GATE Biomedical Engineering Medical Imaging Systems Syllabus

In nuclear medicine, what defines an ideal radiotracer for SPECT imaging?

It should emit gamma photons of suitable energy (~$100\text{–}200\,\text{keV}$) for detection, have a short physical half-life, pure gamma emission (no particulate radiation adding dose), and selective biological uptake in the target tissue.

What is the most commonly used radionuclide in SPECT, its gamma energy, and physical half-life?

Technetium-99m ($\ce{^{99m}Tc}$), which emits gamma photons of about $140\,\text{keV}$ and has a physical half-life of approximately $6\,\text{hours}$.

Describe the basic detector components of a gamma (Anger) camera used in SPECT.

A collimator (defines direction), a large scintillation crystal (usually NaI(Tl)) that converts gammas to light, an array of photomultiplier tubes (PMTs), and position/energy logic circuitry (Anger logic) to compute event location and reject scatter via a pulse-height window.

Why does a gamma camera require a physical collimator while a CT scanner does not?

Gamma photons are emitted isotropically from inside the patient with no inherent directional information, so a lead collimator is needed to accept only photons traveling along defined directions. CT uses an external, directional X-ray source, so geometry is known.

State the law of radioactive decay and define the decay constant $\lambda$.

$N(t) = N_{0}\,e^{-\lambda t}$, where $\lambda$ is the decay constant (probability of decay per unit time). The half-life is $T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$.

Define effective half-life and give its formula in terms of physical and biological half-lives.

Effective half-life accounts for both radioactive decay and biological clearance: $\frac{1}{T_{\text{eff}}} = \frac{1}{T_{\text{phys}}} + \frac{1}{T_{\text{bio}}}$.

What is the fundamental physical principle that distinguishes PET from SPECT?

PET uses positron-emitting radionuclides; an emitted positron annihilates with an electron, producing two $511\,\text{keV}$ gamma photons emitted ~$180^{\circ}$ apart. Detection relies on coincidence detection of these photon pairs rather than physical collimation.

What is the energy of each annihilation photon in PET, and why is this value fixed?

Each photon has energy $511\,\text{keV}$, equal to the rest-mass energy of the electron/positron: $E = m_{e}c^{2} = 0.511\,\text{MeV}$. Two are produced to conserve energy and momentum.

Define a 'line of response' (LOR) in PET and explain electronic (coincidence) collimation.

A line of response is the straight line connecting two detectors that register annihilation photons within a short coincidence timing window. Because the line is defined electronically by simultaneous detection, no physical collimator is needed — this is electronic collimation.

Name the most widely used PET radiotracer and the metabolic process it images.

Fluorine-18 fluorodeoxyglucose ($\ce{^{18}F}$-FDG), a glucose analogue. It images glucose metabolism, with high uptake in metabolically active tissues such as many tumors and the brain.

What is time-of-flight (TOF) PET and what advantage does it provide?

TOF PET measures the small difference in arrival times of the two annihilation photons to localize the annihilation point along the line of response, improving signal-to-noise ratio and image quality.

Why does PET generally offer better spatial resolution and sensitivity than SPECT?

PET uses electronic coincidence detection (no absorptive collimator, so far higher sensitivity) and the back-to-back $511\,\text{keV}$ photons define lines of response precisely, giving better resolution. SPECT's collimator absorbs most photons, lowering sensitivity.

What nuclear property is exploited in magnetic resonance imaging, and which nucleus is primarily imaged?

Nuclear spin / magnetic moment of nuclei with odd nucleon number. MRI primarily images the hydrogen nucleus ($\ce{^{1}H}$, a single proton) due to its high abundance in water and fat in the body.

State the Larmor equation governing nuclear precession in MRI.

$\omega_{0} = \gamma B_{0}$ (or $f_{0} = \frac{\gamma}{2\pi}B_{0}$), where $\omega_{0}$ is the Larmor precession frequency, $\gamma$ is the gyromagnetic ratio, and $B_{0}$ is the static magnetic field strength.

What is the gyromagnetic ratio of the hydrogen proton (in MHz/T)?

$\frac{\gamma}{2\pi} \approx 42.58\,\text{MHz/T}$ for $\ce{^{1}H}$. Thus at $1.5\,\text{T}$ the Larmor frequency is about $63.9\,\text{MHz}$.

Define T1 (longitudinal/spin-lattice) relaxation in MRI.

T1 is the time constant for recovery of longitudinal magnetization $M_{z}$ toward equilibrium after an RF pulse, via energy exchange with the surrounding lattice: $M_{z}(t) = M_{0}\left(1 - e^{-t/T_{1}}\right)$.

