MRI Gradients, Coils, and Quality Assurance – Lecture Vocabulary

Gradient Fundamentals

• Gradient = any magnetic component that varies over space (and/or time) and is super-imposed on the static main field (B_0).
• MRI system contains three orthogonal, independently-driven gradient sets:
  • Z (longitudinal/head–feet)
  • Y (anterior–posterior)
  • X (left–right)
• Purpose: locally increase or decrease B_0 so that frequency (or phase) of proton precession becomes position-dependent → essential for slice selection, phase encoding, frequency/readout encoding.
• Gradients are separate from: main superconducting coils, passive/active shielding coils, and shim coils.

Gradient Coil Designs

• Z-gradient: Helmholtz pair – two identical circular windings mounted at each bore end; produces symmetric field that rises toward each coil.
• X & Y gradients: “Pear-saddle” coils – saddle-shaped windings creating transverse linear fields.
• All gradient sets are resistive; field exists only while current is applied (unlike persistent superconductive main coils).
• Gradient shield windings placed outside primary gradient conductors confine fringe gradient field inside bore → reduces eddy currents in cryostat & limits external RF noise.

Gradient Field Mathematics & Example

• Example: B0 = 3.0\,\text{T}. A z-gradient generates a linear variation Gz = \pm1.5\,\text{T} across bore:
  • At + side: B{tot}=3+1.5=4.5\;\text{T}, 3+1=4.0\;\text{T}, 3+0.5=3.5\;\text{T} • At isocenter (0 point): B{tot}=3.0\;\text{T}
  • At − side: 3-0.5=2.5\;\text{T} … 3-1.5=1.5\;\text{T}
• Reversing gradient current flips polarity; same magnitude, opposite sign.
• “Linear” property: equal distance left/right of isocenter gives equal magnitude but opposite sign change (e.g., \Delta B = \pm1.0\,\text{T} at ±10 cm).

Gradient System Performance Parameters

• Gradient Amplitude: peak strength per unit distance
  G_{max} in \text{mT/m} or \text{G/cm} (10 \text{mT/m}=1\,\text{G/cm}).
• Rise Time: time from 0 to G_{max} (ms).
• Slew Rate: S = G_{max}/\text{rise time} → units \text{mT/m/ms} or \text{T/m/s}; combines power & speed; major spec quoted by vendors (e.g., 120\,\text{mT/m/ms}).
• Duty Cycle: % of each TR that gradient is energized.
• Balanced Gradient: second gradient of equal magnitude & opposite polarity applied to re-phase spins and cancel phase dispersion.

Biological & Safety Considerations

• Rapid switching induces electric fields in conductive tissue → peripheral nerve stimulation, muscle twitch, phosphenes (optic nerve), potential cardiac arrhythmia.
• Duty-cycle & slew-rate limits in software avert PNS and ventricular fibrillation.
• Acoustic noise: gradient vibration against cryostat; up to >100 dB; louder on high-field/higher-slew systems.

Pulse Sequence Context

• Typical spin-echo: 90° RF → TE/2 → 180° RF → echo; gradient “blocks” timed for
  • Slice-select,
  • Phase-encode,
  • Frequency(read)-encode.
• Four separate gradient events can be toggled within 20\,\text{ms}, causing audible “bang–bang”.

Hardware Requirements Synergy

• High B_0 alone is insufficient → must be paired with high-slew, high-amplitude gradients AND high-performance RF coils to obtain speed, resolution, SNR.

RF Coil Taxonomy

• By function:
  • Transmit (Tx)
  • Receive (Rx)
  • Transceiver (Tx/Rx)
• By geometry:
  • Volume (encircle anatomy)
  • Surface (flat/contoured, one side of anatomy)
  • Intracavitary (endorectal, endovaginal, etc.)
• By polarization:
  • Linear (single loop)
  • Quadrature / Birdcage (two orthogonal loops; circularly polarized)
• By channel count:
  • Single-channel
  • Phased-array (multi-element, independently amplified)

Body vs Local Coils

• Body coil (built-in birdcage) usually acts as Tx; distance → poor SNR for Rx.
• Local coil placed directly on anatomy yields SNR increase ≈ distance² law (radio metaphor: farther station → noise).
• Tx/Rx local coils (if available) lower \text{SAR} because RF is confined to region instead of whole torso.

Polarization & Quadrature Advantage

• Quadrature coil delivers a 90° flip using 50 % less power vs. linear → \downarrow SAR.
• Provides ≈40 % SNR improvement (two orthogonal receive channels combined in quadrature).

Phased-Array & Parallel Imaging

• Phased-array = single housing with many decoupled Rx loops.
• Enables:
  • Larger FOV without noise penalty (activate only sections under interest).
  • Parallel imaging (SENSE, ASSET, iPAT) – under-sample k-space in multiple channels → scan-time cut ~40-60 %; cost = lower SNR by factor \sqrt{R} + g-factor.
• Requires:
  • Independent pre-amps,
  • Coil decoupling & tuning each exam.

