A cumulative normal distribution model for simulation of electron beam profiles

Calculation of electron beam depth-dose curves and output factors for arbitrary field shapes

A previously presented method to calculate depth-dose curves and output factors for arbitrarily shaped electron beams is evaluated. The method employs a Gaussian pencil model for direct incident and applicator scattered electrons; the parameter values are derived from measured central axis depth-dose distributions. In addition, an empirical model is used to compute the dose due to electrons scattered by field-defining frames. In this way, the properties of the clinical electron beams are taken into account. In this paper, calculations and measurements for electron beams with energies between 6 and 20 MeV, treatment field dimensions between 3 and 14 cm, and various applicator sizes are compared. The results demonstrate the importance of irregular field dose calculations and the scope of the present method. Agreement better than 3% in dose and 0.2 cm in depth is achieved. For electron beams without applicators, the calculations show the same accuracy. Another method in electron treatment planning that derives values for the radial width parameter of the pencil beam from measured broad beam profiles is also investigated. This method gives good results for dose calculations in beams without applicator scatter. It should be used with care, however, for beams that contain such a scatter component. When electrons scattered by the applicator walls and field-defining frames are neglected, differences between measured and calculated dose up to 8% are found.

Current algorithms for computed electron beam dose planning

The field of electron beam dose planning has been in a state of very rapid development during the last decade. The essentially one-dimensional manual corrections used since the beginning of the sixties, has been replaced by at least two- and sometimes three-dimensional computer algorithms capable of taking all irregularities of the body cross-section and the properties of the various tissues into account. This is achieved by dividing the incoming broad beams in a number of narrow pencil beams, the penetration of which can be described by essentially one-dimensional formalisms. The constituent pencil beams are most often described by Gaussian, experimentally or theoretically derived distributions. The accuracy of different dose planning algorithms is discussed in some detail based on their ability to take the different physical interaction processes of high energy electrons into account. It is shown that those programs that take the deviations from the simple Gaussian model into account give the best agreement with experimental results. With such programs a dosimetric relative accuracy of about 5% is generally achieved except in the most complex inhomogeneity configurations. Finally, the present limitations and possible future developments of electron dose planning are discussed.

Calculation of electron beam dose distributions for arbitrarily shaped fields

A method for the calculation of absorbed dose distributions of arbitrarily shaped electron beams is presented. Isodose distributions and output factors of treatment fields can be predicted with good accuracy, without the need for any dose measurement in the actual field. A Gaussian pencil beam model is employed with two different pencil beams for each electron beam energy. The values of the parameters of the pencil beam dose distributions are determined from a set of measurements of broad beam distributions; in this way the influence of electrons scattered by the applicator walls is taken into account. The dose distribution of electrons scattered from high atomic number metal frames, which define the treatment field contour at the skin, is calculated separately and added. This calculation is based on experimentally derived data. The method has been tested for beams with 6, 10, 14 and 20 MeV electron energy. The distance between calculated and measured isodose lines with values between 10 and 90% is under 0.3 cm. The difference between calculated and measured output factors does not exceed 2%.

Electron beam dose planning using discrete Gaussian beams. Mathematical background

A general method for computerized electron beam dose planning is proposed based on the use of a square or hexagonal grid or matrix of discrete Gaussian elementary beams. Using this method the distribution of absorbed dose in an electron beam of arbitrary cross-section incident on an irregular patient surface can be calculated taking the influence of tissue inhomogeneities into account. The derived expressions for the absorbed dose in narrow and broad uniform beams are compared with experimental data and Monte Carlo calculations. Good agreement is obtained over the clinically significant portion of the absorbed dose distribution at a fairly wide grid spacing of about 0.5 cm.

Cytotoxicity of adriamycin to tumour cells in vivo and in vitro

Two mouse sarcomas have been used to assess the sensitivity to Adriamycin of tumour cells in vivo and in vitro. Both tumours were tissue-culture adapted so that cell survival could be assayed in vitro after treatment either in vivo or in vitro. For both tumours (WHFIB and CBSAF) cells were highly sensitive when treated in vitro yet very resistant to treatment in vivo, whether assayed by cell survival or regrowth delay. Cells from both tumours treated in vitro with Adriamycin immediately after excision were slightly more resistant than the cells maintained in vitro. However, this was not adequate to explain the marked discrepancy between in vivo resistance and in vitro sensitivity. The discrepancy was not due to a failure of drug delivery. Phase of cell growth was the factor was most significantly affecting chemosensitivity in vitro, plateau-phase cells being much more resistant than log-phase cells. Hypoxia was also an important factor leading to reduced chemosensitivity. Tumour diameter, in the range 2-8 mm, did not appear to be important.