Diffusion

As in freezing, diffusion studies have exploited attenuation of the NMR signal; in contrast to freezing, this attenuation results from molecular mobility, and not its absence. Most diffusion imaging experiments make use of the spinecho pulse sequence (Figure 2): briefly, an rf pulse disturbs the magnetisation of the sample nuclei; the nuclei dephase by T2 mechanisms, diffusion and magnetic field nonuniformities; a refocusing pulse is applied; and the signal regains coherency (a spin echo). The refocusing pulse can only reverse dephasing due to a non-uniform magnetic field, not that due to T2 relaxation or diffusion. Diffusion usually produces negligible attenuation under these circumstances. One can enhance attenuation due to diffusion by sequentially imposing two gradients of equal amplitude and opposite polarity during the time between the first rf pulse and acquisition (echo time). The first gradient confers phase upon nuclei dependent on their position; the second, opposite gradient reverses and restores the original phase of stationary nuclei. In the experiment of Figure 2, the refocusing pulse reverses the polarity of magnetisation, hence the second identical gradient reverses the effect of the first gradient. Any nuclei which have moved during the time between the diffusion gradients will retain a phase difference, and the spectrometer receives an out-of-phase, attenuated signal from these nuclei. For a series of experiments varying only the amplitude of the rectangular gradient pulses, the ratio of signal intensities from diffusion-weighted (Sw) and non-weighted (Sn) experiments becomes (Le Bihan, et al., 1988):

where y, G, D, 8, and A denote the gyromagnetic ratio, gradient amplitude, self-diffusion coefficient, duration of the gradient, and time between opposing gradients, respectively (figure 2). Relaxation affects each experiment equally and may be ignored. In the series of experiments proposed above, all parameters except G in the exponential term remain constant; plotting ln(Sw/Sn) vs. G^ 52(A-8/3) for various gradient amplitudes produces a line whose slope yields D, the self-diffusion coefficient.

Diffusion imaging shows promise for mapping of internal temperatures of foods. Changes in temperature alter the apparent self-diffusion coefficient (Dapp) of water, and conversely, knowledge of Dapp provides an estimate of temperature. Temperature mapping by diffusion imaging has already been demonstrated in a medical hypothermia model (Le Bihan et al., 1989) and recently in a model food gel (Sun et al., 1993).

Diffusion imaging can also determine particle size in water/lipid emulsions, by incrementally increasing the time between opposite gradients (A) and noting the interval at which the signal attenuation ceases. In the case of restricted diffusion, a short A will result in the signal attenuation expected in bulk fluid; an appropriately longer A (dependent on particle size) will show less signal

attenuation than in bulk, due to restriction of movement of intraparticle fluid by particle walls. Simply put, small particle size impedes the travel of molecules to areas of varying field strength. Varying the A between gradients will usually result in variation of the echo time (Figure 2), therefore attenuation of the signal requires correction for T2 dephasing. Manufacture of margarines, dressings and cheese would benefit from the non-invasive particle size determination provided by diffusion imaging. Indeed, Callaghan et al. (1983) have estimated fat droplet size in cheese using diffusion spectroscopy.

Sodium imaging allows the non-invasive observation of the progress of sodium chloride diffusion into a milk protein gel, a model of cheese brining during ripening. A simple spin-echo sequence produced the images of Figure 4 (middle and right) without use of diffusion gradients; the spectrometer observed only sodium nuclei, which have a gyromagnetic ratio, hence frequency, different from hydrogen. Here, changes in sodium nuclei density quantify diffusion.

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