Magnetic Resonance RF Pulse Design by Optimal Control With Physical Constraints

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Optimal Control Theory
• Pulse Sequence Design

Background:

• Optimal control is effective for designing radiofrequency (RF) pulses in MRI, but incorporating real-world constraints (e.g., B1 field amplitude, gradient slew rate, slice profile accuracy) remains challenging.
• Existing methods often use quadratic tracking for profile accuracy, which may not fully capture complex error dynamics.

Purpose of the Study:

• To develop and present a novel optimal control method for designing RF and slice-selective gradient pulses that effectively handles inequality constraints.
• To introduce a penalization method for higher-order tracking to improve slice profile accuracy and phase control.
• To demonstrate the application of this method in reducing the power of refocusing pulses for spin echo sequences.

Main Methods:

• A penalization method is introduced, enabling higher-order tracking (approaching infinite order) for improved slice profile accuracy and phase constraints.
• Inequality constraints, including amplitude limits on B1 field and slice-selective gradients, and slew rate limitations, are efficiently handled using semismooth Newton or quasi-Newton methods.
• Joint optimization of RF and slice-selective gradient waveforms is performed.

Main Results:

• The developed method successfully incorporates various amplitude and accuracy constraints in pulse design.
• Numerical experiments demonstrated the reduction of pulse power for simultaneous multislice refocusing pulses, crucial for short echo spacing applications.
• The method's efficacy was validated through phantom and in-vivo experiments.

Conclusions:

• The proposed optimal control approach provides a flexible and efficient framework for designing MRI RF and gradient pulses with complex constraints.
• This method enables significant power reduction in refocusing pulses, enhancing the feasibility of advanced MRI techniques like simultaneous multislice imaging.
• The successful validation in phantom and in-vivo studies confirms the practical applicability and robustness of the developed technique.