Introductory MRI Physics

Transcription

1 C HAPR 18 Introductory MRI Physics Aaron Sodickson EXRNAL MAGNETIC FIELD, PROTONS AND EQUILIBRIUM MAGNETIZATION Much of the bulk of the magnetic resonance imaging (MRI) scanner apparatus is dedicated to producing an extremely strong magnetic field, denoted as B 0. Common present day whole-body clinical systems operate at field strengths of 1.5 Tesla ( times the strength of the earth s magnetic field), although both lower and higher field strength systems are in use. The great majority of clinical MRI applications image protons, present in vast numbers throughout the body in all molecules containing hydrogen nuclei. These protons have a physical characteristic, the nuclear spin, which imparts magnetic properties to the nucleus and which is vital to MR image formation. When placed into the strong B 0 magnetic field, a small excess of the nuclear spins align along rather than opposed to the field direction and their microscopic magnetizations sum into a net equilibrium magnetization vector denoted M 0 (Figure 18.1). The strength of M 0 (and subsequently the maximum available signal strength) scales with the size of B 0, providing the primary motivation for the development and use of higher B 0 field strength systems. LARMOR PRECESSION AND MRI SIGNAL Once M 0 is perturbed away from its equilibrium z-axis, it behaves as a classical bar magnet and precesses about B 0 at a characteristic frequency, the Larmor frequency ω 0 γb 0. This precession frequency scales with the strength of the external magnetic field B 0, with a proportionality constant, the gyromagnetic ratio γ, that is an intrinsic property of the nucleus being interrogated and is the same for all protons throughout the body. At typical clinical MRI field strengths, the proton Larmor frequency is in the megahertz (MHz) or radiofrequency range. When surrounded by a loop of wire, the coil, the timevarying magnetic field created by the precessing magnetization vector induces a current, the signal, which forms the basis for image formation in MRI (Figure 18.2). B 0 Z M 0 B 0 ω 0 M L M ω 0 Y M T X FIG The direction of the external static magnetic field B 0 defines the z-axis, or longitudinal axis of the MRI apparatus. The perpendicular x-y plane is often denoted the transverse plane. A vector sum of the microscopic nuclear spin magnetizations yields the net equilibrium magnetization vector M 0 oriented along the z-axis. FIG Precessing magnetization vector M, separated into its longitudinal component M L which remains fixed along the z-axis and its transverse component M T which precesses about the z-axis in the x-y plane. The time varying magnetic field produced by the precessing magnetization induces an oscillating current in the coil surrounding the magnetization vector. 128

2 RELAXATION 129 RADIOFREQUENCY ENERGY AND RESONANCE In order to precess and induce a signal, M 0 must first be tilted away from its equilibrium longitudinal z-axis orientation and into the transverse x-y plane. In fact, the magnetization vector may best be thought of in terms of its longitudinal component M L which remains fixed along the z-axis and its transverse component M T which precesses about B 0 in the x-y plane (see Figure 18.2). MRI relies on the use of radiofrequency or RF magnetic fields, denoted B 1, to convert longitudinal magnetization into transverse magnetization, or equivalently, to tilt the magnetization vector into the transverse plane. The weak B 1 magnetic fields are aligned in the transverse plane, perpendicular to the z-axis. By its nature, M 0 will precess about any externally applied magnetic field, so this B 1 field will tilt the magnetization away from its equilibrium z-axis. However, the strength of the applied B 1 field is so tiny in comparison to B 0 that if its direction remained fixed, it would have a negligible net effect due to the rapid precession of the magnetization vector about the z-axis. MRI works in this setting by rotating the axis of the B 1 field about the z-axis exactly in concert with the precessing magnetization vector. When the direction of the applied B 1 field is altered in step with the Larmor precession of M 0, the effect of the weak B 1 field can accumulate over time and cause a net tilting of M 0 towards the transverse plane (Figure 18.3). This precise matching of the two frequencies is the resonance criterion from which MRI borrows its name and it sets the B 1 frequency in the megahertz radiofrequency range. Resonant radiofrequency energy is typically applied as RF-pulses, whose combination of amplitude and duration produces a predictable net tilting of the magnetization vector away from the z-axis by a prescribed angle. A 90º pulse takes M 0 from the z-axis fully into the transverse plane, while a 180º pulse produces an excursion from z to the z axis (Figure 18.3). A B C 180 FIG (A) In the presence of the RF field, the magnetization vector spirals down from the z-axis into the transverse plane. (B) Net effect of a 90º RF-pulse. (C) Net effect of a 180º RF-pulse. 