Center for Advanced Imaging Innovation and Research (CAI2R) and Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, New York.
The Sackler Institute of Graduate Biomedical Sciences, New York University School of Medicine, New York, New York.
Magn Reson Med. 2018 Nov;80(5):2256-2266. doi: 10.1002/mrm.27207. Epub 2018 Apr 22.
The ultimate intrinsic signal-to-noise ratio (UISNR) is normally calculated using electrodynamic simulations with a complete basis of modes. Here, we provide an exact solution for the UISNR at the center of a dielectric sphere and assess how accurately this solution approximates UISNR away from the center.
We performed a mode analysis to determine which modes contribute to central UISNR - ζ(r→0). We then derived an analytic expression to calculate ζ(r→0) and analyzed its dependence on main magnetic field strength, sample geometry, and electrical properties. We validated the proposed solution against an established method based on dyadic Green's function simulations.
Only one divergence-free mode contributes to ζ(r→0). The UISNR given by the exact solution matched the full simulation results for various parameter settings, whereas calculation speed was approximately 1000 times faster. We showed that the analytic expression can approximate the UISNR with <5% error at positions as much as 10-20% of the radius away from the center.
The proposed formula enables rapid and direct calculation of UISNR in the central region of a sphere. The resulting UISNR value may be used, for example, as an absolute reference to assess the performance of head coils with spherical phantoms.
通常使用具有完整模式基的电动模拟来计算最终固有信噪比 (UISNR)。在这里，我们提供了介电球体中心处 UISNR 的精确解，并评估了该解在远离中心时对 UISNR 的近似程度。
我们进行了模式分析，以确定哪些模式对中心 UISNR-ζ(r→0)有贡献。然后，我们推导出了一种计算 ζ(r→0)的解析表达式，并分析了其对主磁场强度、样品几何形状和电特性的依赖性。我们通过基于并矢格林函数模拟的已有方法对提出的解决方案进行了验证。
只有一个无散度模式对 ζ(r→0)有贡献。对于各种参数设置，精确解给出的 UISNR 与全模拟结果匹配，而计算速度大约快 1000 倍。我们表明，该解析表达式可以在距中心半径的 10-20%范围内以 <5%的误差来近似 UISNR。
所提出的公式可用于在球体中心区域快速直接地计算 UISNR。所得到的 UISNR 值可用于例如作为评估具有球形仿体的头线圈性能的绝对参考。
