Cardiovascular magnetic resonance physics for clinicians: part I

Abstract

There are many excellent specialised texts and articles that describe the physical principles of cardiovascular magnetic resonance (CMR) techniques. There are also many texts written with the clinician in mind that provide an understandable, more general introduction to the basic physical principles of magnetic resonance (MR) techniques and applications. There are however very few texts or articles that attempt to provide a basic MR physics introduction that is tailored for clinicians using CMR in their daily practice. This is the first of two reviews that are intended to cover the essential aspects of CMR physics in a way that is understandable and relevant to this group. It begins by explaining the basic physical principles of MR, including a description of the main components of an MR imaging system and the three types of magnetic field that they generate. The origin and method of production of the MR signal in biological systems are explained, focusing in particular on the two tissue magnetisation relaxation properties (T1 and T2) that give rise to signal differences from tissues, showing how they can be exploited to generate image contrast for tissue characterisation. The method most commonly used to localise and encode MR signal echoes to form a cross sectional image is described, introducing the concept of k-space and showing how the MR signal data stored within it relates to properties within the reconstructed image. Before describing the CMR acquisition methods in detail, the basic spin echo and gradient pulse sequences are introduced, identifying the key parameters that influence image contrast, including appearances in the presence of flowing blood, resolution and image acquisition time. The main derivatives of these two pulse sequences used for cardiac imaging are then described in more detail. Two of the key requirements for CMR are the need for data acquisition first to be to be synchronised with the subject's ECG and to be fast enough for the subject to be able to hold their breath. Methods of ECG synchronisation using both triggering and retrospective gating approaches, and accelerated data acquisition using turbo or fast spin echo and gradient echo pulse sequences are therefore outlined in some detail. It is shown how double inversion black blood preparation combined with turbo or fast spin echo pulse sequences acquisition is used to achieve high quality anatomical imaging. For functional cardiac imaging using cine gradient echo pulse sequences two derivatives of the gradient echo pulse sequence; spoiled gradient echo and balanced steady state free precession (bSSFP) are compared. In each case key relevant imaging parameters and vendor-specific terms are defined and explained.

Figure 1

MR system components. a) Diagram showing the relative locations of the main magnet coils, x, y, and z gradient coils, integral rf transmitter body coil and rf receiver coils. b) Typical arrangement for a cylindrical bore MR system showing the magnet bore and the reference coordinate axes with the static B_o field direction along the horizontal z axis.

Figure 2

Net Magnetisation, rf pulses and flip angle. a) At equilibrium, the net magnetisation, M_o is at equilibrium, aligned along the a axis. b). When an rf pulse is applied, M_o makes an angle with the z-axis, known as the flip angle, and rotates around the axis in the direction of the curved arrow. At any instant the magnetisation can be split into two components, M_z and M_xy. The rotating M_xy component generates the detectable MR signal. c) The maximum detectable signal amplitude after a single rf pulse occurs when M_o lies entirely in the plane of the x and y axes as this gives the largest M_xy component. This pulse has a 90° flip angle and is referred to as a 90° rf pulse or saturation pulse. d) A 180° rf refocusing pulse is usually applied while there is transverse magnetisation already rotating in the xy plane and is used to instantaneously flip the transverse component of magnetisation through 180° about an axis also rotating in the xy plane. e) A 180° inversion pulse is usually applied at equilibrium and is used to rotates the net magnetisation through 180° from the positive to the negative z axis. This is also know as a magnetisation preparation pulse and is used is the preparation scheme for black blood imaging techniques.

Figure 3

T1 relaxation process. Diagram showing the process of T1 relaxation after a 90° rf pulse is applied at equilibrium. The z component of the net magnetisation, M_z is reduced to zero, but then recovers gradually back to its equilibrium value if no further rf pulses are applied. The recovery of M_z is an exponential process with a time constant T1. This is the time at which the magnetization has recovered to 63% of its value at equilibrium.

Figure 4

Transverse (T2 and T2*) relaxation processes. A diagram showing the process of transverse relaxation after a 90° rf pulse is applied at equilibrium. Initially the transverse magnetisation (red arrow) has a maximum amplitude as the population of proton magnetic moments (spins) rotate in phase. The amplitude of the net transverse magnetisation (and therefore the detected signal) decays as the proton magnetic moments move out of phase with one another (shown by the small black arrows). The resultant decaying signal is known as the Free Induction Decay (FID). The overall term for the observed loss of phase coherence (de-phasing) is T2* relaxation, which combines the effect of T2 relaxation and additional de-phasing caused by local variations (inhomogeneities) in the applied magnetic field. T2 relaxation is the result of spin-spin interactions and due to the random nature of molecular motion, this process is irreversible. T2* relaxation accounts for the more rapid decay of the FID signal, however the additional decay caused by field inhomogeneities can be reversed by the application of a 180° refocusing pulse. Both T2 and T2* are exponential processes with times constants T2 and T2* respectively. This is the time at which the magnetization has decayed to 37% of its initial value immediately after the 90° rf pulse.

Figure 5

Generating a gradient echo. This diagram show how the reversal of a magnetic field gradient is used to generate a gradient echo. The application of the 1^st positive magnetic field gradient causes rapid de-phasing of the transverse magnetisation, M_xy, and therefore the FID signal to zero amplitude. The application of the 2^nd negative magnetic field gradient reverses the de-phasing caused by the first gradient pulse, resulting in recovery of the FID signal to generate a gradient echo at the echo time, TE. Extension of the time duration of the second gradient to twice that of the first gradient causes the FID to then de-phase to zero. The maximum amplitude of the echo depends on both the T2* relaxation rate and the chosen TE.

