Author: William G. Bradley, MD, PhD, FACR

Objectives: Upon the completion of this CME article, the reader will be able to:

1. Define the meaning of the readout axis and the phase-encoded axis.
2. Discuss the meaning of "dwell time", "bandwidth" and the signal-to-noise ratio.
3. Explain how chemical shift artifacts occur and how they can be eliminated from an image.

The generation of an MR image requires the combination of spatial and intensity information. As discussed in Fundamentals of MRI – Part I, spatial information is encoded in the frequencies that comprise the spin echo signal. The frequency of resonance depends on the local value of the magnetic field. Although the main magnetic field is designed to be quite uniform, additional magnetic fields can be temporarily superimposed on the main static field (figure 1). This creates spatial variation in the net magnetic field, resulting in a magnetic field gradient. At each position along this gradient, there is a slightly different resonant frequency. By knowing the exact value of the magnetic field at each point, one can predict the local resonant frequency. Thus the various frequencies in the spin echo indicate the position of the resonating protons, which generated that signal. Since three coordinates (x, y, and z) must be specified to localize a point in space, MR images require three separate gradient fields. In practice these fields are generated by electromagnetic coils that can be turned on and off rapidly.

An MR image is the result of a complicated interplay between RF pulses and intermittently activated gradient fields, all of which are under computer control (figure 2). Depending on the programming, a signal can be acquired from the whole volume simultaneously (three dimensional [3D] acquisition) or from slices or planes within the volume (two dimensional [2D] acquisition). An efficient method of generating images from multiple slices within the volume of interest involves sequential acquisition of adjacent slices (figure 3). Thus while protons in one slice are recovering during the repetition time between pulses (figure 4), other slices can be imaged by selective exposure to RF pulses containing different frequencies. Such selective pulses must be applied in the presence of a slice-selecting gradient so that only protons within the intended slice resonate.

Spatial resolution is determined by the number of frequency-encoded (or readout) projections and phase-encoded projections for a given field-of-view (FOV).

The two axes in an image are thus the "readout" axis and the "phase-encode" axis. For a transaxial image in the traditional orientation (z-axis along the main magnetic field), the z-gradient is used to select the slice (figure 3). The y-gradient may be used for "phase-encoding" and the x-gradient for "frequency-encoding" or "readout" (or vice versa).

During readout, the spin echo signal is "sampled" a certain number of times (figure 5). This changes the analog signal to a string of digits that can be processed by a digital computer. The number of times the spin echo is sampled is equal to the number of "projections" along the readout or frequency-encoded axis, for example, 256. The total period of time the echo is sampled is called the "echo sampling time" and is on the order of 8 msec for a 1.5 T magnet. The interval between samplings of the spin echo is called the "dwell time". Dwell times are typically of the order of 100 m sec. (The inverse of the dwell time is called the "bandwidth". It is a primary determinant of noise.) For 256 readout projections and an echo sampling time of 25.6 msec, the dwell time would be 100 m sec (10^-4 sec) and the bandwidth would be 10 kHz (i.e. 1/10^-4 sec^-1).

An increase in spatial resolution along the phase encode axis requires an increase in the number of phase-encoded projections, N, each with a different strength of the phase encoding gradient. This increases the acquisition time. The only penalty for increasing spatial resolution along the readout axis is that there are fewer protons in the smaller voxels, which decreases the signal-to-noise ratio.

Like the sequence parameter times (TR and TE), spatial resolution must be set prospectively. This is accomplished by specifying the size of the acquisition matrix (N_f x N_p) and the field-of-view (FOV). Larger matrices (covering the same FOV) result in better spatial resolution, but not necessarily in greater lesion detectability. In addition, larger matrices require longer acquisition times since the acquisition time is equal to the product of TR x N_ex x N_p, where N_ex is the number of excitations. Spatial resolution can be increased along the readout axis without increasing the acquisition time.

Other considerations may influence the assignment of the phase encode and readout gradients to particular axes in addition to the image aspect ratio. Motion artifacts (figure 6) in a 2DFT image occur along the phase encode axis, regardless of the direction of motion. Using a sagittal image of the spine as an example, one might assign the phase encode direction to the shorter anterior-posterior axis. However, on heavily T2-weighted images, this might result in projection of motion artifacts (from high intensity flowing CSF) onto the spinal cord itself. When such artifacts are unacceptable, they can be eliminated by swapping the phase-encode and the frequency-encode along the long axis of the spine rather than the FOV.

