Fundamental Limits of Spatial Resolution in PET

In Chapter 17 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss positron emission tomography.

17.10 Positron Emission Tomography

If a positron emitter is used as the radionuclide, the positron comes to rest and annihilates an electron, emitting two annihilation photons back to back. In positron emission tomography (PET) these are detected in coincidence.

Anyone who has looked at PET images will be struck by their low spatial resolution. They provide valuable functional information, but little anatomical detail. Why?

“Fundamental Limits of
Spatial Resolution in PET,”
by William Moses.

In a 2011 article in Nuclear Instruments and Methods in Physics Research A (“Fundamental Limits of Spatial Resolution in PET,” Volume 648, Supplement 1, Pages S236–S240), William Moses analyses what factors contribute to PET spatial resolution.

Abstract: The fundamental limits of spatial resolution in positron emission tomography (PET) have been understood for many years. The physical size of the detector element usually plays the dominant role in determining resolution, but the combined contributions from acollinearity, positron range, penetration into the detector ring, and decoding errors in the detector modules often combine to be of similar size. In addition, the sampling geometry and statistical noise further degrade the effective resolution. This paper quantitatively describes these effects, discusses potential methods for reducing the magnitude of these effects, and computes the ultimately achievable spatial resolution for clinical and pre-clinical PET cameras.

Detector size

The most obvious limitation of spatial resolution comes from the detector size. Usually detection occurs in a scintillator crystal that converts a gamma ray to visible light, which is detected by a photomultiplier. The width of the scintillator limits the spatial solution of the image. A typical detector size is about 4 mm.

Positron range

A positron is emitted with an energy of about a million electronvolts. It then travels through tissue until it slows enough to capture an electron and and give off two 0.511 MeV photons. The range of the positron sets a limit to the spatial resolution. Different isotopes emit positrons with different energies. One of the most widely used isotopes for functional studies is ¹⁸F, which has a range of about half a millimeter. Most other common isotopes used in PET have longer ranges.

Acollinearity

If a positron and electron are at rest when they annihilate, they emit two 0.511 MeV photons. To conserve momentum, these photons must travel in opposite directions. If, however, the positron-electron pair has some kinetic energy when they annihilate, the photons are not emitted exactly in opposite directions. Usually they deviate from 180° by up to 0.25°. This translates into about one to two millimeters of blurring in typical detector rings.

Decoding

Decoding is complicated. Many PET devices have more scintillators than photomultipliers, so the photomultipliers take turns recording from different scintillators (a process called multiplexing). The PET scanner must then decode all this information, and this decoding process is not perfect. Moses estimates that decoding introduces an uncertainty of about a third of the detector width, or around a couple millimeters in spatial resolution.

Penetration

The 0.511MeV photons can penetrate into the ring of detectors used in a PET device, causing blurring. In the illustration below, if the source (green) contains an isotope that emits two photons, then for some angles those photons (red) are detected by a single detector, but for other angles (blue) they are detected by multiple detectors. 

An illustration based on Fig. 2 of
“Fundamental Limits of Spatial Resolution in PET,”
by William Moses, showing how penetration of a
photon into different detectors causes blurring.

Sampling Error

A detector ring is more sensitive to sources at some positions compared to others (see Moses’s Fig. 3 for an explanation). This effect tends to degrade by spatial resolution by about 25%.

 

If you add all these uncertainties in quadrature, you get a spatial resolution of about 6 mm. This is worse resolution that you would have for magnetic resonance imaging or computed tomography, which is why PET images look so blurry. They are often overlaid on an MRI (see Fig. 17.25 in IPMB).

If you decided to build a PET system with the best possible spatial resolution (regardless of complexity or cost), you could eliminate all of the sources of uncertainty except positron range and acollinearity, implying a spatial resolution of about 2 mm (worse for isotopes other than ¹⁸F). PET is never going to image small-scale anatomical detail.