Performance Evaluation of Magnetocardiography Sensor Arrays via Cramér–Rao Bound for Cardiac Source Localization

Magnetocardiography (MCG) source localisation plays a key role in estimating cardiac electrical activity and identifying abnormal activity locations for disease diagnosis. To improve estimation accuracy in clinical applications, evaluating the performance of MCG sensor arrays is crucial for selecting optimal configurations. Such evaluations have traditionally been conducted through various metrics. However, these metrics depend on specific estimation algorithms and fail to directly reflect how the sensor array influences the variance of parameter estimation. Furthermore, the diversity of estimation algorithms hinders the establishment of uniform assessment criteria. To overcome these challenges, we present an evaluation method for MCG arrays focused on minimising the variance in source parameter estimation. The method leverages the Cramér-Rao Bound (CRB), a theoretical limit on the variance of unbiased estimators and independent of the employed algorithm. Aided by the boundary element method, we derive the CRB framework for estimating cardiac source parameters using MCG data and quantify the effect of adding sensors on the CRB. In addition, we utilise the CRB to evaluate the performance of MCG arrays measuring different magnetic field components, quantifying the advantages of three-dimensional (3D) vector field measurements for source estimation. Compared to conventional radial measurements, 3D vector measurements reduce the equivalent uncertainty radius by more than 25.62%. Finally, we apply the approach to optimise sensor arrangements when the number of sensors is limited. Overall, our results show that the CRB effectively evaluates MCG arrays across diverse configurations, making it applicable to various clinical and engineering applications.