The "resolving power" is a useful measure of the machine-determined ability to discriminate a lesion from its background. Resolving power increases with increasing spatial resolution, signal-to-noise ratio (S/N), and object contrast. The S/N from a pixel is proportional to the product of the voxel volume V and the square root of the product of the number of excitations N_ex and the number of phase-encode projections N_p divided by the bandwidth (BW):

Voxel volume is the product of the two inplane pixel dimensions and the slice thickness. Spatial resolution (i.e. pixel dimension) is determined by the FOV divided by the number of pixels along a particular axis in the image. For purposes of further discussion, the matrix will be considered to be square with equal numbers of square pixels along both axes.

Thinner slices and higher spatial resolution carry a signal-to-noise ratio penalty. When higher spatial resolution is achieved by increasing N_p (rather than decreasing the FOV), there is also a time penalty. The signal-to-noise ratio improves as the square root of the number of excitations N_ex increases. This is because as the two (or more) spin echoes of identical acquisitions are "averaged" together, the noise adds randomly and increases only as the square root of N_ex increases while the signal adds linearly with n; the net result is thus N_ex divided by the square root of N_ex equals the square root N_ex increase in S/N. Similarly, as N_p increases, the noise in the multiple spin echoes added together sums randomly (as the square root of N_p), while the signal adds linearly, for a similar net result of N_p divided the square root of N_p equals the N_p increase in S/N (ignoring the separate effect of a smaller voxel volume on the signal-to-noise ratio).

As an example, consider the net effect on the S/N per pixel when the spatial resolution is improved by increasing from a 128x128 to a 256x256 matrix with a constant bandwidth, FOV, TR, TE, slice thickness, and number of excitations (N_ex):

If subscript 1 refers to the high resolution 256x256 image and subscript 2 to the 128x128 image, then:

Thus the S/N per pixel of the 256x256 image is 35 per cent of the 128x128 image . (Also, the acquisition time is twice as long since N_p1, = 2N_p2 and TR and N_ex are the same.) If the acquisition time is to be held constant, then the number of excitations must be halved in the high-resolution images. In this case, the S/N ratio per pixel is:

Thus for equal acquisition times, the S/N of the 256x256 image is one-quarter that of the 128x128 image. It should be noted that spatial resolution along the frequency encode (readout) axis can be improved in two ways: either by doubling the strength of the readout gradient and sampling twice as fast (doubling bandwidth, decreasing the S/N) (figure 7) or by leaving the gradient unchanged and by sampling twice as long (bandwidth and the S/N constant), which increase TE and T2-weighting. The above analysis utilizes the latter technique that leaves bandwidth (and thus the S/N) unchanged.

Perception, like many other biologic processes, is logarithmic, as the eye does not respond linearly to stimuli but rather is more sensitive to differences at low levels and less sensitive at higher levels of the signal-to-noise ratio. The perceived image quality is a logarithmic function of the S/N. If there is a high intrinsic S/N (due to higher fields or reduced bandwidth), then reducing the S/N to 25-35 percent of its previous value may be tolerated without a significant perceptual loss in image quality. However, at lower S/N levels, such losses not only result in a "grainy" appearance to a normal image but in loss of contrast-to-noise such that small lesions may be missed.

The detectability of a small, low contrast lesion is also markedly affected by the slice thickness. While thicker slices have a greater signal-to-noise ratio (due to larger voxel volumes), small, low contrast lesions can easily go undetected due to overwhelming partial volume effects.

Although the majority of the MR signal comes from the hydrogen nuclei of water molecules, lipid protons in fatty tissues can also contribute. Fat and water protons do not resonate at exactly the same frequency. Fat protons resonate at a slightly higher frequency, the difference of which is usually described as a fraction of the resonant frequency. Since the difference in frequencies (or the "chemical shift") is very small, it is expressed as "parts per million" or "ppm". Fat protons resonate at 3.5 ppm, a higher frequency than water protons (figure 8). The absolute frequency difference depends on the strength of the main magnetic field (which determines the Larmor frequency). Thus at 0.35 Tesla (15 MHz resonant frequency), a 3.5 ppm chemical shift will result in fat resonating at a frequency of 52.5 Hz (15 MHz x 3.5 ppm) higher than water. At 1.5 Tesla (64 MHz) fat resonates at a frequency of 224 Hz higher than water.

Spatial information in the MR image is encoded in the specific frequencies comprising the spin echo. Such frequency discrimination is provided through the use of gradient fields (figure 1). The minimum strength of the gradient field is determined by the degree of non-uniformity of the main magnetic field, that is, the net variation in field strength from point to point due to the gradient must be greater than that due to the random non-uniformity in the static field. Stronger static fields with comparable uniformity require stronger gradient fields.

