Outcome/Objectives

To provide the context for the initial developments required for parallel imaging;
To explain the basic parallel imaging methods, their advantages, and pitfalls;
To provide practical examples of the impact of this technique.

Abstract

Although essential for Parallel Imaging, multi-channel array coils were initially introduced for other reasons. The main motivation for using them was to increase the signal-to-noise ratio (SNR) of the images. The use of small coil elements, closer to the region of interest and with a more localized coil sensitivity, enables measurement of the same signal whilst limiting the sample volume which contributes to the received noise. Having an array of small elements makes it possible to keep the spatial coverage of a larger coil with the SNR benefits of a small coil. In 1990, Roemer et al. demonstrated that a nearly-optimal SNR can be obtained by combining the individual coil images by using the sum-of-squares approach¹; this approach had the advantage of not requiring calibration of the coil sensitivities.

A few years later, in 1993, it was suggested that coil encoding could partially replace gradient encoding allowing to speed up image acquisition at the cost of some SNR loss but at the time the demonstrations were limited to phantom experiments². In 1997, Sodickson et al. presented the first in vivo demonstration with a compelling example of a cardiac imaging application³. This was a game-changer since shortening the image readout was essential to make single-shot cardiac imaging feasible and made the community realize that the potential benefits of parallel imaging could in some cases surpass the downside of an SNR penalty. Although the suggested reconstructed algorithm (SMASH) relied on being able to synthesize Fourier spatial harmonics through a linear combination of the coil sensitivities³, and for that reason, it is only compatible with very specific coil geometries (i.e. linear arrays), it paved the way for other approaches.

Soon afterward, an alternative formulation (SENSE) was introduced by Pruessmann et al. who realized that utilizing the image domain representation for both the coil sensitivities and the under-sampled data was a lot simpler and allowed for much more flexibility regarding coil requirements⁴. By using a Cartesian regular under-sampling strategy, it was possible to break the large reconstruction problem into the inversion of many small encoding matrices connecting the groups of aliased image pixels. SENSE became the method of choice, quickly becoming available as a commercial product that could be applied in clinical practice. SENSE enabled to shorten scan times for multi-shot sequences and had a large impact also on single-shot EPI, reducing the duration of the readout window and hence the level of geometric distortions in functional and diffusion MR images.

The SENSE formulation was later extended to allow for more general under-sampling schemes, including Non-Cartesian trajectories, where each pixel will be overlapped with many others⁵. The inversion of a much larger encoding matrix is then required but it can be carried out efficiently through iterative algorithms (e.g. conjugate gradients); this enables to make use of fast implementations of equivalent operators (e.g. fast Fourier transform), without explicitly having to build or invert the full encoding matrix.
A drawback of SENSE is that it requires explicit calibration of the coil sensitivity maps. Although it provides an optimal reconstruction when this is feasible, alternative methods have since been developed which do not present this limitation. GRAPPA⁶ is a k-space-based method that estimates a reconstruction kernel from fully-sampled calibration data. This method is also widely available and enables very fast reconstructions: the estimated kernel implicitly contains coil sensitivity information and can be applied to individual coil k-space data to populate missing k-space positions; after reconstructing the individual coil images, these are combined using Roemer’s¹ sum-of-squares approach.

Parallel Imaging is now used on the majority of MRI acquisitions. The idea of using coil information to encode spatial position has since been applied to separate slices in simultaneous multi-slice (SMS) acquisitions⁷ and has also made it possible to accelerate single-shot EPI scans⁸, with a major impact in both functional⁹ and diffusion MRI¹⁰ studies.

Acknowledgements

Fundação para a Ciência e a Tecnologia (SFRH/BD/120006/2016, PTDC/EMD-EMD/29686/2017) and Programa Operacional Regional de Lisboa 2020 (LISBOA-01-0145-FEDER-029686).