In a conventional spinwarp imaging pulse sequence (2), lines of k-space are acquired one at a time, with a new RF excitation pulse, and newly generated coherent transverse magnetization for each line. This creates two distinct in-plane directions, usually referred to as ‘frequency encoding’ and ‘phase encoding’ directions. In the frequency encoding direction, adjacent data points in k-space are acquired in rapid succession, microseconds apart in time under the influence of the readout or frequency encoding gradient. Thus this direction is traversed and sampled in ‘real time’. In contrast, data points that are adjacent to one another along the phase encoding direction are collected after separate excitations, and at identical times after the excitation pulse. In EPI, a large oscillating readout gradient is applied to traverse kx in a back and forth manner, while small ‘blip’ gradients create incremental steps in ky. A basic EPI (1) pulse sequence and corresponding k-space trajectory are shown in Figure 1. In EPI, both directions are ‘real time’ directions, in that all points in the 2D plane are sampled at different times after the excitation pulse as the trajectory winds down the zig-zag k-space path. However, there is still a strong anisotropy between directions, as the readout direction is sampled quickly (per line), and the blip direction is sampled much slower. EPI is defined by the type of trajectory in k-space, rather than by the methods used for RF excitation or slice selection. An EPI pulse sequence can be a gradient echo sequence as in Figure 1, or a spin echo or stimulated echo, and can be preceded by any magnetization preparation scheme, such as inversion recovery, magnetization transfer, diffusion weighting, arterial spin labeling, etc.

Following excitation, transverse magnetization evolves under three main influences:

1) Applied gradient fields.

2) Transverse relaxation.

3) Resonant frequency offsets unrelated to gradient fields, such as those caused by chemical shift or magnetic susceptibility inhomogeneity.

These can be incorporated into an MRI signal equation as three exponential terms:

$$S(t)\propto\int M_0(r)e^{ik(t)\cdot r}e^{-t/T2^*(r)}e^{i\omega(r)t}dr$$

where M₀ is the transverse magnetization immediately after the excitation pulse. The first exponential term describes the effects of the gradient fields, and with this term alone, the signal in k-space and the transverse magnetization are strictly related to one another by Fourier Transform. The next two terms are modulations arising from relaxation and resonance offsets, respectively. Note that relaxation and resonance offsets both produce simple multiplicative modulations in the data domain. By the Fourier Convolution Theorem (3), this implies that these effects are described by convolutions with point spread functions (PSFs) in the image domain, and that these PSFs are the Fourier Transforms of the modulation terms. While these modulations are naturally functions of time, the k-space trajectory maps these modulations onto k-space. Relaxation produces amplitude modulation across k-space, while resonance offset produces phase modulation. In spinwarp imaging, these effects only produce modulation in the frequency encoding direction. In the phase encoding direction, the signal is not modulated by these effects, and the PSF in that direction is ideal. In EPI, modulations appear in both directions, but because the traversal of k-space in the blip direction is much slower, the effects of modulation is greater in the blip direction, and the non-ideality of the PSF is dominated by blurring and distortion in that direction. Note that the modulation functions are dependent upon the relaxation time T2* and the resonance offset ω, both of which are local properties and typically vary in space. The PSFs are therefore dependent upon the local relaxation and resonance offsets, and result in spatially varying blurring and image distortion, respectively.

The hallmark feature of EPI is the ability to acquire a full plane of k-space after a single excitation. The goal is to cover a sufficiently large patch of k-space with sufficient density to produce a useful image. However, as noted above, the image can be blurred and distorted, and these effects increase with acquisition time. There is therefore a strong motivation to move through k-space as quickly as possible, which in turn places strong demands on gradient performance. The gradient amplitude and slew rate, which are proportional to velocity and acceleration in k-space, explicitly limit the minimum time for complete sampling of 2D k-space. The relative importance of gradient amplitude and slew rate varies with the desired resolution and matrix size, and with the gradient hardware, but for modern whole body human imaging systems, where typical amplitude and slew rate limits are around 50mT/m and 200mT/m/ms, the slew rate is typically more limiting. In this regime, as much or more time may be spent on the ramps of the trapezoidal readout gradient as on the flat portions. Under these conditions, if data is acquired only on the flat portions of the readout gradient, then the SNR suffers both because the duty cycle of the ADC is reduced, and because the TE is lengthened, causing increased T2/T2* decay. Blurring and off-resonance related distortion are increased as well. In response to these problems, many implementations of EPI now acquire data during the ramp portions of the readout gradient as well as the flat portions, This is termed ramp sampling. This can greatly improve the overall time efficiency of the coverage of k-space, but introduces additional complications as well. With ramp sampling, data is typically acquired with uniform sampling in time, and must be resampled to a uniform grid in Kx prior to Fourier Transform. While this step is in principle relatively straightforward, it places much more stringent requirements on the accuracy of the gradient waveform and timing of data acquisition than does a flat readout gradient. In addition, with sharply peaked readout gradients, the readout bandwidth is highest at the center of k-space, reducing the SNR of the estimation of those points in k-space that contain the bulk of the image energy. Thus, while the basic concept of EPI scanning is in principle quite simple, the interdependence between resolution, matrix size, SNR, image artifacts, and hardware requirements generate a relatively complex set of tradeoffs that should be understood in order to optimize the EPI measurement.Single shot EPI represents a prototype 2D pulse sequence in which all of 2D k-space is covered in a single excitation, in a single echo (spin echo or FID). 2D k-space can also be covered using multiple excitations and/or multiple spin echos (4), and the relationship between these approaches is shown schematically in Figure 2. Several of these methods are considered hybrid EPI methods. Two other imaging features that are now commonly used with EPI are coil based parallel acceleration, using approaches in the SENSE (5) or GRAPPA (6) families of methods, and multiband excitation (7), in which multiple slices are excited simultaneously and are disentangled using a combination of parallel acceleration methods and through-slice gradient modulation.