Computational Radiology and Imaging pp 71-100 | Cite as

# Scattered Radiation in Nuclear Medicine: A Case Study on the Boltzmann Transport Equation

## Abstract

The objective in nuclear medicine is to deduce properties of a gamma-ray source inside a patient’s body from measurements of the gamma rays that escape the body. The gamma rays are attenuated and scattered in complicated ways before they emerge from the body, and it is essential to have a good theoretical description of these processes before attempting the inverse problem. In this paper we make use of the Boltzmann transport equation to describe the variation of gamma-ray flux with position, direction and energy. After a tutorial derivation of the Boltzmann equation, we discuss various analytic solutions, showing the relation to the attenuated x-ray transform. Numerical methods are also discussed, and the relation of the gamma-ray distribution to measured data is elucidated. Then some approaches to the inverse-source problem are described.

## Keywords

Inverse Problem Boltzmann Equation Null Space Scattered Radiation Source Distribution## Preview

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