90 RELAXATION T1 and T2 Relaxation After the net magnetization vector has been perturbed away from equilibrium, it will eventually return to its equilibrium state, with restoration of M 0 along the z-axis. This occurs through simultaneous recovery of the longitudinal magnetization component M L along the z-axis via T1 relaxation, and disappearance of the transverse magnetization component M T via T2 relaxation. The two relaxation rates, denoted T1 and T2, are intrinsic features of the underlying tissue (related to tissue structure and microscopic proton motion) and vary with tissue type. Figure 18.4 demonstrates the relaxation curves of the longitudinal and transverse magnetization components following a 90º RF pulse. The 90º pulse converts all of the longitudinal magnetization into transverse magnetization, leaving no residual M L, and a maximal value of M T. M L then re-grows from zero to its equilibrium value M 0 along z, recovering most rapidly for fat and most slowly for CSF. M T decays away to zero at the T2 relaxation rate, with loss of M T (and thus signal strength) occurring most rapidly for fat and most slowly for CSF. T2* Relaxation Signal strength actually decays at the T2 relaxation rate only in an idealized situation in which all spins experience exactly the same external magnetic field. In reality, any source of inhomogeneity in this field causes nearby spins to precess at different frequencies and to dephase more rapidly, resulting in more rapid signal loss with a shortened relaxation time, T2*. Common sources of these inhomogeneities A M 0 M L FAT T1 relaxation WM Time GM CSF B M T FAT T2 relaxation Time CSF GM WM FIG (A) T1-relaxation curves describing recovery of longitudinal magnetization towards equilibrium following a 90º RF pulse. (B) T2-relaxation curves describing the decay of transverse magnetization towards zero following a 90º RF pulse. In sequence from shortest to longest relaxation times (fastest to slowest relaxation rates): fat, white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). As T1 relaxation represents recovery of longitudinal magnetization towards M 0, while T2 relaxation represents decay of transverse magnetization towards zero, the directions of the curves are reversed from (A) to (B).

3 130 CHAPR 18 INODUCTORY MRI PHYSICS include the inability to engineer an absolutely uniform magnetic field and susceptibility effects in which differences in the magnetic properties of nearby materials (air, metal, blood products) distort the magnetic field. IMAGE CONAST MECHANISMS Basic Pulse Sequence and Imaging Parameters and Figure 18.5 outlines a simplified pulse sequence diagram and defines two key variables, and, that may be adjusted to alter image contrast. The echo time,, may be thought of as the delay after the RF pulse during which the signal is gathered. The repetition time,, denotes the time interval between subsequent excitations by RF pulses. The process of creating an image requires numerous repetitions of this basic building block (see below). During each, longitudinal magnetization is allowed to grow back along z, to a degree depending on the tissue s T1 relaxation rate. Adjusting in this pulse sequence thus controls the extent of T1-weighted contrast introduced into the image (see below). Immediately following the subsequent RF pulse, each tissue has its maximal amount of transverse magnetization. This transverse magnetization then decays towards zero during, to a degree depending on the tissue s T2 relaxation rate. Adjusting the length of the delay before collecting the induced signal thus controls the extent of T2- weighted contrast introduced into the image (see below). A Proton-Density, T1-Weighted and T2-Weighted Images The proton density refers to the number of hydrogen nuclei per unit volume. A region with a greater number of spins will contribute more magnetization and thus more signal than an equivalent region containing fewer spins. Proton density images are designed to show purely this underlying density variation. T1- and T2-weighted images then superimpose additional image contrast based on the differing relaxation times of the tissues, to degrees depending on the and values chosen for the scan. It must be emphasized that T1 and T2 are fixed parameters reflecting physical characteristics of the tissue, while and are imaging variables that are adjusted at the MR scanner to accentuate image contrast between tissues. The magnitude