Home
Search
Collections
Journals
About
Contact us
My IOPscience
Letter to the editors (radiotherapy)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 822 (http://iopscience.iop.org/0031-9155/24/4/015) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 129.78.139.28 This content was downloaded on 03/10/2015 at 16:55
Please note that terms and conditions apply.
822
Correspondence
THEEDITOR Sir, In the scientific note on Output Factors and Scatter Ratios for Radiotherapy Units by Ahuja et al. (1978))the introductionof the output factor in the scatterair ratio equation seems to introduce a change in the original expression given by Gupta andCunningham (1966).I n order to understandfully the implications of the equation of Ahuja et al., a more detailed analysis of the SAR equation has been pursued where the primary incident beam is split into components of direct primary radiation from the source and the scattered radiation from the collimator and other shielding materials surrounding the source. It is seen that the expression for SAR of Gupta and Cunningham is the limiting case where the attenuation coefficient in tissue for the radiation scattered from the collimator is taken equal to that for the radiation emanating directly from the source. I n the Ahuja et. derivation of the scatter-air ratio, the collimator scattered component isremoved from the total primaryincident beam (term Picatter(y,A ) of eqn (3) of this note) and asa result theuse of any attenuation coefficient for this component is eliminated. This removes the unknown error, inthe expression of Gupta and Cunningham, introduced by the assumption that the attenuation coefficients for collimator scattered and direct source radiations are equal; an assumption that is nottrue,particularly for large field sizes. TheAhuja et al. definition of scatter-air ratio thus takes the form of the ratio of the total scattered dose (tissue and collimator) to the air dose a t the same point inthe tissue.The advantage of this expression is the elimination of the attenuation coefficient of the collimator scatteredradiation while passing through the tissue. Thus when the scatter-air ratio is defined as the ratio of the tissue scattered dose to the air dose at the same point in tissue it can be expressed mathematically as
SAR(Y,A)= Ds.t(y,A)/Da(Y,A)
(1)
where SAR (y, A ) is the scatter-air ratio for field size A and at depth y in the tissue, Da(y, A)is the dose to a small mass of tissue in air for field size A a t the same point, and D,,(y,A) is the tissue scattered dose as used in the Gupta and Cunningham expression, for field size A and depth y. This scattered dose is the difference between the totaltissue dose and the total primary attenuated dose and can be put as D,(y, A ) - P,(y, A ) and then
where TAR (y, A ) is the tissue-air ratio. The total primary dose in tissue P,(y, A ) is due to total radiation impinging on the tissue phantom and attenuated in the thickness y. The total radiation
Correspondence
823
impinging on the tissue phantom consists basically of two components, one coming directly from the source which would be independent of field size and may be denoted as PrUrce(y,0 ) . The other componentis the radiation scattered from the collimator andother shielding materialsaround the source and which would be dependent on the fieldsize and is denoted as Pp"tter(y,A). The second term on the right hand side of eqn (2) can then be written as
q y ,A ) - Py-(y, 0 )+ p p y y , A ) (3) Da(y,A) Dak, A ) and writing primary tissuedose (4)in termsof primary airdose (D,) attenuated the linear attenuation through thicknessy of the tissue withp1 and p2 as effective coefficients for the direct and scattered primary beam respectively and dm as the depth of maximum dose, the right handside of the above equation reduces to
(assuming TAR (y, 0 ) is a simple exponential). The t,ermD r t t e r ( y ,A ) is the collimator scattered air dose and is also given by Dytter(y,A ) = N ( A ) * D , ( y0) , -Da(y, 0 ) = Da(y,0) ( N ( A )- 1). Introducing this in eqn (4)above,
The expression for the scatter-air ratio, eqn (2)) now takes the form SAR(Y,A) = T A R ( Y , A )
where p2, the effective attenuation coefficient for the radiation scattered from
824
Correspondence
the collimator, is assumed constant with a value somewhat higher than p1 for the radiation emanating directlyfrom the source. If p2 is assumed to equal pl, eqn ( 5 ) above reduces to
which is the same expression as given by Gupta and Cunningham (1966). In theAhuja et al. approach to s m , the term Pt(y, A) in eqn (2) is replaced by Pt(y, 0 ) . Here the SAR' (the prime is used to denote that it is different from the conventional SAR) takes the form of the ratio of the total scatter dose (both from tissue and collimator) to air dose in tissue. The term P y t t e r ( y ,A) in eqn (3) is therefore zero and following through other derivations the second term in the parentheses of the right hand side of eqn ( 5 ) is also zero, and the final expression takes the form l
which is the same as thatproposed by Ahuja et al. This move of lumping allthe scattered dose into one entity removes the discrepancy of assuming a single valued attenuation coefficient for the mixtureof source and collimator scattered incident radiation thereby eliminating the uncertain though small error caused in the SAR value derived from the Gupta and Cunningham expression. The only difficulty, though not very serious for day to day clinical applications, is the need to generate SAR' tables separately for each machine since these SAR' values also incorporate the machine collimator characteristics.
