Spherical harmonic inductive detection coils and their use in dynamic pre-emphasis for magnetic resonance imaging
The issue of eddy currents induced by the rapid switching of magnetic ﬁeld gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic ﬁeld are continuously sensed, through their temporal rates of change, and corrected. In this way, the eﬀects of the eddy currents on multiple spatial harmonic components of the magnetic ﬁeld can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the ﬁeld, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the ﬁeld – an inverse curl operation – and may be of use beyond the speciﬁc problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current eﬀects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI.