OPTIKS: Optimized Gradient Properties Through Timing in K-Space

TL;DR

OPTIKS introduces a differentiable, arc-length-based framework for customizing gradient waveforms to follow pre-defined k-space trajectories while optimizing time-domain properties. By integrating time-domain constraints, PNS limits, mechanical resonance avoidance, and acoustic noise reduction into a single loss, OPTIKS enables rapid, safe, and quiet MRI gradient designs without deviating from prescribed trajectories. The approach is demonstrated on spirals, rosettes, CEPI, and MR fingerprinting trajectories, achieving substantial reductions in back-EMF and acoustic output while maintaining image quality, and is released as an open-source package. The work highlights trade-offs between speed and safety/quietness, and provides a flexible tool for trajectory-constrained gradient synthesis with extensible objective terms.

Abstract

A customizable method (OPTIKS) for designing fast trajectory-constrained gradient waveforms with optimized time domain properties was developed. Given a specified multidimensional k-space trajectory, the method optimizes traversal speed (and therefore timing) with position along the trajectory. OPTIKS facilitates optimization of objectives dependent on the time domain gradient waveform and the arc-length domain k-space speed. OPTIKS is applied to design waveforms which limit peripheral nerve stimulation (PNS), minimize mechanical resonance excitation, and reduce acoustic noise. A variety of trajectory examples are presented including spirals, circular echo-planar-imaging, and rosettes. Design performance is evaluated based on duration, standardized PNS models, field measurements, gradient coil back-EMF measurements, and calibrated acoustic measurements. We show reductions in back-EMF of up to 94% and field oscillations up to 91.1%, acoustic noise decreases of up to 9.22 dB, and with efficient use of PNS models speed increases of up to 11.4%. The design method implementation is made available as an open source Python package through GitHub.

Figures (9)

• Figure 1: Comparison of log-barrier function (purple) to leaky log-barriers with varying relaxations. Smaller $\delta$ values result in steeper slopes beyond $x_{max}$.
• Figure 2: OPTIKS PNS-limited spiral and rosette designs for UHP. a) (TOP) Gradient waveforms for time-optimal (blue) and PNS-limited (orange) spiral (dashed Y channel). (MIDDLE) Slew-rate for the spiral waveforms, dark solid lines indicate magnitude across X and Y channels, faint solid and dashed lines indicate X and Y axes respectively. (BOTTOM) PNS response for spiral waveforms with dashed black line indicating $P_{max}$. b) Gradient waveforms (TOP), slew-rate (MIDDLE), and PNS response (BOTTOM) for rosette designs. c) Resulting k-space trajectories with color indicating speed along curve at each point. OPTIKS traverses k-space in approximately 10% less time for the same PNS threshold in both cases.
• Figure 3: EMF mechanical resonance measurements and designs for UHP and PREMIER systems. a) Gradient waveforms for time-optimal (blue), de-rated (yellow), and OPTIKS mechanical resonance-optimized (orange) CEPI on UHP and MRF spiral on PREMIER. Solid and dashed lines representing X- and Y-axis data respectively. b) Vibration spectra calculated from RMS back-EMF ($\varepsilon$) for UHP and PREMIER gradient systems, along with power spectra for CEPI and spiral waveforms. Mechanical resonances highlighted in red. c) RMS and maximum value of back-EMF measured from time-optimal, de-rated, and OPTIKS waveforms on UHP and PREMIER systems. Dark shorter bar gives RMS value, taller lighter bar gives maximum value. d) Resulting k-space trajectories with color indicating speed along curve at each point for OPTIKS waveforms from b). In each design case OPTIKS significantly reduced power within mechanical resonance bands and the resulting vibration induced back-EMF.
• Figure 4: Field camera measurements and mechanical resonance spiral design. a) Gradient waveforms for time-optimal (blue), de-rated (yellow), and OPTIKS mechanical resonance-optimized (orange) single-shot spiral on UHP. b) (TOP) RMS gradient field oscillation spectra for the 3T GE UHP system on X ( dark blue), Y ( light blue), and Z ( red) axes. Mechanical resonance bands appear as peaks highlighted in red. (BOTTOM) Power spectra for time-optimal, de-rated, and OPTIKS single-shot spiral. c) RMS and maximum gradient field oscillations following time-optimal, de-rated, and OPTIKS waveforms played on the UHP system. Dark shorter bar gives RMS value, taller lighter bar gives maximum value. The OPTIKS spiral greatly reduced power within mechanical resonance bands, and vibration induced gradient oscillations were minimized for CEPI and spiral designs.
• Figure 5: MRF results using time-optimal spiral and OPTIKS spiral. (TOP) Calculated T1 maps for each acquisition and their 10x difference map. (BOTTOM) Calculated T2 maps for each acquisition and their 10x difference map. OPTIKS maintained image quality and quantitative results within reported repeatability margins.