A. S. CHHABRA, Radiation Physics, St. Elizabeth Hospital Medical Center, Youngstown, OH 44501, U.S.A.
2 April 1979
REFERENCES AHUJA, A. S., DUBUQUE,G. L., and HENDEE, W. R., 1978, Phys. Med. Biol., 23, 968. J. R., 1972, Phys. Med. Biol., 17, 42. CUNNINGHAM, P. N., and WILKINSON, J. M., 1972, Comput. Prog. CUNNINGHAM,J. R., SHRIVASTAVA, Biomed., 2, 192. GUPTA, S. K., and CUNNINGHAM, J. R., 1966, Br. J. Radiol., 39, 7. ICRU, 1973, Measurement of Absorbed Dose in a Phantom Irradiated by a Single Beam of X or Gamma Rays, Report 23 (ICRU Publications, P.O. Box 30165, Washington, DC 20014, U.S.A.). of X or ICRU, 1976, Determination of Absorbed Dose in a Patient Irradiated by Beams G a m m R a y s in RadiotherapyProcedures, Report24(ICRUPublications,P.O. Box 30165, Washington, DC 20014, U.S.A.). JOHNS, H. E., and CUNNINQHAM, J. R., 1974, The Physics of Radiology (Springfield, IL: C. C. Thomas).
Search
Collections
Journals
About
Contact us
My IOPscience
Letter to the editors (radiotherapy)
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 822 (http://iopscience.iop.org/0031-9155/24/4/015) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 129.78.139.28 This content was downloaded on 03/10/2015 at 16:55
Please note that terms and conditions apply.
822
Correspondence
THEEDITOR Sir, In the scientific note on Output Factors and Scatter Ratios for Radiotherapy Units by Ahuja et al. (1978))the introductionof the output factor in the scatterair ratio equation seems to introduce a change in the original expression given by Gupta andCunningham (1966).I n order to understandfully the implications of the equation of Ahuja et al., a more detailed analysis of the SAR equation has been pursued where the primary incident beam is split into components of direct primary radiation from the source and the scattered radiation from the collimator and other shielding materials surrounding the source. It is seen that the expression for SAR of Gupta and Cunningham is the limiting case where the attenuation coefficient in tissue for the radiation scattered from the collimator is taken equal to that for the radiation emanating directly from the source. I n the Ahuja et. derivation of the scatter-air ratio, the collimator scattered component isremoved from the total primaryincident beam (term Picatter(y,A ) of eqn (3) of this note) and asa result theuse of any attenuation coefficient for this component is eliminated. This removes the unknown error, inthe expression of Gupta and Cunningham, introduced by the assumption that the attenuation coefficients for collimator scattered and direct source radiations are equal; an assumption that is nottrue,particularly for large field sizes. TheAhuja et al. definition of scatter-air ratio thus takes the form of the ratio of the total scattered dose (tissue and collimator) to the air dose a t the same point inthe tissue.The advantage of this expression is the elimination of the attenuation coefficient of the collimator scatteredradiation while passing through the tissue. Thus when the scatter-air ratio is defined as the ratio of the tissue scattered dose to the air dose at the same point in tissue it can be expressed mathematically as
SAR(Y,A)= Ds.t(y,A)/Da(Y,A)
(1)
where SAR (y, A ) is the scatter-air ratio for field size A and at depth y in the tissue, Da(y, A)is the dose to a small mass of tissue in air for field size A a t the same point, and D,,(y,A) is the tissue scattered dose as used in the Gupta and Cunningham expression, for field size A and depth y. This scattered dose is the difference between the totaltissue dose and the total primary attenuated dose and can be put as D,(y, A ) - P,(y, A ) and then
