A simple method to calculate the signal-to-noise ratio of a circular-shaped coil for MRI

The introduction of the ultrafast imaging sequences has renewed the interest in development of RF coils. The theoretical frame of the SNR of MRI coils is a challenge because it requires a deep mathematical background to master the associated concepts. Here, a simpler method is proposed based on Legendre polynomials. This approximation method, together with a quasi-static approach, was used to derive a signal-to-noise ratio expression for a circular-shaped coil. Legendre polynomials were used instead of a weighting function to simplify the vector potential of the power loss, and an SNR formula was then derived. The simplified version of the SNR formula of a circular coil was compared with the weighting function-derived SNR expression using the quasi-static approach. SNR-vs.-depth plots were computed to theoretically compare both SNR formulas. Results showed a strong agreement between SNR values for the circular-shaped coil. This approach can be used as a tool to derive SNR expressions for more complex geometries. (c) 2006 Wiley Periodicals, Inc.