator sizes are represented in Figure 5. According to the figure, the extent of intensity loss for collimator sizes of 8, 14, and 18 with equal heights are approximately the same except for the 4 mm collimator which showed less intensity attenuation.
Figure 5. Beam attenuation as a function of thickness of tungsten filter (a) and lead (b) for 4, 8, 14, and 18 mm field sizes
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Based on the Table.5, for the simple conical filter with top radius of 0.06mm, 107.52% hot spot has appeared, whereas according to the Figure 4(b) no hot spot was seen for the designed filter with the curved lateral surface. Increasing simple conical filter top radius, the hot spot percentage dropped, while its effect on penumbra reduction width was dramatically lower than our designed filter. Furthermore, the simple conical filter caused more intensity attenuation resulted in more treatment time.
Table 5. The physical penumbra width (90%-50%), penumbra width reduction and beam attenuation for lead conical filter of 8mm height and various top radii.
Conical filter top radius (mm)
Maximum dose at the beam edge (%)
Physical penumbra width (mm)
Penumbra reduction (%)
Beam attenuation (%)
0.06 0.10 0.50 0.90
107.52 107.81 104.98 -
0.32 0.31 0.30 0.59
59.49 60.76 62.03 25.32
21.11 21.88 28.36 35.14
3.2 The effects of increasing SDD The results obtained from SDD changes are listed in Table 6. Unexpectedly, the physical penumbra width (90%-50%) did not show a regular trend with elevation of SDD. As can be seen, the best results were observed for 4 and 8 mm collimators in 1-cm increase, whereby the penumbra width diminished from 0.785 and 0.790 mm to 0.749 and 0.736 mm for 4 and 8 field sizes, respectively.
16 Table 6. The physical penumbra width (90%-50%) for various SDDs at the isocentre depth
Physical penumbra width (90%-50%) (mm) Collimator size (mm)
4 8 14 18
SDD 236 mm
246 mm
256 mm
266 mm
276 mm
286 mm
0.79 0.80 0.82 0.90
0.75 0.74 0.81 0.97
0.77 0.75 0.83 0.93
0.78 0.77 0.79 0.89
0.78 0.78 0.86 0.93
0.79 0.78 0.80 0.94
4. Discussion In this study, some specially designed flattening filters were investigated to reduce the physical penumbra width (90%-50%) of Gamma Knife machine model 4C.To the best of our knowledge, there has been no work on penumbra reduction of Gamma Knife model 4C. There was an appreciable reduction in physical penumbra width of GK single beam, while the maximum dose at the profile edge was not very high especially for 4 mm collimator. The beam penumbra width for optimum compensating filters was reduced by 59.49, 42.50, 39.02, and 34.44% for 4, 8, 14, and 18 mm collimators, respectively. The increase in SDD effect on penumbra width was also studied where small variations were seen in the penumbra width as SDD rose. Adding flattening filter in the radiation beam path led to beam attenuation in the central parts of the filter and increased the primary radiation at periphery [11, 15, 16, 21-23]. On the other hand, the greater fluence at the beam boundaries caused emergence of some hot spots. This effect will grow with elevation of the filter thickness due to increase in the difference between the central and peripheral thickness of the filter [15]. In this study, the compensating filters with different shapes were designed based on the suggestion by Guerrero et al. [15] about using filter with curved lateral surface instead of a linear one to reduce the value of hot spots values appearing near the beam edge. The advantage of our designed filter was a dramatic reduction in the hot spot value appearing near the beam edge when compared to a conical filter with a linear lateral surface as had been predicted [15]. The hot spot percentage reduction in a conical filter can be achieved using elevation of the truncated cone top radius, causing increased penumbra width as well as the lowered beam intensity. This fact, reflect the proper designation of our filter, as it reduces hotspot percentage with a reasonable penumbra reduction and intensity loss (Table.5). The filter designed for 4 mm collimator showed a completely different behavior in creating hot spots as compared to the other collimators. This discrepancy could be due to the less scattered photons in small fields. At this collimator size, there was no hot spot up to 5 mm height for
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tungsten filter (Figure 3(b)). So, based on this observed feature, further elevation of the height to achieve a lower penumbra width was possible. According to the results, greater hot spots were seen with enlargement of the field size for the same filter thickness except for the 18 mm field size, whose hot spots were less than or equal to those of the 14 mm field size. The reason can be attributed to the similar shape of the designed filter for 14 and 18 mm collimators with same thickness as well as the roughly similar behavior of these collimators. The physical penumbra width (90%-50%) diminished by increasing the filter thickness. At very low thicknesses, the penumbra reduction and profile flattening were trivial. Although higher thicknesses resulted in a lower penumbra width, a greater hot point was created near the profile edge. Indeed, the penumbra width and the emergence of hot spots behave in opposite. For all collimator sizes for the filter of 1-cm thickness, the penumbra width difference in filtered and unfiltered mode was greater than the penumbra width difference between the other thicknesses. These observations are in line with the results of Guerrero et al. Another important parameter in the presence of filter is beam attenuation percentage which grew by increasing the filter thickness. According to the results, the smallest penumbra width was obtained in exchange for a greater hot spot and beam attenuation. In addition to tungsten, lead was also studied as a constituent substance of the filter. In the presence of the lead filter, the maximum percentage of dose appearing near the beam edge was lower than that of the tungsten at equal filter thicknesses. As such, the penumbra reduction was also less considerable. This discrepancy is well seen in Figure 4 (b), in which, there are no hot spots up to the height of 8 mm, while for tungsten filters (Figure 3 (b)) they can be seen from 6 mm height. The beam attenuation caused by the lead filter was less than the attenuation induced by the tungsten filter. The reason behind the different behavior of two studied materials is lower linear attenuation coefficient of lead compared with tungsten for 60Cosource which are 0.6252 and 1.025
as investigated by Buyuk and Tugrul [24].