If a 0.2 gauss/cm (2 mT/m) gradient is applied across a 25 cm object, there will be a field difference of 5 gauss across the object and a frequency difference of:

5 gauss x [42 MHz/Tesla] x [1 Tesla/10000 gauss] = 21 kHz

from one end of the object to the other, 10.5 kHz on the positive side of midline and 10.5 kHz on the negative side (figure 7). This 10.5 kHz is called the "Nyquist frequency" and it is the highest frequency received. (The bandwidth in this instance is +/– 10.5 kHz.) If the object is divided into 256 pixels, there will be a frequency difference of 82 Hz (21000/256) per pixel. If fat and water are both present in the pixel, they will resonate at frequencies that are separated by 52.5 Hz at 0.35 Tesla and by 224 Hz at 1.5 Tesla. Thus the frequency difference due to the chemical shift between fat and water is comparable to the frequency difference across 2.7 (224/82) pixels at 1.5 Tesla and 0.6 pixels at 0.35 Tesla. Therefore, at high field the fat image will be shifted 2.7 pixels along the readout (frequency encoded) axis relative to the water image. This chemical shift artifact (illustrated in figure 9) is most noticeable at interfaces between tissues containing different amounts of fat and water.

Although the chemical shift artifact may be more noticeable at high field, it is also increased when the strength of the gradient is reduced. As the intrinsic uniformity of lower field magnets has improved, weaker gradients can be used without sacrificing frequency discrimination. Weaker gradients narrow the bandwidth, which reduces the noise, increasing the signal-to-noise ratio but have the disadvantage of increasing the chemical shift artifact.

While chemical shift artifact is a potential problem in most parts of the body, it is generally not in the brain, although fatty marrow can shift over the brain, creating a pseudo-subdural hematoma (figure 10). Fat in the normal brain is not MR-visible, thus there is no chemical shift artifact either at high field or on intermediate field systems using reduced bandwidth techniques. When a chemical shift artifact is present and bothersome, it can be eliminated by increasing the strength of the gradient fields (at a cost in the signal-to-noise ratio).

1. Gradients. Magnetic field gradients are produced by a pair of electromagnetic coils that add to the main magnetic field above the midplane and subtract below the midplane, leading to a continuous variation in magnetic field from top to bottom.
2. Schematic of MRI System. The largest component is a magnet large enough to fit inside an entire body (and still maintain a very uniform magnetic field). The three gradient coils are the next most important hardware component and are rated in strength (milliTesla per meter [mT/m]) and rise time (in microseconds), bigger being better for the former and shorter being better for the latter. Finally there is an RF (radiofrequency) transmitter and receiver and a computer, which coordinates everything.
3. Multislice acquisition. All three gradients are activated to produce a multislice data set. In this example, the x and y gradients allow image formation within a given plane while the z gradient divides the body into multiple (transverse) axial slices.
4. T1 Recovery. During the time between 90⁰ RF pulses, signal recovers according to the T1 of the substances. During a multislice acquisition, T1 recovery can be occurring at one slice position while another slice is being excited at a different frequency.
5. Echo Sampling Time. The analog spin echo signal is sampled (i.e. digitized) for a period time (echo sampling time) by the analog-to-digital converter (ADC). The number of points used to digitize the spin echo is the same as the number of matrix elements along the readout (frequency-encode) direction in the image. The sampling interval (dwell time) is the inverse of the bandwidth, which is the primary determinant of noise in the image.
6. Motion artifact. Motion in any direction (in this case, inflowing CSF coming out of the plane of the image) results in artifacts along the phase encode axis (in this case, horizontal).
7. Bandwidth vs. gradient strength. For a given field-of-view (FOV), the stronger the gradient, the higher the bandwidth. For a given bandwidth, stronger gradients decrease the FOV.
8. Chemical shift artifact. This diagram of a proton (hydrogen) spectrum shows water resonating at a frequency 3.5 ppm above fat. Since all signals are assumed to come from water resonating at a very specific frequency, fat signal gets mismapped relative to water, producing a chemical shift artifact.
9. Chemical shift artifact. This ruptured dermoid cyst contains fat. When it is next to the CSF in the brain, an artifact is caused by the fat signal being shifted. This leads to high signal at one boundary along the frequency-encode axis and low signal along the other boundary.
10. Pseudo-subdural hematoma. A. This image was acquired with a lower bandwidth (4 kHz) than is usually used, leading to overlap of the shifted fat signal from the calvarial marrow and the brain, simulating a subdural hematoma. B. Using a conventional high field bandwidth (16 kHz) the artifact is no longer present.

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Figure 10 A
Figure 10 B