# Magnetoelectric Nanoparticles for Wireless Peripheral Nerve Stimulation: A Computational Study
## 1 Introduction  
Neuroprostheses are external devices integrated with neuromodulation which reinforce the input or output of a neural system, replacing or enhancing sensory, motor, and cognitive functions, aiming at improving the quality of life of impaired patients [1; 2]. The technological development of recent years has moved towards the enhancement of the connection of such external devices to the human nervous systems to enable a safer, more effective and selective electrical stimulation. As a part of our nervous system, peripheral nerves lie out from the brain and spinal cord and are characterized by different anatomical structures. They act as a conduit, bidirectionally exchanging information between different areas of the body and the central nervous system, communicating signals for both sensations and motor commands. Peripheral nerves are made of mixed nerve fibers: axons of motor or sensory fibers, surrounded by an insulating myelin called endoneurium, are bundled into groups named fascicles. In the context of restoring the functions of the peripheral nervous system, there is a need for neural interfaces which are highly selective and minimal invasive, leading to an unavoidable trade-off between selectivity and invasiveness. Various technologies for neural interfaces have been researched for many years, such as extraneural, intrafacicular, penetrating, and regenerative interfaces. However, some limitations concern these solutions; to mention some, the stiffness of the penetrating electrodes, the difficulty of the implantation technique for the intrafacicular electrodes, and the low signal-to-noise ratio of the extraneural electrodes [3; 4; 5]. In this context, nanotechnology has emerged as a potential novel approach to enhance the coupling between external devices and the neuron system since the dimensions of nanoengineered materials could allow for a non-invasive and highly focal neuromodulation. Particularly, magnetoelectric nanoparticles (MENPs) have demonstrated to be a cutting-edge technology to be used for single-neuron-level stimulation both at the central and peripheral sites [6; 7; 8; 9]. Their unique innovative potential is due to the magnetoelectric (ME) effect, which consists of a coupling between the external applied magnetic field and the generated local electric field, and vice versa. The direct effect occurs when the ME material is placed inside an external magnetic field: the magnetostrictive phase experiences a non-zero strain which is mechanically transferred to the piezoelectric phase, and, in turn, it transduces the mechanical deformation into electrical charges. This property, specific of magnetoelectric composites and of multiferroic solids that simultaneously possess both the ferromagnetic and ferroelectric ordering, has also been recently verified at room temperature, allowing for their use in biomedical applications. The magnitude of the two phases' interaction is defined by the ME coefficient \(\alpha_{\text{E}}=\delta\text{E}/\delta\text{H}\left[\text{V}/\text{cm}\text{ -Oe}\right]\). By this definition of the coupling coefficient, higher-order terms characteristic of the magnetoelectric interactions are ignored, and therefore, a linearity between the external applied magnetic field and the generated local electric field can be assumed [10]. The properties of ME composites depend on the properties of the selected phase materials of the nanostructure, the geometry of the components, such as the phase volume ratio and the particle and sample sizes, the frequency of the external field used to elicit the ME effect, and the quality of the mechanical contact between the two phases [6; 11]. Among all the MENPs described in the literature, the core-shell cobalt ferrite (CoFe\({}_{2}\)O\({}_{4}\)) barium titanate (BaTiO\({}_{3}\)) nanoparticles showed promising properties for biomedical applications, as proven by previous in vivo and in vitro studies [7; 12; 13; 14], and good in vitro and in vivo biocompatibility [7; 15].