Define T2 (transverse/spin-spin) relaxation in MRI.

T2 is the time constant for decay of transverse magnetization $M_{xy}$ due to loss of phase coherence among spins: $M_{xy}(t) = M_{0}\,e^{-t/T_{2}}$. T2 is always $\leq$ T1.

Distinguish T2 from T2* relaxation.

T2 results from intrinsic spin-spin interactions. T2* includes additional dephasing from static magnetic field inhomogeneities: $\frac{1}{T_{2}^{*}} = \frac{1}{T_{2}} + \frac{1}{T_{2,\text{inhomo}}}$, so $T_{2}^{*} \leq T_{2}$. Spin-echo recovers T2; gradient-echo reflects T2*.

What are the roles of repetition time (TR) and echo time (TE) in MRI image weighting?

TR is the time between successive RF excitation pulses; TE is the time from excitation to echo readout. Short TR + short TE = T1-weighted; long TR + long TE = T2-weighted; long TR + short TE = proton-density-weighted.

What is the function of magnetic gradient coils in MRI?

Gradient coils superimpose linear spatial variations on $B_{0}$ so the Larmor frequency becomes position-dependent. They enable slice selection, frequency encoding, and phase encoding — i.e., spatial localization of the signal.

What is k-space in MRI and how is the image obtained from it?

k-space is the spatial-frequency (Fourier) domain where raw MRI data are acquired, with axes determined by phase- and frequency-encoding gradients. The image is reconstructed by applying a 2-D (inverse) Fourier transform to the k-space data.

What is the fundamental relationship between ultrasound propagation speed, frequency, and wavelength?

$c = f\lambda$, where $c$ is the speed of sound in the medium (~$1540\,\text{m/s}$ in soft tissue), $f$ is frequency, and $\lambda$ is wavelength. Higher frequency gives shorter wavelength and better resolution but less penetration.

Define acoustic impedance and give its equation.

Acoustic impedance is $Z = \rho c$, the product of medium density $\rho$ and sound speed $c$ (units rayl, $\text{kg·m}^{-2}\text{s}^{-1}$). Differences in $Z$ at interfaces determine the strength of ultrasound reflections (echoes).

What fraction of ultrasound intensity is reflected at a boundary between two media of impedance $Z_{1}$ and $Z_{2}$?

The pressure reflection coefficient is $R = \frac{Z_{2} - Z_{1}}{Z_{2} + Z_{1}}$, and the intensity reflection coefficient is $R_{I} = \left(\frac{Z_{2} - Z_{1}}{Z_{2} + Z_{1}}\right)^{2}$.

What physical effect underlies ultrasound transducers, and what material is commonly used?

The piezoelectric effect: a material (commonly lead zirconate titanate, PZT) deforms under an applied voltage to generate sound and produces a voltage when deformed by returning echoes, enabling it to both transmit and receive ultrasound.

How is depth (range) of a reflector determined in pulse-echo ultrasound?

From the round-trip echo time $t$: $d = \frac{c\,t}{2}$, where $c$ is the speed of sound and the factor $\frac{1}{2}$ accounts for the sound traveling to the reflector and back.

State the Doppler equation used in ultrasound to measure blood flow velocity.

$f_{d} = \frac{2 f_{0} v \cos\theta}{c}$, where $f_{d}$ is the Doppler frequency shift, $f_{0}$ the transmitted frequency, $v$ the reflector velocity, $\theta$ the angle between the beam and flow, and $c$ the speed of sound.

Compare A-mode, B-mode, and M-mode ultrasound display formats.

A-mode (amplitude): 1-D plot of echo amplitude vs depth. B-mode (brightness): 2-D grayscale image where echo amplitude maps to pixel brightness. M-mode (motion): displays the motion of a structure along one line over time, used for moving structures like heart valves.

What is time-gain compensation (TGC) in ultrasound, and why is it needed?

TGC progressively amplifies echoes returning from greater depths to compensate for attenuation of the beam as it travels deeper into tissue, producing uniform image brightness regardless of reflector depth.

Summarize the key trade-off between ionizing and non-ionizing modalities by classifying CT, PET, SPECT, MRI, and ultrasound.

Ionizing (use radiation, dose concern): X-ray, CT, SPECT, PET — CT/X-ray give anatomy, SPECT/PET give functional/metabolic information. Non-ionizing (no radiation dose): MRI (superb soft-tissue contrast, anatomy + function) and ultrasound (real-time, portable, no dose, operator-dependent).