The plotted profiles indicated that with elevation of the filter thickness, the 90% isodose line approached the profile edge and resulted in a smaller penumbra width. This filter effect on the dose profile agreed with the results reported by Guerrero et al. [15] as well as by Thomas. [11] The shape of unfiltered and low thicknesses filtered profiles is more rounded. This feature is more obvious for 4 mm collimator than for the other ones, highlighting the greater ratio of penumbra width to the field size for small field sizes especially 4 mm field size. Elevation of the filter thickness led to more flattened profiles, but at a critical thickness, with creating higher hot spots despite further reduction in the penumbra width, the profile flatness diminished. In cases of penumbra reduction, it is desirable that the 90% isodose line moves outward while the 50% dose point remains constant. With regard to the profiles calculated for various thicknesses and field sizes (Figures 3 and 4), the 50% dose has also moved toward the beam edge but it is less than 90% dose shifts, so the penumbra reduction was achieved. This dual effect of
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compensating filter on beam profiles resulted in a slight increase in the field size which was in accordance with Thomas’s observations in 1994. The beam attenuation as a function of filter thickness for the collimator sizes of 4, 8, 14, and 18 mm changed almost linearly (Figure 5). This result has also been reported by Guerrero et al. [15]. In addition, the attenuation was nearly the same for the four collimators at the identical filter thicknesses and rose with enlargement of the collimator size. The attenuations of lead filter (Figure 5 (b)) were less than those of the tungsten filter (Figure 5 (a)) for all the studied thicknesses. Optimum compensating filters were selected considering the penumbra width reduction value, the maximum dose near the edge of beam profile, the beam attenuation percentage, and the filter material. The beam attenuation and hot spot area emerged are determinant factors for penumbra reduction, where the filter thickness must be selected such that it results in lower attenuation and fewer hot spots. The maximum dose at the beam edge was acceptable up to 3% of the central axis dose for all collimators [15, 25]. The optimum filter for the 4 mm collimator was the lead filter with a thickness of 8 mm and an attenuation of 30.53%. For this filter, the physical penumbra width dropped by 59.49%. For the 8 mm collimator, the 3 mm lead filter with a 42.50% and 13.67% reduction in penumbra width and beam intensity, respectively was appropriate. The optimum filter for the 14 mm collimator was a 1.5 mm tungsten filter with 11.43% beam attenuation and 39.02% reduction in the beam penumbra width. The lead filter of 2-mm thickness with attenuation and penumbra reduction of 9.82% and 34.44%, respectively was optimum for 18 mm collimator. Since there was no hot spot as limiting factor in penumbra reduction, so a relatively high attenuation was accepted for the 4 mm collimator. In other words, because of high importance of the 4 mm collimator penumbra width, the greater intensity loss was accepted to gain smaller penumbra width. Based on the mentioned results, the maximum and minimum penumbra reduction for optimum compensating filters belonged to 4 and 18 mm collimators, so great reductions were obtained in penumbra for 4 the mm field size. The physical penumbra width did not show a regular trend in reduction with elevation of SDD (Table 6). A reduction in penumbra was expected for each extended SDD value, but for 14 and 18 mm collimators, the penumbra did not diminish by SDD elevation and at the same time increased beyond the penumbra width of standard SDD in some cases. In their work on stereotactic radiosurgery machines, Serago et al. [10] and Thomas [11] found that because of insignificant contribution of geometric penumbra in physical penumbra in such machines, SDD has negligible effects on penumbra width. In order to examine the impact of the designed filters on dose uniformity within the target, dose volume histograms should be calculated using treatment planning system [15] and considering this users are not allowed to manipulate the treatment planning system of the machine, this part can just be proposed to be investigated.
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5. Conclusion External compensating filters located in radiotherapy devices with the aim of increasing the radiation at the beam edges can reduce beam penumbra width. In this study, special shapes of compensating filters were investigated to reduce the physical penumbra width (90%-50%) of Gamma Knife machine model 4C. The designed filters led to considerable reductions in the width of single beam penumbra where a maximum reduction of 59.49% was observed for the 4 mm collimator size with a beam attenuation of 30.53%. The curved lateral surface of filter resulted in a noticeable reduction in the maximum dose emerging near the beam edge in comparison with conical filters. Further, since no significant change was seen due to the increase in SDD, it can be concluded that changing SDD has no dramatic effect on beam penumbra width of Gamma Knife system.
Acknowledgement This research was supported by Tehran University of Medical Sciences as a master thesis number of 32880.
Disclosure of conflicts of Interest Authors have no conflicts of interest.
