**MATHEMATICAL MODELLING and MODERN COMPUTER TECHNOLOGIES in PLANNING RADIOTHERAPY of the CANCER of the BLADDER**MATHEMATICAL MODELLING and MODERN COMPUTER TECHNOLOGIES in PLANNING RADIOTHERAPY of the CANCER of the BLADDER

L.Ya. Klepper, E.V. Molchanova

Central Economic and Mathematical institute of the Russian Academy of Science (CEMI RAS), Moscow

The basic purpose of radiation therapy (RT) consists of a choice of such conditions of irradiation of the center of tumoral disease which will lead to irreversible destruction of tumoral process without serious (irreversible) radiation complications in normal bodies and tissue of an organism. Conditions of the irradiation include a single dose of irradiation, a total dose (TD) and the scheme of realization of the irradiation in time. The determination of optimum conditions of irradiation presents the difficult problem. It is enough to point that to date the choice of a rational tumoral dose, TD, is realized on the base of collective and personal experience of the radiologists.

The purpose of research carried out by us consist:

1. In development mathematical models (MM) for the description of resorbtion probability (RP) the center of tumoral disease as functions from type of tumoral cells, volume of a tumoral tissue and its conditions uniform (with a constant single dose) irradiations (a method of calculation of equivalent conditions of irradiation (CECI)).

2. In creation of MM for the description of tissue complication probability (TCP) in normal bodies and tissue as functions from volumes of tissue and conditions of their irradiation.

3. In use of the created MM for determination of an optimum dose of an irradiation of the center of tumoral disease and a box of the tumoral tissue maximizing criterion of successful radiation treatment F=RP*(1-TCP). Here (1-TCP) there is a probability of absence of tissue complication probability in a box tumours.

4. In application of the developed formalism for direct numerical calculation by means of the COMPUTER optimum TD for a cancer of a bladder.

Adjustment of mathematical models was made on the basis of clinical data about radiation treatment of a transitive-cellular cancer of a bladder which have been systematized in the Republican oncological clinic of Petrozavodsk. As a result of the lead researches the new, theoretically proved and practically confirmed data expressing dependence TD from RP and TCP for various volumes of a tumour of a transitive-cellular cancer of a bladder are received. They can be used as the methodical grant at planning RT of a transitive-cellular cancer of a bladder. The problem of determination optimum TD for a transitive-cellular cancer of a bladder is solved. It has made 49,5 Гр at the scheme of an irradiation: 2 times a day on 1,6 Gy for a session five times a week (RP reaches 71 %, TCP (a radiation cystitis) - 36 %, the volume of a tumour made no more than 5 % from volume of a bladder).