Equivalent Field Calculation to Irregular Symmetric and Asymmetric Photon Fields
Equivalent fields are frequently used for central axis depth-dose calculations of rectangular and irregular shaped photon beam. Since most of the proposed models to calculate the equivalent square field, are dosimetry-based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square for rectangular fields was constructed and then compared with the well-known tables of BJR and Venselaar with the average relative error percentage of 2.5±2.5 % and 1.5±1.5 % respectively. To evaluate the accuracy of this method, the PDDs were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies 6 and 18MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field.
[1] Venselaar, J.L., et al., Is there a need for a revised table of equivalent
square fields for the determination of phantom scatter correction factors?
Phys Med Biol, 1997. 42(12): p. 2369-81.
[2] Yu Jin, H., et al., A simplified method for the calculation of equivalent
squares of irregular photon fields. ConfProc IEEE Eng Med BiolSoc,
2005. 7: p. 7091-4.
[3] McCurdy, B.M. and S. Pistorius, Determination of equivalent photon
fields through integrated 1D convolution kernels. Phys Med Biol, 1999.
44(12): p. 2971-85.
[4] Storchi, P. and E. Woudstra, Calculation of the absorbed dose
distribution due to irregularly shaped photon beams using pencil beam
kernels derived from basic beam data. Phys Med Biol, 1996. 41(4): p.
637-56.
[5] Day, M.J., A note on the calculation of dose in x-ray fields. British
Journal of Radiology 1950. 23(270): p. 368-9.
[6] Day, M.J. and E.G. Aird, The equivalent field method for dose
determinations in rectangular fields. British Journal of Radiology Suppl,
1996. 25: p. 138-51.
[7] Bjärngard, B.E. and R.L. Siddon, A note on equivalent circles, squares,
and rectangles. Med Phys, 1982. 9(2): p. 258-60.
[8] Clarkson, J.R., A note on depth doses in fields of irregular shape. British
Journal of Radiology, 1941. 14: p. 265- 268.
[9] Sathiyan, S., M. Ravikumar, and S.L. Keshava, Relative Output Factors
and Absolute Equivalent Square Fields at Depths for High Energy XRay
and Gamma Ray Beams. Austral Asian Journal of Cancer 2006.
5(4): p. 225-235.
[10] Sterling, T., H. Perry, and J. Weinkam, Automation of radiation
treatment planning. VI. A general field equation to calculate percent
depth dose in the irradiated volume of a cobalt 60 beam. British Journal
of Radiology, 1967. 40(474): p. 463-74.
[11] Vadash, P. and B. Bjärngard, An equivalent-square formula for headscatter
factors. Med Phys, 1993. 20(3): p. 733-4.
[12] Monti, A.F., et al., An equivalent square method for irregular photon
fields. Med Dosim, 1995. 20(4): p. 275-7.
[13] Sanz, D.E., Accuracy limits of the equivalent field method for irregular
photon fields. Phys Med Biol, 2002. 47(17): p. 3073-85.
[14] Thomas, S.J., et al., Equivalent squares for small field dosimetry. Br J
Radiol, 2008. 81(971): p. 897-901.
[15] Araki, F., et al., Dose calculation for asymmetric photon fields with
independent jaws and multileaf collimators. Med Phys, 2000. 27(2): p.
340-5.
[16] Kwa, W., et al., Dosimetry for asymmetric x-ray fields. Med Phys, 1994.
21(10): p. 1599-604.
[17] Day, M.J., The equivalent field method for axial dose determinations in
rectangular fields. British Journal of Radiology, 1972. 11: p. Suppl
11:95-10.
[18] Stathakis, S., et al., An inhomogeneity correction algorithm for irregular
fields of high-energy photon beams based on Clarkson integration and
the 3D beam subtraction method. J ApplClin Med Phys, 2006. 7(1): p. 1-
13.
[19] Heukelom, S., J.H. Lanson, and B.J. Mijnheer, Wedge factor
constituents of high-energy photon beams: head and phantom scatter
dose components. RadiotherOncol, 1994. 32(1): p. 73-83.
[1] Venselaar, J.L., et al., Is there a need for a revised table of equivalent
square fields for the determination of phantom scatter correction factors?
