The statistical distribution of the number of ion pairs per ionizing event in a small volume simulating a tissue sphere was obtained by applying the Expectation-Maximization (EM) algorithm to experimental spectra measured by exposing a Rossi-type spherical proportional counter to γ radiation. The normalized experimental spectrum, r(x), which is the distribution of the number of ion pairs per event from both the primary track and the subsequent electron multiplication, can be represented as$\sum_{{\rm n}}p_{{\rm n}}\cdot f(n,x),\ \text{where the}\ f(n,x)\text{'}{\rm s}\ \text{for}\ n=1,2,3,\ldots $, n are the normalized spectra for exactly 1, 2, 3,..., n primary ion pairs and are calculated by convoluting the single-electron spectrum. The coefficients$p_{{\rm 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 process, and it is represented in analytical form by the Gamma distribution$f(1,x)=a\cdot x^{{\rm b}}\cdot {\rm e}^{{\rm cx}}$, where x is energy, usually in eV, and a, b and c are constants. The EM algorithm is an iterative procedure for computing the maximum likelihood or maximum a posteriori estimates of the mixing proportions$p_{{\rm n}}$, which we also refer to as the primary distribution of ion pairs in a microscopic spherical tissue-equivalent volume. The experimental and primary spectra are presented for simulated tissue spheres ranging from 0.25 to 8 μm in diameter exposed to^{60} Co γ radiation.

Skip Nav Destination

Article navigation

May 1998

Research Article|
May 01 1998

# The Frequency Distribution of the Number of Ion Pairs in Irradiated Tissue

*Radiat Res*(1998) 149 (5): 411–415.

Citation

B. Obelić, D. Srdoč, P. M. Djurić, S. A. Marino; The Frequency Distribution of the Number of Ion Pairs in Irradiated Tissue. * Radiat Res* 1 May 1998; 149 (5): 411–415. doi: https://doi.org/10.2307/3579779

Download citation file:

## Sign in

Don't already have an account? Register

### Client Account

You could not be signed in. Please check your email address / username and password and try again.

### Sign in via your Institution

Sign in via your Institution### Citing articles via

Commonalities Between COVID-19 and Radiation Injury

Carmen I. Rios, David R. Cassatt, Brynn A. Hollingsworth, Merriline M. Satyamitra, Yeabsera S. Tadesse, Lanyn P. Taliaferro, Thomas A. Winters, Andrea L. DiCarlo

Monte Carlo Simulation of SARS-CoV-2 Radiation-Induced Inactivation for Vaccine Development

Ziad Francis, Sebastien Incerti, Sara A. Zein, Nathanael Lampe, Carlos A. Guzman, Marco Durante

Low-Dose Radiation Therapy (LDRT) for COVID-19: Benefits or Risks?

Pataje G. Prasanna, Gayle E. Woloschak, Andrea L. DiCarlo, Jeffrey C. Buchsbaum, Dörthe Schaue, Arnab Chakravarti, Francis A. Cucinotta, Silvia C. Formenti, Chandan Guha, Dale J. Hu, Mohammad K. Khan, David G. Kirsch, Sunil Krishnan, Wolfgang W. Leitner, Brian Marples, William McBride, Minesh P. Mehta, Shahin Rafii, Elad Sharon, Julie M. Sullivan, Ralph R. Weichselbaum, Mansoor M. Ahmed, Bhadrasain Vikram, C. Norman Coleman, Kathryn D. Held

Germicidal Efficacy and Mammalian Skin Safety of 222-nm UV Light

Manuela Buonanno, Brian Ponnaiya, David Welch, Milda Stanislauskas, Gerhard Randers-Pehrson, Lubomir Smilenov, Franklin D. Lowy, David M. Owens, David J. Brenner

RITCARD: Radiation-Induced Tracks, Chromosome Aberrations, Repair and Damage

Ianik Plante, Artem Ponomarev, Zarana Patel, Tony Slaba, Megumi Hada