Nuclear Physics and Instrumentation

Nuclear imaging detects photons emitted from an administered radiopharmaceutical. Image quality depends on radioactive decay, photon interactions, detector performance, collimation, count statistics, and reconstruction.

Radioactive Decay¶

\[ A = A_0e^{-\lambda t} \]

\[ \lambda = \frac{0.693}{T_{1/2}} \]

After each physical half-life, activity decreases by 50%.

Physical half-life: radionuclide decay
Biologic half-life: elimination from the body
Effective half-life: combined physical and biologic clearance

\[ \frac{1}{T_e} = \frac{1}{T_p} + \frac{1}{T_b} \]

Photon Interactions¶

Photoelectric Absorption¶

The photon is completely absorbed. This contributes useful detected events but also patient dose.

Compton Scatter¶

The photon changes direction and loses energy. Scatter reduces contrast and may be detected in the wrong location.

Energy windows help reject scattered photons.

Attenuation¶

Photon intensity decreases as photons pass through tissue:

\[ I = I_0e^{-\mu x} \]

Breast tissue, diaphragm, obesity, and arms may produce apparent perfusion defects. CT or radionuclide transmission imaging can correct for attenuation.

Gamma Camera¶

A conventional Anger camera contains:

Collimator
Scintillation crystal
Photomultiplier tubes
Positioning and energy circuits
Computer and reconstruction software

The sodium iodide crystal converts gamma photons into light. Photomultiplier tubes convert the light into electrical signals and estimate the location and energy of each event.

Collimators¶

Collimators accept photons traveling in selected directions.

Collimator	Typical use
Low-energy high-resolution	Tc-99m cardiac imaging
Low-energy general-purpose	Higher sensitivity with less resolution
Medium-energy	Higher-energy radionuclides
Parallel-hole	Routine planar and SPECT imaging

Higher resolution generally requires lower sensitivity. The collimator must match the photon energy of the radionuclide.

SPECT¶

SPECT cameras rotate around the patient and acquire multiple projections. Reconstruction creates short-axis, vertical long-axis, and horizontal long-axis images.

Modern systems may use:

Dual detector cameras
Solid-state cadmium-zinc-telluride detectors
Iterative reconstruction
Resolution recovery
CT attenuation correction

CZT systems provide greater sensitivity and may permit shorter acquisition times or lower administered activity.

PET¶

PET radionuclides emit positrons. A positron interacts with an electron, producing two 511-keV photons traveling approximately 180° apart.

Coincidence detection localizes the event without a physical collimator.

Advantages include:

Higher sensitivity and resolution
Routine attenuation correction
Short acquisition time
Quantitative myocardial blood flow
Improved detection of multivessel disease

PET Corrections¶

Quantitative PET requires correction for:

Attenuation
Scatter
Random coincidences
Dead time
Radioactive decay
Patient motion

Misregistration between PET and CT can create false perfusion defects.

Image Reconstruction¶

Filtered Back Projection¶

Fast but more sensitive to noise and streak artifact.

Iterative Reconstruction¶

Methods such as OSEM repeatedly compare estimated and measured data.

Advantages include:

Improved noise control
Incorporation of attenuation and resolution correction
Better performance with lower-count studies

Excessive smoothing may conceal small defects; insufficient smoothing increases noise.

Count Statistics¶

Radioactive counts follow Poisson statistics:

\[ \text{Noise} \propto \sqrt{N} \]

\[ \text{Signal-to-noise ratio} \propto \sqrt{N} \]

Obtaining four times as many counts approximately doubles the signal-to-noise ratio.

Low counts may result from insufficient activity, obesity, short acquisition, infiltrated injection, or detector malfunction.

Quality Control¶

Routine quality control includes:

Energy peaking
Detector uniformity
Center-of-rotation testing
Spatial resolution
Sensitivity
SPECT reconstruction checks
PET normalization and calibration
PET/CT or SPECT/CT alignment
Rb-82 generator breakthrough testing when applicable

Quality-control failure should be corrected before clinical imaging continues.

Key Points¶

Scatter and attenuation reduce image contrast.
Collimation trades sensitivity for spatial resolution.
PET uses coincidence detection rather than physical collimation.
More counts improve signal-to-noise by the square-root relationship.
Attenuation-correction misregistration may create new artifacts.
Review quality-control results before attributing an abnormality to the patient.