Spin dynamics during chirped pulses: applications to homonuclear decoupling and broadband excitation

TL;DR

This paper develops a comprehensive framework for analyzing spin dynamics during chirped pulses, enhancing understanding and enabling improved applications in broadband NMR, ESR, MRI, and MRS techniques.

Contribution

It introduces a general expression for chirped pulses and compares numerical methods for calculating spin evolution, including Liouville-von Neumann and Wei-Norman Lie algebra approaches.

Findings

Demonstrates the effectiveness of the methods on PSYCHE pulse for homonuclear decoupling

Shows application to CHORUS sequence for broadband excitation

Provides detailed spin trajectory calculations during chirped pulses

Abstract

Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems during these pulses plays a vital role, not only in describing the mechanism of techniques, but also in enabling new methodologies. In magnetic resonance spectroscopy, broadband inversion, refocusing, and excitation using these pulses are among the most used applications in NMR, ESR, MRI, and $in$ $vivo$ MRS. In the present survey, a general expression for chirped pulses will be introduced, and some numerical approaches to calculate the spin dynamics during chirped pulses via solutions of the well-known Liouville-von Neumann equation and the lesser-explored Wei-Norman Lie algebra along with comprehensive examples are presented. In both cases, spin state trajectories are calculated using the solution of differential equations. Additionally, applications of the proposed methods to study the spin dynamics during the PSYCHE pulse element for broadband homonuclear decoupling and the CHORUS sequence for broadband excitation will be presented.