Linear Radium Sources Research Articles

A simple function describing the absorption in platinum for dose-rate calculations around radium applicators.

The diminution of exposure rate from radium gamma radiation by filtration through platinum can be described very accurately by gamma 0/(1 + mu0d) for wall thickness d from 0.2 mm to 4.0 mm (gamma 0 = 6.356 x 10(-5) A m2/kg2 or 8.869 R cm2 h-1 mg-1; mu0 = 1.501 cm-1). This function fits generally accepted data to within experimental error, to an accuracy not achieved by any single exponential factor. The expression is derived theoretically from a simple approximation to the spectral distribution of radium gamma radiation. With this type of transmission function, the expression for the exposure rate around linear radium sources in platinum tubes (generalized Sievert integral) is readily integrated in terms of elementary functions. Used in place of the Sievert integral in calculations of dose distributions, this new fomulation makes possible straightforward numerical evaluation and avoids the storage of tabulated values in computer programmes.

The M. D. Anderson method for the computation of isodose curves around interstitial and intracavitary radiation sources. I. Dose from linear sources.

A review of the physical factors that are used to compute the dose in rads at points around linear radium sources has included a consideration of the gamma-ray absorption in the radioactive source and the container, the effect of cellularity in the source construction, and the effective absorption coefficients for use with the Sievert integral.The effective attenuation in tissue of the gamma rays of gold 198, iridium 192, cesium 137, radium 226, and cobalt 60 have been considered.In addition, new tables based upon recent experimental data are given for the radiation dose around linear radium sources.

A revised table of tissue correction factors for linear radium sources.

The table of tissue correction factors for linear radium sources which was published in 1964 (Batho and Young) has been revised on the basis of new measurements which have been reported of the ratio of exposure in water to exposure in air. Table I is an abridged version of the revised table*. The original table was based on measurements made by Wootton, Shalek and Fletcher (1954).

TISSUE ABSORPTION CORRECTIONS FOR LINEAR RADIUM SOURCES.

This paper describes a method of correcting γ-ray doses from linear radium sources for apparent absorption in tissue. The tissue correction factors which have been calculated are based on experimental measurements by Wootton et al. (1954). They can be used with any of the dose tables or graphs which have been published for linear radium sources.

RADIATION DISTRIBUTION AROUND DUMBBELL AND INDIAN CLUB RADIUM NEEDLES.

Dumbbell radium needles in contrast with standard radium needles are overloaded at both active ends. Indian club radium needles are overloaded only at the point end. The two types of linear radium sources are useful in radium implants where crossing the ends of the needles is difficult. Isodose distributions around these eccentrically loaded needles have been constructed by calculation (1–3). In this experiment, two types of commercially available dumbbell needles and one type of Indian club needle were studied (see Table I and Fig. 1). The radiation distribution around each needle was measured with fluorods, in accordance with the method described previously (4–6). Study of individual needles Figure 1 illustrates isodose curves around each of the three types of needle. Measurements were made along parallel lines at graded distances ranging from 0.2 to 2.0 cm. from the long axis of the needle. The isodose curves are flattened along the entire active length of the dumbell needle as contrasted with the rounded curves of the standard needle; particularly along the line 0.5 cm. from the axis of the needle, which is the region of interest to the radiotherapist. Figure 2 shows isodose curves in a plane 0.5 cm. above the plane of each radium needle. This is the plane of interest for the stated tumor dose of a planar implant.Comparison of standard radium needles with eccentrically overloaded needles in a single-plane implant. Comparison of Standard Radium Needles with Eccentrically Overloaded Needles in a Single-Plane Implant Figure 3 is a study of the dose distribution in the plane of two radium implants with standard radium needles, and one implant with dumbbell needles. Figure 3A shows the isodose lines at one end of a plane of an implant containing three standard radium needles, 2 cm. active length. Each needle is homogeneously loaded with an equal quantity of radium. All values represent doses measured in a tissue-equivalent medium, relative to 100 rads at a point midway between two needles. The relative dose in the area bounded by the radium sources ranges from less than 80 to 150 rads, The 100-rad isodose area is very small, extending only 0.3 cm. from the midpoint toward either end of the implant, and 0.7 cm. from the active ends toward the center. In order to compensate for the underdosed region, the implant is crossed at the inactive end of the needles. Figure 3B illustrates the isodose lines for a standard radium needle implant crossed at the inactive end by a 1.5 cm. active length radium needle. The values represent doses relative to 100 rads as in Figure 3A. By crossing the needles at the inactive ends, the area of the homogeneous dose is extended to the inactive ends of the needles, a marked improvement. The relative hot spots close to the middle of the radium needles are somewhat reduced. Figure 3C illustrates the isodose lines for a radium implant composed of three dumbbell needles, 3.2 cm. active length. All values represent doses relative to 100 rads midway between any two of the needles.

DOSE TABLES FOR LINEAR RADIUM SOURCES CALCULATED BY AN ELECTRONIC COMPUTER.

