Temporal diffusion spectroscopy: theory and implementation in restricted systems using oscillating gradients.

The theory of temporal diffusion spectra is reviewed. In contrast to q-space spectroscopy, which measures the displacement spectrum of spins in a spatial domain, the spectral density of the velocity correlation function (VCF) in the temporal domain is considered. It is demonstrated that casting diffusion in this domain may facilitate measurements of microscopic geometry and the decomposition of the diffusion signal into components due to disperse flow and restricted diffusion. An oscillating gradient (OG) method of diffusion spectroscopy was developed and implemented. Microscopic pore sizes, surface-to-volume ratios (S/Vs), and diffusion path tortuosities were extracted from model systems using this method. Cases are discussed in which this type of experiment may allow the characterization of pore geometry when spatial domain experiments fail. OGs may be combined with imaging sequences to map complex patterns of diffusion and flow. Moreover, scalar apparent diffusion coefficient (ADC) measurements in complex biological systems may be subtly dependent on specific pulse sequence parameters. Thus, scalar ADC measurements using gradient pulses with different frequency spectra may give different results. Conversely, the frequency dependence of motion-sensitizing gradient pulses may be exploited to deduce the origin of ADC changes.