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

  • Harrison H. Barrett
  • Brandon Gallas
  • Eric Clarkson
  • Anne Clough
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 110)


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.


Inverse Problem Boltzmann Equation Null Space Scattered Radiation Source Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Harrison H. Barrett
    • 1
    • 2
    • 3
  • Brandon Gallas
    • 1
    • 2
  • Eric Clarkson
    • 3
  • Anne Clough
    • 4
  1. 1.Dept. of RadiologyUniversity of ArizonaTucsonUSA
  2. 2.Program in Applied MathematicsUniversity of ArizonaTucsonUSA
  3. 3.Optical Sciences CenterUniversity of ArizonaTucsonUSA
  4. 4.Dept. of MathematicsMarquette UniversityMilwaukeeUSA

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