Numerical solution of an applied biophysics inverse problem

The problem of reconstruction of the radionuclide intake dynamics using results of lifetime measurement of the Sr-90 incorporated in the enamel of human teeth is considered. This problem is a part of the system of dose reconstruction for the population exposed to ionizing radiation as a result of radioactive contamination of the environment. The approach to the solution of this task results in formulation of a mathematical inverse problem whose type depends on the biophysical properties of investigated radionuclide and the instrumental technique used for measurements. The problem results in two nonlinear integral equations with inexact known right parts. The basic method of research is linearization of this system and further regularization of linear integral equations. The main approach to solving these types of problems is based on minimization of the smoothing functional. Numerical procedure was carried out simultaneously by a direct minimization (method of Hook and Jeeves) and by a necessary condition analysis of extremum of the appropriate finite-dimensional problem. The solution obtained in such a way has biological and physical meaning and is in a good agreement with biological data.