MR images are generated based on the assumption that the magnetic field at any given spatial location is precisely known. With this knowledge, the MR signal can be quantified as:

$$S(t) = \int_x \int_y \int_z M_{xy0}(x,y,z) e^{-i\gamma \int_0^t (G_x(\tau)x + G_y(\tau)y + G_z(\tau)z + \Delta B_0(x,y,z))d\tau} dx dy dz$$

However, any magnetic field inhomogeneity, $$$\Delta B_0$$$, could have spatial gradient components along the $$$x$$$, $$$y$$$, and $$$z$$$ directions, either globally or locally, resulting in geometric distortions and/or signal losses. To minimize this inhomogeneity, the magnetic field needs to be “shimmed”. The recent advent of high field MRI scanners further exacerbated the image artifacts due to field inhomogeneity, demanding even greater shimming capabilities.

There are multiple layers of shimming technologies embedded in a typical MRI scanner to address both the intrinsic (e.g., arising from the magnet itself) and extrinsic (e.g., arising from the human subject inside the bore) magnetic field inhomogeneities.

Correcting intrinsic magnetic field inhomogeneity

Both passive shimming and active superconducting shimming approaches are typically used to compensate for the intrinsic inhomogeneities arising from the magnet itself.

Passive shimming

Passive shimming, judging by its name, is a field-correction method that relies on the use of passive ferromagnetic materials such as iron rods or patches placed in specific configurations inside the magnet (Hoult et al., 1985). For example, iron rods can be inserted into or iron patches can be lined along the magnet bore in specific patterns. The passive shimming process can be time-consuming and tedious, as a large number of iterations (mapping the magnetic field and tweaking the shim elements) may be needed to determine the optimal pattern of the spatial arrangements for the passive shim elements. Although passive shimming is an effective and economical solution, the shimming materials are usually heat-sensitive. Fortunately, many modern scanners have liquid-cooled gradient coils, mitigating the heating-induced magnetic field drifts.

Active superconducting shimming

Many MRI manufacturers also implement active superconducting shim coils within the cryogen chamber, based on spherical harmonics (SH) functions of various orders (Romeo et al., 1985). The mathematical foundation is based on the solution of Laplace’s equation, $$$\nabla^2B=0$$$, which is derived from Maxwell’s equations in regions with no current sources. This solution is a linear combination of SH functions. Typical 3T scanners are equipped with SH shim coils up to the 3rd order ($$$X, Y, Z, ZX, ZY, XY, X^2-Y^2, Z^2, Z^2X, Z^2Y, ZXY, Z(X^2-Y^2), Z^3$$$), while scanners with higher magnetic fields such as 7 Tesla may have SH shim coils up to the 5th order or even higher. The advantages of active superconducting shimming are two-fold: first, it is more stable, and second, it allows for an efficient shimming procedure as all currents can be determined based on the known orders of SH.

Together, passive shimming and active superconducting shimming coils ensure a uniform magnetic field under the factory setting, typically reaching a magnetic field uniformity < 0.1 ppm.

Correcting extrinsic magnetic field inhomogeneity

As effective as they are, one common and main shortcoming of passive and active superconducting shims is that they are usually permanent and only address static magnetic field inhomogeneity. When a human subject enters the MRI scanner, the magnetic field inhomogeneity inside the human body is dependent on that particular person, so that it cannot be easily corrected by the permanent shims. Instead, adjustable shims are necessary, giving rise to the advent of active resistive shimming coils and local shimming solutions.

Active resistive shimming

Active resistive shimming is based on the same SH functions as used in active superconducting shimming, with the difference being that coils are located within the scanner bore at room temperature. Note that since the onboard $$$X$$$, $$$Y$$$, and $$$Z$$$ gradient coils already produce magnetic field gradients of the first order, there are no separate $$$X$$$, $$$Y$$$, and $$$Z$$$ shim coils. As such, resistive coils are almost always used for higher-order shimming. Structurally, these coils can be placed along the cylindrical surface in the space between the magnet and the gradient coils, and oftentimes they are integrated with the gradient coils. Ring-shaped resistive coils correct for spherical harmonics in the z-direction, for example, the $$$Z^2$$$ and $$$Z^3$$$ terms, while saddle-shaped coils correct for crossing terms such as $$$XY, ZY, ZXY, Z^2Y$$$, etc.

As mentioned earlier, one main advantage of resistive shimming over passive and superconducting shimming is that the currents through resistive shims can be changed dynamically. This allows shimming to be performed on a subject-by-subject basis, or even dynamically on a slice-by-slice basis within the same subject (Morrell et al., 1997).

Local shimming

Although SH shimming has been the standard practice for the past three decades of human MRI, local shimming methodologies have been gaining momentum in recent years. Since the magnetic field inhomogeneities arising from the human anatomy can be highly localized and are thus not always best solved by combinations of SH functions, it may be more effective to design and implement local coils that are close to the sources of magnetic field perturbation, such as the nasal sinus, the oral cavity, or the ear canal, which contain (paramagnetic) air spaces.