of the signal collected for a given tissue type is determined by multiplying the underlying proton density distribution by the values of the T1 and T2 relaxation curves of Figure 18.5 for each particular tissue at the chosen and times. The appropriate choices of and values are contained in Table 18.1 and discussed below. Proton-Density Images Proton density images rely on a very long value to eliminate T1-weighted contrast and a very short value to eliminate T2-weighted contrast. The long allows recovery of full equilibrium magnetization for all tissues. The next RF pulse transfers these magnetizations to the transverse plane, where they precess and induce the signal that is recorded immediately (at a very short ) before significant T2 relaxation can take place. The resulting image then reflects the spatial distribution of proton density across the patient, without additional T1- or T2-weighted contrast. B M 0 M L T1W C M T T2W T1-Weighted Images T1-weighted images rely on relatively short values of to introduce T1-weighted contrast and very short values to eliminate T2-weighting. The short value of establishes differences in longitudinal magnetization values for different tissue types (see Figure 18.5B). Following the subsequent RF pulse to transfer this magnetization to the transverse plane, the induced signal is collected rapidly FIG (A) Schematic pulse sequence diagram. (B) T1 relaxation occurs during each repetition time () between subsequent 90º RF pulses. Choice of thus determines the extent of T1 weighting in the image. (C) T2 relaxation occurs during each echo time (), which defines the timing of signal collection after each RF pulse. Choice of thus determines the amount of T2 weighting in the image. and ranges to produce T1-weighted and T2-weighted images are bracketed in (B) and (C). T ABLE 18-1 Appropriate choices of and to create T1-weighted, T2-weighted and proton density images Proton density T1-weighted T2-weighted As long as Relatively As long as possible short possible As short as As short as Relatively possible possible long

4 IMAGE CONAST MECHANISMS 131 (at short ) to minimize T2-weighting. This combination produces a T1-weighted image while eliminating the confounding effects of T2-weighting. T2-Weighted Images T2-weighted images rely on a very long value to eliminate T1-weighting and a relatively long value to introduce T2-weighted contrast by creating differences in transverse magnetization between different tissue types. The long allows recovery of full equilibrium magnetization for all tissues. Following the subsequent RF pulse to transfer this magnetization to the transverse plane, signal is not collected until enough time has passed to highlight differences in transverse magnetization based on T2-relaxation differences (see Figure 18.5C). This combination produces a T2-weighted image while eliminating the confounding effects of T1-weighting. Figure 18.6 shows examples of the different image types, achieved by appropriate adjustment of and. Inversion Recovery Inversion recovery sequences add an additional 180º RF pulse to the basic pulse sequence building block of Figure Following this pulse, there is a delay time τ before the subsequent 90º pulse and signal collection at (Figure 18.7). and are chosen to produce T2-weighted images, but the additional τ imaging variable provides a mechanism to use T1 relaxation differences to uniformly suppress signal from a tissue of interest (water in FLAIR images and fat in STIR images). FLAIR In FLAIR (fluid attenuated inversion recovery) images, τ is chosen to correspond to the zero-crossing point in the T1 relaxation curve of water. The 90º RF pulse is applied at just the moment that the longitudinal magnetization of cerebrospinal fluid crosses through zero, so that there is no formation of transverse magnetization to produce signal from the CSF. Other tissue types with faster T1 relaxation A B C D E FIG Different types of image contrast in a patient with melanoma metastases. (A) Proton density, (B) T2-weighted, (C) FLAIR, (D) T1-weighted and (E) T1-weighted following intravenous gadolinium administration. Note the slightly lower signal intensity of white matter relative to gray matter on the T2-weighted and FLAIR images, as opposed to its slightly higher relative intensity on the T1-weighted image. In (E), the metastases enhance due to the T1-shortening effect of gadolinium in regions where it enters tissues across a disrupted blood brain barrier. The shorter T1 time leads to greater recovery of longitudinal magnetization during each and produces greater signal after the subsequent RF pulse. In (C) the FLAIR image eliminates the signal from CSF, while continuing to demonstrate the vasogenic edema surrounding the metastases.

