Quantification of radioactivity in PET
Radioactive atoms are unstable and spontaneously disintegrate (decay) into other atoms, releasing energy by the emission of ionizing radiation. When a positron-emitting radionuclide decays, the decay energy is shared between positron (β+) and neutrino (υe, which is not detected). The positron travels a short distance (positron range) in tissue before losing enough energy to be able to interact with an electron. This leads to the annihilation of the positron and electron, and two 511 keV gamma photons arise, travelling in approximately opposite direction from the site of annihilation. The emitted gamma radiation makes it possible to quantify and locate the radioactive material.
Event is a generic term referring to the PET scanner's detection of a gamma ray. There are four types of events: prompt, delayed (or random), true, and multiple.
The units of measured radioactivity ("activity") are related to the rate at which they decay. The standard unit of radioactivity is Becquerel, and it is equal to one decay per second. An old unit is Curie, which equals to 37 GBq.
Radioactive decay is a random process, and therefore the measurement of radioactivity must be treated with statistical methods. We have to observe a number of events (counts) with the detectors over time to achieve an acceptable level of fluctuations (standard deviation) of the mean value (counts/time). If the radioactivity in the sample is low, we have to measure it for a longer time, increase the size of the sample, or use a more sensitive detector system, to achieve sufficient count statistics. In case of ex vivo blood and tissue samples, the measurement time could be extended until sample radioactivity is reduced to the background radioactivity level, although in practice equipment will be needed for the measurement of other samples before that. In in vivo imaging the measurement time is limited by the fact that radioactivity of the "sample" is changing due to physiological dynamic (re)distribution of the radiotracer. Therefore the in vivo radioactivity measurement must be divided into time frames, that are short enough to record the dynamic changes in radioactivity concentration, and long enough to achieve sufficient count statistics.
Temperature or mass can be measured repeatedly to determine the mean value and standard deviation with good accuracy. Also radioactive sample can be measured repeatedly, if there is radioactivity left, and if the sample otherwise does not change. But radioactive in vivo "sample" is changing, and therefore it can only be measured once - and only for a short time.
The result of radioactivity measurement is the number of detected events (counts) per measurement time. This is much lower than the number of actual disintegrations during that time. Detection efficiency is different for each detector system (and changes over time, is affected by humidity and temperature, etc). Therefore all radioactivity measurement devices (PET scanners, well counters, dose calibrators, blood on-line detectors, ...) need to be cross-calibrated using a sample with known radioactivity. Cross-calibrations provide us with calibration coefficient for each device, which are used to convert the device-dependent counts per second (cps) values to comparable Bq values.
Sample size is taken into account in the calibration process at the latest. The "activities" that we actually are using in PET data analyses are concentrations of radioactivity: Bq/mL (millilitre = cubic centimetre = cm3), or Bq/g in case of ex vivo data.
Accuracy of scanner calibration could be monitored by comparing image-derived blood or urine (bladder) activity concentrations to those measured from blood or urine samples (Maus et al., 2014 and 2018).
Reconstruction of PET images produces 4D data, consisting of pixels (voxels). Pixels have a known volume (in units cm3, often shortened as cc, or mL), and each pixel has the number of events (counts) collected during the time frame as its value. Average radioactivity concentration, in units cps/mL, inside a pixel is calculated by dividing the number of counts with the frame length (duration, in seconds) and the pixel volume. Physical decay of the isotope label is corrected to the start of PET scan, and prior to the analysis, to the tracer administration start time (t=0), if PET scan was started later. Image is then calibrated to units Bq/mL by multiplying pixel values with a calibration coefficient that is based on previously scanned cylinder containing liquid with known radioactivity concentration. Image pixels can be used in analyses as such, producing "parametric" 3D images, or as groups of pixels, regions-of-interest (ROIs, or volumes-of-interest, VOIs). The radioactivity concentration of a pixel or ROI at different frame times (over the 4th image dimension) is called time-activity curve (TAC).
The limited image resolution of PET systems leads to partial volume effects, which can cause substantial under- or overestimation of the radioactivity concentration in a small lesion. With new scanner generations and advanced image reconstruction techniques, these errors will decrease. This also means that previously set cut-off limits in diagnostic studies need to be redefined, and that scanners and reconstruction methods need to be standardized in multi-centre studies (Kuhnert et al., 2016).
Arterial cannulation enables fast and accurate blood sampling for obtaining the input function for quantitative data analysis. Sample tube is weighed before and after blood sampling, and placed in a well counter, where the radioactivity is measured. Measurement time may be automatically adjusted to achieve sufficient count statistics. Background radioactivity is corrected. Then the physical decay that happened during the radioactivity measurement of the sample can be corrected precisely. Radioactivities are also corrected to the time of radioligand administration, and calibrated to units kBq/g or kBq/mL.
Radioactivity of plasma samples is measured similarly, except that weighing the tubes is not necessary, if a known plasma volume is pipetted from the blood to the sample tube.
When blood radioactivity is measured using automatic online sampling system, the blood is flowing through the tubing at a certain flow rate, passing the detectors. Thus it is not possible to measure exactly same blood sample for a certain time, but instead we have to integrate the counts during a pre-set time "frame", usually 1 or 5 s, that is required to achieve sufficient count statistics. Thus the sampling frequency is limited by the count statistics. The sample time has to be corrected for the time that it took for the blood to flow from the artery to the detector.
- Units of radioactivity in PET data
- Radioactivity measurement of blood samples
- PET data
- Molar activity
- Decay correction
- Branching factor
- Attenuation correction
- Processing input data
- Simulation of PET time frames
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Updated at: 2023-04-17
Created at: 2014-01-30
Written by: Vesa Oikonen