Measuring Practical Coil Array Performance with Respect to Ultimate Intrinsic SNR: A Tool for Array Design and Assessment. Presentation # 424, at the 14th ISMRM

Abstract

Introduction As the number of available receiver channels on modern MR systems increases, increasing attention will be paid to the design and performance of many-element RF coil arrays. Questions regarding the balance of coil-noise and sample-noise or the suitability of any particular array design for parallel imaging-already areas of great practical interest to coil designers -promise to take on new significance as the number of elements increases. In this context, it would be useful to have a concrete metric of coil performance, in order not only to compare different designs but also to determine how much room for improvement there may be in any particular design. Recent studies have shown that there is an inherent electrodynamic limitation to the achievable SNR for any physically realizable coil array (assuming sampledominated noise), and have modeled the behavior of ultimate intrinsic SNR either in the absence Materials and Methods The best possible SNR can be found by substituting coil sensitivities in the image reconstruction algorithm with a complete set of basis functions that are valid solutions of Maxwell's equations. The electric field associated to these basis functions is used to compute the noiseresistance matrix Ψ which specifies the noise power associated with any linear combination of coil sensitivities. Using the weak SENSE reconstruction algorithm for parallel MRI [4], which has unit sensitivity at the pixel of interest and zero at the aliased positions, the ultimate intrinsic SNR can be expressed as: where ω is the Larmor frequency, M 0 is the equilibrium magnetization, k B is Boltzmann's constant, T S is the temperature of the sample and B is the encoding matrix as defined in [2]. The net field inside a cylindrical-shaped uniform phantom was expressed as a linear combination of cylindrical harmonics (having the form e ikz e imφ J m (k'ρ), with integer m and suitable values of k and k') satisfying Maxwell's equations in a source free medium where V is the voxel volume, θ is the flip angle, N acq is the number of acquired k-space data points, NEX is the number of repetitions, NF is the noise figure of the preamplifiers and BW is the bandwidth. Performance maps for the coil array were computed as the ratio of the actual SNR to the scaled ultimate SNR, as a function of position inside the sample of interest, for various acceleration factors. Results and Discussion The choice of basis functions was found to have a significant influence on the convergence behavior and the numerical tractability of the ultimate intrinsic SNR calculations, and this motivated our choice of cylindrical harmonic functions matched to the geometry of the phantom, as opposed to the plane wave Conclusions We have described a method to evaluate the absolute performance of any particular coil array. This procedure can be used to improve the design of receiver coils for sequential or parallel imaging applications. Future investigations will evaluate larger numbers of array elements and higher accelerations