[Methods for geometric and nonlinear optimization of the structure of interstitial implants for interstitial x-ray therapy of malignant tumors].

In 1990 G. K. Edmundson suggested a geometric optimization method for determination of the effective structure of interstitial implants. In 1997 Y. Anacak, M. Essassolak, A. Aydin, et al. used this method for two-level interstitial implantation. It was shown in their work that the geometric optimization method provided higher efficiency of the dose distribution than conventionally used dose distributions produced by interstitial implants with equal exposure times. In 1983 the problem of optimization of the interstitial implant structure was formulated in our works. Its mathematical interpretation was also suggested. The goal of this work was to show that the geometric optimization method does not always provide high efficiency of the dose distribution, even in comparison with conventionally used dose distributions produced by interstitial implants with equal exposure times. The interstitial implant structure can be optimized by solving special mathematical programming problems.