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Quality assurance of stereotactic alignment and patient positioning mechanical accuracy for robotized Gamma Knife radiosurgery
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Med. Biol. 59 N221 (http://iopscience.iop.org/0031-9155/59/23/N221) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.140.28.22 This content was downloaded on 11/11/2014 at 06:00
Please note that terms and conditions apply.
Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) N221–N226
Physics in Medicine & Biology doi:10.1088/0031-9155/59/23/N221
Notes
Quality assurance of stereotactic alignment and patient positioning mechanical accuracy for robotized Gamma Knife radiosurgery Lijun Ma1, Joshua Chiu, Jocelyn Hoye, Christopher McGuiness and Angelica Perez-Andujar Department of Radiation Oncology, University of California, San Francisco, CA, USA E-mail: [email protected] Received 5 August 2014, revised 23 September 2014 Accepted for publication 6 October 2014 Published 10 November 2014 Abstract
The automatic patient positioning system and its alignment is critical and specified to be less than 0.35 mm for a radiosurgical treatment with the latest robotized Gamma Knife Perfexion (GKPFX). In this study, we developed a quantitative QA procedure to verify the accuracy and robustness of such a system. In particular, we applied the test to a unit that has performed >1000 procedures at our institution. For the test, a radiochromic film was first placed inside a spherical film phantom and then irradiated with a sequence of linearly placed shots of equal collimator size (e.g. 4 mm) via the Leksell Gamma Knife Perfexion system (PFX). The shots were positioned with either equal or unequal gaps of approximately 8 mm both at center and off-center positions of the patient positioning system. Two independent methods of localizing the irradiation shot center coordinates were employed to measure the gap spacing between adjacent shots. The measured distance was then compared with the initial preset values for the test. On average, the positioning uncertainty for the PFX delivery system was found to be 0.03 ± 0.2 mm (2σ). No significant difference in the positioning uncertainty was noted among measurements in the x-, y- and z-axis orientations. In conclusion, a simple, fast, and quantitative test was developed and demonstrated for routine QA of the submillimeter PFX patient positioning system. This test also enables independent verification of any patient-specific shot positioning for a critical treatment such as a tumor in the brainstem.
1
Author to whom any correspondence should be addressed. Professor in Residence, University of California San Francisco, 505 Parnassus Avenue, Room L-08, San Francisco, CA 94143, USA 0031-9155/14/23N221+6$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA N221
L Ma et al
Phys. Med. Biol. 59 (2014) N221
Keywords: gamma-ray, stereotactic radiosurgery, quality assurance, patient positioning (Some figures may appear in colour only in the online journal) 1. Introduction Gamma Knife has been the hallmark delivery system for intracranial stereotactic radiosurgery (Wu et al 1990, Phillips et al 1994, Snell et al 1995, Sahgal et al 2009). The mechanical accuracy of the system has consistently been reported to be less than 0.35 mm at the isocenter (Snell et al 1995, Mack et al 2002, Ma et al 2008, Novotny et al 2014). With the latest Gamma Knife Perfexion (GKPFX) system (Regis et al 2009), a major change in the physical design of the Gamma Knife system has been introduced (Sahgal et al 2009). In contrast to the previous models where all radioactive Co-60 sources are fixed in a stationary position, the Co-60 sources of the GKPFX are partitioned into eight separate sectors which can each independently slide along the axial directions to produced collimated beams of variable aperture sizes (i.e. 4 mm, 8 mm and 16 mm). Furthermore, the patient positioning system (PPS) has been fully robotized to integrate with a high-precision automatic couch, where the entire patient body can be shifted for each isocentric alignment and treatment delivery. This is in contrast to the PPS of the previous Gamma Knife models where only the patient head can be shifted when setting up the stereotactic coordinates for each isocenter. As a result, the stereotactic alignment between the source and PPS are critical for administering a GKPFX treatment. This raises the question as to whether the dynamic shifting of the source in conjunction with the active manipulations of the PPS system would achieve the same level of stereotactic targeting accuracy as the traditional GK unit where both parts were mechanically fixed during the treatment setup and delivery. The mechanical specification for the PPS accuracy has been reported to be within 0.35 mm by the manufacturer. However, quantitative clinical validation of such a specification in conjunction with radioactive source alignment for actual patient setups has yet to be reported. In order to independently verify the alignment of the PPS and source positioning in setting up the stereotactic coordinates for Gamma Knife stereotactic radiosurgery (GKSRS), we developed a practical routine quality assurance test procedure. For the study, we implemented such a procedure for a clinical GKPFX system that was initially calibrated and installed more than seven years ago at our institution. Given the natural wear-and-tear of the system from over one thousand procedures, the results of our study also serve as the first validation report on the robustness of the GKPFX in maintaining submillimeter stereotactic targeting accuracy for a GKSRS treatment. 