Modeling real shim fields for very high degree (and order) B0 shimming of the human brain at 9.4 T

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One of the many challenges of high field strengths in MRI is the inhomogeneity of the B0 field. Clinical human MRI systems are usually equipped with spherical harmonic shim coils up to either first‐ or second‐degree shim terms. However, as the field strength of MRI systems increases to ultrahigh field strengths such as 7 and 9.4 Tesla (T), B0 inhomogeneity becomes even more severe and therefore requires more attention.
B0 inhomogeneity directly affects the image quality. Various artifacts can result from poor B0 homogeneity, such as signal dropout, geometric distortion, blurring, curved slice profiles, and Moiré artifacts 1. Echo‐planar imaging (EPI) sequences are especially susceptible to many of these artifacts 5. B0 homogeneity is even more important for MR spectroscopy (MRS), as some of the peaks that need to be separated differ by only a few hertz (eg, the characteristic splitting of lactate is only 7 Hz) 6. Poor B0 homogeneity results in the broadening of linewidths. Furthermore, any water and fat‐suppression technique will be compromised by inhomogeneity 8.
Current state‐of‐the‐art B0 shimming hardware either extends the degrees (and orders) of the spherical harmonic terms to third‐degree 9 and even fourth‐degree systems 10, or alternatively, discard the spherical harmonic paradigm for more localized multicoil shim arrays 11. The multicoil shimming approach uses a large array of small coils to shim the B0 field. In the case of Juchem et al 11, 48 coils were used. The advantages of the multicoil shim system is that there are more degrees of freedom. The advantages of spherical harmonic shimming are that the hardware is normally available with the MRI scanner or otherwise can be purchased commercially, and that the shim coils generate orthogonal shim fields and are based on analytical models.
Both of these systems require knowledge of the real shim field produced by each coil for calibration so that they can be used in the B0 shimming algorithm 12. Spherical harmonic shim systems are based on analytical models (from the Legendre polynomials), and vendor‐implemented B0 shimming algorithms assume that the shim fields generated by each of the shim coils are identical to the desired spherical harmonic function 15 (ie, shim fields are usually assumed to be ideal). If the shim coils generate fields that are similar to the ideal fields, this assumption is feasible. However, if this is not the case, then to improve the shim, the shimming needs to be done iteratively until sufficient convergence is achieved 12. Alternatively, field reference maps can be acquired for each shim coil to correct for field imperfections. This has been done previously for very high‐degree (or very high‐order) shim systems used on a 7T magnet, in which the higher‐degree shim coils do not generate ideal fields 9. Field reference maps were successfully used to shim using up to second 12 and third‐degree shim terms 9, and even fourth with partial fourth‐plus‐degree shim terms 18.
The advantage of using modeled shim fields (as opposed to directly using the field reference maps, which was done previously) is that there are no problems with either noise or different field of views (FOVs) or different resolutions or different position offsets. Furthermore, because the reference maps are compressed into the analytical model, the reference maps do not need to be stored on the system. This makes the B0 shimming algorithm less cumbersome without sacrificing the quality of the shim. Furthermore, by using the analytical models instead of reference maps to characterize the shim fields, we can account for any nonlinearity of the shim amplifiers. Modeling of the shim fields has been reported previously in 10, where they used up to third‐degree shim coils.

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