Magnetic Resonance Relaxation Lecture Notes

This set of vocabulary flashcards covers the fundamental principles of T1 and T2 relaxation in Magnetic Resonance, including relaxation mechanisms, molecular motion effects, and practical applications in carbon-13 NMR and MRI.

Relaxation

The processes that return the spin magnetisation $M$ to thermal (Boltzmann) equilibrium following a perturbation such as an RF pulse.

$T_1$ (Spin-Lattice) Relaxation

The longitudinal relaxation of the $z$ component of the magnetisation $M$ involving energy exchange with surroundings.

$T_2$ (Spin-Spin) Relaxation

The transverse relaxation involving the irreversible decay of the $xy$ component of the magnetisation $M$ to zero.

Lattice

The surroundings of nuclear spins with which energy is exchanged to achieve Boltzmann equilibrium during $T_1$ relaxation.

Correlation time ($au_c$)

The characteristic timescale for molecular motions, such as molecular tumbling, which drives relaxation.

Dipolar interaction

The direct magnetic interaction between pairs of spins $I$ and $S$, serving as the primary source of relaxation for spin-$rac{1}{2}$ nuclei where the rate is proportional to rac{ ext{1}}{T_1} ext{ ∝ } rac{ ext{γ}_I ext{γ}_S}{r^6}.

Quadrupolar relaxation

A highly effective source of relaxation for nuclei with I > rac{1}{2} that typically leads to very short relaxation times, making peak resolution difficult.

Isotopic enrichment

A technique to improve the sensitivity of $^{13}C$ NMR; for example, $100\%$ $^{13}C$ provides $90 imes$ more signal than natural abundance ($1.1\%$).

$^{1}H$ Decoupling

The process of using RF irradiation at the $^{1}H$ NMR frequency while acquiring $^{13}C$ spectra to cause protons to flip rapidly, effectively averaging out $J_{CH}$ couplings.

Decoherence

The random process where fluctuations in local magnetic fields cause spins to get "out of sync," leading to the exponential decay of the $xy$ magnetisation as defined by $M(t) = M(0) ext{exp}(-t / T_2)$.Rose

$T_1$-weighted images

MRI scans that use a short recycle delay to emphasize regions with short $T_1$ relaxation times, such as fat versus water.

NMR Linewidths

The finite widths of NMR resonances that are a direct consequence of $T_2$ relaxation and instrumental factors like field homogeneity.

Spontaneous relaxation

The relaxation of higher energy spin states without external forcing, which is negligibly slow because the rate scales as $u^3$.