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References [1] Pignol J-P, Keller BM. Electron and photon spread contributions to the radiological penumbra for small monoenergetic x-ray beam (≤ 2 MeV). J. Appl. Phys. 2009;105(10):102011-5. [2] Keller BM, Beachey DJ, Pignol JP. Experimental measurement of radiological penumbra associated with intermediate energy x‐rays (1MV) and small radiosurgery field sizes. Med. Phys. 2007;34(10):3996-4002. [3] Romano F, Sabini M, Cuttone G, et al. Geant4-based Monte Carlo Simulation of the Leksell Gamma Knife®: Nuclear Science Symposium Conference Record; 26 Oct.-3 Nov. 2007; Honolulu, HI, USA: IEEE; 2007. P. 2581-6. [4] Cheung JY, Yu KN, Yu CP, et al. Monte Carlo calculation of single‐beam dose profiles used in a gamma knife treatment planning system. Med. Phys. 1998;26(7):1252-6. [5] Xiong W, Huang D, Lee L, et al., editors. Implementation of Monte Carlo simulations for the Gamma Knife system. J. Phys: Conference Series 2007:1-10. [6] Battistoni G, Cappucci F, Bertolino N, et al. FLUKA Monte Carlo simulation for the Leksell Gamma Knife Perfexion radiosurgery system: homogeneous media. Physica Medica. 2013;29(6):656-61. [7] Al-Dweri FM, Lallena AM. A simplified model of the source channel of the Leksell Gamma Knife®: testing multisource configurations with PENELOPE. Phys. Med. Biol. 2004;49(15):3441-53. [8] Moskvin V, DesRosiers C, Papiez L, et al. Monte Carlo simulation of the Leksell Gamma Knife®: I. Source modelling and calculations in homogeneous media. Phys. Med. Biol. 2002;47(12):1995-2011. [9] O'Malley L, Pignol J-P, Beachey DJ, et al. Improvement of radiological penumbra using intermediate energy photons (IEP) for stereotactic radiosurgery. Phys. Med. Biol. 2006;51(10):2537-48. [10] Serago CF, Houdek PV, Hartmann GH, et al. Tissue maximum ratios (and other parameters) of small circular 4, 6, 10, 15 and 24 MV x-ray beams for radiosurgery. Phys. Med. Biol. 1992;37(10):1943-56. [11] Thomas S. Factors affecting penumbral shape and 3D dose distributions in stereotactic radiotherapy. Phys. Med. Biol. 1994;39(4):761-71. [12] Pignol J-P, Keller BM. Electron and photon spread contributions to the radiological penumbra for small monoenergetic x-ray beam (≤ 2 MeV). J. Appl. Phys. 2009;105(10):102011-5. [13] Keller BM, Pignol JP, Presutti J, et al. Intermediate energy photons (1MV) to improve dose gradient, conformality, and homogeneity: Potential benefits for small field intracranial radiosurgery. Med. phys. 2009;36(1):33-9. [14] Yarahmadi M, Allahverdi M, Nedaie HA, et al. Improvement of the penumbra for small radiosurgical fields using flattening filter free low megavoltage beam Zeitschrift für Medizinische Physik. 2013;23(4):291-9. [15] Guerrero M, Li XA, Ma L. A technique to sharpen the beam penumbra for Gamma Knife radiosurgery. Phys. Med. Biol. 2003;48(12):1843-53. [16] Bender ET. Increasing dose gradient and uniformity in small fields using modulation: Theory and prototypes for cone‐based stereotactic radiosurgery. Med. phys. 2014;41(5): 051706-7. [17] Rogers D, Walters B, Kawrakow I. BEAMnrc users manual. Nrc Report Pirs. Ottawa, Canada. National Research Council of Canada; 2017. [18] Mahmoudi A, Shirazi A, Geraily G, Hadisi nia T, Bakhshi M, Maleki M. Penumbra width determination of single beam and 201 beams of Gamma Knife machine model 4C using Monte Carlo simulation. Journal of Radiotherapy in Practice. 2019; 18(1):82-7. [19] Rogers D, Walters B, Kawrakow I 2011 DOSXYZnrc users manual. Nrc Report Pirs. Ottawa, Canada. National Research Council of Canada; 2017. [20] McGowan H, Faddegon B, Ma C 2007 STATDOSE for 3D dose distributions. [21] Laughlin JS, Mohan R, Kutcher GJ. Choice of optimum megavoltage for accelerators for photon beam treatment. Int. J. Rad. Oncol. Biol. Phys. 1986;12(9):1551-7. [22] Biggs PJ, Shipley WU. A beam width improving device for a 25 MV x ray beam. Int. J. Rad. Oncol. Biol. Phys. 1986;12(1):131-5.
21 [23] Brugmans MJ, van der Horst A ,Lebesque JV, et al. Beam intensity modulation to reduce the field sizes for conformal irradiation of lung tumors: a dosimetric study. Int. J. Rad. Oncol. Biol. Phys. 1999;43(4):893-904. [24] Buyuk B, Tugrul AB. Comparison of lead and WC-Co materials against gamma irradiation. Acta Phys Pol A. 2014;125(2):423-5. [25] Korevaar EW, van Vliet RJ, Woudstra E, et al. Sharpening the penumbra of high energy electron beams with low weight narrow photon beams. Radiother. Oncol. 1998;48(2):213-20.
Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation Atefeh Mahmoudi , Ghazale Geraily , Tahereh Hadisi Nia , Alireza Shirazi , Milad Najafzadeh PII: DOI: Reference:
S0169-2607(19)31997-2 https://doi.org/10.1016/j.cmpb.2019.105261 COMM 105261
To appear in:
Computer Methods and Programs in Biomedicine
Received date: Revised date: Accepted date:
4 November 2019 30 November 2019 4 December 2019
Please cite this article as: Atefeh Mahmoudi , Ghazale Geraily , Tahereh Hadisi Nia , Alireza Shirazi , Milad Najafzadeh , Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation, Computer Methods and Programs in Biomedicine (2019), doi: https://doi.org/10.1016/j.cmpb.2019.105261
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Highlights
Considerable reduction in physical penumbra was achieved using the designed filters The most penumbra reduction was seen for lead filter of 4 mm collimator The curved lateral surface of the filters led to lower hot spots near the beam edge Lead filters caused lower hot spots and beam attenuation than to the tungsten filters Negligible variations were seen by increasing SDD parameter
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Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation Atefeh Mahmoudi1, Ghazale Geraily*2, Tahereh Hadisi Nia3, Alireza Shirazi4, Milad Najafzadeh5 1 MSc of Medical Physics, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran. Email: [email protected] 2 Associate Professor, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran Email: [email protected] 3 PhD Student, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran. Email: [email protected] 4 Full Professor, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences, Tehran, Islamic Republic of Iran. Email: [email protected] 5 MSc of Medical Physics, Department of Radiology, Faculty of Para-Medicine, Hormozgan University of Medical Sciences, Bandar Abbas, Islamic Republic of Iran. Email: [email protected]
*Corresponding author: Ghazale Geraily, Assistant Professor, Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Tehran University of Medical Sciences. Islamic Republic of Iran. Email: [email protected] Phone number: +989124308726
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Beam penumbra reduction of Gamma Knife machine model 4C using Monte Carlo simulation Atefeh Mahmoudi1, Ghazale Geraily*2, Alireza Shirazi3, Tahereh Hadisi Nia4, Milad Najafzadeh5
Abstract Background and objective: In small radiation fields used in stereotactic radiosurgery penumbra is an important portion of the field size especially when critical organs at risk are located near the treatment sites. This study was aimed to reduce penumbra width (90%-50% isodose lines) of Gamma Knife (GK) machine by investigating of source to diaphragm distance (SDD) and designing compensating filter. Methods: Compensating filters at the end of the helmet collimators with the aim of reducing penumbra as well as reducing hot spots appeared near the edge of beam were modeled using Monte Carlo simulation code. Moreover, the SDD parameter was increased as one of the effective factors on penumbra width. Results: Results showed that single beam penumbra width using optimal design of filters was decreased by 59.49%, 42.50%, 39.02% and 34.44% with attenuation of 30.53%, 13.67%, 11.43% and 9.82% for 4, 8, 14 and 18 mm field sizes, respectively. Conclusions: The designed filters lead to considerable reductions in single beams penumbra width as well as a noticeable reduction in maximum dose emerged near the beam edge due to the curved lateral surface of filters. Keywords: Gamma Knife, physical penumbra width, compensating filter, SDD
1. Introduction Stereotactic radiosurgery (SRS) is an advanced form of radiotherapy technique with high precision in which intracranial tumors and functional disorders are treated with multiple high focused non-coplanar arcs of x-ray or gamma radiation beams. Stereotactic target localization and dose delivery have caused minimum radiation dose to be imparted to adjacent normal structures [1, 2, 3]. Nowadays, SRS is performed using linac-based radiosurgery, cyberknife systems, and Gamma Knife machine. Gamma Knife is a highly accurate radiation device invented by Lars Leksell in 1968. It is internationally recognized as a feasible alternative modality to treat brain tumors either benign or malignant which are inaccessible for brain surgery [4, 5, 6]. Converged radiation beams directed
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at the tumor from 201 cobalt-60 sources deliver a single high dose to the localized target with a precision greater than 0.3 mm and sharp dose gradient while preserving nearby critical tissues intact [4, 7, 8]. Radiosurgery treatment can sometimes be challenged by the small tumor grown near the vital structures such as trigeminal neuralgia treatment. In such cases, the penumbra is a leading factor for the dose received by normal tumor-bound tissues. The penumbra is defined qualitatively as the region of high dose gradient at the edge of a beam and from a quantitative aspect as the distance between the 80%-20% or the 90%-50% isodose lines at a defined depth [9]. Thus, the penumbra must be considered especially in SRS treatments in which the prescribed radiation dose is high and subsequently, the dose delivered to the penumbra region will be high [9]. Several methods have been proposed to reduce the beam penumbra width in stereotactic radiosurgery. The source to diaphragm distance (SDD) has been evaluated in small radiosurgery fields as one of the factors affecting the geometric penumbra width. Although the penumbra width is expected to shrink by increasing the SDD, no dramatic changes have been observed because of the inappreciable contribution of the geometric penumbra to the physical penumbra [10, 11]. On the other hand, scatter photons and secondary electrons contribute to radiological penumbra. However, in radiation fields especially smaller than 2 cm, scattered photons are negligible so secondary electrons are considered as the primary cause of radiological penumbra. Under these circumstances, use of low megavoltage beams leads to diminished ranges of secondary electrons thus shrinking the beam penumbra [2, 9, 12-14]. Compensating filters which reduce penumbra through increasing primary radiation at the beam edges have been investigated in standard and radiosurgery fields as another factor for penumbra reduction. Thomas [11] and Guerrero et al. [15] studied the flattening filter effect on penumbra width in linac-based radiosurgery and Gamma Knife, respectively. Reduced penumbra and greater field homogeneity were reported using compensating filters in small circular fields. Bender et al. [16] also reduced small field penumbra by inserting needles as compensators within conical collimators. The purpose of this study was to reduce beam penumbra of Gamma Knife machine model 4C with lower hot spots emerging near the beam edge which are relatively high in conical filters used in Guerrero et al.’s work. To this aim, first different designed flattening filter shapes of various materials were modeled for 4, 8, 14, and 18 mm collimators. Then, the increase in the source to diaphragm distance (SDD) was studied using Monte Carlo simulation.
