Sebastian Rosenzweig^{1,2}, H. Christian M. Holme^{1,2}, Robin N. Wilke^{1,2}, and Martin Uecker^{1,2}

Simultaneous multi-slice (SMS) MRI allows for the acquisition of several slices at the same time. We propose a novel reconstruction technique for radial SMS MRI based on Regularized Nonlinear Inversion (NLINV). This method does not require a priori knowledge of the coil sensitivities. We present the simultaneous estimation of images and coil sensitivities of two slices of a phantom from 10-fold undersampled data. Image quality is analyzed for different sampling schemes and compared to single-slice acquisitions. Clinical relevance is demonstrated by in-vivo imaging of two slices of a human heart in real-time at a time-resolution of 30.8 ms per frame.

**Introduction and Purpose**

Increasing imaging speed is of utmost importance in in-vivo MRI. With simultaneous multi-slice (SMS) MRI¹ we can simultaneously acquire several slices of an object, which allows for higher undersampling factors compared to single- or conventional multi-slice measurements by exploiting axial coil sensitivity information. Furthermore, SMS MRI benefits from an inherently increased SNR which contributes to an improved overall image quality.

In
SMS MRI, we can use a
specific encoding scheme and the
spatial encoding information provided
by the
multi-coil receiver system to
disentangle the superposed
information of the simultaneously excited slices. Common
reconstruction
strategies
make
use of previously
estimated
coil sensitivities to
solve a linear equation.
Here,
we extend
the novel reconstruction
approach based on
Regularized
Nonlinear
Inversion (NLINV)^{2}
from Cartesian
SMS MRI^{3} to radial data.
For this
method no
prior knowledge
of the coil sensitivities
is required,
which is particularly
beneficial
for real-time
imaging where coil sensitivities vary due to motion or
interactive changes of slice positions.

**Method**

**
Phantom**

For static measurements we utilize a custom-made phantom made of ABS bricks (LEGO) and pure water (Fig. 1). It is designed such that the proton density of the top and bottom part of the phantom apparently differ. We use this property to demonstrate the capability of SMS-NLINV to disentangle simultaneously excited slices.

**SMS
sequence**

We utilize a 2D radial FLASH sequence with multiband RF excitation pulses generated by a superposition of single-slice pulses. For the acquisition of $$$mb$$$ slices ($$$mb$$$: multi-band factor) we perform $$$mb$$$ (undersampled) measurements and in each measurement $$$p=1,...,mb$$$ the simultaneously excited slices $$$q=1,..,mb$$$ are modulated with a phase (Fourier encoding) $$\Xi_{pq}:=\exp\left(-2\pi i \cdot (p-1)(q-1)/mb\right).$$ We obtain $$$mb$$$ different k-spaces $$$Y_p$$$ (one for each measurement) and define $$$\boldsymbol{Y}:=(Y_1,...,Y_{mb})$$$. For each measurement $$$p$$$ we use complementary radial k-space trajectories to avoid redundancy and to guarantee a maximum coverage of k-space. A schematic of this turn-based sampling strategy for $$$mb=2$$$ slices and 3 spokes is shown in Fig. 2a.

**SMS-NLINV
reconstruction**

$$$\boldsymbol{X}:=(X_1,...,X_{mb})$$$
is the vector we want to reconstruct. Its elements
$$$X_q=(m_q,\boldsymbol{c}_q)$$$
contain the object function
$$$m_q(x)$$$
and the coil sensitivities $$$\boldsymbol{c}_q(x)$$$
of slice $$$q$$$.
We set up the nonlinear equation
$$F(\boldsymbol{X})=\boldsymbol{Y},$$
where
$$$F$$$
is the forward operator, and solve it with the Iteratively
Regularized Gauss-Newton Method (IRGNM).³ The extension to non-Cartesian trajectories is performed by employing
a technique that is similar to convolution-based SENSE,
where $$\mathcal{F}^{-1}\boldsymbol{P}_{\vec{k}}
\mathcal{F}$$ is
used as the point spread function.^{4,5}
Here $$$\mathcal{F}$$$ and
$$$\mathcal{F}^{-1}$$$ are the Fourier Transform and its inverse and
$$$\boldsymbol{P}_\vec{k}$$$ is the projector onto the k-space
trajectories.

