Undergraduate · 20 min

PET imaging: timing a positron tracer

Compare the decay curves of ¹⁸F, ¹¹C, ⁶⁸Ga and ¹⁵O, see why hospitals pair a cyclotron with a radiochemistry lab, and follow the positron annihilation that lights up the scan.

Goal

Match each tracer's half-life to its logistics, apply $N/N_0 = (1/2)^{t/T_{1/2}}$ to plan a scan, and explain the $\beta^+$ → $2\gamma$ signal.

Apparatus and reagents

Virtual bench: decay curves of four positron emitters plus the annihilation scheme $\ce{e+ + e- -> 2\gamma}$ (511 keV each).

Procedure

Select ¹⁸F-FDG. Check the curve at 110 min, 220 min and 330 min: what fractions remain?
Switch to ¹⁵O (T½ = 2 min). How much activity is left after 8 minutes? Why can it only be made on-site?
Compare ¹¹C and ⁶⁸Ga: which one survives a 90-minute synthesis, and which fits a 20-minute chemistry?
Use the compare preset to rank the three isotopes by decay speed, then connect each to cyclotron, generator or regional distribution.

What to observe

After one half-life exactly half remains, after three only an eighth — the grey 0.5 line and red tick always intersect the curve at T½.
¹⁵O loses 15/16 of its activity in 8 minutes while ¹⁸F keeps about 95% — half-life dictates how far a tracer can travel.
The detected signal is not the positron itself but the two back-to-back 511 keV γ-rays from its annihilation with an electron.

Explanation

A proton-rich nucleus like $\ce{^{18}F}$ decays by $\beta^+$ emission: $\ce{p -> n + e+ + ν_e}$ . The positron flies a millimetre or so, meets an electron and annihilates into two 511 keV photons emitted back-to-back; a ring of detectors catching both at once draws a line through the annihilation point, and millions of lines rebuild the tracer map. Activity follows $A = A_0(1/2)^{t/T_{1/2}}$ , so the half-life sets the whole logistics: ¹⁵O demands an on-site cyclotron, ¹¹C fits fast chemistry, ⁶⁸Ga is milked from a ⁶⁸Ge generator, and ¹⁸F (110 min) can be shipped to regional hospitals.

History of the experiment

Positron emission was predicted by Dirac in 1931 and confirmed by Irène and Frédéric Joliot-Curie in 1934. PET took shape in the 1970s when Michel Ter-Pogossian's team built the first tomograph at Washington University, and the glucose mimic ¹⁸F-FDG — devised by Louis Sokoloff's group and synthesised in 1976 — became its workhorse tracer.

Chemists behind it

Marie Curie Frederick Soddy