Novel Numerical Modelling of Lumped Circuit Elements in RF Coils for Identifying Resonant Frequencies

Introduction: Many different numerical approaches have been investigated in the past that are related to the topic of this research [1], but there seems to be an ever increasing need to model RF coils in real time, to better understand the field behaviour when an imaging sample is present. In this work the discrete numerical solution to Maxwell’s equation is investigated, with the aim of modelling lumped element RF coils in real time, without the need to superimpose signals from different rungs or channels. Equivalent circuit theory when applied to RF coil design is somewhat limited, because it does not take account of the fact that RF coils are loaded when operational, and the consequent design using equivalent circuit theory cannot accurately predict any shifts on the resonant frequency and signal intensity losses that may be incurred due to the electromagnetic properties of the load. Past experiments have provided some interesting results, for example, RF head coils [2] and in parallel imaging at high field [3], but these are not without some limitations and modelling assumptions. The problem in modelling RF coils in terms of numerical approximations has to do with errors in the discretisation process. Errors such as lattice capacitance and inductance play important roles when numerical discretisation of the continuous Maxwell’s equations is performed, and in this work, the aim is to considerably reduce these errors. The approach used here is not dissimilar to that used in antenna theory, for example [4, 5], and to some extent in circuit theory [6, 7]. The proposed numerical modelling approach aims to better simulate RF coils when a load is present (e.g. a head), whether it is a birdcage coil [2], or a multi channel arrangement [3]. When numerical models are used to predict certain phenomena, the simulations should provide sufficient data in time to allow for the prediction of indicators like field inhomogeneity (i.e. loss of intensity) and SAR levels.