The Extended Phase Graph (EPG) calculus [1-3] can be understood as a solution of the Bloch equation using its k‑space representation. It is especially well suited for the characterization of spin systems that are strongly dephased by switched gradients as takes place in MRI sequences [1-3]. The ability to represent magnetization in phase state configurations frequently enables an intuitive and pictorial understanding of echo formation and assignment. A class of functions that allows for the easy calculation and simulation of EPGs for a broad variety of arbitrary, i.e. non-periodic, MR sequences was developed (EPGspace). Its key points are presented and the EPGspace source code is made publically available for download in the internet (or through the author also).

All functions of EPGspace are defined within the MATLAB® environment (The Mathworks Inc., Natick, USA). Each phase state is described by a small EPG struct knowing its k value and type (transversal ‘F’ or longitudinal ‘Z’) and the corresponding population. An arbitrary number of states can be grouped to a 'stack' of EPG states and, thus, fully depict a spin system at any given point of time. Consecutive events of RF pulses, phase evolution and relaxation - characterizing the basics of an MRI sequence -, are provided by operator functions. These act on the EPG states and stacks and modify them in accordance to the underlying physical principles.

EPGspace allows for both, using ‘virtual’ integral values of k, which are common in literature [1-3], and ‘real’ absolute k values. The latter can be provided by additional gradient structs that can define rectangular and asymmetric trapezoidal gradients via amplitude and both ramp and flat top durations.

Special operators allow to include diffusion or flow effects as well, which is also a current point of further development and improvement of EPGspace.

For visualization, EPGspace offers a variety of display functions, among them histograms of phase state configurations and the flow of magnetization in the EPG versus time.

EPGspace was developed to offer a rather simple and neat approach to EPGs, particularly regarding educational aspects. Its focus is flexibility and not computational speed. It does not necessitate a regular temporal grid like common EPG codes do because of a much lower complexity.

Further importance lies on visualization besides quantitative signal values. Additional functions provide practical algorithms for sorting of states, error handling, and - quite important here - quantization errors due to floating point notation issues.