The simplest solutions for local shimming may be the use of specially-shaped paramagnetic materials that can be placed near the anatomical regions causing the magnetic field disturbance. For example, a mouth piece made of paramagnetic material can effectively compensate for the field inhomogeneity arising from the oral cavity (Wilson et al., 2002). Similar to the previously mentioned whole-body passive shimming solutions, these local passive shimming materials cannot be readily adjusted for different subjects. In addition, they can be uncomfortable to use.

Recent effort has been made in developing active local shimming solutions (Hsu et al., 2005). Specifically, a set of direct current (DC) loops, placed closely to the imaging sample, showed promise in achieving a highly uniform magnetic field (Juchem et al., 2010). While effective, one limitation in this approach is that it requires a separate array of coils, which takes up additional space and could reduce either SNR or shimming efficiency depending on its spatial arrangement with respect to the RF array.

The most recent, and perhaps the most effective and efficient, solution for local shimming is based on the newly proposed framework known as integrated parallel reception, excitation, and shimming (iPRES) (Han et al., 2013; Truong et al., 2014; Stockmann et al., 2016). Specifically, a single coil array can simultaneously and inherently accommodate both alternating currents (AC) for parallel RF reception/excitation and DC currents for local $$$B_0$$$ shimming, thereby providing an integrated solution to acquire MR images with high spatial fidelity. The main advantage is that, by inherently enabling $$$B_0$$$ shimming within the same RF coil array, one can achieve greatly improved magnetic field homogeneity over existing shimming technologies, while still maintaining the same high RF performance.

Auto-shimming procedures

To provide fast and effective shimming solutions across all subjects, auto-shimming procedures (Webb et al., 1991; Gruetter et al., 1993) are essential in routine MRI exams to ensure high image quality, especially in diffusion MRI, functional MRI, and MR spectroscopy. Whether it is for linear shimming or higher-order shimming, most auto-shimming procedures require fast and accurate magnetic field mapping, as well as effective determination of required currents in either SH coils or local shimming coils. While most modern scanners are equipped with adequate auto-shimming routines, some applications such as MR spectroscopy may still require manual shimming over specific regions.

While conventional shimming methodologies can usually ensure a magnetic field homogeneity < 0.1 ppm and are adequate for anatomical scans in human subjects, at times they may not be sufficient for functional or diffusion MRI, which can result in signal losses (in the case of $$$B_0$$$ inhomogeneity along the slice-encoding direction) or geometric distortions (in the case of $$$B_0$$$ inhomogeneity in-plane). For example, there are still marked signal losses in gradient-echo echo-planar imaging (EPI) (e.g., for functional MRI application) and geometric distortions in spin-echo EPI (e.g., for diffusion MRI application) in the ventral frontal region influenced by the air cavity in the nasal sinus, even after high-order shimming, as illustrated in Fig. 1.

In this section, we discuss some examples of advanced shimming applications that can overcome these remaining challenges. One solution to recover signal losses is a technique known as z-shimming (Frahm et al., 1988; Yang et al., 1998). However, one cannot simply set the z shim to compensate for signal loss, for example, in the ventral frontal regions, as it will distort other regions that are otherwise homogeneous. Instead, two (or more) images (one with z-shim, and one without) need to be combined (example shown in Fig. 2) to generate a uniform image (Glover et al., 1999), leading to a somewhat reduced throughput, even in the case of the more efficient single-shot solutions (Song, 2001, Truong and Song, 2008).

Because of its local nature, a natural solution to correct the magnetic field inhomogeneity such as that in the ventral brain region is local shimming. Shown in Fig. 3 is an example illustrating the promise of the aforementioned iPRES technique. By using the local shimming inherently embedded in the RF array, the magnetic field uniformity was greatly improved from 55.3 Hz (root mean square error) to 9.2 Hz, and geometric distortions were corrected to restore the spatial fidelity of the frontal lobe and the anterior horns of the ventricles. Green contours were derived from a $$$T_1$$$-weighted anatomical image.

Having a homogeneous magnetic field is an essential requirement to ensure high image quality in MRI. Significant field inhomogeneity can result in severe signal losses or geometric distortions. To achieve the desired uniformity, effective and efficient shimming strategies are needed. Specifically, passive and active shimming strategies have been developed to correct for both the intrinsic and extrinsic magnetic field inhomogeneities. Advantages and disadvantages of these various solutions are reviewed. In addition, specific applications in imaging experiments for some advanced shimming strategies are discussed, when the conventional shimming solutions are inadequate. With the ever increasing demand for higher magnetic field and higher spatial resolution, magnetic field shimming will remain a highly active research field for many years to come.