Exact and Computationally Robust Solutions for Cylindrical Magnets Systems with Programmable Magnetization.

Magnetic systems based on permanent magnets are receiving growing attention, in particular for micro/millirobotics and biomedical applications. Their design landscape is expanded by the possibility to program magnetization, yet enabling analytical results, crucial for containing computational costs, are lacking. The dipole approximation is systematically used (and often strained), because exact and computationally robust solutions are to be unveiled even for common geometries such as cylindrical magnets, which are ubiquitously used in fundamental research and applications. In this study, exact solutions are disclosed for magnetic field and gradient of a cylindrical magnet with generic uniform magnetization, which can be robustly computed everywhere within and outside the magnet, and directly extend to magnets systems of arbitrary complexity. Based on them, exact and computationally robust solutions are unveiled for force and torque between coaxial magnets. The obtained analytical solutions overstep the dipole approximation, thus filling a long-standing gap, and offer strong computational gains versus numerical simulations (up to 106 , for the considered test-cases). Moreover, they bridge to a variety of applications, as illustrated through a compact magnets array that could be used to advance state-of-the-art biomedical tools, by creating, based on programmable magnetization patterns, circumferential and helical force traps for magnetoresponsive diagnostic/therapeutic agents.

The Myokinetic Control Interface: How Many Magnets Can be Implanted in an Amputated Forearm? Evidence From a Simulated Environment.

We recently introduced the concept of a new human-machine interface (the myokinetic control interface) to control hand prostheses. The interface tracks muscle contractions via permanent magnets implanted in the muscles and magnetic field sensors hosted in the prosthetic socket. Previously we showed the feasibility of localizing several magnets in non-realistic workspaces. Here, aided by a 3D CAD model of the forearm, we computed the localization accuracy simulated for three different below-elbow amputation levels, following general guidelines identified in early work. To this aim we first identified the number of magnets that could fit and be tracked in a proximal (T1), middle (T2) and distal (T3) representative amputation, starting from 18, 20 and 23 eligible muscles, respectively. Then we ran a localization algorithm to estimate the poses of the magnets based on the sensor readings. A sensor selection strategy (from an initial grid of 840 sensors) was also implemented to optimize the computational cost of the localization process. Results showed that the localizer was able to accurately track up to 11 (T1), 13 (T2) and 19 (T3) magnetic markers (MMs) with an array of 154, 205 and 260 sensors, respectively. Localization errors lower than 7% the trajectory travelled by the magnets during muscle contraction were always achieved. This work not only answers the question: "how many magnets could be implanted in a forearm and successfully tracked with a the myokinetic control approach?", but also provides interesting insights for a wide range of bioengineering applications exploiting magnetic tracking.