“Shimming” on spatially localized signals

The advent of surface coils (I, 2) and the use of selective pulses in conjunction with transiently applied field gradients (3-6) have spurred investigators to obtain spectra from localized regions of large samples. For example, spatial localization may be used to examine the spectrum of a tumor in a person or animal, while excluding signal from surrounding tissue. However, the main magnetic field over the region of interest may well be inhomogeneous, perhaps due to localized susceptibility effects which are present when the sample is heterogeneous or is oddly shaped, or even due to incorrect shim coil settings. Whatever the reason may be, it appears not to be generally recognized that if the volume of interest is remote from the origin of the shim coil set, as is often the case, it is exceedingly difficult, if not impossible, to shim the magnet in the conventional manner by observation of the free induction decay, or spectral peak amplitude as the shim settings are varied. Mathematically, the above statement is a manifestation of the fact that spherically harmonic fields (the various fields created by the shim coils) are only orthogonal over a spherical volume centered on the origin. Movement of the origin by an amount greater than or comparable to the radius of the spherical volume of interest renders the shim set hopelessly nonorthogonal, and all the current adjustments interact. To appreciate the gravity of this statement, consider the gross simplification of Fig. la, where we show only a one-dimensional perturbation of the field by, say, a tumor, at position z = 10 cm, and we restrict our shim set to only two variables, z and z2. The tumor has a frequency spread of 100 Hz, and it is quite clear by inspection of the region centered on 10 cm and bounded by 10 f 1.5 cm (the selected volume) that the field is of the form 12. AvO=a!+pz’-yz , Iz’/ < 1.5, 111