Image Encoding

To create an image, the spatial distribution of the protons has to be resolved. Spatial encoding is achieved with the use of spatially and temporally varying magnetic fields. In the first step, the signal-generating volume is reduced to a slice (two-dimensional imaging) or volume (three-dimensional imaging) by selective excitation. A linear magnetic field gradient is superimposed onto the main magnetic field in the slice (or volume) direction simultaneously with the RF excitation. Consequently, the resonance frequency of the spin system is linearly varying as well. The RF system generates a pulse that excites not only a single precession frequency but all the frequencies contained in the desired slice or volume. Spins located outside the desired volume are not excited because their precession frequency is higher or lower than the frequency band covered by the RF excitation. Theoretically, this concept could be repeated in orthogonal directions ultimately to excite only a single point in the object, and then repeat the measurement until all points in the image are sampled. However, a much more efficient approach is Fourier encoding, whereby each sampled signal contains contributions from all spins in the object, therefore dramatically increasing the SNR of the acquisition. Figure 81-2 shows a basic example for a Fourier-encoded two-dimensional acquisition in the form of a pulse sequence diagram that illustrates the timing for RF excitation, the gradients, and data acquisition.

FIGURE 81-2 Basic gradient echo pulse sequence for two-dimensional Fourier transform k-space scanning. An RF pulse and slice-encoding gradient, followed by a refocusing gradient, are played out simultaneously to excite spins in a slice. Frequency encoding is achieved with a linear gradient applied during data acquisition, resulting in the sampling of k-space along the frequency encoding direction k_x. A prewinding gradient is required to start the acquisition with negative spatial frequencies. The measurement is repeated with stepwise changing phase-encoding gradients for sampling along the frequency-encoding direction with different offsets in the phase-encoding direction k_y. The signed area under the gradients steers the sampling path, here shown for two phase-encoding settings (orange and blue) and their characteristic time points A, B, C, and D.

A second linear field gradient, called the frequency-encoding gradient, is applied during data sampling so that the precession frequency of the net magnetization varies linearly. Thus, the detected signal becomes a summation of all encoded frequencies and its spatial distribution can be derived by a one-dimensional Fourier transform. This encoding scheme makes MRI a spectroscopic imaging method. Unfortunately, the second spatial dimension cannot be encoded simultaneously during readout because this would result in a nonunique allocation of frequency and spatial location. Instead, the gradients are applied sequentially, with the drawback of extended imaging times.

The third gradient, called the phase-encoding gradient, is switched on and off prior to the frequency-encoding gradient. This leads to a linearly varying phase of the net magnetization vectors along the direction of that gradient, providing encoding for a single spatial frequency. In other words, with properly controlled gradients, the time-dependent MR signal actually samples the spatial frequencies of the object in two dimensions. Figure 81-2 shows how the sampling trajectory in the spatial frequency space, also called k-space, is controlled by the area under the gradient waveforms.

If that experiment is repeated several times with varying phase-encoding gradients, then multiple spatial frequencies are sampled in the phase-encoding direction as well and an image can be reconstructed via inverse two-dimensional Fourier transform. Figure 81-3 shows an example of a sagittal head scan. The received signal is digitized by an analog to digital converter and a discrete inverse two-dimensional Fourier transform generates the corresponding image, which contains magnitude (length of the transversal magnetization) and phase information (position in the transverse plain in respect to the coil axis) for each voxel. Most MRI relies on the magnitude image only. However, in some applications, such as phase contrast MRA, the phase information plays an essential role in generating image contrast.

FIGURE 81-3 Two-dimensional (2D) Fourier transform pair. The acquired complex k-space data are reconstructed into image space via a 2D Fourier transform. The resulting signal has a magnitude and a phase component, representing the transversal magnetization M_xy and its position φ in a unit circle in respect to a receiver axis. The highest signal can be obtained with a flip angle of α = 90 degrees, which tips the magnetization vector completely into the transversal plane. Note that the k-space magnitude is shown on a logarithmic scale.

Suppose an acquisition matrix contained 256 data points in the frequency and 256 data points in the phase-encoding direction. The reconstructed image is also described by a 256 × 256 matrix. For a two-dimensional acquisition, the total scan time is given by the number of phase-encoding steps multiplied by the repetition time (i.e., TR). Volumetric imaging can be accomplished by successive imaging of two-dimensional slices (i.e., two-dimensional MRA), or by excitation of an entire imaging volume (i.e., three-dimensional MRA) and the use of phase encoding in the third dimension for a true three-dimensional data acquisition. Either option prolongs the total scan time proportional to the number of slices (two-dimensional) or partitions (three-dimensional) in the volume.

