Yudong Zhu^{1}

In a way that augments existing encoding, signal coding promotes a multiplying effect of SNR and flexibility of scan acceleration. Its essence is to push for noise decimation by acquiring sums of marked signals from all components where the marking can be achieved by RF, gradient or other means. Its application to multi-slice MRI opens up a regime that enjoys both a √N SNR enhancement, as analogous to that of volumetric MRI, and flexibility with scan time budget, as equal or superior to that of existing multi-slice MRI.

In a way that augments existing encoding, the new approach promotes a multiplying effect of SNR and flexibility of scan acceleration. Its essence, hereby termed signal coding or echo composition, is to push for noise decimation by acquiring sums of marked signals from all components (Fig.1). The present work focuses on applying the new approach to multi-slice MRI.

The Fourier signal-coding strategy (Fig.2) gives rise to a full-fledged 3D k-space framework, one that
supports analysis and practice of signal-coding SMS much the same way as a standard
3D k-space framework does for volumetric MRI. The framework suggests, for instance, i) acceleration
along slice direction by skipping signal-coding steps, i.e., under-sampling *k*, causes aliasing or folding, ii) parallel MRI principle is readily applicable
to effect acceleration in up to 3 dimensions simultaneously, and iii) there is considerable
flexibility sampling the *k*_{x}-*k*_{y}-*k* space, options including,
e.g., incorporation of random sampling and compressed sensing, addition of SMS’
view-to-view phase modulation, and implementation of non-Cartesian trajectories. Of particular significance, setting up
multi-slice MRI in this framework ensues an SNR scaling analogous to that of
volumetric MRI. In cases of even sampling in *k*_{x}-*k*_{y}-*k*,
an analysis similar to that of SENSE^{5} gives signal-coding image SNR
as:

SNR^{sc}=SNR^{full}/(*g*√R)

where* R* is the product of in-plane and
slice-direction acceleration factors, and SNR^{full}
represents image SNR of a non-accelerated counterpart. Note that noise
decimation and SNR^{full }scale with √N, a multiplying effect that allows SNR^{sc} to
track, within a *g*-factor penalty, √*total
acquisition time*. This is in contrast to that of conventional multi-slice
or modern SMS, where noise averaging and decimation is under-exploited for
relatively large *N*. Modern SMS can be viewed as a special case where
only *k*=0 is sampled and *R*_{s}
is tied to *N*_{SMS} (*R*_{s}=*N*_{SMS}) – its SNR under-performs when practical *R*_{s} cannot reach *N* and it must repeat to cover *N* slices.

Signal-coding SMS was evaluated in simulation studies. k-space data corresponding to various
multi-slice and *k*_{x}-*k*_{y}-*k* sampling configurations were synthesized
based on a 32-channel volumetric data set from repository http://mridata.org. Sensitivity calibrations were performed separately
using 12x12 center k-space.
SENSE-type algorithms were used for image reconstructions.

A first study
used a Fig.2C-type strategy, with spiral trajectories employed at each sampled *k*, to
signal-code and spatial-encode 12 transaxial slices. The sampling involved under-sampling of outer *k*_{x}-*k*_{y} space (varying-density spirals) and
3x under-sampling of *k* (RF-based phase modulations). Signal-coding SMS yielded
results (Fig.3C) that are in excellent agreement with the original (Fig.3A). In a further study targeting 12 coronal slices, the
k-space sampling trajectory was composed of line segments parallel to *k*_{y}.
Sampling of *k*_{x}-*k* used
a pseudo-random pattern reflecting a 9x acceleration (Fig.3D). These two studies demonstrated incorporation of fast spiral
trajectories, 3D acceleration, and random sampling spokes – signal-coding SMS
promises to offer greater opportunities for rapid imaging than modern SMS does.

A third study used Fig.2C-type
strategy to signal-code and spatial-encode multiple
coronal slices, with Cartesian trajectories
employed at each sampled k. Three evaluated cases indicated flexible
tradeoffs between speed, *N* and SNR as enabled by signal-coding SMS (Figs.4
and 5). Notice in particular the SNR gain in accordance with √*N * (Fig.5) – this contrasts with modern SMS’
limited SNR multiplying effect.

1. Barth M, Breuer F, Koopmans PJ, Norris DG, Poser BA. Simultaneous Multislice (SMS) Imaging Techniques, Magn Reson Med 75:63-81, 2016.

2. Breuer FA, Blaimer M, Heidemann RM, Mueller MF, Griswold MA, Jakob PM. Controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) for multi-slice imaging. Magn Reson Med 53:684–691, 2005.

3. Setsompop K, Gagoski BA, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped-controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor penalty. Magn Reson Med 67:1210–1224, 2012.

4. Macovski A, Noise in MRI, Magn Reson Med, 36:494-497, 1996.

5. Pruessmann KP, Weiger W, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI, Magn Reson Med, 42:952-962, 1999.

**Fig.3** The first study targeted 12 slices of 19mm center-to-center spacing (A). The parallel receive data reflected 3x acceleration sampling *k* and a same 16-arm *k _{x}-k_{y}* spiral sampling trajectory for all four