Magnetic Resonance Spectroscopy (MRS) and MRI Physics

MRI: where the (water) signal is → an image. MRS: which molecules are present in one region → a spectrum.
Same physics. MRS reads small frequency differences between molecules instead of using frequency to encode position.

Water ≈ 55 M, metabolites ≈ 1–10 mM, so metabolite peaks are ~1/10,000 of the water peak.
Unsuppressed, the water peak and its tails swamp the small peaks and use up the receiver's dynamic range.

The electrons around a nucleus react to B0 with a small opposing field (shielding), so the nucleus feels B0(1 − σ) and resonates at f = (γ/2π)·B0·(1 − σ).
Different chemical environment → different σ → slightly different frequency.
Trap: the slides write δ for the shielding constant; δ is normally the shift in ppm.

They pull electrons away → less shielding → higher frequency → higher ppm.
Example from the slides: H bonded to O (OH) resonates higher than H bonded to C (CH).

δ = (f − f_ref)/f_ref × 10^6, with f_ref from a reference compound (TMS = 0 ppm for 1H).
Dividing by f_ref makes δ independent of B0, so spectra from different field strengths line up on the same ppm axis.

Hz separations grow in proportion to B0: 1 ppm = 600 Hz at 14.1 T, 400 Hz at 9.4 T, 128 Hz at 3 T.
Glutamate H2 (3.75) to H4 (2.34) = 1.41 ppm ≈ 846 Hz at 14.1 T vs ≈ 564 Hz at 9.4 T: same ppm, 1.5× more Hz. (The slide labels this 1280 vs 850 Hz, which doesn't match its own ppm values; the 1.5× ratio is the point.)

≈ 4.7 ppm (it shifts slightly with temperature). At 600 MHz that is 4.7 × 600 Hz ≈ 2820 Hz above the 0 ppm reference.
It is a relative label, not a frequency of 4.7 Hz: the water protons still precess at ~600 MHz.

Increasing ppm to the LEFT. Left = "downfield" = higher frequency = less shielded. Right = "upfield" = lower frequency = more shielded.
Most brain metabolites lie between ~1 and 4.5 ppm, water at 4.7.

Splitting of a peak into a multiplet by neighbouring nuclear spins, transmitted through the electrons of the chemical bonds (scalar or spin–spin coupling).
Each neighbour being "up" or "down" slightly shifts the nucleus's frequency, so one peak becomes several.

Protons coupled to n equivalent neighbours give n + 1 lines with Pascal's-triangle intensities (1:1, 1:2:1, 1:3:3:1 …), spaced by J (in Hz).

CH3 at 1.31 ppm has 1 CH neighbour → doublet. CH at 4.10 ppm has 3 CH3 neighbours → quartet (1:3:3:1). J ≈ 7 Hz.
In vivo the 1.31 ppm doublet is the one used (4.1 ppm sits close to water).

J stays fixed in Hz (field-independent), while chemical-shift differences in Hz grow with B0.
So at higher field multiplets look narrower on the ppm axis and overlap less.

Weak (Δf ≫ J): clean n + 1 multiplets (e.g., heteronuclear 13C–1H). Strong (Δf comparable to J, e.g., Glu, Gln, GABA at low field): distorted patterns with the "roof effect" (inner lines taller, outer smaller). Equivalent protons (Δf = 0) show no splitting: one line.
Higher B0 increases Δf while J (Hz) stays the same, so systems become more weakly coupled: simpler spectra. Trap: J itself does not decrease.

Coupled multiplets keep evolving during TE (180° pulses don't fully refocus J), so their shape and amplitude change with TE.
Short TE (≤ 10 ms preclinically) minimises J-evolution and T2 loss → more accurate quantification.

Its fixed pattern of peaks: positions from the chemical shifts of its proton groups, splittings from J-coupling, relative areas from how many protons are in each group.
The spectrum is the sum of all signatures on a macromolecule baseline, so small or similar metabolites overlap; fitting (set 10) separates them.

Similar structures → overlapping multiplets (around 2.0–2.5 and 3.75 ppm).
They need high B0 (bigger Hz spread) and a good shim: merged at 100 MHz, separated at 400–600 MHz.

