Simple , accurate and efficient multilayer integral method for eddy current simulation in thin volumes of arbitrary geometry produced by MRI gradient coils

Introduction: Eddy currents are invoked when the time-varying magnetic fields produced by the gradient coils interact with the surrounding conducting structures of the MRI scanner including RF coils. These currents in turn produces acoustic noise, power heating, magnetic field asymmetries, unpleasant acoustic noise, electronic malfunctioning, frequency shift in the RF coil and imaging artifacts [1]. In this abstract we present a new fast, accurate and efficient eddy current simulation method capable of calculating induced currents in thin (finite thickness) conducting and non-magnetic volumes of arbitrary geometry induced by arbitrary arrangements of gradient coils. We assumed that one of the linear Cartesian dimensions is much smaller than the rest and that the volume is divided in thin layers along the smallest Cartesian dimension. This novel method has been experimentally validated using a z-gradient coil and its performance tested against COMSOL and the Fourier Network method (FNM) [2]. We present an example to demonstrate the capabilities of the method in terms of predicting the induced currents, power losses and pre-emphasis simulations using the excited eigenvalue corresponding to the surrounding structure. The method is accurate and fast enough to be performed in a laptop (Intel core(TM) i7 CPU) 8 GB RAM. Method: We assumed a thin but finite thickness, smooth, non-magnetic and conducting domain of arbitrary shape is immerse in a time-varying magnetic field produced by a known current source Js(r,t) of arbitrary geometry. The displacement current is much smaller than the conduction current at the given frequency ω=2πf where f is given in Hz. The domain is divided along the smallest dimension into N layers of thickness h, where h is much smaller than the skin depth δ [2]. Each surface is approximated to a connected set of discrete mesh of plane triangles and the surface current density Ji(r,t) is represented as a finite set of linear basis functions [3]. The Stokes theorem holds in each thin layer and no current flows through the boundaries containing each layer; hence that the layers are inductively coupled but resistively decoupled. The boundary conditions and the edges of the domain are enforced to satisfy the continuity equation. The differential form of the diffusion equation is solved for time-harmonic or transient solution when the coil is driven with an arbitrary current pulse s(t):