Extended phase graphs: dephasing, RF pulses, and echoes - pure and simple

Area of Science:

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

Background:

• The extended phase graph (EPG) concept is a valuable tool for analyzing magnetic resonance (MR) sequences.
• EPGs describe magnetization behavior using "configuration states" and matrix operations, simplifying the analysis of gradients, RF pulses, relaxation, and motion.
• Despite its utility, EPGs are underutilized due to perceived complexity.

Purpose of the Study:

• To demystify the extended phase graph (EPG) concept for a wider audience.
• To elucidate the foundational principles and mathematical underpinnings of EPGs.
• To explore advanced applications, limitations, and extensions of the EPG method, including diffusion phenomena.

Main Methods:

• Review of the theoretical framework of extended phase graph (EPG) modeling.
• Analysis of matrix operations representing MR sequence components (gradients, RF pulses, relaxation, motion).
• Discussion of the relationship between EPG diagrams and quantitative calculations, including software examples.

Main Results:

• EPGs offer a robust method for fast and precise quantitation of echo intensities in complex MR sequences.
• EPG diagrams enhance the understanding of various echo types and their associated echo times.
• The review provides insights into incorporating advanced phenomena like diffusion into the EPG framework.

Conclusions:

• The extended phase graph (EPG) method provides a powerful and accessible framework for MR sequence analysis and simulation.
• Understanding EPGs facilitates the comprehension and application of complex MR phenomena.
• This review aims to bridge the gap between EPG theory and practical application, encouraging wider adoption in research and clinical settings.