Efficient 3D Low-Discrepancy k -Space Sampling Using Highly Adaptable Seiffert Spirals.

Area of Science:

• Medical Imaging
• Magnetic Resonance Imaging (MRI)
• Biophysics

Background:

• Efficient k-space sampling is crucial for reducing 3D MRI scan times.
• Current methods for accelerating MRI acquisition have limitations in k-space coverage.
• Undersampling strategies combined with advanced reconstruction techniques offer potential for faster imaging.

Purpose of the Study:

• To introduce and evaluate a novel 3D center-out k-space trajectory, Seiffert's spiral.
• To demonstrate the trajectory's ability to achieve low-discrepancy k-space coverage with fewer readouts.
• To assess the acceleration capabilities of Seiffert's spiral using undersampling and compressed sensing (CS) reconstruction.

Main Methods:

• Development of a versatile 3D center-out k-space trajectory based on Jacobian elliptic functions (Seiffert's spiral).
• Simulation of point-spread functions and discrepancy evaluations comparing Seiffert's spiral with the 3D cones approach.
• Acquisition and reconstruction of in vivo knee images using both Nyquist and undersampled datasets with CS.

Main Results:

• Seiffert's spiral provides low-discrepancy k-space coverage with a reduced number of readouts compared to existing methods.
• The trajectory supports efficient undersampling, enabling significant acceleration when combined with CS reconstruction.
• In vivo imaging demonstrated comparable quality for undersampled datasets reconstructed with CS to Nyquist sampled data.

Conclusions:

• Seiffert's spiral is an efficient 3D k-space trajectory suitable for accelerated MRI acquisition.
• The trajectory's properties facilitate faster 3D dataset acquisition, even for single-shot applications like with hyperpolarized media.
• This approach, particularly with CS, holds promise for improving the efficiency and applicability of advanced MRI techniques.