Abstract

Magnetic localizers have been widely investigated in the biomedical field, especially for intra-body applications, because they don’t require a free line-of-sight between the implanted magnets and the magnetic field sensors. However, while researchers have focused on narrow and specific aspects of the localization problem, no one has comprehensively searched for general design rules for accurately localizing multiple magnetic objectives. In this study, we sought to systematically analyse the effects of remanent magnetization, number of sensors, and geometrical configuration (i.e. distance among magnets—Linter-MM—and between magnets and sensors—LMM-sensor) on the accuracy of the localizer in order to unveil the basic principles of the localization problem. Specifically, through simulations validated with a physical system, we observed that the accuracy of the localization was mainly affected by a specific angle (theta = tan−1(Linter-MM / LMM-sensor)), descriptive of the system geometry. In particular, while tracking nine magnets, errors below ~ 1 mm (10% of the length of the simulated trajectory) and around 9° were obtained if θ ≥ ~ 31°. The latter proved a general rule across all tested conditions, also when the number of magnets was doubled. Our results are interesting for a whole range of biomedical engineering applications exploiting multiple-magnets tracking, such as human–machine interfaces, capsule endoscopy, ventriculostomy interventions, and endovascular catheter navigation.

Highlights

  • Building on this, in this study we sought to systematically analyse the effects of remanent magnetization (Br), number of sensors, L­ inter-magnetic markers (MMs) and ­LMM-sensor on the accuracy of the localizer, in order to unveil some of the basic principles of the localization problem or, in other words, define effective guidelines for optimal myokinetic controllers

  • We systematically analysed the effects of the (i) magnetization grade, (ii) number of sensors, (iii) L­ inter-MM and (iv) ­LMM-sensor on the accuracy of a multi-magnet localizer, in a planar, simulated configuration, and we verified the validity of the simulations comparing the outcomes with those from equivalent physical systems

  • Our results confirm the sparse information found in the literature, i.e., that larger compound/cumulative errors are obtained as ­LMM-sensor ­increases[6,9,14,17,18], and ­Linter-MM decreases 14

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Summary

Introduction

In this study we sought to systematically analyse the effects of remanent magnetization (Br), number of sensors, L­ inter-MM and ­LMM-sensor on the accuracy of the localizer, in order to unveil some of the basic principles of the localization problem or, in other words, define effective guidelines (or design tips) for optimal myokinetic controllers. Results ­from[18,19] highlighted that a better accuracy can be achieved when the sensors are aligned with the magnetization axis of the magnet, as the signal to noise ratio is increased Generalizing these outcomes from a single to multiple magnets (and all that it entails) represents a fundamental step towards the understanding of the underlying phenomena and the development of a new class of magnetic localizers. Taking our previous study as a starting ­point[14], here we simulated different setups in which the number of MMs was fixed at nine, while their remanent magnetization Br, ­LMM-sensor, ­Linter-MM and the number of sensors were varied. In the case of a myokinetic control interface, they represent an important step forward towards the development of a highly intuitive and physiologically appropriate controller for limb prostheses

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