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A generalized formulation of diffusion effects in μm resolution nuclear magnetic resonance imaging
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1989
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A generalized diffusion‑related NMR signal formulation derived from a random walk model extends beyond time‑specific spectroscopy analyses, enabling continuous‑time domain studies relevant for high‑gradient NMR microscopy. The study extends the diffusion theory to two‑dimensional imaging, providing an analytical formula for continuous‑time diffusion‑affected signals under time‑variant gradients. The authors derive the formula and incorporate the line‑spreading effect into a computer simulation to evaluate overall diffusion impacts in micrometer‑resolution NMR imaging. The results show that diffusion causes significant resolution loss and SNR reduction, and the intensity variation during acquisition produces line broadening whose full width at half maximum exceeds both bandwidth‑limited and intrinsic diffusion resolutions.
A generalized formulation of the diffusion related nuclear magnetic resonance (NMR) signal is derived from a random walk model. Previous analyses performed in the NMR spectroscopy were the formulations of the diffusion related signal amplitude at a specific time, such as the spin echo formation time. They are, in general, not applicable to continuous time domain analyses. In this paper, we have extended the theory to the two‐dimensional imaging case and derived an analytical formula useful for the computation of the diffusion affected signal as a function of continuous time for a time variant gradient. This formulation will be useful in NMR imaging, especially in NMR microscopy where the diffusion associated signal attenuation is serious due to the strong gradient fields (100–1000 G/cm), and at the same time data are acquired continuously for the acquisition period. In addition to the loss of the resolution and signal‐to‐noise ratio due to the random phase fluctuation by diffusion, the variation of the intensity during the data acquisition period introduces a line broadening whose full width at half‐maximum is found to be much larger than the bandwidth‐limited resolution or diffusion related intrinsic resolution. This line spreading effect is integrated in a computer simulation and is evaluated as an integral part of the overall diffusion effects in μm resolution NMR imaging or NMR microscopy.