Photon-absorbed fractions for cylindrical geometry: a TLD photon-absorbed fraction model

The purpose of this study is to develop a mathematical model and calculate photon-absorbed fractions in a homogeneous nonradioactive cylinder placed inside off-center and outside a cylindrical homogeneous distribution of activity. In the second case, both the radioactive cylinder and the nonradioactive one are placed in a tissue-equivalent nonradioactive medium. The values of the photon-absorbed fractions are investigated for various geometrical configurations using water as the material filling the cylinders and the medium in between and an isotope commonly used in Nuclear Medicine, 99mTc. The calculations for off-center cylinders allows for modeling inhomogeneous distributions of activity within a tumor by placing several "cold" cylinders of various sizes in a radioactive finite cylinder. This three-dimensional model calculates photon-absorbed fractions for inhomogeneous activity distributions that can be used in quantitative nuclear medicine for self-absorption correction, thus introducing a more realistic correction than the one-dimensional corrections. These calculations are also used to model the response of a cylindrical TLD (thermoluminiscent dosimeter) placed inside a homogeneous radioactive cylinder and outside the homogeneous radioactive cylinder, in an absorbing nonradioactive surrounding medium. The purpose of these calculations is to evaluate the photon-absorbed fraction in the TLD as an instrument of measuring the time-integrated activity of a homogeneous radioactive source versus an inhomogeneous one. The dependence of the TLD-absorbed fraction on the position of the TLD with respect to the radioactive cylinder is investigated.