Remote magnetic navigation is used for the manipulation of untethered micro and nanorobots, as well as tethered magnetic surgical tools for minimally invasive medicine. Mathematical modeling of the magnetic fields generated by magnetic navigation systems is a fundamental task in the control of such tools for biomedical applications. In this article, we describe and compare several existing and newly developed methods for representations of continuous magnetic fields using interpolation in the context of remote magnetic navigation. Clinical-scale electromagnetic navigation systems feature nonlinear magnetization and magnetization interactions between electromagnets, which renders accurate magnetic field modeling challenging. We first introduce a method that can adapt existing linear models to correct for nonlinear magnetization, with similar performance to the current state-of-the-art nonlinear model. Furthermore, we present a method based on convolutional neural networks.

Electromagnetic Navigation Systems (eMNS) can be used to control a variety of multiscale devices within the human body for remote surgery. Accurate modeling of the magnetic fields generated by the electromagnets of an eMNS is crucial for the precise control of these devices. Existing methods assume a linear behavior of these systems, leading to significant modeling errors within nonlinear regions exhibited at higher magnetic fields, preventing these systems from operating at full capacity. In this paper, we use a random forest (RF) and an artificial neural network (ANN) to model the nonlinear behavior of the magnetic fields generated by an eMNS. Both machine learning methods outperformed the state-of-the-art linear multipole electromagnet model (MPEM). The RF and the ANN model reduced the root mean squared error (RMSE) of the MPEM when predicting the field magnitude by approximately 40% and 87%, respectively, over the entire current range of the eMNS. At high current regions, especially between 30 and 35 A, the field-magnitude RMSE improvement of the ANN model over the MPEM was 37 mT, equivalent to 90% error reduction. This study demonstrates the feasibility of using machine learning to model an eMNS for medical applications, and its ability to account for complex nonlinear behavior at high currents. The use of machine learning thus shows promise in developing accurate field predicting models, and ultimately improving surgical procedures that use magnetic navigation.