Figure 1. Hypothetical proton magnetic resonance signals from water and oil differ in frequency and relaxation times. Frequency varies linearly with magnetic field strength; the higher electron affinity of oxygen in water as compared to carbon in oil provides less electronic shielding for water protons than for oil protons. For a given magnetic field, protons of water experience a stronger local field and resonate at a higher frequency. Relaxation times vary inversely with line width. The relatively long decay constant of water protons (67 ms) results in a line width of 4.75 Hz, while the shorter relaxation time of oil (25 ms), yields a line width of 12.7 Hz. oj electrons of protons from the effect of the applied magnetic field. The actual field experienced by protons in a molecule decreases with electronic shielding, thereby requiring a lower radiofrequency (rf) for resonance:

where C denotes shielding field strength in gauss or Tesla. The greater electronegativity or electron affinity of oxygen compared to carbon provides less electron shielding (higher frequency) to water protons than to oil protons (lower frequency) at a given magnetic field strength.

The decay of the MR signal results from relaxation; in its absence, the perturbed nuclei would emit no signal. Temperature influences molecular mobility, which in turn induces changes in relaxation rates, manifested in the rate of signal decay. Viscosity, another quality related to mobility, affects relaxation rates in the same way. Molecular structure also determines mobility; larger or more hindered structures move less easily than do smaller or more open structures. This discussion will deal with two mechanisms of MR relaxation, spin-lattice, or Ti relaxation, and T2, or spin-spin relaxation. Ti relaxation occurs as energy transfers from the high-energy spin state nucleus to the surroundings, or lattice, usually as heat, manifested as molecular rotation close to the resonance frequency. Ti, the reciprocal of the exponential relaxation rate, denotes the time constant of the return of perturbed magnetisation to its equilibrium state in alignment with the external field (Farrar, 1989):

where Mz(t) and Mo denote the magnetisation aligned with the magnetic field at time t and at equilibrium, respectively. T2 relaxation occurs via exchange of spin states with nearby nuclei, thereby dephasing the signal and averaging it to zero:

where Mt denotes the observed signal at time t. Only fast processes (molecular motion frequencies near that of resonance) affect Ti relaxation, while both fast and slow processes (less than resonance frequency) affect T2 relaxation (Farrar, 1989). For this reason the T2 relaxation rate (I/T2) often exceeds 1/Ti. Mobility affects relaxation rates in a non-linear manner. Efficiency of relaxation increases with mobility until the correlation time, Tc (roughly the expected duration the nucleus remains in one position) equals the period corresponding to the resonant frequency:

Any deviation in correlation time from this value decreases the relaxation rate; at low frequencies (low magnetic field strength), the high mobility and short correlation time of bulk water slows its relaxation. In contrast, hydrogen atoms in an oil molecule, attached to the chain of carbons, rotate relatively slowly with the molecule, lengthening the correlation time and increasing the relaxation rate of oil relative to water. Relaxation rate differences allow discrimination between signals originating from oil and water. The magnetisation of oil recovers its alignment with the external magnetic field more quickly than does bulk water; a rapid succession of rf pulses may prevent the magnetisation of the water from recovering to equilibrium and diminish the water signal with respect to that of the oil. Conversely, the water signal also decays more slowly than does the oil signal, allowing water signal enhancement simply by delaying acquisition. Figure 1 illustrates a similar situation, in which the water signal at a chemical shift of 25 Hz decays to zero with an exponential rate constant of 0.015 t, while the relaxation of the oil signal at a chemical shift of 100 Hz proceeds with a time constant of 0.04 t. A wait of 100 ms before acquisition of the composite signal would nearly eliminate the contribution from the 100 Hz component (Figure 1). The term "T2 weighting" refers to an image or spectrum acquired in this way. The resonance at 100 Hz in the frequency spectrum has a wider spread of frequencies, or line width, than does the resonance at 25 Hz; ideally, the line width at half height of the resonance (Figure 1) varies inversely with T2:

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