Nuclear Medicine: Radiopharmaceuticals, Instrumentation, and Decay Math
The imaging chain
A radionuclide must emit a penetrating gamma of suitable energy with a half-life long enough to image but short enough to limit dose. Tc-99m dominates: 6-hour half-life, 140 keV photon, eluted from a Mo-99/Tc-99m generator (Mo-99 half-life 66 hours) with sterile saline. Generator quality control includes testing for Mo-99 breakthrough and alumina column breakthrough - a classic exam item.
Camera and collimator trade-offs
The collimator defines the image: spatial resolution and sensitivity are inversely related. High-resolution collimators give detail with long acquisition times; high-sensitivity collimators give counts with poorer resolution; pinhole collimators magnify small organs such as the thyroid. The NaI(Tl) crystal converts photons to light, PMTs amplify and localize, and the pulse-height analyser windows around the photopeak (typically ±10–20%), rejecting Compton scatter.
Decay mathematics
Activity decays as A = A₀e^(−0.693t/T½); in whole half-lives, activity halves each time. Pre-dispensing, residual-activity, and post-therapy exposure questions are almost always simple half-life arithmetic.
Study-specific knowledge and traps
Know localization and normal biodistribution: MDP bone scan (kidneys/bladder, growth plates), sestamibi myocardial perfusion (gallbladder, bowel), V/Q for PE, HIDA for biliary patency, iodine uptake for thyroid. Traps include:
- Confusing I-123 (imaging) with I-131 (therapy) and omitting thyroid blocking or breastfeeding interruption.
- Forgetting that F-18 FDG has a ~110-minute half-life, requires ~60 minutes uptake, and is affected by blood glucose and insulin.
- Ignoring that PET uses 511 keV annihilation photons detected in coincidence, not collimation.
- Assuming lead aprons are equally effective at all energies - they are less so at 140 keV, so time and distance dominate.
Worked example
800 MBq eluted at 08:00. At 14:00 (one 6-hour half-life), activity = 400 MBq; at 20:00, 200 MBq.