Peter Roemer^{1}

Fundamental limits of Signal-to-Noise(SNR) ratio exist that cannot be exceeded even with an idealized noiseless receiver coil. These limits can be approached in certain circumstances with proper coil design. The objective is to provide the audience with an understanding of these limits and their relationship to practical aspects of coil design. In turn this will help guide the choice of coil element size, array extent, and total coil count for imaging a specific anatomical location.

Target Audience

The research engineer or scientist interested in the basics of RF receive coil and array design and the applications scientist wishing to better understand the limits of array coil performance.Discussion

The intrinsic SNR[1] is defined as the SNR after subtracting the coil and receiver noise, limited only by the electrical noise emitted by the patient. The intrinsic SNR is a function of the depth of the region of interest[2,3]. The greater the amount of tissue between the receive coil and the region of interest, the lower the SNR for that location. To approach the intrinsic limit for a given depth, the coil elements largest dimension should be less than the shallowest depth of interest. The overall dimensions of the array should be made as large or larger than the greatest depth of interest. It is the array overall extent, not the individual coil element size, that determines the best SNR at depth. This is often misunderstood and leads to incorrect coil element size and in turn reduced SNR of the array. A key consideration in array design is the SNR variation over the desired imaging volume. The area of lowest SNR becomes the limiting factor in scan time or resolution. Therefore, coil elements in an array should be similar in size to minimize the variation of the SNR in directions parallel to the patient surface. The SNR variation as a function of depth is still present and cannot be overcome by adjusting coil size. Simply increasing the coil density with more channels and smaller coils ultimately leads to a plateau in the SNR at depth. Any further increase in coil density results in reduced SNR at depth when considering the finite noise of the coil and its electronics [4]. Thus, fundamental limits of intrinsic SNR and practical coil design result in relatively well defined upper limits on the useful number of coil elements in an array. As general guidance, the benefits of increased channel count for torso and head image start to diminish above 50 coils with limited and potentially diminishing benefits above 100 channels[5]. Understanding the coil size/density limits is critical in design. Regarding component technology, the fundamentals of coil-to-coil decoupling remain largely unchanged for 1.5T and 3.0T field strengths when compared with the methods introduced with the development of the Phased Array [5]. The methods require minimizing the mutual inductance between nearby coils and the use of low input impedance preamplifiers for a further decrease in coil coupling. However, the miniaturization of the preamplifier, while at the same time improving the preamplifier’s overall noise performance, has had a profound impact on coil design. This miniaturization allowed Integrating the preamplifier into the coil making practical higher channel count array while shrinking the size of the signal cables. A key measure of a coil’s preamplifier performance is its relative noise contribution to the signal. The preamplifier has lowest noise contribution at a certain electrical input impedance. A coil array used at various anatomical locations or with different body size and can result in a large variation in electrical impedance. A critical measure of a preamplifiers performance is the noise contribution under these non-ideal conditions. This allows the coil array to maintain high performance over a variety of conditions. Another practical consideration is preamplifier gain and stability within an array. Various interactions can result in unwanted oscillations and cross talk that degrade coil performance.Conclusions

The fundamental limits of intrinsic SNR and its variation as a function of depth combined with the practical limits preamplifier and coil noise performance place limits on the quantity and size of RF coils. The useful number of receiver coils active is not unlimited. Modern research and commercial systems are approaching these limits.[1] Edelstein WA, Glover GH, Hardy CJ, Redington RW. “The Intrinsic Signal-to-Noise Ratio in NMR Imaging, MRM 3, 604-619 (1986)

[2] Roemer PB, Edelstein WA. "Ultimate Sensitivity Limits of Surface Coils. "SMRM, Sixth Annual Conference, New York City, New York, August\1987. Book of Abstracts, pp.\ 410.

[3] Wiesinger F, “Parallel Magnetic Resonance Imaging: Potential and Limitation at High Fields”, Doctoral Dissertation, Swiss Federal Institute of Technology, Zurich, Diss. ETH no 16010

[4] Boskamp EB, Lindsay SA, Lorbiecki JE. On the coil noise contribution to SNR versus coil diameter, temperature, frequency, and load distance. In: Proceedings of the 13th Annual Meeting of ISMRM, Miami Beach, FL, USA, 2005 (Abstract 916).

[5] Hardy CJ Et al, 128-Channel Body MRI With a Flexible High- Density Receiver-Coil Array, JOURNAL OF MAGNETIC RESONANCE IMAGING 28:1219–1225 (2008) [6] Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson Med 1990;16:192–225.(2008)

[6] Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson Med 1990;16:192–225.