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2. Materials and methods Geometry simulations and photon transports were performed using Monte Carlo-based BEAMnrc code built on the EGSnrc. The EGSnrc is an extended version of the EGS4 code in which transport physics is substantially improved when compared with EGS4 [17]. Initial gamma rays emitted by 60Co source decays and secondary electrons are conducted to the isocentre point by passing through the Gamma Knife channel. Each beam channel consists of a fixed collimator placed in the machine body and helmet collimator which defines the final beam diameter at the focus point [5, 7, 8] (Figure 1). One of the unique features of the BEAMnrc code is availability of pre-made geometries called component module impressively improving the facility and reducing the time of geometric modeling in radiotherapy applications. Single channel geometry was modeled using FLATFILT module. The outer aperture diameter of helmet collimator (d) is 2.5, 5.0, 8.5, and 10.6 mm for 4, 8, 14, and 18 mm collimators, respectively.
Figure 1. The view of the single channel geometry
In order to simulate the source, a 1.25 MeV point source at the active center of the 60Co cylindrical source was considered [7]. The accuracy of the simulated geometry was validated through comparing the simulated profiles with film dosimetry results [18].
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2.1 Compensating filter design The shape of the compensating filter was derived from the particles planar fluence distribution generated by beamdp code. Since the collimated output particles distribution was Gaussian and non-uniform, the required filter thickness in the beam path was calculated using the Lambert’s law equation: I = I0 Where, I is the least fluence and I0 is fluence at different points with different thicknesses x of filter, whereby the overall shape of the filter was obtained. FLATFILT module was selected to mode the filter geometry. The filter placed at the end of the helmet collimator [11, 15] was composed of multiple truncated cones with various heights and radii. The coronal cross-section of the simulated filter at the outer collimator aperture and the three-dimensional shape of the modeled filter for 4-mm collimator can be observed in Figure 2.
Figure 2. Coronal view (X-Z) of the modeled filter at the end of the single channel (left), tridimensional shape of filter (right) for 4 mm collimator. The height of filter is 5 mm.
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Two different materials, tungsten (74W) and lead (82Pb), with linear attenuation coefficients of 1.025 and 0.6252
and densities of 19.3 and 11.34
, respectively were used as materials of
the filters. The initial studies of the designed filter with the thickness obtained from the Lambert equation showed that value of generated hot spots was very high. So, new filters were designed in which the thickness of all points was reduced to the same ratio. Accordingly, totally 56 configurations with different filter heights and two materials were modeled for collimator sizes of 4, 8, 14, and 18 mm. The flattening filters designed for all studied thicknesses and materials were made of 9, 12, 12, and 13 truncated cones for 4, 8, 14, and 18 mm field sizes, respectively. The bottom radius of the first truncated cone of filters (R 1T) was equal to the output aperture radius of helmet collimators. But for the top radius of the last truncated cone of filters (R 2T), all considered modes, according to the mentioned fluence calculation, was 0.06, 0.13, 0.21, and 0.80 mm for 4, 8, 14, and 18 mm collimators, respectively. The electron and photon transport cut-off energies were set to 0.7 and 0.01 MeV, respectively. Specifically, 6×108 initial photon trajectories were simulated for each beam diameter. DOSXYZnrc code which is a general purpose MC EGSnrc user-code for three-dimensional dosimetry was implemented in energy deposition calculations [19]. For this purpose, the voxelbased cubic phantom made of Plexiglas (PMMA) was used. The phantom was made of 0.25 mm voxel sizes for 4 and 8 collimators and 0.50 mm voxel sizes for 14 and 18 mm collimators along the X and Y axes [15]. In the present study, because of the insignificant contribution of voxel sizes along Z axis in dose calculation, the intersecting voxel with other axes was only considered small. The phase space file generated through BEAMnrc execution was used as the phase space source in DOSXYZnrc code. The number of histories assigned to obtain the statistical errors less than 1% was 6×109 and 8×109 for 0.25 and 0.50 mm voxel sizes, respectively. Then, STATDOSE program was employed to calculate the single beam profiles at the isocentre depth through reading the “.3ddose” file (output file from DOSXYZnrc) [20]. Physical penumbra width (90%-50%) was measured for different field sizes in MATLAB software. Additionally, to assess the beam attenuation due to the presence of filter, filtered and unfiltered profiles for each thickness were compared with each other. Given the similarity of X and Y profiles, only Xprofiles were evaluated. In order to verify our filter efficiency in diminishing of the hot spots appeared near the beam edge, one simple lead conical filter with a height of 8mm for 4mm collimator which produces a larger penumbra-field radius ratio compared to the other collimators was designed. .