2. Materials and methods A series of GKSRS treatment plans (n = 9) were created for the study such that radiation of 5 Gy administered from 4 mm collimators was targeted at equal or unequal gaps of approximately 8 mm both at center and off-center positions of the patient positioning system, concentrated along the x-axis (n = 3), y-axis (n = 3), and z-axis (n = 3). Radiochromic EBT2 self-developing dosimetry films (n = 9) were cut so that they would fit into the Elekta ABS spherical phantom used for quality assurance checks. Each film was irradiated according to the treatment plan, and then removed with gloved hands to be scanned by an Epson film scanner (Model 10 000 XL) at 600 dpi resolution. The images were analyzed using ImageJ, N222
L Ma et al
Phys. Med. Biol. 59 (2014) N221
an edge-detection software, to find the center of each shot developed on the film. This was done using two independent analysis methods. All films were background subtracted and pixel value calibrated. For the first method, a line tool in ImageJ was used to create an axis for a central line profile along all exposed shots that was analyzed to reveal a plot of pixel intensity values (figure 1(a)). The peaks in the plot profile are indicative of the centers of the radiation shots produced by initial preset values of the plan. The exact peak pixel values were found by choosing a gray scale value below the peak and above the valley (such as along the red line pictured in figure 1(b)) and then finding the pixel value where the red line and the curve intersect to the right and left of each peak and averaging these values to find the center of the peak. Once the center peak pixel values were determined, then the distance (pixel) between each peak was found. These distances were converted to mm using the 600 dpi pixel resolution or the conversion factor of 25.4 mm/600 pixels. The same method was repeated to compare distance from valley to valley. The second method involved using the ellipse tool in ImageJ to draw circles around each dot whose diameter was used to determine the center pixel value of each dot (figure 1(c)). The distances in pixels between the centers of each dot were calculated. The pixel distances were converted to mm in the same manner as the first method. The measured distance was then compared with the initial preset values for the test determined by the GKSRS treatment plan, resulting in deviation from expected values. Mean deviation from expected value was determined for each film in the x-, y-, and z-axis orientations, and then all independently measured directional deviation values were combined in quadrature sum. Error was determined using the spread in the data from each method and propagated uncertainty analysis. 3. Results Figure 2 summarizes the film analysis results in the x-, y-, and z-axis orientations with the mean deviation from expected value and one standard deviation from the mean for each orientation indicated by solid and dashed lines respectively. Twenty-nine measurements were made in the x-orientation, which had a mean difference of Δx = 0.003 mm ± 0.368 mm (2σ). None of the x-orientation deviation values exceeded 0.4 mm and 93% of the values fell within a 2σ interval. Similarly, twenty-nine measurements were made in the y-orientation, which yielded a mean deviation of Δy = 0.03 mm ± 0.24 mm (2σ). The maximum deviation in this orientation was less than 0.3 mm with 93% of the values falling within a 2σ interval. Finally, forty-two measurements were made in the z-orientation, which had a mean deviation of Δz = 0.007 mm ± 0.239 mm (2σ) from the expected value. In this orientation, 95% of the values fell within a 2σ interval and the maximum deviation was less than 0.35 mm. No significant difference in the positioning uncertainty was noted among measurements in the x-, y- and z-axis orientation (Unpaired t-test, p > 0.1). Combining all independently measured directional deviation values in quadrature sum, the 3D deviation vector distance was found to be Δ ≡ (Δx2 + Δy2 + Δz2)1/2 = 0.03 mm ± 0.20 mm (2σ), where the composite uncertainty was calculated via error propagation of the formula. 4. Discussion In this technical note, a fast quality assurance test was demonstrated for checking the alignment accuracy between the automatic stereotactic patient positioning system and central N223
L Ma et al
Phys. Med. Biol. 59 (2014) N221
Figure 1. Illustration of the film measurement results: (a) shows an irradiated
radiochromic film in the z-plane orientation where the horizontal shots are each separated by 8.0 mm. A straight line was defined through the centers of each shot. (b) shows the method of localizing the center of each shot via examining the central line profile. (c) shows the method of localizing the center of each shot via using a circular template where the center of each circle was taken as the central coordinates of the corresponding shot. (d) shows the method of localizing the center of each shot on irradiated radiochromic film with ‘smiley face’ pattern to illustrate measurements in the x and z-plane orientations.