Tables of dose factors for linear radium sources have been calculated using an electronic computer. These Tables are more detailed than have been published previously. They give values of a function proportional to the dose-rate at points on a rectangular grid surrounding the source. Each Table is applicable to any source of the specified filtration and diameter. The paper discusses the values of the constants used in the calculations. In particular, the value of the absorption coefficient of radium γ rays in platinum has been taken as a function of the absorber thickness.

Computer Evaluation of Dose Rates Around Multiple Radium Sources

Two programs have been developed to determine the dose-rate distribution resulting from an arbitrary array of radium sources. Both programs have been written for an IBM 1620 Data Processing System with 20 K memory and with the automatic division and indirect addressing special features. The constants incorporated in the programs pertain to radium sources of 1 cm. active length with 1 mm. Pt filter, and to any number of such sources up to 6. The constants and the number limitation may be changed rather easily. The first program is written in FORTRAN, the second in SPS. Either program may be used to calculate the dose rate at selected points (entered on punched cards) or at an automatically indexed grid of points (horizontal or vertical plane). For these alternatives, the computer yields a tabular print-out of the coordinates and of the corresponding total dose rates (r/hr.). An additional alternative is available with the SPS program, that of a graphic print-out (again, horizontal or vertical plane). Here the typed output page is an array of points characterized by specific letters which have been assigned to predetermined dose-rate levels. Sketching connections through like letters gives all isodose chart for the distribution. For each patient, as many input cards are required as there are sources. The following information is required on each card: measured angles and relative spatial position of the source (taken directly from anteroposterior and lateral roentgenograms), the estimated magnification of each roentgenogram, the activity of the source, and indexing numbers to distinguish the sources. Information such as patient name and number, date, and number of the application, if included on the first card, will be repeated in the output as the first line typed. The strength of the several sources will also be repeated in the output headings. The method of calculation is the same in both programs. Greenfield et al. (1) have recalculated dose-rate tables for linear radium sources. These data have been revised to the present value for the emission constant of radium and then reduced to analytical form. Six zones of polar angle (measured from the axis of a source) suffice to describe the tabular data in the analytical form chosen. The basic form is common throughout all zones; the constants selected are specific to each zone, and in three a calculated correction is also included. With such selection, the dose rate at a point is evaluated for each source in turn and accumulated for output presentation. The time required depends on the number of sources and the number of points required. A typical gynecological application (5 sources) requires about fifteen minutes for tabulation or plotting of the results for one plane covering an area 16 × 16 cm. Upon request, arrangements can be made to duplicate the programs.

Dosage tables for linear radium sources filtered by 0.5 and 1.0 mm. of platinum.

The dosage tables for linear radium sources filtered by 0.5 mm. platinum computed by Quimby (1) continue to be extremely useful in the planning of radium therapy. No corresponding table exists, however, for linear sources filtered by 1.0 mm. of platinum, which are also commonly used in radium therapy. We have computed such a table, therefore, using Sievert's integrals (2). An extensive check of the table by application of the principles of symmetry and similitude (see below) shows that the computed dose rates are internally consistent to about 1 per cent. A similar check of Quimby's table (1) reveals inconsistencies of the order of 10 per cent. To remove these inconsistencies we have also computed a dosage table for linear radium sources filtered by 0.5 mm. platinum. The tables are presented in the same form as that used by Quimby. Readers are referred to her paper (1) or to the standard text of Glasser et al. (3) for instructions as to their use. Method The tables were computed by linear interpolation from Sievert's integrals. Absorption coefficients used were 0.15 cm.−1 for radium sulfate, 2.00 cm.−1 for 0.5 mm. platinum and 1.94 cm.−1 for 1.0 mm. platinum (2). The radium was assumed to be uniformly distributed on a thin line at the center of the needle. The thickness of the radium salt was taken as the difference between the measured needle thickness and the thickness of the platinum filter. For 1.0 mm. and 0.5 mm. Pt, the radium sulfate thicknesses were, respectively, 1.5 and 0.65 mm. A value of 9.33 r∕mg.-hr. was taken as the dose rate 1.0 cm. from an unfiltered source of radium. This value is consistent with the figure of 8.4 r∕mg.-hr. from a point source of radium filtered by 0.5 mm. of platinum and is in satisfactory agreement with both calculated and experimental values (4). The scattering and absorption of the gamma rays in tissue was ignored. A thorough investigation of the tables applying principles of symmetry and similitude (see below) indicates an internal consistency of 1.0 per cent or better throughout. At least half the entries were checked in this way. In addition, all entries were checked graphically. Assuming the validity of the basic assumptions, the accuracy is about 1 per cent for those regions in which the dose rate is in excess of 0.2 r∕mg.-hr. In the regions where the dose rates are smaller, Sievert's integrals lead to small differences in two large numbers, so that the inaccuracies are somewhat larger. Fortunately, in the low dose rate regions far from the needles, high degrees of accuracy are not necessary. The symmetry principle is readily demonstrated by the following example: the dose rate from the center of a 2.0-cm. needle should be exactly the same as the intensity from the end of a 1.0-cm. needle with the same total radium content.

