Matthew A. McCready^{1}, William B. Handler^{1}, and Blaine A. Chronik^{1}

^{1}Physics and Astronomy, Western University, London, ON, Canada

### Synopsis

Delta relaxation enhanced magnetic resonance (dreMR) is a field-shifting quantitative molecular imaging method using activatable MR probes. The dreMR method may be used to produce images with signal proportional to concentration of contrast agent and eliminate signal due to unbound agent. In this work we outline a novel design method for dreMR coils, using an inner layer of windings determined by the boundary element method (BEM). This new design method produces a strong, highly homogeneous field shift which, when coupled with a 0.5T MRI system and activatable MR probes, can reliably image on a larger volume than previous designs.

### INTRODUCTION

Delta relaxation enhanced magnetic resonance (dreMR) is a promising
field-cycling based quantitative molecular imaging method for contrast-enhanced
MRI and molecular imaging. DreMR uses a *B*_{0} insert magnet to
shift the magnitude of the main magnetic field of an MRI as a pulse preparation
phase of the pulse sequence. Using field-dependent longitudinal relaxivity (*r*_{1}) contrast agents, images
taken at different field strengths provided by the dreMR insert can be
subtracted, resulting in signal proportional to the concentration of these
agents. Furthermore, with the use of “activatable” MR probes —contrast agents
which have strong *r*_{1} field
dependence when bound, this image subtraction technique can create images based
upon bound agent only.^{1} Many contrast agents such as *VivoTrax*
and *Feraheme*, and activatable probes such as *Ablavar* experience
higher field dependence at 0.5T than standard clinical field strengths (1.5T,
3T). This means that if imaging is done at a lower field strength, specifically
at 0.5T, a dreMR insert can be developed with a high contrast resulting from a
small field shift, decreasing the amount of current and number of windings
required. To explore possible dreMR inserts for a new MR system at 0.5 T, a
novel approach has been taken to improve upon previous designs by using the
boundary element method (BEM)^{2-4} to correct for field inhomogeneity
in the dreMR system, resulting in a dreMR coil with greatly improved
homogeneity compared to previous designs (~5% for Alford et al and Harris et al).^{1,5}
An active shield designed by the BEM can easily be added, using the methods
outlined in previous work.^{5}### METHODS

Our approach begins by choosing the number of radial
and axial windings (*NR*, *NZ*) of the outer solenoid required to
bring us close to the desired field shift (*ΔB*_{0})
with the available amplifier which would be composed of square hollow wire of
known width. A mesh of regular triangles is created in a meshing program to use as a
surface on which current can flow to correct the homogeneity. This surface is located just inside the
solenoid radially and is intended to be constructed from finer wire than the
hollow, water cooled solenoid, and be cooled by its proximity. The wire pattern
of the solenoid is used to calculate the field at random points (*P*) on a
spherical surface with radius 75% that of the coil’s inner radius using
Biot-Savart’s Law. Differences between the field at *P* and the field at
the isocenter were then used as field targets for the BEM –previously used for
designing gradient coils and their shims, to create a current density on the
mesh that would negate these differences and thus homogenize the dreMR field.
Given the cylindrical symmetry of the problem, the stream function calculated
by the BEM on a regular mesh can be averaged to remove irregularities in the
solution. As a preliminary study of the design space, the diameter of spherical
volume (*DSV*) with field inhomogeneity
below 1% was found for each coil design by changing the number of windings
radially and axially, and by varying the inner radius (*a1*) for a picked coil winding. Designs were evaluated based on
their *ΔB*_{0}
and *DSV<1%*. This is only a first step and a more complete
exploration of the design space will be carried out before construction.### RESULTS

**Figure 1** Shows a diagram of a BEM corrected dreMR coil.
The *DSV<1%* for a coil with *NR*=4 and *NZ*=44 over varying radius is shown in **Figure 2** and a grid
search of *DSV<1%* for varying
windings at *a1*=13.6cm is shown in **Figure
3**. *VivoTrax*, *Feraheme*, and *Ablavar* longitudinal
relaxivity data for varying *B*_{0}
can be found in **Figure 4**. **Table 1** compares the properties of
coils designed with BEM correction.### DISCUSSION

It was found that as *a1* was increased and axial length held constant, the *DSV<1%* and *ΔB*_{0} decreased. Therefore, coils designed with this
method should have the minimum *a1*
feasible for the desired imaging region, though as
seen in **Table 1** larger coils are feasible. A grid search of
solenoid windings showed that as the total number of windings (*N*) increased, *ΔB*_{0} and *DSV<1%* increased. While
coils with many windings could be designed with strong *ΔB*_{0} and high homogeneity, the weight and space
requirements of such coils become strong limiting factors and require a move
away from the optimal Fabry parameter.^{6} Going forward the space
available for a dreMR system and heating considerations will constrain designs,
but it is important to note that the homogeneity in the imaging region of a
field shifting coil can be greatly improved using the addition of a field
correction layer. A full exploration of
the parameter space for the design method will likely yield even more
improvement.### CONCLUSION

Here we have outlined a new
method for the development of homogeneous field shifting dreMR insert coils,
using the BEM to correct the field of a standard solenoid. It has been seen
through simulation that such coils, if used in a 0.5T field strength MRI system,
may produce significant signal from active MR probes and contrast agents for a
small field shift, and thus greatly benefit from improved homogeneity.### Acknowledgements

The authors would like to acknowledge financial support from NSERC, the Ontario Research Fund, and the Ontario Graduate Scholarship.### References

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