source positioning for the latest Gamma Knife Perfexion system. The manufacture specified tolerance level of 0.35 mm is more than 10 times larger than our measured mean alignment result of 0.03 mm. Additionally, no significant difference in the positioning uncertainty was noted for the centrally aligned shot sequence locations versus the peripherally aligned shot sequence locations. Considering the overall caseload of more than 1000 patients treated at our institution, our quality assurance measurement results strongly attest to the accuracy and robustness of the current GKPFX system. N224
L Ma et al
Phys. Med. Biol. 59 (2014) N221
Figure 2. Results for the measurements along the x-, y-, and z-axis orientations. The
positional coordinates for the extreme and selected data point values are given in the parentheses with the hyphen denoting the two reference shot coordinates for the measurements. Figure 2(a) is the measured positional deviations (n = 29) along the xaxis showing Δx = 0.003 mm ± 0.368 mm (2σ); figure 2(b) is the measurement results for the y-axis (n = 29) showing Δy = 0.03 mm ± 0.24 mm (2σ); figure 2(c) is the measurement results for the z-axis (n = 42) showing Δz = 0.007 mm ± 0.239 mm (2σ). The mean values are plotted in solid lines and the upper and the lower 2σ bounds are plotted in dash lines. N225
L Ma et al
Phys. Med. Biol. 59 (2014) N221
In summary, we have developed a simple and effective quality assurance test procedure that may be applied for routine QA of submillimeter patient positioning system of GKPFX. This test also enables independent verification of long-term couch stability as well as patientspecific shot positioning for a critical SRS treatment such as trigeminal neuralgia or tumor in the brainstem. Conflict of Interests Ma is currently on the board of ISRS (International Stereotactic Radiosurgery Society). References Ma L, Chuang C, Descovich M, Petti P, Smith V and Verhey L 2008 Whole-procedure clinical accuracy of gamma knife treatments of large lesions Med. Phys. 35 5110–4 Mack A, Czempiel H, Kreiner H J, Durr G and Wowra B 2002 Quality assurance in stereotactic space. A system test for verifying the accuracy of aim in radiosurgery Med. Phys. 29 561–8 Novotny J, Bhatnagar J P, Xu Y and Huq M S 2014 Long-term stability of the Leksell Gamma Knife Perfexion patient positioning system (PPS) Med. Phys. 41 031711 Phillips M H, Stelzer K J, Griffin T W, Mayberg M R and Winn H R 1994 Stereotactic radiosurgery: a review and comparison of methods J. Clin. Oncol. 12 1085–99 Regis J, Tamura M, Guillot C, Yomo S, Muraciolle X, Nagaje M, Arka Y and Porcheron D 2009 Radiosurgery with the world’s first fully robotized Leksell Gamma Knife PerfeXion in clinical use: a 200-patient prospective, randomized, controlled comparison with the Gamma Knife 4C Neurosurgery 64 346–55 discussion 55–6 Sahgal A et al 2009 Advances in technology for intracranial stereotactic radiosurgery Technol. Cancer Res. Treat. 8 271–80 Snell M, Bova F, Larson D, Leavitt D, Lutz W, Podgorsak E and Wu A 1995 Stereotactic Radiosurgery, Report of TG42 (Madison, WI: Medical Physics) Wu A, Lindner G, Maitz A H, Kalend A M, Lunsford L D, Flickinger J C and Bloomer W D 1990 Physics of Gamma Knife approach on convergent beams in stereotactic radiosurgery Int. J. Radiat. Oncol. Biol. Phys. 18 941–9
N226
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My IOPscience
Quality assurance of stereotactic alignment and patient positioning mechanical accuracy for robotized Gamma Knife radiosurgery
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Med. Biol. 59 N221 (http://iopscience.iop.org/0031-9155/59/23/N221) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.140.28.22 This content was downloaded on 11/11/2014 at 06:00
Please note that terms and conditions apply.
Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) N221–N226
Physics in Medicine & Biology doi:10.1088/0031-9155/59/23/N221
Notes
Quality assurance of stereotactic alignment and patient positioning mechanical accuracy for robotized Gamma Knife radiosurgery Lijun Ma1, Joshua Chiu, Jocelyn Hoye, Christopher McGuiness and Angelica Perez-Andujar Department of Radiation Oncology, University of California, San Francisco, CA, USA E-mail: [email protected] Received 5 August 2014, revised 23 September 2014 Accepted for publication 6 October 2014 Published 10 November 2014 Abstract
The automatic patient positioning system and its alignment is critical and specified to be less than 0.35 mm for a radiosurgical treatment with the latest robotized Gamma Knife Perfexion (GKPFX). In this study, we developed a quantitative QA procedure to verify the accuracy and robustness of such a system. In particular, we applied the test to a unit that has performed >1000 procedures at our institution. For the test, a radiochromic film was first placed inside a spherical film phantom and then irradiated with a sequence of linearly placed shots of equal collimator size (e.g. 4 mm) via the Leksell Gamma Knife Perfexion system (PFX). The shots were positioned with either equal or unequal gaps of approximately 8 mm both at center and off-center positions of the patient positioning system. Two independent methods of localizing the irradiation shot center coordinates were employed to measure the gap spacing between adjacent shots. The measured distance was then compared with the initial preset values for the test. On average, the positioning uncertainty for the PFX delivery system was found to be 0.03 ± 0.2 mm (2σ). No significant difference in the positioning uncertainty was noted among measurements in the x-, y- and z-axis orientations. In conclusion, a simple, fast, and quantitative test was developed and demonstrated for routine QA of the submillimeter PFX patient positioning system. This test also enables independent verification of any patient-specific shot positioning for a critical treatment such as a tumor in the brainstem.
1
Author to whom any correspondence should be addressed. Professor in Residence, University of California San Francisco, 505 Parnassus Avenue, Room L-08, San Francisco, CA 94143, USA 0031-9155/14/23N221+6$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA N221
L Ma et al
Phys. Med. Biol. 59 (2014) N221
Keywords: gamma-ray, stereotactic radiosurgery, quality assurance, patient positioning (Some figures may appear in colour only in the online journal) 1. Introduction Gamma Knife has been the hallmark delivery system for intracranial stereotactic radiosurgery (Wu et al 1990, Phillips et al 1994, Snell et al 1995, Sahgal et al 2009). The mechanical accuracy of the system has consistently been reported to be less than 0.35 mm at the isocenter (Snell et al 1995, Mack et al 2002, Ma et al 2008, Novotny et al 2014). With the latest Gamma Knife Perfexion (GKPFX) system (Regis et al 2009), a major change in the physical design of the Gamma Knife system has been introduced (Sahgal et al 2009). In contrast to the previous models where all radioactive Co-60 sources are fixed in a stationary position, the Co-60 sources of the GKPFX are partitioned into eight separate sectors which can each independently slide along the axial directions to produced collimated beams of variable aperture sizes (i.e. 4 mm, 8 mm and 16 mm). Furthermore, the patient positioning system (PPS) has been fully robotized to integrate with a high-precision automatic couch, where the entire patient body can be shifted for each isocentric alignment and treatment delivery. This is in contrast to the PPS of the previous Gamma Knife models where only the patient head can be shifted when setting up the stereotactic coordinates for each isocenter. As a result, the stereotactic alignment between the source and PPS are critical for administering a GKPFX treatment. This raises the question as to whether the dynamic shifting of the source in conjunction with the active manipulations of the PPS system would achieve the same level of stereotactic targeting accuracy as the traditional GK unit where both parts were mechanically fixed during the treatment setup and delivery. The mechanical specification for the PPS accuracy has been reported to be within 0.35 mm by the manufacturer. However, quantitative clinical validation of such a specification in conjunction with radioactive source alignment for actual patient setups has yet to be reported. In order to independently verify the alignment of the PPS and source positioning in setting up the stereotactic coordinates for Gamma Knife stereotactic radiosurgery (GKSRS), we developed a practical routine quality assurance test procedure. For the study, we implemented such a procedure for a clinical GKPFX system that was initially calibrated and installed more than seven years ago at our institution. Given the natural wear-and-tear of the system from over one thousand procedures, the results of our study also serve as the first validation report on the robustness of the GKPFX in maintaining submillimeter stereotactic targeting accuracy for a GKSRS treatment. 