Nomographic Aids in Calculating Radium Dosage for Plane and Point Sources

Abstract

Calculations of radium dosage were considerably simplified by the contributions of Paterson and Parker (1, 2). For radium sources, filtered by 0.5 mm. Pt or its equivalent, distributed on square or circular areas, the number of milligram hours required to deliver 1,000 gamma roentgens could be determined from a group of graphs. The same data can be put in the form of an alignment chart or nomogram. The advantages of a nomogram are that it is compact and that no interpolation is required in order to obtain intermediate values. With very little practice, nomograms can be used with facility and speed. The nomogram (Fig. 1) presented for this purpose consists of three vertical scales. On the left-hand scale is found the area in square centimeters. On the scale in the center is found the treatment distance in centimeters. The right-hand scale has divisions on both sides. The divisions on the right side of this scale are labeled at the top “Mg. Hrs.”; the divisions on the left side of this scale are labeled at the top “%“ To find the number of milligram hours required to deliver 1,000 gamma roentgens, one finds the area on the left-hand scale and the treatment distance on the scale in the center. Then, a straight edge, e.g., a ruler, preferably transparent, is placed across the chart through the points selected on these two scales. The straight edge intersects the right-hand scale at a certain point. The figures on the right side of this scale give the same result as the Paterson and Parker area graphs but expressed per square centimeter. When this figure is multiplied by the area, the number of milligram hours required to deliver 1,000 gamma roentgens is obtained. For filtration equivalents other than 0.5 mm. Pt, the Paterson and Parker correction figures are used (Table I). The figures on the lefthand side of the third scale are discussed below. For square areas, Paterson and Parker gave definite distribution rules specifying the amount of radium to be placed on lines added within the square separated by twice the treatment distance. Unfortunately, the exact linear strengths and lengths that these rules require are rarely available. It usually turns out that the figure of practical importance is the percentage of the total amount of radium that must be placed on the lines added within the square. The figures on the left-hand side of the third scale, labeled at the top “%,” are these percentages, i.e., they give the percentage of the total amount of radium that must be placed within the periphery of a square. These figures apply when more than one line is added. If only one line is added, the percentage is always 11 per cent. These percentage figures may also be used for rectangular areas up to the point at which one side is twice as long as the other. Corrections for more elongated rectangles are given in Table II. These figures for rectangles apply when more than one line is added.