A simple method for projecting isodose charts of linear radium sources on planes oblique to the longitudinal axis.

This method of graphic projection of isodose curves for linear radium sources was devised to enable isodose charts to be used for the determination of two orthogonal films of a radium applicator. The commonest use for these charts is dosage calculation in radium therapy of cancer of the cervix uteri according to the method described by Fletcher, Wall, Bloedorn, Shalek and Wootton (1953). A contour of the pelvic brim with the position of the radium sources in the tandem and in the ovoids is traced on transparent paper on the antero-posterior film. Isodose charts of the three components of the radium applicator are then placed under the contour, superimposed on one another, on an illuminator. In most cases, however, the longitudinal axis of the tandem lies on a plane oblique to the frontal plane of the pelvis (Fig. 1). Therefore, the angle of the tandem to the frontal plane should be first measured on the lateral film and then the appropriate chart should be applied to the tandem as seen in the antero-poste...

Method of dosage calculation for linear radium sources.

As a routine procedure in intracavitary or interstitial radium treatment, every patient is radiographed in order to visualize the distribution of sources after implantation. Frequently it is discovered that the planned arrangement of sources differs from what is accomplished in the operating room. Sources are found to be well spaced in one region and far apart in another, so that, although one area of tumor is properly dosed, another is inadequately dosed. Sometimes the arrangement is found to be such that there are “hot spots” in regions which tolerate radiation poorly. Of particular interest are cases of cervical cancer under treatment by an intracavitary technic, since sources in the uterus and vagina can be so situated as to deliver a harmful dose to the rectum or bladder. Meredith (1) has considered this problem in detail. Calculation of the amount of radiation reaching such points of interest is often neglected, the dose being expressed simply as the number of milligram-hours. The range is from 5,00...

Two Diagrams for the Computation of Dosage Rates from Linear Radium Sources

In Radium Therapy it is frequently necessary to calculate dosage-rates at various points near rectilinear sources. Such sources include not only the single needle or container, but also intracavitary tubes and rows of needles in plaques and implants. The Parker-Paterson methods are satisfactory in many cases, but they only give the average dosagerate in a strictly defined area or volume, and also it is not always possible to conform to their rules for the distribution of the radium. The two types of diagrams for calculating dosagerates near rectilinear sources, described in this paper, are easy to construct and simple to use, and have been found useful in this department. One diagram of either type will deal with all sources which have the filtration for which it is designed. The dosage-rate, D r/hr., at a point P (Fig. 1), near a radium source AB, of unit linear density and with a wall thickness equivalent to d mm. of platinum, is given by the equation: μ=the absorption coefficient of γ radiation in plat...

Assessment of Dosage from Linear Radium Sources

A device comprising sets of curves combined with a nomogram is described, by means of which the dosage at any point in the vicinity of a linear radium source may be quickly determined. It is applicable to the proposed new types of non-uniformly loaded needles. A special protractor for use in conjunction with the device is also described.

Calculator Circuit for Tandems of Screened Linear Radium Sources

A circuit is given by means of which a calculator for screened linear radium sources, described in a previous paper, can be used for investigating the combined dosage due to a small number of sources in tandem when the line densities of the constituent sources differ. An example of the application of this circuit to the problem of the treatment of cylindrical surfaces by axial sources is given, showing that the apparatus developed makes it possible to consider in detail the dosage distribution in individual cases in a manner not hitherto considered practicable. A number of other applications are also indicated.

Dosage Table for Linear Radium Sources

The expression of tissue dosage in terms of roentgens is becoming general in x-ray and radium therapy. For interstitial radium or radon sources, the literature contains data for several satisfactory methods of determining the minimum dose delivered within a volume implanted with needles or seeds in accordance with certain general principles. In the case of single linear sources, however, such as are commonly employed in the treatment of cervical and rectal cancer, information is not so accessible. The most generally used charts, those of Paterson and Parker (1), give the number of milligram-hours necessary to deliver 1,000 rγ at points in a plane perpendicular to the source at its mid-point, up to 3 cm. distance. For positions not in this central plane, or for greater distances, they are not helpful. Sievert (2) and Laurence (3) have presented extensive data, but in rather complicated mathematical forms. Mayneord and Honeyburne (4) have published a general method for drawing isodose curves around any part...

Linear Radium Source Dose Calculators

Dosage calculators for both unscreened and screened linear radium sources are described. The calculator for unscreened sources may be used for a small number of sources in tandem, including arrangements in which the sources have different line densities. The calculator for screened sources incorporates an electrical method of integration, and takes into account both obliquity and nonhomogeneity of the radiation. It may be used for one source only, or for a small number of sources in tandem provided the sources possess the same line density.