A Study of the Explicit Distribution of Radiation in Interstitial Implantations

Abstract
In interstitial radiation therapy, the calculation of the explicit dose distribution throughout an implant is so laborious that it is rarely done by manual methods except for model cases. Systems have been developed which permit the calculation of a single dose rate that is taken as representative of a radium implant. The two methods in common use are the Quimby system (1) and the Paterson-Parker system (2). Both require that the needles be implanted to form standard geometrical patterns with the radium distributed according to the “;rules”; of the system. Ideal geometry, however, is seldom possible in practice; indeed, in some cases there is a deliberate deviation from rigid geometry in order to fit the anatomy or the disease. In any case, only one dose rate is given for an arrangement of needles about which there is a complex radiation distribution. As a result, the radiotherapist often must make decisions based on inadequate knowledge of the dose delivered from an interstitial implant. The advent of the automatic electronic computer has made possible a new approach to the dosimetry of interstitial needle implants. With a large digital computer it is feasible to calculate the dose to thousands of points and to plot automatically the isodose patterns in planes through the implant for individual patients (3). The method to be described here requires a small amount of human effort and a modest amount of machine time on an IBM 709 computer. In this paper the method of calculation will be discussed. The application of the method to more than 100 cases and the resulting analysis have been presented in an earlier issue of this journal (4). A subsequent paper will reexamine the interstitial dosimetry systems, the meaning of the dose thus derived, and deviations resulting from imperfect implant geometry. METHOD The logic of the machine calculation is much the same as would be utilized for a manual calculation. The dose contributed by each needle to the grid of points in chosen planes is summed at each point and points of equal dose are allowed to define isodose curves. Implants which can be calculated by the computer method are those composed of an array of approximately parallel needles, with or without perpendicular crossing needles. Cross-sectional views of the implant are obtained by one of several methods: transverse tomography (5), perpendicular-section technic (6), or three-dimensional reconstruction (7). The use of the latter two methods has been explained (8). These cross-sectional cuts are the planes of calculation and should be perpendicular to the average direction of the vertical needles. Input data on punched cards specify locations and types of needles in the implant. In a given plane of calculation the points locating the vertical needles are placed on a coordinate system, the position of each needle determined by an x and y. If there are crossing needles, projections of the ends are located in the plane of calculation. The IBM 709 computer utilizes approximately 29,000 storage locations and six tape units for this calculation. To make the problem amenable to calculation, the needle is divided equally into four parts by five planes, as shown in Figure 1. In preliminary calculations for each plane, two-dimensional tables of the dose rates for each type of radium needle in stock were calculated to points on a 1.0 mm. grid by a numerical evaluation of the Sievert integral (9), thus making full allowance for oblique filtration of the gamma rays in the case of the needle. The tables developed in this manner are stored on magnetic tape and made available for transfer to the core memory of the computer as needed.