PL-ESTIMATES WITH FINITE FLOW DISPERSION AT A POINT

E.N. Donskoi
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.3. С. 48-58.

            For homogeneous and heterogeneous media with a similar chemical composition PL-estimates with finite flow dispersion at a point are developed Two approaches to the construction of PL-estimates for a homogeneous medium considered namely: the approach based on trajectory invariancy of the Markovian process related to the transport equation. The second approach allows to construct PL-analogs for well known local estimates of flow at a point, and the first one allows to develop new PL-estimates prototypes of which are artificial and not used in Monte-Carlo calculations. The principal features of the developed PL-estimates of flow at a point are the following: imbiasedness, dispersion finiteness with rather weak limitations on the source function and functional under the approach based on invariancy of the transport equation’s Green function and computation, estimation discontinuity as a detection point function at all points of the estimated functional discontinuity.
      It is shown that PL-estimates of flow at a point may be efficiently used for solving problems of radiation therapy. Essential (up to 100 time and higher in heterogeneous medium and more than 1000 times in homogeneous medium) computation time reduction, a possibility of computing a dose in the given points direct computation time dependance on a number of points, absence of statistical fluctuations on dose and isodose curves are to be stated as the advantages of using these estimates as comparable to standart estimates by the Monte-Carlo method.