Application of Optimal Control to CPMG Refocusing Pulse Design

TL;DR

This paper uses optimal control theory to design robust refocusing pulses for the CPMG sequence, modeling their effects as a dephasing Pauli channel, and demonstrates high refocusing efficiency over wide resonance offsets and RF inhomogeneities.

Contribution

It introduces a quantum information-inspired model for CPMG refocusing dynamics and applies optimal control to create broadband pulses with high robustness.

Findings

Refocusing over 98% of magnetization at large offsets.

Pulses effective under +/- 10% RF inhomogeneity.

Model accurately describes residual pulse errors.

Abstract

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B0 and B1 offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10 t180 that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of +/- 10% RF inhomogeneity.