New Parameters of the Power Law for Tumor-Air Ratios for Cobalt-60 Radiation

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Abstract
The British Institute of Radiology has recently published a comprehensive revised survey of depth-dose tables (Suppl. No. 10, Brit. J. Radiol., 1961) superseding those first published in 1953 (Suppl. No. 5). In particular, the tumour-air ratios (now referred to as “tissue-air ratios”) for cobalt 60 have been newly calculated and differ slightly from the earlier ones. It therefore became of interest to recalculate the parameters K and m in the power law (Pfalzner 1960) for tumour-air ratios, using the new values of R of Suppl. No. 10. As in the earlier publication (Pfalzner 1960), R(t,A t ) is the tumour-air ratio for field area A t, thickness of overlying tissue t, and K(t) and m(t) are constants for a given value of t. The new values of K and m are given in Table I together with other parameters useful in the conversion relations for axial depth dose (Pfalzner 1961). K and m values listed here were obtained as part of a larger program (extending over a wide range of half-value thicknesses) with the aid of the IBM 650 Data Processing System at the Computing Center, University of Western Ontario, London. The calculations were based on least-squares solutions of the logarithmic form of relation (1) above, utilizing as data the tumour-air ratio values for all of the nine non-zero square field areas of Table 6.5, Suppl. No. 10, i.e., 4 × 4, 5 × 5, 6 × 6, 7 × 7, 8 × 8, 10 × 10, 12 × 12, 15 × 15, and 20 × 20 cm. It will be seen that the new values of K and m differ from those published by the author in 1960, first because the earlier values were based on least-square solutions for four field areas only, namely 4 × 4, 6 × 6, 8 × 8, and 10 × 10 cm., second because the actual values of R are now slightly different. Values of the slope, m, now continue to increase with depth. It may also be pointed out here that the physical meaning of 100K(t)/K(0.5) may easily be shown to be the per cent axial depth dose for infinite SSD for unit field area (A = 1 sq. cm.). In Table II a comparison is shown between central axis depth-dose values as given in Suppl. No. 10, Table 6.3, for a field of 10 × 10 cm., 80 cm. SSD, and as calculated from the relation for axial depth dose, P, derived from the power law (1): It is seen that agreement between calculated and experimental values is now substantially better at all depths than that shown in Table II of the author's earlier publication (1960). Part of the original discrepancy was due to the fact that the P* values were for a circular field area of 100 sq. cm., whereas the parameters K and m had been calculated from R values for square field areas.

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