|Fig. 1: PET-CT Scanner (Source: Wikimedia Commons)|
Noninvasive imaging is the hallmark of modern medicine, as it allows one to look into a patients body without cutting it open, providing for more proactive treatment. Positron Emission Tomography (PET) is a noninvasive radionuclide imaging method used to help diagnose and monitor diseases such as cancer. A positron emitting tracer molecule that acts as the disease biomarker is detected to produce images of its 3-D biodistribution. [1,2] Tracer molecules, usually intravenously administered to the patient, accumulate and concentrate in tracer-specific regions of the body. These radioactive molecules emit positrons that annihilate with an electron within a short distance, releasing two photons traveling in opposite directions. [1,3] PET systems image the tracer biodistribution in the body by collecting and quantifying (i.e. detecting) the pairs of oppositely directed photons from this annihilation event. Each photon for PET tracers is 511 kilo-electron Volt (keV). [1-3] Since PET images the biology of the body, it is usually used in conjunction with other imaging modalities, such as CT, that image the anatomy of the body (see Fig. 1). Due to PET's complexity and detector-material cost, development of PET centers can cost upwards of $5 million.  Thus, PET imaging is typically exclusive to relatively wealthy clinics.
Conventional PET employs coincidence detection to reconstruct an image of the radioactive source.  In the typical ring geometry, a ring of detectors surrounds the patient. Each annihilation event generated from a positron emitted from the radioactive source produces two photons traveling antiparallel to each other.
When a photon reaches the detector and interacts with it, an electric signal is produced. If two signals occur at opposite detectors within a small time-window, they are called coincident and are presumed to have originated from the same positron. As the two photons producing this coincidence are considered collinear, each coincidence forms a line of response (LOR). The annihilation event must have occurred somewhere along this line.  Over the duration of a PET scan, multiple LORs are acquired, and image reconstruction algorithms are used to produce an image of the source, usually at the intersection of the majority of LORs.
One of the largest limitations to the coincidence-detection method is the occurrence of Compton Scatter events. While a photon travels, it passes through many different media including human tissue, air, and the detector surfaces.  In doing so, it often bounces off electrons in the absorbing medium, transferring some of its kinetic energy to the electron. This process, known as Compton Scatter, results in the photon losing some of its energy in addition to changing its trajectory by an angle θ.  Lower energies of photons impinging upon the detectors cause weaker signals, resulting in a noisier image, i.e. with a lower signal to noise ratio. Additionally, the spatial resolution of the image itself is impaired by the change in trajectory, as many of the LORs now do not pass through the annihilation site. The probability of Compton scattering per unit length of absorbing medium is linearly proportional to the atomic number of the medium. The angular distribution of scattering is independent of medium but dependent on the energy of the photons. 
© Sreyas Misra. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 J. M. Ollinger and J. A. Fessler, "Positron-Emission Tomography," IEEE 560323, IEEE Signal Processing Magazine 14, No. 1, 43 (1997).
 G. Muehllehner and J. S. Karp, Positron Emission Tomography, Phys. Med. Biol. 51, R117 (2006).
 M. E. Phelps, PET: Physics, Instrumentation, and Scanners (Springer, 2006).
 R. G. Evens eta l., "Cost Analyses of Positron Emission Tomography For Clinical Use," Am J. Roentgenol. 141, 1073 (1983).