Monte Carlo-based Spencer-Attix and Bragg-Gray tissue-to-air stopping power ratios for ISO beta sources.

Spencer-Attix (SA) and Bragg-Gray (BG) mass-collision-stopping-power ratios of tissue-to-air are calculated using a modified version of EGSnrc-based SPRRZnrc user-code for the International Organization for Standardization (ISO) beta sources such as (147)Pm, (85)Kr, (90)Sr/(90)Y and (106)Ru/(106)Rh. The ratios are calculated at 5 and 70 µm depths along the central axis of the unit density ICRU-4-element tissue phantom as a function of air-cavity lengths of the extrapolation chamber l = 0.025-0.25 cm. The study shows that the BG values are independent of l and agree well with the ISO-reported values for the above sources. The overall variation in the SA values is ∼0.3% for all the investigated sources, when l is varied from 0.025 to 0.25 cm. As energy of the beta increases the SA stopping-power ratio for a given cavity length decreases. For example, SA values of (147)Pm are higher by ∼2% when compared with the corresponding values of (106)Ru/(106)Rh source. SA stopping-power ratios are higher than the BG stopping-power ratios and the degree of variation depends on type of source and the value of l. For example, the difference is up to 0.7 % at l = 0.025 cm for the (90)Sr/(90)Y source.