5 132 CHAPR 18 INODUCTORY MRI PHYSICS B ω τ 90 B 0 ω 0 x x M 0 M L have recovered significant portions of their equilibrium magnetization, so the 90º pulse does produce transverse magnetization and MR signal for these tissues. Figure 18.6C provides a sample image. STIR τ STIR FAT CSF τ FLAIR In STIR (short tau inversion recovery) images, τ is chosen to match the zero-crossing point in the T1 relaxation curve of fat. As a result, STIR provides a robust method of uniform fat suppression and is particularly helpful in accentuating soft tissue edema within fat-containing tissues such as bone marrow. MAKING AN IMAGE Spatial Localization by Magnetic Field Gradients τ FIG Immediately following the 180º inversion pulse, all of the equilibrium magnetization has been flipped to the z axis. The longitudinal magnetization recovers from z to z at the characteristic T1 relaxation rates of the different tissues. Appropriate selection of τ eliminates subsequent signal production from water in FLAIR images and from fat in STIR images. Spatial localization in MR images is primarily achieved through magnetic field gradients. These gradients, G, are spatially varying magnetic fields whose strength increases linearly with position along a given direction and are applied in addition to the uniform B 0 field that is present at baseline. For example, when an x-axis gradient G x is applied, the total magnetic field strength is slightly weaker on one side of the imaging volume ( x locations) and stronger on the other ( x locations) (Figure 18.8). Because the Larmor precession frequency is directly proportional to magnetic field strength, the result is that signal from one FIG In the presence of the magnetic field gradient, magnetic field strength B varies linearly with position. As a result, corresponding precession frequencies vary linearly with position. side of the patient oscillates at slightly slower frequencies than signal from the other side of the patient. All of these signal components are simultaneously detected in the surrounding coil, but may be separated into the individual frequency components through use of the Fourier transform. The amount of signal oscillating at a given frequency corresponds to the amount of magnetization precessing at the corresponding magnetic field strength, which determines the spatial location of that magnetization along the gradient direction. In this way, magnetic field gradients create a mapping of frequency to position, a property which is crucial to MR image formation. k-space The concept of frequency-to-position mapping produced by magnetic field gradients is most intuitive in a single dimension, but is more challenging to conceptualize in multidimensional images. The k-space formalism is a convenient way to describe gradient encoding along one or more dimensions. Magnetic Field Gradients, Spatial Frequencies and k-space As magnetic field gradients establish different precession frequencies across the imaging volume, evolution in a gradient over a specified time creates a spatial distribution of magnetization that varies along the gradient direction. Greater amounts of evolution in the gradient produce progressively tighter spatial oscillations across the patient, or oscillations of progressively higher spatial frequency (Figure 18.9A). The basic tenet of Fourier transform mathematics is that any given shape may be defined as an appropriate combination of spatially oscillating distributions. k-space tabulates the contributions of these spatial frequency components. It is the mathematical domain in which MRI signal is collected and is in fact related to the actual image by means of Fourier transformation. Each data point of collected signal occupies a particular location in k-space and contains information about

