Thermal noise calculation method for precise estimation of the signal-to-noise ratio of ultra-low-field MRI with an atomic magnetometer

摘要

In recent years, there has been considerable interest in developing an ultra-low-field magnetic resonance imaging (ULF-MRI) system using an optically pumped atomic magnetometer (OPAM). However, a precise estimation of the signal-to-noise ratio (SNR) of ULF-MRI has not been carried out. Conventionally, to calculate the SNR of an MR image, thermal noise, also called Nyquist noise, has been estimated by considering a resistor that is electrically equivalent to a biological-conductive sample and is connected in series to a pickup coil. However, this method has major limitations in that the receiver has to be a coil and that it cannot be applied directly to a system using OPAM. In this paper, we propose a method to estimate the thermal noise of an MRI system using OPAM. We calculate the thermal noise from the variance of the magnetic sensor output produced by current-dipole moments that simulate thermally fluctuating current sources in a biological sample. We assume that the random magnitude of the current dipole in each volume element of the biological sample is described by the Maxwell-Boltzmann distribution. The sensor output produced by each current-dipole moment is calculated either by an analytical formula or a numerical method based on the boundary element method. We validate the proposed method by comparing our results with those obtained by conventional methods that consider resistors connected in series to a pickup coil using single-layered sphere, multi-layered sphere, and realistic head models. Finally, we apply the proposed method to the ULF-MRI model using OPAM as the receiver with multi-layered sphere and realistic head models and estimate their SNR.