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2.1 Increase in source-to-diaphragm distance (SDD) In order to investigate the effect of SDD parameter on the physical penumbra width of single beam, SDD was elevated in five 1-cm steps for 4, 8, 14, and 18 mm collimator sizes. Increase in SDD was performed by raising the helmet collimator height. With increase in every 1-cm step, the SDD values changed to 24.6, 25.6, 26.6, 27.6, and 28.6 cm. The method discussed for the dose and profile calculations in section 2.1 was also applied in this section.
3. Results 3.1 simulated compensating filters Physical penumbra width (90%-50%) values in the presence of the designed filters as well as beam attenuation are presented in Tables 1-4 for 4, 8, 14, and 18 mm field sizes. Use of filters led to reduced beam penumbra width. With enlargement of the filter thickness, greater penumbra reductions were achieved. This decline was small for low heights especially for 4 mm collimator. Furthermore, a greater intensity loss of filters with a higher thickness was seen, where the filter attenuation was less for the lead filter with equal heights to tungsten filters. The simulated filters for 4 mm collimator showed a different behavior than the other collimators. For this reason, filter thicknesses up to 8 mm were studied. The penumbra width (90%-50%) of 4 mm radiation field size without filter was 0.79 mm, which decreased by 11.21% and 63.06% as the tungsten filter thickness varied from 1 to 8 mm.
9 Table 1. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 4 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5 6 7 8
Penumbra Penumbra width (mm) reduction (%) 0.79 0.70 0.68 0.64 0.53 0.46 0.35 0.32 0.31 0.29
12.86 13.92 19.00 32.91 41.77 55.70 59.49 60.76 63.29
Lead Beam attenuation (%)
Penumbra width (mm)
7.46 10.94 14.37 20.73 26.42 31.81 36.76 41.33 45.54
0.79 0.72 0.72 0.71 0.62 0.57 0.49 0.43 0.36 0.32
Beam Penumbra reduction (%) attenuation (%) 8.86 8.86 10.13 21.52 27.85 37.97 44.57 54.43 59.49
4.42 6.67 8.78 12.86 16.84 20.45 23.81 27.29 30.53
Table 2. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 8 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5
Penumbra Penumbra width (mm) reduction (%) 0.80 0.58 0.48 0.42 0.34 0.26 0.21
27.50 40.00 47.50 57.50 67.50 73.75
Lead Beam attenuation (%)
Penumbra width (mm)
7.55 11.22 14.54 21.00 26.86 32.13
0.80 0.69 0.59 0.56 0.46 0.38 0.33
Penumbra Beam reduction (%) attenuation (%) 13.75 26.25 30.00 42.50 52.50 58.75
4.93 7.04 9.25 13.67 17.78 21.51
10 Table 3. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 14 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5
Penumbra Penumbra width (mm) reduction (%) 0.82 0.61 0.50 0.47 0.45 0.43 0.42
25.61 39.02 42.68 45.12 47.56 49.78
Lead Beam attenuation (%)
Penumbra width (mm)
7.78 11.43 14.79 21.27 27.16 32.75
0.82 0.69 0.60 0.55 0.47 0.46 0.45
Penumbra Beam reduction (%) attenuation (%) 15.86 26.83 32.93 42.68 43.90 45.12
4.78 7.16 9.43 13.91 17.87 21.85
Table 4. The physical penumbra width (90%-50%) and beam attenuation values for various thicknesses of tungsten and lead filters designed for the 18 mm collimator
Tungsten Filter thickness (mm)
0 1 1.5 2 3 4 5
Penumbra Penumbra width (mm) reduction (%) 0.90 0.62 0.59 0.57 0.51 0.45 0.38
31.11 34.44 36.67 43.33 50.00 57.78
Lead Beam attenuation (%)
Penumbra width (mm)
8.18 11.78 15.34 22.10 28.42 33.97
0.90 0.77 0.63 0.59 0.59 0.55 0.51
Penumbra Beam reduction (%) attenuation (%) 14.44 30.00 34.44 34.44 38.89 43.33
5.07 7.63 9.82 14.35 18.56 22.74
Figures 3 and 4 display the half-beam profiles calculated at the isocentre depth for collimator sizes of 4, 8, 14, and 18 mm with and without the flattening filters made of tungsten and lead materials, clearly representing the effect of filter on the beam profiles. All profiles were normalized to the central axis dose. As shown on the figures, as the filter thickness grows, the internal useful area of the beam becomes flattened further. The filter usage caused appearance of hot spots near the beam edge and horn-shaped profiles. These spots grew by increasing the filter
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height. The filters made of lead produced lower hot spots than the tungsten filters at the profile edges (Figure 4).
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Figure 3. Half-beam profiles calculated along X axis at isocentre depth in Plexiglas cubic phantom in the presence of tungsten filters for collimator sizes of a) 4mm (h=1-3mm), b) 4mm (h=4-8mm), c) 8mm (h=1-2mm), d) 8mm (h=35mm), e) 14 mm (h=1-2mm), f) 14 mm (h=3-5mm) and g) 18 mm (h=1-2mm), h) 18 mm (h=3,4mm)
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Figure 4. Half-beam profiles calculated along X axis at isocentre depth in Plexiglas cubic phantom in the presence of lead filters for collimator sizes of a) 4mm (h=1-3mm), b) 4mm (h=4-8mm), c) 8mm (h=1-2mm), d) 8mm (h=35mm), e) 14 mm (h=1-2mm), f) 14 mm (h=3-5mm) and g) 18 mm (h=1-2mm), h) 18 mm (h=3-5mm)
The percentages of beam attenuation in different thicknesses of tungsten and lead filters for four collimator sizes are represented in Figure 5. According to the figure, the extent of intensity loss for collimator sizes of 8, 14, and 18 with equal heights are approximately the same except for the 4 mm collimator which showed less intensity attenuation.