6 MAKING AN IMAGE 133 A B C D k 0 ±1 ±2 ±3 G freq G phase k phase FIG (A) Creation of spatial distributions via gradient evolution. Relative to the center position, rightward magnetizations precess at increasing clockwise rates, leftward magnetization at increasing counterclockwise rates. The top row is a uniform distribution of magnetization prior to gradient evolution, lower rows show the spatial distribution after progressive steps of gradient evolution. (B) Corresponding spatial distributions and k-space values. (C) and (D) Equivalent gradient evolution steps: (C) frequency encoding approach, with fixed gradient strength and increasing evolution time intervals; (D) phase encoding approach, with fixed evolution times, but increasing gradient strengths. the corresponding spatial frequency of magnetization distributed across the imaging volume. The k 0 data point represents magnetization uniformly distributed across the imaging volume. The k 1 data points describe distributions of magnetization with a single cycle of oscillation from one end of the imaging volume to the other, k 2 with two cycles of oscillation, and so on (Figure 18.9B). A complete set of these data points specifies the amount of each spatial frequency component and uniquely determines the true spatial map of magnetization. This k-space map of spatial-frequencies is converted via the Fourier transform to the spatial domain to produce the image. Each spatial frequency component is interrogated by creating the appropriate spatial oscillation via increasing intervals or steps of gradient evolution. In practice, this may be done by allowing evolution for longer time intervals under a gradient of fixed strength the frequency encoding approach (Figure 18.9C), or by producing evolution for a fixed time interval under gradients of increasing strength the phase encoding approach (Figure 18.9D). The signal produced by each gradient evolution step reflects the size of the corresponding spatial frequency component and fills the corresponding k-space position. Frequency Encoding During the signal collection phase of the pulse sequence, a frequency-encoding gradient or readout gradient is applied. This gradient maps precession frequency to spatial position. Fourier transformation decomposes the collected signal into its component frequencies, whose magnitudes correspond to the amount of magnetization at each position, and yield a one-dimensional image. In the k-space description, gradient evolution steps are defined by successive time intervals under a readout gradient of fixed strength. Each associated signal data point fills the corresponding k-space position (Figure 18.10). All of the data points needed to fill the complete line of k-space may be acquired after a single RF pulse and Fourier transformation yields a one-dimensional image. Phase Encoding Phase encoding is used to encode spatial information in the second dimension and uses a gradient along an axis perpendicular to the frequency encoding direction. Unlike frequency encoding, phase-encoding steps are achieved via stepwise changes in the strength of the phase-encoding gradient, with the evolution interval remaining fixed (see Figure 18.10). Phase encoding is otherwise entirely analogous to frequency encoding, as each encoding step provides information about a different spatial frequency component and fills the corresponding position in k-space. Each phase encoding evolution step must be performed after a new RF pulse, which requires numerous repetitions of the pulse sequence building block in order to collect all of the required signal data. Data collected after a full set of frequency and phase encoding steps then fills a full plane of k-space, which may be Fourier transformed into a two-dimensional image. Slice Selection k freq FIG Spatial encoding technique combining frequency and phase encoding. Signal collected during each frequency encoding gradient fills a horizontal line in k-space (straight arrows). Each phase encoding gradient step toggles to the next vertical k-space position (curved arrows). After a complete set of phase encode steps, a full plane of k-space data is filled, allowing 2D image reconstruction. In order to spatially encode the third dimension, a slice selection step is often employed, in which the RF pulses are applied in the presence of a slice-selection magnetic field gradient. The RF pulses contain an adjustable range of frequencies. As discussed in the section on radiofrequency