Figure 81-4 provides some insight about the signal distribution in k-space. For this image, most of the signal energy is located around the origin of k-space. This area defines the weighting for the low spatial frequencies, which define the coarse outline of the imaged object yet lacks information on edges. The broad pattern of the phantom can be identified even with less than 0.5% of the k-space samples from the full-resolution image. However, all the detail is lost, which is defined in the unsampled higher spatial frequencies. The difference in images between the low-resolution images and the fully sampled image reveals the errors caused by limiting the acquisition to lower spatial frequencies only.

FIGURE 81-4 A high-resolution phantom scan reconstructed from different k-space subregions. The upper row is reconstructed when the central 512 × 512 (full resolution), 128 × 128, 64 × 64, and 32 × 32 samples are used for the reconstruction. This is equivalent to using 100%, 6.25%, 1.6%, or 0.4% of all sampled data. The lower row represents reconstruction results when the remaining peripheral k-space data are used for the image reconstruction instead. Whereas the central k-space samples define the low spatial frequencies and most of the image contrast, the peripheral k-space data define the higher spatial frequencies and, therefore, fine structures and edges.

The basic signal-to-noise ratio (SNR) in MR acquisitions is given by

(2)

where T_acq represents the data acquisition time.³ Based on this relationship, one notes that the desirable properties for MRA, such as small voxel size for higher spatial resolution imaging and short acquisition times for fast scans, are detrimental to the obtainable SNR. Frequently, compromises in scan parameter choices are necessary for optimization of MRA for imaging individual vascular territories, with each offering unique challenges for proper visualization by MRA.

Magnetic Resonance Scanner

Each MR scanner is designed to provide a magnetic field, B₀, that is homogeneous over the imaging volume, stable over time, and against the influence of external sources. The magnetic induction of the field, also frequently referred to as the magnetic field strength, is measured in tesla (T) or gauss (G), where 1 T = 10⁴ G. The most common modern MR scanners used in clinical practice are whole-body scanners that rely on a superconducting magnet with a field strength of 1.5 or 3 T. For comparison, the field strength of a 1.5-T MR scanner is about 30,000 times stronger than the earth’s magnetic field (~0.5 G). Superconducting MR scanners contain several coils that run in series to form a solenoid and create a cylindrically symmetrical magnetic field, with the main magnetic field aligned with the z-axis of the cylindrical housing (Fig. 81-5). They operate near absolute zero temperature (~4 K, or −270° C) to effectively eliminate electrical resistance in the coil wires, allowing large currents that generate high magnetic fields. Other MR scanner designs include resistive magnetic fields (without superconductivity) that operate at lower magnetic field strengths (<0.15 T), permanent magnetic fields that have intermediate field strength (<0.7 T), smaller bore diameter MR scanners for extremity imaging, and open bore designs (usually <0.7 T) to improve patient comfort and reduce claustrophobia. Imaging at lower field strengths reduces some of the problems encountered at higher fields, such as reduced RF penetration and increased energy absorption. However, MRA applications greatly benefit from imaging at higher field strength because the SNR increases linearly with field strength. MR scanners with field strengths of 3 T are becoming more prevalent in clinical settings and favorable results have been reported with these systems⁴; more recently, higher field 7-T research MR systems are being investigated.⁵

FIGURE 81-5 A 1.5-T MR system with a superconducting magnet, gradient coils, and a body transmit-receive RF system enclosed in the housing. The patient table, connectors for external transmit-receive or receive-only coils, and physiologic monitoring equipment are also shown. The main magnetic field is aligned with the table axis, called the z-axis by convention.

Gradient System

The magnetic field gradient system typically consists of three orthogonal gradient coils embedded within the housing of the scanner. Gradient coils are designed to produce a spatially varying magnetic field that can be temporally altered. Although these additional magnetic fields are dramatically smaller than the main magnetic field, they are an essential component for spatial encoding of the signal distribution in the imaging volume of interest. Gradients are rated by their maximum gradient strength (the higher the better) and the time needed to rise to the maximum gradient strength (slew rate—the faster the better). The gradient waveforms in Figure 81-2 are idealized in that they can be switched on and off instantaneously.

