THE FREQUENCY-DISTRIBUTION OF THE NUMBER OF ION-PAIRS IN IRRADIATED TISSUE

The statistical distribution of the number of ion pairs per ionizing e vent in a small volume simulating a tissue sphere was obtained by appl ying the Expectation-Maximization (EM) algorithm to experimental spect ra measured by exposing a Rossitype spherical proportional counter to gamma radiation. The normalized experimental spectrum, r(x), which is the distribution of the number of ion pairs per event from both the pr imary track and the subsequent electron multiplication, can be represe nted as Sigma(n)p(p) . f(n, x), where the f(n,x)'s for n = 1, 2, 3,... , n are the normalized spectra for exactly 1, 2, 3,..., n primary ion pairs and are calculated by convoluting the single-electron spectrum. The coefficients p(n) represent the mixing proportions of the spectra corresponding to 1, 2, 3,..., n ion pairs in forming the experimental spectrum. The single-electron spectrum used in our calculations is the distribution of the number of ion pairs due to the multiplication pro cess, and it is represented in analytical form by the Gamma distributi on f(1,x) = a . x(b) . e(-cx), where x is energy, usually in eV, and a , b and c are constants. The EM algorithm is an iterative procedure fo r computing the maximum likelihood or maximum a posteriori estimates o f the mixing proportions p(n), which we also refer to as the primary d istribution of ion pairs in a microscopic spherical tissue-equivalent volume. The experimental and primary spectra are presented for simulat ed tissue spheres ranging from 0.25 to 8 mu m in diameter exposed to C o-60 gamma radiation. (C) 1998 by Radiation Research Society.