frequency, to investigate different types of molecules. In MRI, we want images. Thus the resonant frequency stays similar, but the main field is modified by the addition of a linearly varying field. This makes the resonance frequency linear in position, in direction ‘x’. Each pixel or voxel now contributes with a slightly different frequency. Before applying this gradient, another perpendicular gradient is applied in the third direction, for a short while. This makes spins precess faster in that direction for a short while, thus when this ‘phase-encode’ gradient is switched, they get back to their previous frequency of rotation, but with an additional dephasing proportional to their ‘y’-coordinate. Thus, when we ‘read’ the magnetization, what we read is the contribution from each pixel, but weighted by a term dependent on position, and the gradients applied. It is not too hard to see that this term can be written e−ikx x+ky y , where k is a function of gradients and when they were switched on and off. This is the k-space often described for MRI and the measured signal corresponds to a Fourier transform. It is actually possible to excite an entire 3D volume and, for example, frequency encode the x direction and phase encode the y, z directions, although this is relatively slow.

Relaxation If left alone, the spins interact with their environment and with each other, leading to exponential decays, which are the source of the main image contrasts (T1 and T2) mentioned below.

11.2.3.1 Characteristics of the 3D MRI Data

As for CT, classical MRI is thus a 3D modality, which can be imagined as a stack of 2D slices. The most common acquisition is indeed to excite one slice at a time, and frequency encode and phase encode in two directions in that plane. MRI can be acquired directly as a full 3D volume. This means phase-encoding two directions. It is possible to have non-standard, non-lattice acquisition patterns, such as radial, spiral and rose-like. Modern advances in reconstruction theory have led to the use of different types of random sampling patterns.

Image Quality and Artifacts The most typical artifacts for MR acquisition are ‘Nyquist’ artifacts, also known as ‘aliasing’ artifacts, which are artifacts related to a spatial sampling rate that is too low. 3D MR acquisitions can be particularly affected by them. In particular, Gibbs ringing artifacts are frequent near edges. These are due to unavoidable truncations in the acquisition. Further to this, the contrast of the image is determined by the center of the k-space. It can happen that outer parts are then undersampled, leading to blurred images. The phase encode direction is the slowest to acquire. So, to make scans faster, this direction may be undersampled. This can lead to foldover or wrap-around artifacts, where parts of the image which are out of the field-of-view seem to fold inside it. Related motion artifacts are also more visible in this direction. Examples of MRI artifacts are shown in Fig. 11.4.

Apart from the main magnetic field, all fields change with time. This creates eddy currents, which induce fields and thus distort the picture. The typical artifact

Fig. 11.4 Examples of MRI artifacts—(a) aliasing causing wrap-around near the sides of the image and (b) intensity inhomogeneity (brightness at the center) and ringing (wave-like patterns inside dark prostate region) in an image taken with a transrectal coil

due to such eddy currents is a distortion, possibly affine (shear, etc.). See Erasmus et al. [27] for further reading on MRI artifacts.

A different type of artifact can arise due to the main field being non-uniform or the gradients not being perfectly linear functions. Such inhomogeneities lead to spatial distortions of the image. There are also local imperfections of the magnetic field due to local changes in magnetic susceptibility. These artifacts lead to non-affine, localized distortions at interfaces; for example, tissue-air. So, unlike CT, it cannot be guaranteed that MRI is a geometrically correct representation of the patient.

Resolution δx is inversely proportional to the width in k-space, δx 1/ k. Small voxels are also noisier, thus there is always a trade-off between resolution and other desirable qualities of the image, such as SNR. This again is something that can be decided by operators, thus might be influenced by the application. Typical resolutions for human, in vivo MRI, are between 1 mm and 2 mm, with typical image sizes between 128 × 128 to 256 × 256.

MR images are, from the Fourier transform reconstruction, complex by nature, with the magnitudes of the complex numbers being used to display the image. Although noise in MRI is Gaussian, provided we consider their complex form, the noise on the displayed magnitudes is Rician. It is important for the computer scientists performing post-processing operations to keep this in mind.

Standard MR modalities have sufficient SNR that the noise can be approximated as Gaussian (with some correction factors) but for some other techniques, such as diffusion MRI (see Sect. 11.6), this is usually not true. We refer the reader to Rajan et al. [66] for more details on SNR in MRI.

Note that there are always trade-offs. With longer scan times, we can improve SNR at the risk of augmenting sensitivity to motion.

Contrasts: There is a wealth of different contrast weighting in MRI, thus, for a specific 3D application, it is nearly always useful to discuss the requirements with MR physicists, as it is often possible to tune the scan. However, one should keep in mind that, in most cases, these contrasts are not mutually exclusive. Images are weighted more towards one type of property, but always contain some element of the other.

The simplest contrast conceptually is the proton density scan, but this has few clinical applications. Typical clinical images are ‘T1’ or ‘T2’-weighted, which means that the contrast is a relaxation rate relating to the spin-lattice or spin-spin