No abstract

Objective. Transcranial magnetic stimulation (TMS) can be used to safely and noninvasively activate brain tissue. However, the characteristic parameters of the neuronal activation have been largely unclear. In this work, we propose a novel neuronal activation model and develop a method to infer its parameters from measured motor evoked potential signals. Approach. The connection between neuronal activation due to an induced electric field and a measured motor threshold is modeled. The posterior distribution of the model parameters are inferred from measurement data using Bayes' formula. The measurements are the active motor thresholds obtained with multiple stimulating coil locations, and the parameters of the model are the location, preferred direction of activation, and threshold electric field value of the activation site. The posterior distribution is sampled using a Markov chain Monte Carlo method. We quantify the plausibility of the model by calculating the marginal likelihood of the measured thresholds. The method is validated with synthetic data and applied to motor threshold measurements from the first dorsal interosseus muscle in five healthy participants. Main results. The method produces a probability distribution for the activation location, from which a minimal volume where the activation occurs with 95% probability can be derived. For eight or nine stimulating coil locations, the smallest such a volume obtained was approximately 100 mm 3 . The 95% probability volume intersected the pre-central gyral crown and the anterior wall of the central sulcus, and the preferred direction was perpendicular to the central sulcus, both findings being consistent with the literature. Furthermore, it was not possible to rule out if the activation occurred either in the white or grey matter. In one participant, two distinct activations sites were found while others exhibited a unique site. Significance. The method is both generic and robust, and it lays a foundation for a framework that enables accurate analysis and characterization of TMS activation mechanisms.

An analytical formula for the shape derivative of the magnetic field integral equation (MFIE) method of moments (MoM) system matrix (or impedance matrix) is derived and validated against finite difference formulas. The motivation for computing the shape derivatives stems from adjoint variable methods (AVM). The Galerkin system matrix is constructed by means of Rao-Wilton-Glisson (RWG) basis and testing functions. The shape derivative formula yields an integral representation which is of same singularity order as the integrals appearing in the traditional MFIE system matrix.Index Terms-Adjoint variable method (AVM), magnetic field integral equation (MFIE), method of moments (MoM), sensitivity analysis, shape optimization, strongly singular integrals.

This paper presents the vibration analysis and results of an induction motor through two kinds of magnetomechanical coupling methods. The computation results are validated by comparing them with the vibration measurements of the motor. The role of both the magnetic forces and magnetostriction are examined and distinguished based on their contribution to the vibration behavior of the machine. It was found that the pole pair number of an induction machine can affect the way the vibrations caused by magnetostriction and magnetic forces either add up or oppose each other.

No abstract