Giuseppe Carluccio^{1,2}, Karthik Lakshmanan^{1,2}, and Christopher Michael Collins^{1,2}

^{1}Radiology, Center for Advanced Imaging Innovation and Research (CAI2R), New York, NY, United States, ^{2}Radiology, Bernard and Irene Schwartz Center for Biomedical Imaging, New York, NY, United States

### Synopsis

We present a tool to quickly estimate the noise induced by
the resistance of a surface coil and the noise induced by the coil in a sphere.
The tool relies on two analytical solutions, and results depend on many
parameters. We show plots of the dissipated power in the sample and the coil as
function of some of these parameters such as the diameter of the coil, the
distance of the coil from the sphere and the wire diameter of the coil. The
tool can be useful in the design process of coils, especially dense receive
arrays.

### Purpose

To
develop a tool to quickly estimate the power dissipated in an arbitrary
spherical sample and circular surface coil for evaluating the balance of sample
and coil noise in MRI at any frequency.### Introduction

For a given sample and coil, the proportionality between the
frequency of the $$$B_1$$$ field the strength of $$$B_0$$$ results in big differences in the RF fields
distribution between low-field and high-fields MRI systems. At low fields, the $$$B_1$$$ field distribution and noise levels are more
dependent on the coil than the sample. In fact, at very low fields the magnetic
field $$$B_1$$$ is quasi-static, and the induced electric
field is very low. At higher fields, the $$$B_1$$$ fields tend to propagate in the sample more like
a wave, and the electric field becomes more significant, so that in the
computation of SNR the noise is more strongly related to the electric fields in
the sample (resulting in sample noise dominance), while in low-field systems
the coil resistance may be the only significant contributor to noise (coil
noise dominance). The noise related to the coil resistance increases with
frequency with $$$f^{1/4}$$$ due to variation in skin depth with frequency,
while the noise related to the sample increases with $$$f$$$ ^{1,2}.
Frequency is not the only parameter which
determines the balance between coil noise and sample noise. Noise is also
conditioned by parameters such as the size of the sample, the size of the coil,
the distance of the coil from the sample, etc. For example, Wiggins
observed that due to the small coil size in a 96-element head array, the impact
of coil noise resulted in a reduction of SNR deep within the sample compared to
SNR of arrays with fewer, larger coils^{3}.
In this work, we utilize analytical
solutions to rapidly estimate the noise induced by the resistance of the coil
and the noise induced by the sample for a surface coil near a sphere. We use
these methods to estimate the variation of the noise according to different
parameters.### Methods

The noise induced by the sample is
proportional to the square root of the power dissipated in the sample. A method
to estimate the power loss in a spherical sample per unit current in a circular
surface coil (Fig. 1) was provided by Keltner^{4}. The computed power
depends on the operating frequency, the radius and the dielectric properties of
the sphere, the distance of the coil from the center of the sphere and the
radius of the surface coil. We validated our implementation of this analytical
solution with the numerical commercial software XFDTD (Remcom).
The noise induced by the coil resistance is computed by
estimating the resistance per unit length in the coil. Considering that for
good conductors used in MRI and for frequencies in the order of MHz the skin
depth is much smaller than the cross section of the coil, we estimate the
resistance by approximating the effective cross-sectional of the conductor as having
width equal to the perimeter and thickness equal to the skin depth. We have developed a tool to estimate the two noise
contributions with the commercial software Matlab (The Mathworks), and we have
computed and plotted the two contributions by varying three parameters: the
diameter of the coil, the distance of the coil from the sample, and the
diameter of the wire of the coil.### Results and Discussion

For a frequency of 64 MHz, the power dissipated in the
sample and in the coil as functions of the coil diameter are shown in Fig. 2, as
a function of the distance of the coil from the sample are shown in Fig. 3, and
as a function of the diameter of the wire of the coil are shown in Fig. 4. In
each plot many parameters need to be set, and the reported plots can change
depending on the value assigned to the other parameters.
The tools developed can be used in the design process of
coils, including dense receive arrays. For example, the tool can be used to
determine the minimum size of coil that will still allow for sample noise
dominance, which affects the arrangement and the number of coils of an array of
a given overall geometry (e.g., surrounding the head or covering the torso).
The tool will be publicly available on the website of our
institution.### Acknowledgements

No acknowledgement found.### References

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2. Myers W, Slichter D, Hatridge M, Busch S, Mößle M,
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detected with SQUIDs and Faraday detectors in fields from 10μT to 1.5 T.
Journal of Magnetic Resonance. 2007 Jun 30;186(2):182-92.

3. Wiggins GC, Polimeni JR, Potthast A, Schmitt M, Alagappan
V, Wald LL. 96‐Channel receive‐only head coil for 3 Tesla: design optimization
and evaluation. Magnetic Resonance in Medicine. 2009 Sep 1;62(3):754-62.

4. Keltner JR, Carlson JW, Roos MS, Wong ST, Wong TL,
Budinger TF. Electromagnetic fields of surface coil in vivo NMR at high
frequencies. Magnetic resonance in medicine. 1991 Dec 1;22(2):467-80.