2. Materials and methods A series of GKSRS treatment plans (n = 9) were created for the study such that radiation of 5 Gy administered from 4 mm collimators was targeted at equal or unequal gaps of approximately 8 mm both at center and off-center positions of the patient positioning system, concentrated along the x-axis (n = 3), y-axis (n = 3), and z-axis (n = 3). Radiochromic EBT2 self-developing dosimetry films (n = 9) were cut so that they would fit into the Elekta ABS spherical phantom used for quality assurance checks. Each film was irradiated according to the treatment plan, and then removed with gloved hands to be scanned by an Epson film scanner (Model 10 000 XL) at 600 dpi resolution. The images were analyzed using ImageJ, N222
L Ma et al
Phys. Med. Biol. 59 (2014) N221
an edge-detection software, to find the center of each shot developed on the film. This was done using two independent analysis methods. All films were background subtracted and pixel value calibrated. For the first method, a line tool in ImageJ was used to create an axis for a central line profile along all exposed shots that was analyzed to reveal a plot of pixel intensity values (figure 1(a)). The peaks in the plot profile are indicative of the centers of the radiation shots produced by initial preset values of the plan. The exact peak pixel values were found by choosing a gray scale value below the peak and above the valley (such as along the red line pictured in figure 1(b)) and then finding the pixel value where the red line and the curve intersect to the right and left of each peak and averaging these values to find the center of the peak. Once the center peak pixel values were determined, then the distance (pixel) between each peak was found. These distances were converted to mm using the 600 dpi pixel resolution or the conversion factor of 25.4 mm/600 pixels. The same method was repeated to compare distance from valley to valley. The second method involved using the ellipse tool in ImageJ to draw circles around each dot whose diameter was used to determine the center pixel value of each dot (figure 1(c)). The distances in pixels between the centers of each dot were calculated. The pixel distances were converted to mm in the same manner as the first method. The measured distance was then compared with the initial preset values for the test determined by the GKSRS treatment plan, resulting in deviation from expected values. Mean deviation from expected value was determined for each film in the x-, y-, and z-axis orientations, and then all independently measured directional deviation values were combined in quadrature sum. Error was determined using the spread in the data from each method and propagated uncertainty analysis. 3. Results Figure 2 summarizes the film analysis results in the x-, y-, and z-axis orientations with the mean deviation from expected value and one standard deviation from the mean for each orientation indicated by solid and dashed lines respectively. Twenty-nine measurements were made in the x-orientation, which had a mean difference of Δx = 0.003 mm ± 0.368 mm (2σ). None of the x-orientation deviation values exceeded 0.4 mm and 93% of the values fell within a 2σ interval. Similarly, twenty-nine measurements were made in the y-orientation, which yielded a mean deviation of Δy = 0.03 mm ± 0.24 mm (2σ). The maximum deviation in this orientation was less than 0.3 mm with 93% of the values falling within a 2σ interval. Finally, forty-two measurements were made in the z-orientation, which had a mean deviation of Δz = 0.007 mm ± 0.239 mm (2σ) from the expected value. In this orientation, 95% of the values fell within a 2σ interval and the maximum deviation was less than 0.35 mm. No significant difference in the positioning uncertainty was noted among measurements in the x-, y- and z-axis orientation (Unpaired t-test, p > 0.1). Combining all independently measured directional deviation values in quadrature sum, the 3D deviation vector distance was found to be Δ ≡ (Δx2 + Δy2 + Δz2)1/2 = 0.03 mm ± 0.20 mm (2σ), where the composite uncertainty was calculated via error propagation of the formula. 4. Discussion In this technical note, a fast quality assurance test was demonstrated for checking the alignment accuracy between the automatic stereotactic patient positioning system and central N223
L Ma et al
Phys. Med. Biol. 59 (2014) N221
Figure 1. Illustration of the film measurement results: (a) shows an irradiated
radiochromic film in the z-plane orientation where the horizontal shots are each separated by 8.0 mm. A straight line was defined through the centers of each shot. (b) shows the method of localizing the center of each shot via examining the central line profile. (c) shows the method of localizing the center of each shot via using a circular template where the center of each circle was taken as the central coordinates of the corresponding shot. (d) shows the method of localizing the center of each shot on irradiated radiochromic film with ‘smiley face’ pattern to illustrate measurements in the x and z-plane orientations.
