The gradient system (fig. 1) of an MRI is responsible for the spatial encoding of the received signals. The gradient system consists of a gradient coil, including three orthogonal axes which generate rapidly switched magnetic fields using high voltages and currents, and a gradient amplifier which provides these high currents and voltages.

The maximum gradient strength in mT/m and the rise time, normally specified as “slew-rate” in T/m/s, are the main characteristics of a gradient system and determine its performance.

The improvements in resolution and speed in recent MRI scanner generations were only possible with the development of high-performant gradient systems. Present gradient technology allows gradient amplitudes of up to 80mT/m and slew rates of up to 200T/m/s simultaneously for conventional whole-body systems. Even higher amplitudes and slew rates are possible using dedicated coils like head gradient coils or special research gradient systems. A major advantage of head gradient coils is that the high amplitudes can mostly be switched in short rise times without restrictions due to peripheral nerve stimulation (PNS) (1,2). With special diffusion gradient systems (3), the highest possible gradient amplitudes are applied in the shortest possible time for the diffusion lobes, combined with an echo-planar imaging (EPI) pulse sequence to encode diffusion at the shortest possible echo time (TE).

An ideal gradient system would only produce the rapidly switching gradient field in the desired FOV. The objectives are maximum gradient strength and minimum rise time. Since the performance of the amplifier is limited to a certain voltage, the inductance of the coil has to be minimized. The required voltage V and current I in a gradient coil of an inductance L and a resistance R are described by:

$$V(t)=R\cdot I(t)-L\frac{dI(t)}{dt}$$

The realization of an ideal wire pattern for a gradient coil requires not only knowledge of the amplifier but also of the magnet, because the linearity of the gradient coil has to be adapted to the available magnet homogeneity. Normally, a high linearity in the field of view is desired.

The nonlinearity in a defined volume is defined by: $$$\Delta B=\frac{max(|B_{z}-G_{ideal}|)}{max(G_{ideal})}$$$

However, for “real” gradients additional effects have to be taken into account, like stray fields on conductive layers inside the gradient coil (RF screen) and on surrounding surfaces. Outside the gradient coil, the most dominant source of eddy currents are the conductive layers inside the magnet, one of them is the so-called “cryo-shield” (or shields). The induced eddy currents (due to the law of inductance $$$\frac{\partial }{\partial t}\int \overrightarrow{B}\cdot d\overrightarrow{A} =-\oint\overrightarrow{E}\cdot d\overrightarrow{s}$$$) will spoil the image quality in the FOV, and the gradient induced heat load inside the magnet will lead to Helium boil-off. Therefore, nearly all gradient coils are “shielded gradient coils” (4), i.e. every gradient axis consists of a primary layer which produces the main field and a secondary layer which is designed to prevent stray fields. There are different approaches possible to achieve the optimal solution, like the stream function method, the target field approach as well as other numerical methods. An overview is described in a review by Turner (9,10). For a numerical approach, so-called “mesh currents” are optimized for primary and secondary surface (see fig. 2) under the following condition:

Minimize $$Q=({\bf B}_{s}-{\bf Z})^2+w_{b}\cdot \frac{1}{2}{\bf I}^{Tr}\cdot{\bf L}\cdot{\bf I}+w_a\cdot({\bf Mn}\cdot{\bf I})$$

The first part of the function is the deviation of the desired field in the FOV; the second part reflects the field energy, and the third describes the eddy current field in the FOV.

Other undesirable side effects like the rigid-body forces as a result of the switched gradient fields in a non-ideal homogeneous main magnet are given into the optimization as constraints. Other constraints are geometric boundaries derived from the available radial space or current densities derived from the performance of the amplifier (maximum current and voltage). This numerical method allows the use of arbitrary surfaces for the wire pattern, not necessary just cylindrical ones.

There are limitations to the usage of the possible technical performance because of physiological conditions, in particular peripheral nerve stimulation (5). The interaction of the switched electro-magnetic fields with the human physiology lead to induced electrical fields in the human body causing nerve stimulation. These limits can be influenced by using special head gradient coils or to some amount by adapting the linearity volume of the gradient coil; a restricted linearity volume will allow higher gradient performance. There are approaches to simulate the effect of the switching gradient fields on the human body; but for the determination of the relevant limits a “clinical trial” with a defined set of test sequences and a defined amount of volunteers is the method required by the regulations (6).