where TAR (y, A ) is the tissue-air ratio. The total primary dose in tissue P,(y, A ) is due to total radiation impinging on the tissue phantom and attenuated in the thickness y. The total radiation
Correspondence
823
impinging on the tissue phantom consists basically of two components, one coming directly from the source which would be independent of field size and may be denoted as PrUrce(y,0 ) . The other componentis the radiation scattered from the collimator andother shielding materialsaround the source and which would be dependent on the fieldsize and is denoted as Pp"tter(y,A). The second term on the right hand side of eqn (2) can then be written as
q y ,A ) - Py-(y, 0 )+ p p y y , A ) (3) Da(y,A) Dak, A ) and writing primary tissuedose (4)in termsof primary airdose (D,) attenuated the linear attenuation through thicknessy of the tissue withp1 and p2 as effective coefficients for the direct and scattered primary beam respectively and dm as the depth of maximum dose, the right handside of the above equation reduces to
(assuming TAR (y, 0 ) is a simple exponential). The t,ermD r t t e r ( y ,A ) is the collimator scattered air dose and is also given by Dytter(y,A ) = N ( A ) * D , ( y0) , -Da(y, 0 ) = Da(y,0) ( N ( A )- 1). Introducing this in eqn (4)above,
The expression for the scatter-air ratio, eqn (2)) now takes the form SAR(Y,A) = T A R ( Y , A )
where p2, the effective attenuation coefficient for the radiation scattered from
824
Correspondence
the collimator, is assumed constant with a value somewhat higher than p1 for the radiation emanating directlyfrom the source. If p2 is assumed to equal pl, eqn ( 5 ) above reduces to
which is the same expression as given by Gupta and Cunningham (1966). In theAhuja et al. approach to s m , the term Pt(y, A) in eqn (2) is replaced by Pt(y, 0 ) . Here the SAR' (the prime is used to denote that it is different from the conventional SAR) takes the form of the ratio of the total scatter dose (both from tissue and collimator) to air dose in tissue. The term P y t t e r ( y ,A) in eqn (3) is therefore zero and following through other derivations the second term in the parentheses of the right hand side of eqn ( 5 ) is also zero, and the final expression takes the form l
which is the same as thatproposed by Ahuja et al. This move of lumping allthe scattered dose into one entity removes the discrepancy of assuming a single valued attenuation coefficient for the mixtureof source and collimator scattered incident radiation thereby eliminating the uncertain though small error caused in the SAR value derived from the Gupta and Cunningham expression. The only difficulty, though not very serious for day to day clinical applications, is the need to generate SAR' tables separately for each machine since these SAR' values also incorporate the machine collimator characteristics.
A. S. CHHABRA, Radiation Physics, St. Elizabeth Hospital Medical Center, Youngstown, OH 44501, U.S.A.
2 April 1979
REFERENCES AHUJA, A. S., DUBUQUE,G. L., and HENDEE, W. R., 1978, Phys. Med. Biol., 23, 968. J. R., 1972, Phys. Med. Biol., 17, 42. CUNNINGHAM, P. N., and WILKINSON, J. M., 1972, Comput. Prog. CUNNINGHAM,J. R., SHRIVASTAVA, Biomed., 2, 192. GUPTA, S. K., and CUNNINGHAM, J. R., 1966, Br. J. Radiol., 39, 7. ICRU, 1973, Measurement of Absorbed Dose in a Phantom Irradiated by a Single Beam of X or Gamma Rays, Report 23 (ICRU Publications, P.O. Box 30165, Washington, DC 20014, U.S.A.). of X or ICRU, 1976, Determination of Absorbed Dose in a Patient Irradiated by Beams G a m m R a y s in RadiotherapyProcedures, Report24(ICRUPublications,P.O. Box 30165, Washington, DC 20014, U.S.A.). JOHNS, H. E., and CUNNINQHAM, J. R., 1974, The Physics of Radiology (Springfield, IL: C. C. Thomas).