7 134 CHAPR 18 INODUCTORY MRI PHYSICS energy and resonance, the RF excitation frequency must match the spin precession frequency in order to tilt magnetization into the transverse plane. As a result, each RF pulse only excites spins with a matching range of precession frequencies, which corresponds to a predictable range of locations along the gradient direction (Figure 18.11). Expanded Pulse Sequence Diagram and 2D Versus 3D Imaging Techniques Figure contains a simplified schematic pulse sequence diagram for two-dimensional imaging, in which slice selection, phase encoding and frequency encoding extract spatial information along each of the three perpendicular axes. For each slice selection step, in-plane spatial encoding is performed with a combination of phase RF frequencies Gradient Frequency Slice Position FIG Slice selection. The position of the slice is determined by the center frequency of the RF pulse and the slope of the magnetic field gradient, while the slice thickness is determined by the range of frequencies in the RF pulse and by the slope of the gradient. G freq G phase G slice FIG Schematic two-dimensional imaging pulse sequence diagram (several practical details omitted). The slice-selection gradient is applied during the RF pulses. The phase encoding gradients step in amplitude during successive repetitions. The frequency encoding gradients are applied during signal readout. and frequency encoding. Each slice requires a full set of phase encoding steps, each of which in turn requires its own. It is primarily this need to repeat numerous excitations with different slice-selection and phase-encoding steps that accounts for the lengthy scan times of MRI (although in reality data acquisition from different slices may be interleaved to save some time). Rather than performing slice selection as above, threedimensional imaging techniques instead add an additional nested phase-encoding cycle to spatially encode the third dimension, again requiring repetition through multiple excitations. Echoes In actual practice, it is generally necessary to acquire signal data from both positive and negative sides of k-space. In order to do this, data are collected during symmetric echoes, with the center point of the echo corresponding to k 0. There are two general techniques to do this, called, respectively, spin echo and gradient echo. Spin Echoes Spin echoes are formed by placing a 180º pulse in the center of the time (left out of the pulse sequence diagrams for simplicity). This additional 180º pulse has the effect of refocusing any dephasing of transverse magnetization caused by persistent magnetic field inhomogeneities as discussed above. The result is an echo height determined by T2 rather than T2*, which not only produces greater signal strength, but also better reflects intrinsic tissue properties. A commonly used analogy is to visualize runners on a track, who run in one direction for /2 before the sound of a whistle (the 180º pulse) causes them all to reverse directions but to maintain their individual speeds. After the second /2, they all rejoin one another in an echo at the starting line before again beginning to de-phase around the track in the other direction. Gradient Echoes Gradient echoes do not use any additional RF pulses during. Instead, the strength of the frequency encoding readout gradient is reversed to form an echo. The track runner analogy to a gradient echo is that after running for a length of time, the whistle (the gradient reversal) causes the fastest and slowest runners each to adopt the other s previous running speed. After an equivalent time interval, the two again meet, coming momentarily back in phase with one another. Because fixed magnetic field inhomogeneities are not corrected by gradient echo sequences, such sequences are more prone to susceptibility effects. These may be intended, as with use of gradient echo sequences to improve

8 REFERENCES 135 detectability of subtle foci of hemorrhage, or undesired, in the form of susceptibility artifacts arising from dental or surgical metal, or from air/tissue interfaces in diffusion weighted images. CONCLUSION This chapter has introduced many of the key conceptual underpinnings of MRI physics. Several good references contain extensive sections that expand further upon these crucial concepts and typical imaging methods [1 4]. A basic understanding of these principles is vital to a firm grasp of clinical MR image content and forms the foundation for understanding more advanced MR imaging techniques. REFERENCES 1. Stark DD, Bradley WG (1999). Magnetic Resonance Imaging, 3rd edn. Mosby, St Louis. 2. Edelman RR, Hesselink JR, Zlatkin M (2005). Clinical Magnetic Resonance Imaging, 3rd edn. Saunders, Philadelphia. 3. Hornak JP The Basics of MRI htbooks/mri/ 4. Higgins CB, Hricak H, Helms CA (1996). Magnetic Resonance Imaging of the Body, 3rd edn. Lippincott-Raven, Philadelphia.