**Experiments**

All measurements were conducted on a SIEMENS Skyra 3T scanner. For the static measurements we used a 20-channel head coil. For the in-vivo measurement we utilized 26 channels of a body/spine coil.

*Phantom.*
We measured two slices (base resolution 192, slice thickness 5mm, flip angle 15°, TE 2.0ms, TR 3.1ms) at a distance of 50mm
and acquired
31 spokes per measurement (10-fold undersampling),
using

(1) two independent single-slice acquisitions,

(2) a SMS acquisition without turn-based trajectory scheme (Fig. 2b),

(3) a SMS acquisition with turn-based trajectory scheme (Fig. 2a).

*In-vivo.
*To
demonstrate the real-time capability of our reconstruction technique,
we simultaneously
measured two
slices of
a human heart (short-axis view) with
the turn-based scheme at a time-resolution of 30.8
ms for
two slices
(7
spokes
per measurement, base resolution 160, slice thickness 6mm, flip angle 8°, TE 1.4ms, TR
2.2ms).

**Results ****and Discussion**

*Phantom.*
The SMS-NLINV reconstruction can reproduce both slices without
significant artifacts (Fig. 3). The SMS scheme (2) gives better
results than the single-slice measurements (1) due to the
$$$\sqrt{mb}$$$ SNR benefit. The
turn-based scheme (3) provides a distinctly higher image quality than
the scheme without turns (2). Further preliminary experiments (not depicted) show that the method also works well for higher multi-band factors.

*In-vivo.*
Fig. 4 shows two exemplary
frames (end systole and end diastole) for both slices of
the real-time in-vivo measurement.
The images provide a
clinically relevant-time resolution and
image quality.

**Conclusion and ****Outlook**

In this work, we developed a radial multi-band FLASH sequence and extended the method of Regularized Nonlinear
Inversion to radial SMS MRI. We successfully reconstructed highly
undersampled SMS data without prior knowledge of the coil
sensitivities both for a phantom and in-vivo with
real-time-resolution. In the future we will implement the
reconstruction algorithm on GPUs^{5 }to allow for online
live-reconstructions and evaluate the method in clinical studies.

^{ }

1. D. Larkman et al. “Use of multicoil arrays for separation of signal from multiple slices simultaneously excited”. J. Magn. Reson. Imaging 13 (2001), pp. 313–317.

2. M. Uecker et al. “Image reconstruction by regularized nonlinear inversion—joint estimation of coil sensitivities and image content”. Magn. Reson. Med. 60 (2008), pp. 674–682.

3. S. Rosenzweig and M. Uecker. “Reconstruction of multiband MRI data using Regularized Nonlinear Inversion”. In: Proc. Intl. Soc. Mag. Reson. Med. 24 (2016), p. 3259.

4. F. Wajer and K. Pruessmann. "Major speedup of reconstruction for sensitivity encoding with arbitrary trajectories". In: Proc. Intl. Soc. Mag. Reson. Med. 9 (2001), p. 767.

5. M. Uecker et al. “Nonlinear inverse reconstruction for real-time MRI of the human heart using undersampled radial FLASH”. Magn. Reson. Med. 63 (2010), pp. 1456–1462.

**Fig. 2:** Schematic of
two radial sampling schemes (multi-band factor
mb=2 and 3 spokes per measurement). The numbers indicate the order of
acquisition.

a) Turn-based scheme: The spokes of all measurements are complementary to guarantee optimal coverage of the k-space.

b) Non-turn-based scheme: For all measurements the same spokes are used.

**Fig. 3:**
Reconstructed slices (2 slices, 50mm slice distance, 5mm slice
thickness, 31 spokes per measurement, base resolution 192) acquired
from the brick phantom (see Fig. 1). A zoom-in of the inner part as indicated by a red rectangle is shown as inset on the bottom right.

a) Single-slice acquisition and NLINV reconstruction for each slice.

b) SMS acquisition and SMS-NLINV reconstruction
(multiband factor mb=2) **without** turn-based sampling.

c) SMS
acquisition and SMS-NLINV reconstruction (mb=2) **with**
turn-based sampling.