Klaus Scheffler^{1,2}, Jonas Bause^{1}, Ali Aghaeifar^{1}, Theodor Steffen^{1}, Bernhard Schölkopf^{1}, and Alexander Loktyushin^{1}

^{1}Max Planck, Tuebingen, Germany, ^{2}University of Tuebingen, Tuebingen, Germany

### Synopsis

We
introduce the principles of a novel approach for the acceleration of signal
acquisition that is based on a rapid and unique modulation of localized
magnetic fields superimposed to the conventional linear gradient-based spatial
encoding.

**Introduction**

Spread-spectrum MRI is based on rapid dynamic (up to
MHz) and local modulation of magnetic fields produced in local current loops.
Current localized gradient encoding techniques such as PatLoc, O-space imaging and FRONSAC (1-3) rely on static or quasi-static (<kHz) local magnetic field profiles that are
essentially constant (compared to the Larmor frequency) during each MR echo
acquisition. In spread-spectrum MRI, these fields are modulated dynamically
during signal acquisition to imprint local and distinct signal characteristics
into the spin arrangement, which can be interpreted as a unique fingerprint
onto confined regions within the object. Spread-spectrum MRI distributes or
spreads the basic bandwidth of gradient-encoded resonance frequencies along the
encoding axis using distinct carrier frequencies (or other time courses such as
orthogonal noise patterns) originating from a certain spatial portion of the
object. This spatially unique information can then be used to resolve aliasing
in undersampled acquisition, and thus to drastically boost imaging speed.

**Methods**

Local magnetic
fields, for example, can be generated by a set of current loops that are placed
close to the object. An example is shown in Fig. 1 that consists of 8
independent magnetic field coils that are placed on a cylinder (5cm x 5 cm, 25
windings). A temporal current variation induces a locally varying magnetic
field that modifies the local Larmor frequency of the magnetization. In Fig. 1, a 1 kHz and 1 A current produces a 1kHz
varying local magnetic field that generates a locally confined frequency
modulation of the free induction decay, visible as side bands. Different
frequencies and phases can be applied to each coil separately during the
acquisition of the MR signal to improve localization. Using this additional
local information, the conventional imaging process can be accelerated.
In Fig. 2 we
illustrate the effect of injecting currents in different local B0 coils on the
image reconstructed with inverse Fourier transform without taking into account
additional encoding components due to an oscillating field. However, in the
presence of local oscillating magnetic fields, a linear model for
image reconstruction can be used.
S(t) is the measured signal and m(r) the image to be reconstructed. Gx, Gy and
Gz are the linear gradients, and Bc(r) are the local sensitivities or B0-field
maps of the coils driven with a sine wave of amplitude A. In order to
reconstruct the image m, a linear system has to
be solved. E is the linear operator
that aggregates the exponential encoding terms and performs the summation
(integration) over the spatial domain. To reconstruct the image, we solve the
following regularized optimization problem:
The
regularization coefficient
sets the weight of the total variation term TV
that penalizes high-frequency artifacts in the reconstruction. An extension of
the model to the case of accelerated acquisition is straightforward and
involves decreasing the number of rows in the matrix E subject to the spectral
undersampling pattern.**Results**

Fig.
3 shows an example where the local field modulations have been used to accelerate
image acquisition. Fig. 3 (reference) is the corresponding reference. In Fig 3
(2-fold undersampling) k-space of the 2D gradient echo sequence was 2-fold
undersampled resulting in a N/2 ghosting artifact. Application of alternating
currents of 3A and 5kHz all channels with a phase shift of 45° between channels
during each readout period of the gradient echo sequence, and using the
reconstruction algorithm shown above gives the 2-fold accelerated image shown
in Fig. 3 (spread spectrum MRI). Additionally, we performed a simulation
experiment where we evaluated reconstruction performance at different
acceleration factor, modulation frequency and current combinations. In Fig. 3
bottom right, we show normalized root mean square errors between the reconstructed
images and the reference.**Discussion**

In preliminary experiments, we could demonstrate
an acceleration factor of 2 with only minor imaging artifacts. The proposed
method is essentially based on an increased acquisition bandwidth, as local
frequency modulations will increase the spectral bandwidth of MR signals.
Therefore, image acquisition acceleration based on spread spectrum MRI will go
with a decrease in SNR proportional to the square root of acquisition time.
However, optimal arrangements of local B0 coils and combination of spread
spectrum MRI with Parallel Imaging based on local B1 coils might open novel and
currently unforeseen possibilities and applications.### Acknowledgements

Reinhart Koselleck-Projekt DFG SCHE 658### References

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