"Imaging Diffusion with Non-Uniform B₁ Gradients"

K. Woelk, B. L. J. Zwank, J. Bargon, R. J. Klingler, R. E. Gerald II, and J. W. Rathke, in "Spatially Resolved Magnetic Resonance", P. Blümler, B. Blümich, R. Botto, E. Fukushima (Eds.), 103-110, Wiley-VCH, Weinheim (1998).

• Rotating-frame imaging with the mathematically well-defined, non-uniform magnetic field gradient of toroid cavity detectors represents a new technique for evaluating diffusion in solids, fluids, or mixed-phase systems.

• While conventional NMR methods for measuring diffusion utilize constant (i.e., uniform) magnetic field gradients and, therefore, constant k-space wave numbers across the sample volume, the hyperbolic B₁ fields of toroid cavity detectors exhibit large ranges of wave numbers radially distributed around the central conductor. As a consequence, signal amplitudes decay, depending on the radial distance from the center axis of the torus.

• Applying a numerical finite-difference procedure to solve partial differential transport equations makes it possible not only to determine diffusion in toroid detectors to a high precision, but also to include and accurately reproduce transport phenomena at or through singularities, such as phase transitions, membranes, or impermeable boundaries.

K. Woelk, September 25, 2000