NAA 2.01 ppm: neuronal marker (density/viability); falls after brain injury; precursor of NAAG.
Cr + PCr 3.03 and 3.9 ppm: energy buffer (PCr stores high-energy phosphate).
Cho 3.2 ppm: membrane synthesisreakdown; acetylcholine precursor.
mI (myo-inositol) 3.56 ppm: glial marker, osmolyte.
Lac 1.31 ppm: end product of anaerobic glycolysis; also an inflammation marker.

Glu: main excitatory neurotransmitter. Gln: made from Glu in astrocytes. GABA: main inhibitory neurotransmitter (excitatory in the immature brain). Asp: excitatory neurotransmitter. GSH (glutathione): antioxidant. Tau (taurine): osmolyte, antioxidant, inhibitory neuromodulator. Lipids (0.9–1.3 ppm): membrane degradation, or contamination from outside the voxel.
At 9.4–14.1 T over 18 metabolites are resolved in rodent brain, down to ~0.5 mM.

Myelination/cell proliferation, energy metabolism, osmoregulation, neurotransmitter metabolism, antioxidants.
1) Myelination/proliferation: NAA, PCho, GPC, PE.
2) Energy: Cr, PCr, Glc, Lac, Ala.
3) Osmoregulation: mI, Tau.
4) Neurotransmission: Glu, Gln, GABA, Asp, NAAG.
5) Antioxidants: GSH, Asc.

Through the linewidth: FWHM = 1/(π·T2*). Better shim → narrower, taller peaks → better resolution and SNR.
Human 7 T example: 9 Hz excellent, 11.5 Hz adequate, 13.5 Hz acceptable, 25 Hz poor (small metabolites lost).

Better: SNR ↑, chemical-shift dispersion in Hz ↑ (resolution), strong-coupling effects ↓ → more precise and accurate quantification.
Worse: T2* shortens, so linewidth in Hz grows (shimming matters more), and B1 inhomogeneity and SAR grow.

The simplest experiment: one pulse θ, record the FID, repeat every TR and average; Fourier transform → spectrum.
It is not localized (the whole coil volume contributes). With short TR, the Ernst angle gives the most signal per unit time.

A narrow-band, frequency-selective 90° pulse tips only the water magnetization, then a spoiler gradient dephases it. Usually repeated a few times just before the localization sequence.
When the metabolites are excited, water has almost no Mz left.

VAPOR uses 7 water-selective pulses with optimized flip angles (powers) and inter-pulse delays, so suppression stays good over a range of T1 and B1 values.
CHESS is simpler but more sensitive to B1 errors and T1 recovery.

Frequency carries the chemical identity. A readout gradient would mix position with chemical shift.
So single-voxel MRS localizes with slice-selective RF pulses and records with gradients off.

Slice selection uses frequency, so metabolites at different shifts are selected at slightly shifted positions: each one "sees" a displaced voxel.
Shift = Δf_cs / ((γ/2π)·G) = (Δf_cs / BW_RF) × slice thickness. Worked: 1 ppm at 14.1 T = 600 Hz; with BW = 5 kHz the voxel shifts by 12% of its size.

Use high-bandwidth RF pulses (with correspondingly strong gradients).
180° pulses usually have lower bandwidth at a limited peak B1, so their directions show larger CSDE. CSDE in Hz terms also grows with B0.

1) The 90° with a gradient gives Mxy only in slab 1.
2) The 1st 180° refocuses only spins also in slab 2.
3) The 2nd 180° refocuses only spins also in slab 3.
Only the intersection forms the final echo; crusher gradients around the 180°s dephase everything else. One pulse with one gradient can only select a slab.

90°–180°–180°, each slice-selective on a different axis → double spin echo from the voxel.
Strengths: full signal, single shot, insensitive to motion. Weaknesses: longer TE (more T2 loss and J-evolution); the 180°s need high peak B1 and have narrow bandwidth → larger CSDE.