source positioning for the latest Gamma Knife Perfexion system. The manufacture specified tolerance level of 0.35 mm is more than 10 times larger than our measured mean alignment result of 0.03 mm. Additionally, no significant difference in the positioning uncertainty was noted for the centrally aligned shot sequence locations versus the peripherally aligned shot sequence locations. Considering the overall caseload of more than 1000 patients treated at our institution, our quality assurance measurement results strongly attest to the accuracy and robustness of the current GKPFX system. N224
L Ma et al
Phys. Med. Biol. 59 (2014) N221
Figure 2. Results for the measurements along the x-, y-, and z-axis orientations. The
positional coordinates for the extreme and selected data point values are given in the parentheses with the hyphen denoting the two reference shot coordinates for the measurements. Figure 2(a) is the measured positional deviations (n = 29) along the xaxis showing Δx = 0.003 mm ± 0.368 mm (2σ); figure 2(b) is the measurement results for the y-axis (n = 29) showing Δy = 0.03 mm ± 0.24 mm (2σ); figure 2(c) is the measurement results for the z-axis (n = 42) showing Δz = 0.007 mm ± 0.239 mm (2σ). The mean values are plotted in solid lines and the upper and the lower 2σ bounds are plotted in dash lines. N225
L Ma et al
Phys. Med. Biol. 59 (2014) N221
In summary, we have developed a simple and effective quality assurance test procedure that may be applied for routine QA of submillimeter patient positioning system of GKPFX. This test also enables independent verification of long-term couch stability as well as patientspecific shot positioning for a critical SRS treatment such as trigeminal neuralgia or tumor in the brainstem. Conflict of Interests Ma is currently on the board of ISRS (International Stereotactic Radiosurgery Society). References Ma L, Chuang C, Descovich M, Petti P, Smith V and Verhey L 2008 Whole-procedure clinical accuracy of gamma knife treatments of large lesions Med. Phys. 35 5110–4 Mack A, Czempiel H, Kreiner H J, Durr G and Wowra B 2002 Quality assurance in stereotactic space. A system test for verifying the accuracy of aim in radiosurgery Med. Phys. 29 561–8 Novotny J, Bhatnagar J P, Xu Y and Huq M S 2014 Long-term stability of the Leksell Gamma Knife Perfexion patient positioning system (PPS) Med. Phys. 41 031711 Phillips M H, Stelzer K J, Griffin T W, Mayberg M R and Winn H R 1994 Stereotactic radiosurgery: a review and comparison of methods J. Clin. Oncol. 12 1085–99 Regis J, Tamura M, Guillot C, Yomo S, Muraciolle X, Nagaje M, Arka Y and Porcheron D 2009 Radiosurgery with the world’s first fully robotized Leksell Gamma Knife PerfeXion in clinical use: a 200-patient prospective, randomized, controlled comparison with the Gamma Knife 4C Neurosurgery 64 346–55 discussion 55–6 Sahgal A et al 2009 Advances in technology for intracranial stereotactic radiosurgery Technol. Cancer Res. Treat. 8 271–80 Snell M, Bova F, Larson D, Leavitt D, Lutz W, Podgorsak E and Wu A 1995 Stereotactic Radiosurgery, Report of TG42 (Madison, WI: Medical Physics) Wu A, Lindner G, Maitz A H, Kalend A M, Lunsford L D, Flickinger J C and Bloomer W D 1990 Physics of Gamma Knife approach on convergent beams in stereotactic radiosurgery Int. J. Radiat. Oncol. Biol. Phys. 18 941–9
N226
