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

Abstract

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.