Coil Selection Best Practices

• Choose coil that is:
  1. Smallest footprint completely covering anatomy.
  2. Physically closest to tissue (maximize filling factor).
  3. Highest channel count (more SNR/parallel options).
  4. Quadrature or multi-channel rather than linear.
  5. Tx/Rx if SAR or high-field constraints present.
• Example: neonatal brain often fits knee volume coil (smaller diameter, proximity) → may outperform 16-ch adult head coil; must empirically compare.
• Surface coil penetration ≈ radius of loop; use volume coil for deep organs (liver, pancreas).

Large vs Small Coil Trade-offs

• Large coil: uniform field, relaxed positioning, but ↓SNR, ↑risk of aliasing (wrap) when FOV < coil coverage.
• Small coil: sharp drop-off outside sensitive region → high SNR, low aliasing, but precise placement critical.

RF Shielding & Zipper Artifact

• Entire room enclosed in Faraday cage (copper/aluminum walls, floor, ceiling, penetrations, window with copper mesh).
• Stops external RF (radio, TV, cell) in 10–300 MHz band used by MRI (same band as Larmor frequencies).
• Breach → zipper artifact (vertical line noise) on image.
  • Causes: door opened during scan, broken light bulb filament, faulty equipment, physical tear in shield.
• All conduits enter via filtered penetration panel.

Patient Tables & Workflow

• Fixed table (attached) vs detachable dock-able table.
• Dock-able benefits:
  • Rapid patient turnover (pre-load outside),
  • Emergency egress without ferromagnetic stretcher,
  • Redundancy (second top).
• Cost/benefit analysis depends on daily volume (e.g., saving 2 h/day ~ 4–6 extra cases worth ).

Control & Computer Rooms

• Control room: technologist console, ECG/patient monitoring, communication, observation through RF window (mesh embedded glass).
• Computer/equipment room: pulse-sequence controller, gradient amplifiers, RF amplifiers & receivers, digitizers, cryogen & environmental monitors.

Quality Assurance (QA) & Quality Control (QC)

• Personnel requirements:
  • MRI technologist ARRT or ARMRIT certified.
  • Board-certified radiologist.
  • Qualified MR physicist.
• Accreditation bodies: ACR, Joint Commission, RadSite; renewal every 3 yr; include phantom & clinical submissions.

Daily QA

• Quick phantom scan (~10 min) to log: SNR, center frequency, Tx gain, geometric accuracy.
• Visual checks: coil integrity, table motion, room temp/humidity, cryogen level.

Weekly (QC) – ACR Protocol

• Visual tests of patient transport, laser alignment, gradient/door interlocks, viewing monitors.
• ACR 7 quantitative tests (done with ACR head phantom):
  1. Table position accuracy (\pm2\,\text{mm}).
  2. Center frequency (e.g., 63.8\,\text{MHz} for 1.5 T).
  3. Transmitter gain (attenuation calibration).
  4. Geometric accuracy (Slice 5 must read 190\pm2\,\text{mm} in both axes).
  5. High-contrast resolution (resolve 0.9–1.1 mm holes).
  6. Low-contrast resolution (≥ 9 spokes visible).
  7. Artifact evaluation (no zipper, ghost, distortion).

ACR Phantom Testing Steps

1. Level phantom in head coil; align lasers to central fiducial; acquire sagittal localizer.
2. Acquire 11 axial slices per ACR protocol.
3. Measurements:
   • Slice 1: high-contrast holes.
   • Side localizer: table offset \le\pm2\,\text{mm}.
   • Slice 5: geometric calipers top–bottom & left–right =190\pm2\,\text{mm}.
   • Slice N (contrast cylinders): count for low-contrast index (need ≥9).
   • Spectrum plot: verify center frequency & fat–water separation (e.g., 220\,\text{Hz} at 1.5 T).
4. Record in ACR QC form; call service if any parameter outside tolerance.

Key Equations & Numerical References

• Larmor (precession) frequency: \omega = \gamma B0 with \gamma{\text{H}}\approx42.58\,\text{MHz/T}.
  • B0=1.5\,\text{T}\Rightarrow f\approx63.8\,\text{MHz}. • B0=3.0\,\text{T}\Rightarrow f\approx127.7\,\text{MHz}.
• Chemical shift (fat–water) separation: \Delta f = 3.5\,\text{ppm}\times B_0 → \approx220\,\text{Hz} @1.5 T.
• Gradient amplitude–unit conversion: 10\,\text{mT/m}=1\,\text{G/cm}$$.

Practical/Clinical Implications & Ethics

• Coil mis-selection lowers diagnostic accuracy; knowledge prevents repeat exams, lowers cost & patient burden.
• Ignoring duty-cycle / slew-rate limits risks patient PNS or arrhythmia → ethical obligation to respect manufacturer limits.
• Regular QA/QC ensures image reliability, avoids misdiagnosis and costly downtime – technologist’s professional duty.