With the introduction of fast MRI techniques, the acoustic noise also became more relevant. Without any counter-measures, the noise level can cause discomfort or harm to patients and personnel (7). The reason for the noise is vibration of the gradient coil body which is produced by Lorentz forces on the wires in the coil. When a current passing through a wire is exposed to a magnetic flux, a force perpendicular to the current and the magnetic flux is generated. Mathematically this is expressed by the vector product:

$$\overrightarrow{F}(t)\sim \overrightarrow{I}(t) \times \overrightarrow{B}_0$$

If the excitation of the Lorentz forces matches the eigenmodes of the gradient coil, the noise level will increase (fig. 3). These eigenmodes are determined by the geometric dimensions and the material properties of the gradient coil, like weight and stiffness. There have been ideas to minimize the vibration by de-tuning the excitation by means of altering the wire pattern, to suppress the most relevant eigenmodes of the gradient coil (8). But due to the desired performance of the coil and restricted available space, the achievements are limited.

Limitations in radial space and the high amount of energy which is deposited inside the coil volume due to the losses in the wires require an efficient cooling system (see fig.4). There are different approaches for such a cooling system, but for state-of-the-art gradient systems with high performance, water cooling is necessary. Water can be provided either in plastic piping, copper tubes or in hollow conductors, dependent on the different requirements and vendors.

The thinner the gradient coil, the less efficient the coil is due to the shielding. This means that there are limits for the patient bore, unless the magnet inner bore is increased, leading to higher costs. It is possible to combine gradient coil and body coil to overcome these radial limitations. But for these alternative approaches, other drawbacks like an increase of local SAR exist, and the benefits are restricted. The smaller the distance between the primary and secondary layers becomes, the more sensitive the coils get to manufacturing tolerances. A shift of 0.5mm in z-direction between both layers leads to undesirable stray fields and to eddy currents of higher orders. Whereas residual linear eddy currents can be compensated (eddy current compensation, ECC), the higher-order eddy currents normally cannot be compensated and can lead to fat saturation problems.

A restriction in length can lead to alternative solutions for the gradient coil. The so-called 3D gradient coils (fig. 5) combine the primary layer and the secondary layer with connectors at both ends and can achieve a shorter design with comparable performance and linearity specification.

For the manufacturing process of a gradient coil, it is important to use the available space to combine the three gradient layers for the primary coil and the secondary coil with the necessary cooling layers as effectively as possible. The distance between the field-generating layer and the shielding layer should be maximized to increase the sensitivity of the coil. The space in between can be used for different shim options like second-order shim coils or, if necessary, for passive shimming (iron plates). In addition, the high-voltage isolation between the different layers has to be guaranteed. Therefore, the transversal gradient axes can be made of punched copper plates, which are fixed on isolation plates or isolated copper wires, which in turn are glued on to GRP plates. The plates are later rolled to obtain the necessary shape. In the case of copper plates, the variable wire thickness will reduce the DC resistance and the power consumption, but for higher frequencies the eddy currents inside the copper have to be considered (11). Slotting the copper areas is a possibility to reduce the eddy currents. A conventional Z-gradient coil is wound with copper wire, but hollow conductors for the z axis can combine the cooling requirement and the field generation. As an alternative to additional support structures like GRP tubes, a special vacuum-potting process can be applied to fulfill the different requirements of the gradient system. This casting process should guarantee the mechanical stiffness and provide a sufficient thermal conductivity. The high mechanical stiffness is necessary to withstand the mechanical forces, especially in ultra-high-field systems with magnetic fields of 7T or more. The high density of conductive layers inside the coil and the high voltages, which are necessary to reach the performance, are an additional challenge. If there are any shrinkage cavities in the casting compound, partial discharge will spoil the image quality and will damage the internal structure of the gradient coil. This makes the partial-discharge measurement essential for every coil, to ensure image quality with respect to artefacts like spikes.

A shift of more than 0.5mm between the primary and the secondary coil can lead to undesirable image artifacts, like eddy currents of higher orders. Therefore, it is necessary to check every individual example not only for the most relevant electrical parameters like resistance and inductance, but also to check the resulting magnetic field.

Until now, the improvements in gradient performance have been essential for the development in fast MRI. For nearly all technical restrictions, solutions are possible, like split gradient coils and stronger amplifiers, and even higher parameters can be reached. But the limitations, caused by peripheral nerve stimulation and in some cases going to the limits of cardiac stimulation, seem to make it questionable to go in that direction.

Patient comfort, like a bigger patient bore or reduced vibration and noise, or reduced energy consumption within the gradient system, are additional targets, which have already got into the focus. Therefore, the most important consideration prior to the electrical design is to prioritise the different requirements for the gradient system.