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Nuclear magnetic resonance (NMR) spectroscopic imaging of {sup 23}Na holds promise as a non-invasive method of mapping Na{sup +} distributions, and for differentiating pools of Na{sup +} ions in biological tissues. However, due to NMR relaxation properties of {sup 23}Na in vivo, a large fraction of Na{sup +} is not visible with conventional NMR imaging methods. An alternate imaging method, based on stochastic excitation and oscillating gradients, has been developed which is well adapted to measuring nuclei with short T{sub 2}. Contemporary NMR imaging techniques have dead times of up to several hundred microseconds between excitation and sampling, comparable to the shortest in vivo {sup 23}Na T{sub 2} values, causing significant signal loss. An imaging strategy based on stochastic excitation has been developed which greatly reduces experiment dead time by reducing peak radiofrequency (RF) excitation power and using a novel RF circuit to speed probe recovery. Continuously oscillating gradients are used to eliminate transient eddy currents. Stochastic {sup 1}H and {sup 23}Na spectroscopic imaging experiments have been performed on a small animal system with dead times as low as 25{mu}s, permitting spectroscopic imaging with 100% visibility in vivo. As an additional benefit, the encoding time for a 32x32x32 spectroscopic image is under 30 seconds. The development and analysis of stochastic NMR imaging has been hampered by limitations of the existing phase demodulation reconstruction technique. Three dimensional imaging was impractical due to reconstruction time, and design and analysis of proposed experiments was limited by the mathematical intractability of the reconstruction method. A new reconstruction method for stochastic NMR based on Fourier interpolation has been formulated combining the advantage of a several hundredfold reduction in reconstruction time with a straightforward mathematical form.

Three dimensional nuclear magnetic resonance spectroscopic imaging of sodium ions using stochastic excitation and oscillating gradients