ABMP MRI Physics cheat sheet

Nuclear spin arises when a nucleus has an odd number of protons or neutrons; 1H (single proton) has spin 1/2 and is the dominant imaging nucleus.

Gyromagnetic ratio γ relates Larmor frequency to field: ω0 = γB0; for 1H, γ/2π ≈ 42.58 MHz/T.

Net magnetization M0 grows as spins populate the lower energy state; Boltzmann excess is small (~ppm at clinical fields).

Equilibrium M0 is proportional to proton density and to B0 (Curie behavior, M0 ∝ B0/T at thermal equilibrium).

Bloch equation: dM/dt = γM × B − (Mx i + My j)/T2 − (Mz − M0)k/T1.

A 90° pulse rotates M0 into the transverse plane; flip angle θ = ∫γB1(t)dt.

Resonance condition: RF at ω0 transfers energy; off-resonance reduces the effective flip angle.

T2* combines reversible field inhomogeneity with true T2: 1/T2* = 1/T2 + 1/T2′.

T1 recovery: Mz(t) = M0(1 − e^(−t/T1)); after a 90° pulse, Mz returns toward M0 with time constant T1.

T2 decay: Mxy(t) = Mxy(0)e^(−t/T2); T2 is always ≤ T1 for tissue.

Signal equation (gradient echo, flip α): S ∝ ρ sinα (1 − e^(−TR/T1)) e^(−TE/T2*) / (1 − cosα e^(−TR/T1)).

Spin-echo signal: S ∝ ρ (1 − e^(−TR/T1)) e^(−TE/T2); long TR + short TE = PD weighting, long TR + long TE = T2 weighting.

Short TR and short TE favor T1 weighting; TR controls T1 contrast, TE controls T2 contrast.

Inversion recovery: Mz(t) = M0(1 − 2e^(−TI/T1)); null point when TI = T1 ln2 (≈0.693 T1).

STIR nulls fat (TI ≈ 0.69 × T1_fat, ~150 ms at 1.5T); FLAIR uses a long TI to null CSF.

Ernst angle (gradient echo) maximizes signal at α = arccos(e^(−TR/T1)).

Slice selection: RF bandwidth Δf and slice-select gradient Gss set slice thickness Δz = Δf/(γGss).

Frequency encoding applies a readout gradient so position maps linearly to Larmor frequency along x.

Phase encoding applies a brief gradient whose area sets ky; number of phase-encoding steps sets matrix size in y.

k-space: FOV = 1/Δk and resolution = 1/(k_max); readout sampling interval Δt with gradient G gives Δk = γGΔt.

Gradient amplitude determines maximum spatial frequency (resolution); gradient duration/area determines ky spacing.

Two-dimensional Fourier reconstruction maps k-space samples to image via inverse 2D FT.

Slice profile is the FT of the RF envelope; sinc RF gives a rectangular (idealized) slice profile.

Chemical shift in pixels = Δf / (bandwidth per pixel); fat–water offset ≈ 3.5 ppm.

Coil SNR improves with proximity to tissue; surface coils give high SNR near the coil but limited field of view.

Quadrature (circularly polarized) coils improve SNR by √2 versus linear coils and reduce transmit power needs.

Body/volume coils provide uniform B1 for transmit; phased-array receive coils combine element signals for high SNR over large FOV.

Coil noise dominance: when sample noise exceeds coil noise, SNR scales with B0; at low fields coil noise may dominate.

B1 field homogeneity affects flip-angle uniformity; B1 mapping and parallel transmit address high-field inhomogeneity.

Receive bandwidth: wider bandwidth lowers SNR (more noise) but reduces chemical-shift artifact.

Gradient hardware limits slew rate (dB/dt) and maximum amplitude; peripheral nerve stimulation thresholds relate to dB/dt.

RF power deposition (SAR) scales approximately with B0² and with flip angle squared for a given sequence.

Nyquist criterion: sampling interval must satisfy Δt ≤ 1/(bandwidth) to avoid aliasing; undersampling k-space produces wrap.

Aliasing (wrap) occurs when FOV is smaller than the object; remedies include larger FOV, oversampling, or saturation bands.

Truncation (Gibbs) artifact arises from finite k-space sampling; manifests as ringing near sharp edges.

Motion artifact appears as ghosting along the phase-encode direction because motion modulates ky lines.

Chemical-shift artifact shifts fat relative to water along the frequency-encode direction.