Gradient systems have undergone dramatic improvements over the last decade and modern equipment can provide maximum gradient strengths of about 50 mT/m and slew rates of 200 T/m/s. MRA applications greatly benefit from high-performance gradients because they enable faster imaging for higher temporal sampling of data, which can be used to improve spatial or temporal resolution. Faster imaging speeds are particularly helpful to assess the dynamic progression of a contrast bolus using multiphase or time-resolved MRA, or to ensure sufficient spatial resolution during a single breath-hold MRA acquisition. The minimization of imaging parameters such as the echo time, TE, or the repetition time, TR, are facilitated by the availability of high-performance gradients and provide additional benefits for image quality (see later).

Radiofrequency System

The RF system serves the purpose of converting pulsed oscillating currents from a power amplifier into an oscillating magnetic field, also referred to as the B₁ field, for the excitation of the nuclear spin system. This is accomplished by a transmitter coil tuned to the resonance frequency of the spin system under investigation. Such coils are designed to provide a uniform B₁ field over the imaging volume to ensure uniform spin excitation. So-called birdcage coils are well suited for this purpose and exist as whole-body coils built into the scanner housing and as specialty coils, such as for head or knee imaging (Fig. 81-6).

FIGURE 81-6 RF coils used for MR scanning. Bird cage coils for head (A) and knee (B) imaging are single-coil transmit and receive coils with a very homogeneous B₁ field. Single-channel surface coils such as the shoulder coil (C) or general purpose flex coil (D) are designed to have a high local sensitivity. Multielement coil arrays can combine the benefits of local sensitivity and larger coverage, here shown for an eight-channel neurovascular coil (E), eight-channel body phased-array coil (F), four-channel lower extremity coil (G), and eight-channel lower leg coil (H).

A receiver coil is used to detect the RF field created by the precessing magnetization of the nuclear spins after their excitation. The same coil may be used for transmitting and receiving the RF signals, which are referred to as transmit-receive coils (see Fig. 81-6A and B). However, in many applications, it is advantageous to use special local coils that are sensitive only to the signal from the region close to the coil. Such local coils can have a significantly better SNR, as described by equation 2, especially compared with the whole-body transmit-receive coil that encounters noise contributions from the whole volume within it that is much larger than that of smaller local coils. Figure 81-6 shows examples of such local coils, including a shoulder coil (C) and a multipurpose flex coil (D).

Coil arrays consist of multiple local receiver coils to provide a larger coverage with the SNR advantage of local coils. These multielement RF coils have become very common and are available for many applications in many body regions (Fig. 81-6E-H). Figure 81-7 demonstrates the local coil sensitivities of an eight-channel head coil in a three-dimensional TOF MRA and the cumulative image obtained from combining all channels. Data from multiple coils cannot be combined during acquisition and must be stored individually. Therefore, the acquired data size increases linearly with the number of coils, and image reconstruction must be completed for each channel before they can be combined. However, current reconstruction engines are prepared to handle the additional workload for 8 to 16 channels without significant delays.

FIGURE 81-7 TOF angiography data set acquired with an eight-channel head coil. Shown are images reconstructed for each individual coil with increased local sensitivity (small images) and after combining all images as the square root of the sum of the squares from all individual coil images.

(Courtesy of Dr. Alexej Samsonov, University of Wisconsin-Madison, Madison, Wis.)

Parallel Imaging

More recently, scan time reduction methods were developed that explore the redundancy in the information contained in multiple receiver coils with partly overlapping sensitivity regions. SMASH (simultaneous acquisition of spatial harmonics),⁶ SENSE (sensitivity encoding),⁷ and GRAPPA⁸ are acquisition and reconstruction methods from this group referred to as parallel imaging, which have found rapid commercial adaptation for cardiovascular imaging, especially CE-MRA. With this approach, the equivalent of multiple-phase encoding steps is acquired during a single readout. Although the advantage of accelerated imaging comes at the expense of a reduction in SNR, it can be highly beneficial in situations in which there is sufficient SNR and rapid image acquisition is desired. Basically, all CE-MRA applications fall into this category because faster imaging can improve the frame rate for dynamic acquisitions or reduce breath-hold lengths or other artifacts related to patient motion. As shown in Figure 81-8, attention has to be paid to potential local noise amplifications from the reconstruction process, frequently described as g-factor maps, when using high acceleration factors.

