Question 3 of 6: MRI and CT Tomographic Imaging

Question 3: MRI and CT Tomographic Imaging (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. MRI spatial encoding rests on three cooperating subsystems — a static main field, switched linear gradient fields, and an RF transmit/receive subsystem — that together make the resonance frequency and phase of tissue protons carry spatial information; CT and MRI resolution and shielding follow directly from what each modality actually uses (x-rays vs. RF/magnetic fields), and the titanium-hip case is worked through each of the resulting hazard mechanisms in turn.

(i) MRI spatial encoding

The main field $B_0$ (a superconducting magnet, typically 1.5 or 3 T clinically) aligns the net nuclear magnetic moment of hydrogen protons (abundant in water and fat) along its axis and sets each proton's Larmor precession frequency $\omega_0=\gamma B_0$, where $\gamma$ (the gyromagnetic ratio, $\approx$42.58 MHz/T for ¹H) is fixed by the nucleus. Without anything else, every proton in the body precesses at the same frequency and no spatial information exists. The orthogonal gradient fields $G_x, G_y, G_z$ (produced by three sets of gradient coils, whose current is switched rapidly — the $dx/dt$, $dy/dt$, $dz/dt$ notation refers to these time-varying gradient waveforms) are superimposed linearly on $B_0$, so the local field — and hence the local Larmor frequency — becomes a known linear function of position. This is exploited in three stages of a pulse sequence: a slice-select gradient applied during RF excitation restricts excitation to a single slab whose Larmor frequency matches the transmitted RF bandwidth; a phase-encode gradient, applied briefly and stepped in amplitude over repeated excitations, imparts a spatially-dependent phase shift along a second axis; and a frequency-encode (readout) gradient, applied during signal acquisition, spatially encodes frequency along the third axis. The RF field has a transmit component $B_1^+$, a circularly-polarised field at the Larmor frequency that tips the net magnetization away from $B_0$ by a chosen flip angle (exciting the signal), and a receive component $B_1^-$, the same coils (or dedicated receive-only surface/phased-array coils) sensing the weak RF signal (free induction decay or echo) re-radiated as the tipped magnetization precesses and relaxes. Each combination of phase- and frequency-encode steps fills one line of "k-space" (spatial-frequency space); once enough lines are collected, a 2D/3D inverse Fourier transform of k-space reconstructs the final image.

(ii) Characterizing and monitoring spatial resolution

MRI resolution is set by the field of view divided by the acquisition matrix (in-plane voxel size) and by the slice-select gradient/RF bandwidth (through-plane thickness); a steeper gradient spreads a given anatomical distance over a wider range of frequencies, allowing finer spatial discrimination at the cost of reduced signal-to-noise ratio per voxel. It is characterized and monitored using a resolution phantom (a block containing bar patterns or point sources of known spacing) imaged periodically, from which the point-spread function or modulation transfer function (MTF) is measured; routine quality-assurance scans (e.g. under an ACR MRI accreditation programme) track this alongside geometric distortion and signal-to-noise ratio. CT resolution is set by detector element size, x-ray focal-spot size, and the reconstruction kernel/algorithm chosen; it is characterized with a wire or thin-edge phantom (from which the MTF is computed) and a line-pair phantom (resolution quoted in line pairs per cm), with routine QA also checking CT-number linearity, uniformity and noise using a standard accreditation phantom (e.g. the ACR CT phantom).

(iii) Shielding: MRI vs. CT

MRI requires two distinct kinds of shielding because its hazards are non-ionizing: an RF shield (a continuous copper-mesh or sheet Faraday cage lining the scan room) prevents external RF sources (broadcast radio, WiFi, other hospital telemetry) from contaminating the extremely sensitive receive coils, and equally prevents the scanner's own RF pulses from radiating out into the hospital; separately, passive (steel) or active shim/shielding coils confine the static fringe field so the 5-gauss line (the boundary beyond which ferromagnetic objects and pacemakers are considered safe) stays within the controlled room. CT shielding is entirely different in kind: because CT uses ionizing x-rays, the room is lined with lead (or lead-equivalent barium plaster) sized by a radiation-protection calculation (NCRP/CSA methodology) that accounts for workload, use factor and the occupancy of adjacent areas, to keep scattered and leakage x-ray dose to staff and the public below regulatory limits. The two shielding designs differ because the underlying hazard differs: MRI's is RF/magnetic-field interference and exposure, CT's is ionizing-radiation dose, and no amount of lead helps against the former, nor copper mesh against the latter.

(iv) Titanium hip implant: MRI safety concerns

Titanium is paramagnetic (only very weakly magnetic, essentially non-ferromagnetic), so the translational (projectile) force and torque that a strong ferromagnetic implant would experience in $B_0$ are minimal for a pure titanium prosthesis, and most titanium hip implants are labelled MRI-conditional. Several concerns remain nonetheless: (1) RF heating — a metal implant, especially an elongated or looped conductive structure, can concentrate RF-induced eddy currents from the $B_1^+$ field, particularly at higher field strength (3 T) or with high-specific-absorption-rate (SAR) sequences, causing localized tissue heating around the implant; the scan's SAR must be checked against the implant's conditional labelling and reduced (lower flip angle, fewer slices, or a lower-SAR sequence) if needed. (2) Image artifact — the difference in magnetic susceptibility between titanium and surrounding tissue locally distorts $B_0$, producing a signal void and geometric distortion around the joint (a susceptibility artifact) that can obscure adjacent anatomy; this is reduced with metal-artifact-reduction sequences (wider receiver bandwidth, view-angle tilting, or dedicated techniques such as SEMAC/MAVRIC). (3) Residual mechanical risk — while the titanium stem/cup itself experiences little force, many "titanium" hip systems include other components (cobalt-chromium liners, steel screws, or other alloyed parts) that may be more strongly magnetic; the actual implant composition and its MR-conditional labelling/implant card must be confirmed before scanning, not assumed from the word "titanium" alone. (4) Any electrically conductive loop formed by modular implant components can still support induced currents even without significant ferromagnetism, so scan-parameter limits on the implant's conditional label must be respected.