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Abstract

Introduction Bloch simulations based on phase distribution graphs (PDG) provide a fast and exact simulation of arbitrary MRI imaging sequences, outperforming classical isochromat based approaches1. Pulseq2 is an open-source project that defines a file format for sequence definitions with implementations for scanners of different vendors, which makes reproducible in vivo measurements possible. The presented simulation can as well interpret pulseq files and thus execute the exact same sequence in silicio. Methods A pulseq interpreter capable of reading pulseq 1.2.0 to 1.4.0 files was written. The imported sequence is then converted into the internal representation used by the simulation. As the focus of simulation lies in imaging techniques, the sequence is additionally simplified by using instantaneous pulses and merging events if it does not change the measurement. The simulation then executes the sequence on a virtual phantom to produce a complex signal that can then be reconstructed in the same way as a signal obtained by a physical scanner. All code is written in python, a schematic of the whole process can be seen in figure 1. Results The interpreter was successfully tested on the example sequences provided by the official pulseq GitHub repository3. The duration of the simulation of the tested sequences ranged between 70 ms and 16 s, or between 0.5 and 13 times the duration of the sequence itself. The resolution of the sequences ranged from 128² to 256² while the virtual phantom was fixed to 128². Figure 2 shows the reconstruction of an imperfect spin echo sequence with spiral trajectory. PDG allows splitting of the signal into different parts like FID or stimulated echoes to obtain additional insight into the inner workings of the sequence. Discussion A fast simulation of arbitrary MRI sequences defined by pulseq files is a universal tool usable by any project that allows the use of pulseq sequences. In contrast to measurement on physical systems, simulations are readily available. Furthermore, PDGs can provide additional information about the acquired signal that cannot be obtained in a measurement1 and the simulation is fully analytically differentiable, which together makes it a valuable tool in the research of novel imaging and reconstruction techniques, or end-to-end optimization approaches like MRzero4.