Susceptibility artifact produces signal loss and geometric distortion near metal/air-tissue interfaces, worse with gradient echo.

Zero-filling interpolates but does not add true resolution; it reduces Gibbs ringing appearance.

Partial Fourier and parallel imaging reduce scan time at the cost of SNR and potential unfolding artifacts.

Echo-planar imaging (EPI) fills k-space rapidly after a single excitation; susceptible to geometric distortion and T2* blurring.

Parallel imaging (SENSE/GRAPPA) uses coil sensitivity to skip phase-encode lines; acceleration reduces SNR by roughly √R.

SENSE unfolds in image space using coil sensitivity maps; GRAPPA reconstructs missing lines in k-space.

Turbo/fast spin echo uses multiple 180° refocusing pulses per TR to fill multiple k-space lines.

Balanced SSFP gives high SNR with T2/T1 contrast; sensitive to off-resonance banding.

Compressed sensing exploits sparsity and incoherent sampling to reconstruct from undersampled data.

Simultaneous multislice (SMS) excites multiple slices at once and separates them with coil sensitivity encoding.

Non-Cartesian trajectories (radial, spiral) offer motion robustness and efficient sampling but require gridding reconstruction.

Specific absorption rate (SAR) = deposited RF power per unit mass (W/kg); regulatory limits exist for whole-body and localized exposure.

SAR scales approximately with B0², flip angle², and duty cycle; reducing flip angle or TR increases safety margin.

RF heating risk increases near conductive implants and leads; long resonant leads can concentrate induced currents.

Static field limits: the main field attracts ferromagnetic objects; projectile risk is the primary hazard.

Gradient-induced electric fields can cause peripheral nerve stimulation; dB/dt limits are sequence-dependent.

Acoustic noise arises from gradient coil vibration; hearing protection is required.

Pregnancy and implanted-device status must be verified; device MR-conditional status specifies allowed field and SAR conditions.

Daily QA typically checks SNR, geometric accuracy, slice thickness, and image uniformity with a phantom.

SNR can be measured as mean signal divided by standard deviation of background noise (with correction for magnitude bias).

Geometric accuracy is verified by comparing known phantom distances to measured distances.

Ghosting/phase stability is assessed by measuring signal in a background region across phase-encode direction.

Coil element failure shows as signal dropout or nonuniformity in a specific region; compare element images.

Center frequency and transmit gain drift indicate hardware or coil tuning issues.

Artifact troubleshooting: identify direction (frequency vs phase encode), then match to sampling, motion, or hardware cause.

Acceptance testing establishes baseline values against manufacturer or protocol specifications before clinical use.

T1 mapping: variable flip angle or inversion-recovery methods fit signal to recovery models; B1 correction is required.

T2 mapping uses multi-echo spin echo with exponential decay fitting; T2* mapping uses multi-echo gradient echo.

ADC maps from diffusion-weighted imaging quantify water mobility; high cellularity lowers ADC.

DWI signal: S = S0 e^(−b·ADC); b-value depends on gradient amplitude, duration, and diffusion time.

MR elastography derives tissue stiffness from shear-wave propagation measured with phase-contrast sequences.

Quantitative susceptibility mapping (QSM) estimates tissue susceptibility from phase data after dipole inversion.

Perfusion (DCE/DSC) quantifies flow and volume from tracer kinetics; requires arterial input function modeling.

Machine-learning reconstruction and synthetic contrasts are emerging; validation against reference standards is required.

Larmor frequency: f0 = (γ/2π)B0; at 1.5 T, 1H precesses at ~63.9 MHz; at 3 T, ~127.7 MHz.

Spin angular momentum and magnetic moment are related by μ = γS; only nuclei with net spin show MR signal.

RF excitation tips M0 by angle θ; a 180° pulse inverts Mz to −M0.

Free induction decay (FID) is the signal after a single RF pulse as Mxy dephases.

Bloch equation describes precession and relaxation of the macroscopic magnetization vector.

T1 and T2 are intrinsic tissue time constants; T2* includes additional dephasing from field inhomogeneity.

Boltzmann distribution: the small population difference between spin states produces the measurable net magnetization.

T1 is spin-lattice (longitudinal) recovery; T2 is spin-spin (transverse) decay.

Signal in spin echo: S = k·ρ·(1 − e^(−TR/T1))·e^(−TE/T2).

Inversion recovery nulls a tissue when TI = T1·ln2; STIR nulls fat, FLAIR nulls CSF.

