DATA ACQUISITION AND IMAGE RECONSTRUCTION

MRI is based on the nuclear magnetic resonance phenomenon, which arises in atoms with an odd number of protons and/or an odd number of neutrons. Almost all clinical MRI, including angiography applications, is based on the signal from the hydrogen nucleus, ¹H, a single, positively charged proton that is the most abundant in the body (mainly in H₂O but also in fat and other compounds). From a classic physics perspective, each proton has a magnetic dipole moment and behaves like a tiny bar magnet when interacting with a magnetic field. In the absence of an external magnetic field, the axes of the magnetic dipole moments are randomly arranged so that they in aggregate cancel each other out and result in a net magnetization of zero. However, in the presence of an external magnetic field, or B₀, the magnetic dipole moments of the protons will align parallel or antiparallel with the external field. In thermal equilibrium, slightly more spins are aligned parallel than antiparallel with the external magnetic field because it requires less energy. The result is a net magnetization that becomes the signal source in MR experiments. As shown in Figure 81-1A, this vector quantity is aligned with the direction of the main magnetic field. To measure signal from the net magnetization, it has to be “tipped” away from its orientation along the main magnetic field into the transverse plane. Once it is tipped away from the longitudinal axis, the magnetization vector rotates, or precesses, around that axis with a characteristic frequency, as given by the Larmor equation:

FIGURE 81-1 A, In thermal equilibrium, the net magnetization is aligned with the direction of the main magnetic field, B₀. B, With an RF system that generates an RF field tuned to the resonance frequency of the spin ensemble, the net magnetization (M₀) can be tipped into the transverse plane. C, The transverse magnetization, M_xy, precesses at the Larmor frequency, ω₀, thereby creating an oscillating signal that can be measured with a receiver coil.

(1)

where ω₀ is referred to as the Larmor frequency, γ is the gyromagnetic ratio of protons (42.58 MHz/T) and B₀ is the magnetic field flux of the main field. The precessing transversal magnetization M_xy creates a weak radiofrequency (RF) field that can be recorded with a properly tuned coil (e.g., 63.87 MHz at B₀ = 1.5 T) circularly polarized about the axis of precession. As illustrated in Figure 81-1B, the tipping of the net magnetization vector is accomplished with a second RF system that can generate an oscillating magnetic field, B₁, close to the resonance frequency, a concept called RF excitation. In practice, the RF pulse is played out very shortly (in the order of milliseconds) and a remarkably small B₁ field is sufficient for RF excitation (e.g., ~50 mT in comparison to B₀ = 1.5 T).

Once the RF field is turned off, the spin system returns into its thermal equilibrium state. The rate of regrowth for the longitudinal magnetization follows an exponential waveform described by its characteristic time constant, called T1, referred to as the longitudinal relaxation time. The regrowth rate depends on the properties of the nucleus and its interactions with the environment. Meanwhile, the signal decrease in the transversal magnetization component is described by the exponential time constant called T2, the transversal relaxation time, and reflects dephasing caused by interactions between neighboring nuclei; also, it does not depend on the nucleus or chemical compound alone. Additional parameters contribute to the T2 relaxation, so that the T1 and T2 relaxation processes cannot be predicted from one another.

Multiple RF excitations are needed to acquire enough data for a two-dimensional image. The time between successive excitations is controlled by the MRI parameter repetition time (TR). The time between an RF excitation and the recording of the signal is controlled by the MRI parameter echo time (TE). Both of these parameters have an impact on the measured MR signal because they dictate how much time is allowed for the decay of the transversal magnetization (TE) or the regrowth of the longitudinal magnetization (TR). The actual measured MR signal depends on the T1 and T2 relaxation times, proton density, choice of TR and TE, and other imaging parameters, but also on factors such as motion, diffusion, and temperature. In MRA, the goal is to generate high signal differences between blood and surrounding background tissues, which is achieved by incorporating the motion of the blood using noncontrast MRA techniques or T1 shortening of blood by a circulating Gd chelate contrast agent using CE-MRA. Typical relaxation times are T1/T2 = 1200/250 ms for arterial blood and T1/T2 = 1200/220 ms for venous blood at 1.5 T.² Whereas T1 increases with field strength for most tissues (1600 ms for arterial blood), the T2 undergoes a small decrease.

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.

TECHNICAL REQUIREMENTS

The basic components of an MRI system are (1) a magnet that creates a strong static magnetic field, (2) an RF system that excites nuclei with a magnetic moment via RF pulses and detects the electrical signals created by the excited nuclei, and (3) a set of gradient coils that generates secondary static magnetic fields in a controlled fashion to superimpose linear field gradients onto the main field for spatial encoding.

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.