k and q Dedicated to Paul Callaghan

Area of Science:

• Magnetic Resonance Imaging
• Scattering Experiments
• Transport Phenomena

Background:

• The symbols k and q represent wave numbers in scattering and NMR imaging.
• Paul Callaghan's seminal works focused on k and q in Magnetic Resonance Microscopy and Translational Dynamics.
• This work reviews aspects of k and q explored in a lecture at the ISMAR Conference in Shanghai (2015).

Purpose of the Study:

• To revisit and expand upon the concepts of wave numbers k and q in NMR imaging.
• To introduce novel gradient pulse schemes for enhanced velocity measurements.
• To explore applications in acceleration and higher-order transport coefficient measurements.

Main Methods:

• Revisiting definitions of q, distinguishing between diffusive displacement (q) and coherent flow (qv).
• Developing novel pulsed field-gradient NMR schemes using three or more gradient pulses.
• Applying numerical analysis differentiation rules to design gradient modulation schemes.

Main Results:

• Demonstrated that anti-phase pulsed field-gradient schemes can be replaced by multi-pulse schemes in the short gradient pulse limit.
• Developed practical gradient modulation schemes with finite pulse widths for accurate velocity measurement.
• Showcased potential for expansion to measure acceleration and higher-order transport coefficients.

Conclusions:

• The novel gradient pulse schemes offer improved accuracy for velocity measurements in NMR.
• This approach provides a foundation for measuring complex flow dynamics and restricted diffusion.
• The study extends the application of k and q concepts in NMR imaging, building on Callaghan's legacy.