90°–90°–90° on three axes → stimulated echo.
Strengths: short TE; 90° pulses have broader bandwidth (smaller CSDE) and are less B1-sensitive than 180°s. Weakness: only half the magnetization forms the echo (50% signal).
During the mixing time TM, magnetization is stored along z, so it decays slowly with T1, not T2.

Inversion pulses are switched ON/OFF across scans and the results are added/subtracted so only the voxel survives (1D: 2 scans; 3D: 8 scans).
Magnetization stays along z during localization and the signal is an FID → no T2 loss (popular for 31P). Weakness: relies on subtraction across scans → sensitive to motion and instability.

Excitation followed by pairs of adiabatic full-passage 180° pulses (6 in LASER).
Adiabatic pulses give the same flip angle over a wide range of B1 → insensitive to B1 inhomogeneity (ideal with surface coils), sharp profiles, small CSDE, full signal. Weaknesses: longer TE (15–28 ms), high peak B1 and SAR.

1D ISIS (inversion ON/OFF along one axis) + a slice-selective spin echo on the other two axes.
Strengths: full signal, very short TE (2.8 ms), insensitive to B1 inhomogeneity along the ISIS axis (LASER is still the least B1-sensitive overall). Weaknesses: needs 2 scans (subtraction) → more motion-sensitive; the 180° direction has more bandwidth/CSDE issues.

STEAM: 50% signal, TE ≈ 2 ms, single shot. SPECIAL: 100%, TE ≈ 2.8 ms, two shots. LASER: 100%, TE 15–28 ms, single shot, best localization and least B1-sensitive, but needs T2 knowledge for quantification.

Saturation bands (selective 90° + spoiler) placed on tissue around the voxel, especially lipid-rich skull, skin and muscle, so it cannot contaminate the spectrum.
Mz recovers by T1, so the bands are applied every TR.

1) Detects signal from the voxel (VOI).
2) Suppresses signal from outside it.
3) Minimal CSDE (high pulse bandwidth).
4) Insensitive to B1 inhomogeneity, especially with surface coils.
5) Efficient water suppression.

Tiny voxels (rat 50–150 µL, mouse 2–15 µL) → ultra-high field (≥ 9.4 T) and strong gradients (≥ 400 mT/m vs ~70 mT/m on 7 T human systems).
Many tissue interfaces in a small head → strong B0 inhomogeneity → efficient shimming (FAST(EST)MAP, B0 mapping).

It probes mechanisms human MRS can't; it complements human research and is not a clinical or veterinary diagnostic tool.
1) Biology: a living organism, controlled genetics and environment (less group variance), short lifespan (fast long-term studies), validation against brain extracts.
2) Physics: ≥ 9.4 T; long motion-free scans; small coils need little RF power and B1radient limits are looser, so pulses can be chosen for SNR and CSDE (heating still matters at ultra-high field).

For small samples the coil's own thermal noise dominates, so cooling the coil cuts the noise → 2–5× SNR.

Ultra-short TE (≤ 10 ms) and fully relaxed TR (4–5 s); scans can last > 4 h (humans: ~45 min in 10-min blocks).
Anaesthesia reduces stress, pain and motion but depresses breathing and heart rate and can affect metabolism, and the animal cannot give feedback, so physiology must be monitored.

Respiration rate and body temperature, held constant so every group has the same anaesthesia depth.
Rats: 35–80 breaths/min, 37.5–38.5 °C. Mice: 50–90 breaths/min, 36.5–37.5 °C. Pulse oximetry and ECG add control if available. Awake-rodent MRS is rare: long training, with serum cortisone and heart rate monitored.

31P (~100% abundant, no label needed): energy metabolism and pH; spectrum shows PCr (0 ppm reference), Pi and the three ATP phosphates (γ, α, β).
13C (1.1%), 2H (0.015%), 15N (0.37%) are rare, so labelled substrates are infused: 13C glucose/acetate → metabolic fluxes (TCA, Glu–Gln cycle); 2H glucose; 15N nitrogen metabolism. Rare isotope = almost no background.
All are far less sensitive than 1H.

1H 600 MHz, 31P 243 MHz, 13C 151 MHz, 2H 92 MHz, 15N 61 MHz (f ∝ γ).
Each needs its own coil tuning and transmiteceive channel.