Figure 5. Beam attenuation as a function of thickness of tungsten filter (a) and lead (b) for 4, 8, 14, and 18 mm field sizes
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Based on the Table.5, for the simple conical filter with top radius of 0.06mm, 107.52% hot spot has appeared, whereas according to the Figure 4(b) no hot spot was seen for the designed filter with the curved lateral surface. Increasing simple conical filter top radius, the hot spot percentage dropped, while its effect on penumbra reduction width was dramatically lower than our designed filter. Furthermore, the simple conical filter caused more intensity attenuation resulted in more treatment time.
Table 5. The physical penumbra width (90%-50%), penumbra width reduction and beam attenuation for lead conical filter of 8mm height and various top radii.
Conical filter top radius (mm)
Maximum dose at the beam edge (%)
Physical penumbra width (mm)
Penumbra reduction (%)
Beam attenuation (%)
0.06 0.10 0.50 0.90
107.52 107.81 104.98 -
0.32 0.31 0.30 0.59
59.49 60.76 62.03 25.32
21.11 21.88 28.36 35.14
3.2 The effects of increasing SDD The results obtained from SDD changes are listed in Table 6. Unexpectedly, the physical penumbra width (90%-50%) did not show a regular trend with elevation of SDD. As can be seen, the best results were observed for 4 and 8 mm collimators in 1-cm increase, whereby the penumbra width diminished from 0.785 and 0.790 mm to 0.749 and 0.736 mm for 4 and 8 field sizes, respectively.
16 Table 6. The physical penumbra width (90%-50%) for various SDDs at the isocentre depth
Physical penumbra width (90%-50%) (mm) Collimator size (mm)
4 8 14 18
SDD 236 mm
246 mm
256 mm
266 mm
276 mm
286 mm
0.79 0.80 0.82 0.90
0.75 0.74 0.81 0.97
0.77 0.75 0.83 0.93
0.78 0.77 0.79 0.89
0.78 0.78 0.86 0.93
0.79 0.78 0.80 0.94
4. Discussion In this study, some specially designed flattening filters were investigated to reduce the physical penumbra width (90%-50%) of Gamma Knife machine model 4C.To the best of our knowledge, there has been no work on penumbra reduction of Gamma Knife model 4C. There was an appreciable reduction in physical penumbra width of GK single beam, while the maximum dose at the profile edge was not very high especially for 4 mm collimator. The beam penumbra width for optimum compensating filters was reduced by 59.49, 42.50, 39.02, and 34.44% for 4, 8, 14, and 18 mm collimators, respectively. The increase in SDD effect on penumbra width was also studied where small variations were seen in the penumbra width as SDD rose. Adding flattening filter in the radiation beam path led to beam attenuation in the central parts of the filter and increased the primary radiation at periphery [11, 15, 16, 21-23]. On the other hand, the greater fluence at the beam boundaries caused emergence of some hot spots. This effect will grow with elevation of the filter thickness due to increase in the difference between the central and peripheral thickness of the filter [15]. In this study, the compensating filters with different shapes were designed based on the suggestion by Guerrero et al. [15] about using filter with curved lateral surface instead of a linear one to reduce the value of hot spots values appearing near the beam edge. The advantage of our designed filter was a dramatic reduction in the hot spot value appearing near the beam edge when compared to a conical filter with a linear lateral surface as had been predicted [15]. The hot spot percentage reduction in a conical filter can be achieved using elevation of the truncated cone top radius, causing increased penumbra width as well as the lowered beam intensity. This fact, reflect the proper designation of our filter, as it reduces hotspot percentage with a reasonable penumbra reduction and intensity loss (Table.5). The filter designed for 4 mm collimator showed a completely different behavior in creating hot spots as compared to the other collimators. This discrepancy could be due to the less scattered photons in small fields. At this collimator size, there was no hot spot up to 5 mm height for
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tungsten filter (Figure 3(b)). So, based on this observed feature, further elevation of the height to achieve a lower penumbra width was possible. According to the results, greater hot spots were seen with enlargement of the field size for the same filter thickness except for the 18 mm field size, whose hot spots were less than or equal to those of the 14 mm field size. The reason can be attributed to the similar shape of the designed filter for 14 and 18 mm collimators with same thickness as well as the roughly similar behavior of these collimators. The physical penumbra width (90%-50%) diminished by increasing the filter thickness. At very low thicknesses, the penumbra reduction and profile flattening were trivial. Although higher thicknesses resulted in a lower penumbra width, a greater hot point was created near the profile edge. Indeed, the penumbra width and the emergence of hot spots behave in opposite. For all collimator sizes for the filter of 1-cm thickness, the penumbra width difference in filtered and unfiltered mode was greater than the penumbra width difference between the other thicknesses. These observations are in line with the results of Guerrero et al. Another important parameter in the presence of filter is beam attenuation percentage which grew by increasing the filter thickness. According to the results, the smallest penumbra width was obtained in exchange for a greater hot spot and beam attenuation. In addition to tungsten, lead was also studied as a constituent substance of the filter. In the presence of the lead filter, the maximum percentage of dose appearing near the beam edge was lower than that of the tungsten at equal filter thicknesses. As such, the penumbra reduction was also less considerable. This discrepancy is well seen in Figure 4 (b), in which, there are no hot spots up to the height of 8 mm, while for tungsten filters (Figure 3 (b)) they can be seen from 6 mm height. The beam attenuation caused by the lead filter was less than the attenuation induced by the tungsten filter. The reason behind the different behavior of two studied materials is lower linear attenuation coefficient of lead compared with tungsten for 60Cosource which are 0.6252 and 1.025
as investigated by Buyuk and Tugrul [24].