Phys Med Biol, 1997. 42(12): p. 2369-81.
[2] Yu Jin, H., et al., A simplified method for the calculation of equivalent
squares of irregular photon fields. ConfProc IEEE Eng Med BiolSoc,
2005. 7: p. 7091-4.
[3] McCurdy, B.M. and S. Pistorius, Determination of equivalent photon
fields through integrated 1D convolution kernels. Phys Med Biol, 1999.
44(12): p. 2971-85.
[4] Storchi, P. and E. Woudstra, Calculation of the absorbed dose
distribution due to irregularly shaped photon beams using pencil beam
kernels derived from basic beam data. Phys Med Biol, 1996. 41(4): p.
637-56.
[5] Day, M.J., A note on the calculation of dose in x-ray fields. British
Journal of Radiology 1950. 23(270): p. 368-9.
[6] Day, M.J. and E.G. Aird, The equivalent field method for dose
determinations in rectangular fields. British Journal of Radiology Suppl,
1996. 25: p. 138-51.
[7] Bjärngard, B.E. and R.L. Siddon, A note on equivalent circles, squares,
and rectangles. Med Phys, 1982. 9(2): p. 258-60.
[8] Clarkson, J.R., A note on depth doses in fields of irregular shape. British
Journal of Radiology, 1941. 14: p. 265- 268.
[9] Sathiyan, S., M. Ravikumar, and S.L. Keshava, Relative Output Factors
and Absolute Equivalent Square Fields at Depths for High Energy XRay
and Gamma Ray Beams. Austral Asian Journal of Cancer 2006.
5(4): p. 225-235.
[10] Sterling, T., H. Perry, and J. Weinkam, Automation of radiation
treatment planning. VI. A general field equation to calculate percent
depth dose in the irradiated volume of a cobalt 60 beam. British Journal
of Radiology, 1967. 40(474): p. 463-74.
[11] Vadash, P. and B. Bjärngard, An equivalent-square formula for headscatter
factors. Med Phys, 1993. 20(3): p. 733-4.
[12] Monti, A.F., et al., An equivalent square method for irregular photon
fields. Med Dosim, 1995. 20(4): p. 275-7.
[13] Sanz, D.E., Accuracy limits of the equivalent field method for irregular
photon fields. Phys Med Biol, 2002. 47(17): p. 3073-85.
[14] Thomas, S.J., et al., Equivalent squares for small field dosimetry. Br J
Radiol, 2008. 81(971): p. 897-901.
[15] Araki, F., et al., Dose calculation for asymmetric photon fields with
independent jaws and multileaf collimators. Med Phys, 2000. 27(2): p.
340-5.
[16] Kwa, W., et al., Dosimetry for asymmetric x-ray fields. Med Phys, 1994.
21(10): p. 1599-604.
[17] Day, M.J., The equivalent field method for axial dose determinations in
rectangular fields. British Journal of Radiology, 1972. 11: p. Suppl
11:95-10.
[18] Stathakis, S., et al., An inhomogeneity correction algorithm for irregular
fields of high-energy photon beams based on Clarkson integration and
the 3D beam subtraction method. J ApplClin Med Phys, 2006. 7(1): p. 1-
13.
[19] Heukelom, S., J.H. Lanson, and B.J. Mijnheer, Wedge factor
constituents of high-energy photon beams: head and phantom scatter
dose components. RadiotherOncol, 1994. 32(1): p. 73-83.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65111", author = "N. Chegeni and M. J. Tahmasebi Birgani", title = "Equivalent Field Calculation to Irregular Symmetric and Asymmetric Photon Fields", abstract = "Equivalent fields are frequently used for central axis depth-dose calculations of rectangular and irregular shaped photon beam. Since most of the proposed models to calculate the equivalent square field, are dosimetry-based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square for rectangular fields was constructed and then compared with the well-known tables of BJR and Venselaar with the average relative error percentage of 2.5±2.5 % and 1.5±1.5 % respectively. To evaluate the accuracy of this method, the PDDs were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies 6 and 18MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field.
", keywords = "Equivalent field, asymmetric field, irregular field, multi leaf collimators.", volume = "7", number = "9", pages = "1430-6", }
