Real-Time Gradient Waveform Design for Arbitrary $k$-Space Trajectories.

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Medical Physics
• Signal Processing

Background:

• Designing gradient waveforms for arbitrary k-space trajectories is crucial for advanced MRI techniques.
• Existing methods often face limitations in real-time applicability and hardware compliance.

Purpose of the Study:

• To develop a real-time, hardware-compliant method for designing time-optimal gradient waveforms.
• To accommodate arbitrary k-space trajectories in MRI gradient waveform design.

Main Methods:

• A recursive approach solves gradient waveforms under slew-rate and trajectory constraints, forming a quadratic equation.
• Gradient constraints are enforced using L2-norm thresholding and escape velocity.
• Discrete-Time Forward and Backward Sweep strategy refines slew-rate constraints.
• Trajectory and gradient reparameterization enhance generality and sampling accuracy.

Main Results:

• Achieved over 89% reduction in computation time and over 98% reduction in slew-rate error.
• Computation time was consistently shorter than the gradient duration, confirming real-time capability.
• Demonstrated imaging feasibility through phantom and in vivo experiments.

Conclusions:

• The developed method enables real-time, hardware-compliant gradient waveform design.
• Significant reductions in computation time and slew-rate overshoot were observed compared to prior methods.
• This represents the first method for real-time gradient waveform design for arbitrary k-space trajectories.