The Calculation of Percentage Depth Doses

Abstract

AN analysis of percentage depth dose data reveals some simple numerical relationships which exist between the magnitude of this dose and the size of the portal, the focal distance, and the half value in copper of the incident beam. These relations can be put to practical use in the calculation of approximate doses under widely different conditions of radiation. The percentage depth dose is found by dividing the intensity measured at a depth by that measured at the surface. The latter consists of the intensity of the beam in air plus that of the back-scattered radiation. These terms are illustrated in Table I by two examples taken from Grebe and Nitzge's tables. In the first example, the surface intensity amounts to 118 per cent (the intensity of the incident beam is called 100 per cent; to this is added back-scattered radiation, which in this case amounts to 18 per cent). The actual intensity at 10 cm. depth is 34 per cent of that of the incident beam. The percentage depth dose is, therefore, or 29 per cent. In the second example, the percentage depth dose is the same as in the first, but the actual depth and surface intensities are not. It is apparent that the percentage depth dose gives no information as to the actual values of these factors from which it is derived. In the following discussion only percentage depth doses at a depth of 10 cm. will be considered. I.—The Effect of Portal Area on the 10 cm. Percentage Depth Dose The magnitude of the 10 cm. percentage depth dose increases in a definite way with increasing portal areas. The most convenient method of showing this is to compare the magnitudes of doses found under different areas with that obtained under a portal of 50 sq. cm. In Table II are given the results of an analysis of data obtained from various sources. In each case the value of the dose for the 50 sq. cm. area is made unity, and the doses obtained under larger portals are expressed as percentages of the first. Space does not permit the presentation of all of the data;1 in the table only the averages derived from many observations are given. In these sets of measurements the focal distances range from 30 to 120 cm., and the half values of the incident beams, from 0.30 to 5.2 mm. of copper. It will be seen that the ratios set down under each portal area agree among themselves fairly well, except those for the largest portal. Here the values given by Grebe and Nitzge are uniformly much larger than any of the others. Those of Quimby and her collaborators are lower than the average. The averaged values of all of the available data are given on the lowest line of Table II. When these are plotted against the logarithms of the areas, they are found to lie along an exponential curve. From this it is possible to determine with reasonable accuracy how much greater or less than the dose under the 50 sq. cm. portal, will be the doses under portals of other sizes. The nomogram (Fig. 1) simplifies this calculation.