FIGURE 81-8 MRA data reconstructed with a SENSE (1) based parallel imaging reconstruction using all the data from a fully sampled acquisition. The enlargements (bottom row) demonstrate good image quality for R = 2 but a decreased SNR and local noise enhancements for R = 3, which renders the images nondiagnostic, for a reduction of R = 4 with dramatic noise enhancements that obscure vessel anatomy. 100% reduction factor R = 1; 50% (R = 2); 33% (R = 3); 25% (R = 4).

(Courtesy of Dr. Alexej Samsonov, University of Wisconsin-Madison, Madison, Wis.)

The scan time reduction factor that can be obtained with parallel imaging depends on the number of independent coil elements and their arrangement. Therefore, further increases in the number of coil elements and receiver channels promise even greater reductions in scan time. Consequently, the recent progress in parallel imaging has led to renewed interest in coil design and receiver systems. New MRI platforms provide the ability to connect many coil elements and acquire the signal from as many as 16 to 32 receivers simultaneously and systems with even more channels are being explored. With higher receiver coil counts, the SNR and coverage can be further improved or higher acceleration factors can possibly be obtained. Current design problems, such as with the decoupling of individual coil elements, has limited commercial coil designs to 8 to 32 elements. In research settings, systems with up to 128 receiver channels have been recently evaluated and demonstrated regional SNR benefits and high acceleration factors for cardiovascular applications as compared with lower count coil arrays.⁹ However, the lack of penetration for small coils might limit additional benefits for regions of interest that are more distant from the body surface. It remains to be seen at which point additional coil elements are still beneficial, especially when the noise in the MR system becomes dominated by electrical noise from the receiver system, instead of intrinsic noise contributions caused by random motion of electrons in the patient’s tissue.

Patient Monitoring

Patient monitoring systems are crucial components for vascular imaging because several approaches require synchronization with the cardiac cycle or feedback on the respiratory motion for optimized image quality. To accommodate these needs, most MR systems are equipped with a pulse oximeter probe, an electrocardiogram (ECG) gating system, and stress transducer systems worn as a belt around the abdomen to track abdominal distention during respiration.

The most precise synchronization with the cardiac cycle is obtained with R wave detection from an ECG signal. It requires the placement of three or four MR-compatible electrodes on the subject’s chest and the connection to an amplifier system. ECG readings from within the MR scanner are often suboptimal for proper diagnostic ECG interpretation because of magnetohydrodynamic effects, which most notably manifest themselves as enlarged T waves. These enlarged T waves can cause problems in gated acquisitions when they are mistaken as the trigger point from the R wave. Vector gating systems that process multiple leads simultaneously, as well as careful electrode placement, can minimize erroneous ECG gating results. Another source for suboptimal gating results can be unwanted signal perturbations into the ECG leads from gradient switching and RF transmission. Heavy shielding or shortening of the ECG cables can minimize these effects. Use of fiberoptic ECG cables for extended connections can also reduce these concerns. An alternative to ECG gating is to use optically based arterial blood oxygen saturation monitors (Sao₂) in the form of finger probes or reflectance probes for cardiac imaging synchronization. The setup for these measurements is simple but the signal has a less distinct peak within the cardiac cycle for gating, making it less desirable for acquisitions that need precise synchronization.

Stress transducer systems provide a similarly simple approach for the tracking of the respiratory cycle. However, they can lack precision because they track the abdominal circumference instead of the targeted image area, can undergo baseline drifts, and can pose difficulties in shallow breathers. A more precise but also more complex approach is the use of navigator echoes that track the position of the lung-liver interface (i.e., hemidiaphragm) and determine the respiratory cycle of the patient, typically during tidal respiration.

Power Injector

For CE-MRA, a Gd-based contrast agent is injected intravenously, usually into an antecubital vein. The injection of the contrast agent is followed by the injection of sterile saline to flush the contrast material out of the delivery system and ensure that the contrast bolus is sufficiently central within the body. Although manual injections are possible, the use of a computer-controlled, MR-compatible power injector is usually preferred. The power injector is more precise in delivering reproducible injection rates and its use omits the need for an operator in the scan room during imaging. Power injectors also provide features to assist in dynamic timed studies and breath-hold maneuvers and allow for multiphase injections. A typical system consists of a delivery component in the scan room and a user console in the operator room (Fig. 81-9). Manual injections have the advantage that the physician is right next to the patient and can better monitor the administration of contrast agent and the status of the patient.

FIGURE 81-9 MR-compatible power injector during patient preparation. A computer-controlled delivery system injects the contrast agent and the saline flush into the antecubital vein through a common line.

Contrast-Enhanced Magnetic Resonance Angiography