The plotted profiles indicated that with elevation of the filter thickness, the 90% isodose line approached the profile edge and resulted in a smaller penumbra width. This filter effect on the dose profile agreed with the results reported by Guerrero et al. [15] as well as by Thomas. [11] The shape of unfiltered and low thicknesses filtered profiles is more rounded. This feature is more obvious for 4 mm collimator than for the other ones, highlighting the greater ratio of penumbra width to the field size for small field sizes especially 4 mm field size. Elevation of the filter thickness led to more flattened profiles, but at a critical thickness, with creating higher hot spots despite further reduction in the penumbra width, the profile flatness diminished. In cases of penumbra reduction, it is desirable that the 90% isodose line moves outward while the 50% dose point remains constant. With regard to the profiles calculated for various thicknesses and field sizes (Figures 3 and 4), the 50% dose has also moved toward the beam edge but it is less than 90% dose shifts, so the penumbra reduction was achieved. This dual effect of
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compensating filter on beam profiles resulted in a slight increase in the field size which was in accordance with Thomas’s observations in 1994. The beam attenuation as a function of filter thickness for the collimator sizes of 4, 8, 14, and 18 mm changed almost linearly (Figure 5). This result has also been reported by Guerrero et al. [15]. In addition, the attenuation was nearly the same for the four collimators at the identical filter thicknesses and rose with enlargement of the collimator size. The attenuations of lead filter (Figure 5 (b)) were less than those of the tungsten filter (Figure 5 (a)) for all the studied thicknesses. Optimum compensating filters were selected considering the penumbra width reduction value, the maximum dose near the edge of beam profile, the beam attenuation percentage, and the filter material. The beam attenuation and hot spot area emerged are determinant factors for penumbra reduction, where the filter thickness must be selected such that it results in lower attenuation and fewer hot spots. The maximum dose at the beam edge was acceptable up to 3% of the central axis dose for all collimators [15, 25]. The optimum filter for the 4 mm collimator was the lead filter with a thickness of 8 mm and an attenuation of 30.53%. For this filter, the physical penumbra width dropped by 59.49%. For the 8 mm collimator, the 3 mm lead filter with a 42.50% and 13.67% reduction in penumbra width and beam intensity, respectively was appropriate. The optimum filter for the 14 mm collimator was a 1.5 mm tungsten filter with 11.43% beam attenuation and 39.02% reduction in the beam penumbra width. The lead filter of 2-mm thickness with attenuation and penumbra reduction of 9.82% and 34.44%, respectively was optimum for 18 mm collimator. Since there was no hot spot as limiting factor in penumbra reduction, so a relatively high attenuation was accepted for the 4 mm collimator. In other words, because of high importance of the 4 mm collimator penumbra width, the greater intensity loss was accepted to gain smaller penumbra width. Based on the mentioned results, the maximum and minimum penumbra reduction for optimum compensating filters belonged to 4 and 18 mm collimators, so great reductions were obtained in penumbra for 4 the mm field size. The physical penumbra width did not show a regular trend in reduction with elevation of SDD (Table 6). A reduction in penumbra was expected for each extended SDD value, but for 14 and 18 mm collimators, the penumbra did not diminish by SDD elevation and at the same time increased beyond the penumbra width of standard SDD in some cases. In their work on stereotactic radiosurgery machines, Serago et al. [10] and Thomas [11] found that because of insignificant contribution of geometric penumbra in physical penumbra in such machines, SDD has negligible effects on penumbra width. In order to examine the impact of the designed filters on dose uniformity within the target, dose volume histograms should be calculated using treatment planning system [15] and considering this users are not allowed to manipulate the treatment planning system of the machine, this part can just be proposed to be investigated.
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5. Conclusion External compensating filters located in radiotherapy devices with the aim of increasing the radiation at the beam edges can reduce beam penumbra width. In this study, special shapes of compensating filters were investigated to reduce the physical penumbra width (90%-50%) of Gamma Knife machine model 4C. The designed filters led to considerable reductions in the width of single beam penumbra where a maximum reduction of 59.49% was observed for the 4 mm collimator size with a beam attenuation of 30.53%. The curved lateral surface of filter resulted in a noticeable reduction in the maximum dose emerging near the beam edge in comparison with conical filters. Further, since no significant change was seen due to the increase in SDD, it can be concluded that changing SDD has no dramatic effect on beam penumbra width of Gamma Knife system.
Acknowledgement This research was supported by Tehran University of Medical Sciences as a master thesis number of 32880.
Disclosure of conflicts of Interest Authors have no conflicts of interest.
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