Ernst angle α = arccos(e^(−TR/T1)) maximizes gradient-echo signal for given TR and T1.

Long TR reduces T1 weighting; long TE increases T2 weighting.

Proton density weighting uses long TR and short TE to minimize T1 and T2 effects.

Contrast agents shorten T1 (and T2*) to increase signal on T1-weighted images.

Slice thickness Δz = Δf/(γGss); thinner slices need larger gradient or narrower RF bandwidth.

Frequency encoding maps position to frequency via a readout gradient; phase encoding uses gradient area to set ky.

FOV = 1/Δk; resolution = 1/(k_max); both depend on gradient amplitude and sampling.

k-space center holds low-frequency contrast; periphery holds high-frequency edge detail.

Inverse 2D Fourier transform reconstructs the image from k-space samples.

Slice profile equals the Fourier transform of the RF pulse envelope.

Chemical shift (pixels) = Δf/(bandwidth per pixel); fat–water separation ~3.5 ppm.

Surface coils give high SNR near tissue but nonuniform sensitivity; phased arrays combine elements for large FOV.

Quadrature coils improve SNR by √2 relative to linear coils.

Body coils transmit uniform B1; local receive coils improve SNR for reception.

Receive bandwidth affects SNR: wider bandwidth admits more noise but reduces chemical-shift artifact.

B1 inhomogeneity worsens with field strength; B1 mapping and parallel transmit mitigate it.

SAR scales approximately with B0² and flip angle²; gradient slew rate limits dB/dt.

Coil noise vs sample noise determines whether SNR scales with B0 in a given regime.

Aliasing/wrap occurs when FOV is smaller than the object; oversampling or saturation bands prevent it.

Gibbs (truncation) ringing results from finite k-space sampling near sharp edges.

Motion ghosts appear along the phase-encode direction because ky lines are modulated inconsistently.

Chemical-shift artifact displaces fat along the frequency-encode direction.

Susceptibility artifact causes signal loss and distortion near metal and air–tissue interfaces.

Zero-filling interpolates but does not improve true resolution.

Parallel imaging and partial Fourier reduce scan time at the cost of SNR and possible unfolding artifacts.

EPI fills k-space after one excitation; prone to geometric distortion and T2* blurring.

Parallel imaging (SENSE/GRAPPA) uses coil sensitivities to skip phase-encode lines; SNR falls roughly with √R.

Turbo spin echo uses multiple 180° refocusing pulses per TR to acquire multiple lines.

Balanced SSFP gives T2/T1 contrast with high SNR; sensitive to off-resonance banding.

Compressed sensing exploits sparsity and incoherent sampling to reconstruct undersampled data.

Simultaneous multislice excites multiple slices and separates them using coil sensitivity encoding.

Non-Cartesian radial/spiral trajectories improve motion robustness but require gridding reconstruction.

SAR is RF power absorbed per unit mass (W/kg); limits differ for whole-body and localized exposure.

SAR scales approximately with B0², flip angle², and duty cycle.

Conductive implants and leads can concentrate RF currents, increasing local heating risk.

The static field attracts ferromagnetic objects; projectile hazard is the primary safety concern.

Gradient-induced electric fields can cause peripheral nerve stimulation; dB/dt limits apply.

Acoustic noise from gradient vibration requires hearing protection.

Device MR-conditional status specifies allowed field strength and SAR conditions.

Daily QA checks SNR, geometric accuracy, slice thickness, and uniformity with a phantom.

SNR is measured as mean signal divided by background noise standard deviation, with magnitude-bias correction.

Geometric accuracy compares known phantom distances with measured distances.

Ghosting is assessed by signal in a background region along the phase-encode direction.

Coil element failure appears as regional signal dropout or nonuniformity.

Center frequency and transmit gain drift indicate tuning or hardware issues.

Artifact troubleshooting starts with direction (frequency vs phase encode) to identify the cause.

T1 mapping uses variable flip angle or inversion recovery with B1 correction.

T2 mapping uses multi-echo spin echo; T2* mapping uses multi-echo gradient echo.

DWI signal: S = S0·e^(−b·ADC); higher b-values emphasize restricted diffusion.

ADC maps quantify water mobility; high cellularity lowers ADC.

MR elastography measures tissue stiffness from shear-wave propagation.

QSM estimates tissue susceptibility from phase data after dipole inversion.

DCE/DSC perfusion quantifies flow and volume using tracer kinetics and an arterial input function.