Figure 6

Generating a spin echo. The presence of magnetic field inhomogeneities causes additional de-phasing of the proton magnetic moments. The Larmor frequency is slower where the magnetic field is reduced and faster where the field is increased resulting in a loss or gain in relative phase respectively. After a period of half the echo time, TE/2, the application of a 180° rf pulse causes an instantaneous change in sign of the phase shifts by rotating the spins (in this example) about the y axis. As the differences in Larmor frequency remain unchanged, the proton magnetic moments the move back into phase over a similar time period, reversing the de-phasing effect of the magnetic field inhomogeneities to generate a spin echo. In addition to the effect of the 180° refocusing pulse, gradients are applied to de-phase and re-phase the signal for imaging purposes. Note that for spin echo pulse sequences, the second gradient has the same sign as the first, as the 180° pulse also changes the sign of the phase shifts caused by the first gradient.

Figure 7

Image formation, Step 1 - Selecting a slice. For step 1 of image formation process, a slice of tissue is selected by applying a magnetic field gradient G_S at the same time as the rf excitation pulse. The position along the gradient (in this example along the z axis) determines the Larmor frequency and resonance only occurs where this matches the frequency of the rf pulse, f₀, defining a plane (slice) of tissue perpendicular to the z axis. In practice the rf pulse is applied over a small range of frequencies, thus defining the thickness of the slice.

Figure 8

Image formation, Steps 2 & 3 - Phase and frequency encoding. For step 2 of the image formation process, a phase encoding gradient, G_P, is applied in a direction along the selected image plane (in this case the phase encoding direction is along the y direction). This causes a range of phase shifts of the proton magnetic moments dependent on their position along the gradient as well as the slope and duration of the gradient. For step 3, following the phase encoding gradient, the frequency encoding gradient, G_F, is applied also in the plane of the selected slice but perpendicular to the phase encoding direction. The MR signal echo is measured during this period. The frequency encoding gradient determines the Larmor frequency according to position along its direction (in this case, the x direction). The detected MR signal from the slice of tissue is therefore comprised of many different frequencies. The field of view is predefined and matched to a specific range of frequencies, referred to as the receiver bandwidth. See also Additional File 1.

Figure 9

Image formation - pulse sequence diagram. A pulse sequence diagram showing the relative timing of the rf and gradient pulses applied as part of the three step process to localise and encode the MR signal for image formation. The frequency-encoded MR signal echo is measured during a sampling period centred at the echo time, TE. Additional gradient pulses (shown outlined in red) are required immediately after the slice selection gradient and immediately before the frequency encoding gradient. These additional pulses ensure that any de-phasing of the transverse magnetisation caused by the imaging gradients is cancelled once the echo time, TE, is reached. This results in the echo reaching its maximum possible signal at this point.

Figure 10

Image reconstruction - frequency encoding. The frequency encoded signal is analysed by a Fourier Transform to determine the contribution of each of the frequency components to each location along the frequency encoding gradient within the pre-defined field of view.

Figure 11

Phase encoding steps and repetition time, TR. To acquire sufficient information for image reconstruction, the pulse sequence is repeated a number of times, with an increment in the strength (or slope) of the phase encoding gradient being applied each time. In this example, 7 values of phase encoding gradient slope are used (shown by the dotted lines). Note that as the strength of the phase encoding gradient increases, this increases the amount of de-phasing along the gradient. When the strength (or slope) of the phase encoding gradient is zero (step 4), there is no de-phasing and the signal has its maximum possible amplitude. The time interval between each repetition is known as the repetition time, TR.

Figure 12

Image reconstruction, k-space and image space. The MR signals derived from each phase encoding step are stored in a raw data matrix, known as k-space. A two-dimensional Fourier transformation of this matrix results in the reconstruction of the image. The number of phase encoding steps determines the number of pixels in the image along the phase encoding direction. The coordinates of the image are the spatial coordinates x and y. The distribution of MR signal components in the image is determined by their frequency along the frequency encoding direction (in this case, x) and by their change in phase with each phase encoding step along the phase encoding direction (in this case, y). The Coordinates of k-space are the spatial frequencies k_x = 1/x and k_y = 1/y. The data points in k-space (the sampled MR signals) therefore represent the spatial frequencies content of the image. In a Cartesian data acquisition, the data points are stored line by line along the k_x direction, with each line corresponding to a separately sampled MR signal. The position along k_x depends on the time point during the sampling period. The location of each line of data points in the k_y direction is determined by the amplitude and duration of the phase encoding direction at each phase encoding step.

Figure 13

k-space and spatial frequencies. A single point in k-space defines a spatial frequency that can be represented as a wave in image space. A point close to the centre of k-space contributes a low spatial frequency, represented by a wave with broad peaks and troughs. This provides the signal content for large regions of uniform signal in the image and therefore the image contrast. A point at the edge of k-space contributes a high spatial frequency and is represented by a fine 'toothcomb' wave. The highest spatial frequency content defines the spatial resolution limit of the image.

Figure 14

k-space order. Standard Cartesian MR data acquisition fills k-space by starting at one edge of k-space incrementing line by line until the opposite edge of k-space is reached. This is known as linear k-space order. 'Centric' or 'lo-hi' k-space order starts at the centre of k-space and fills lines of k-space outward to both edges in an alternating fashion.

Figure 15

T1-weighted spin echo. T1 and T2 relaxation curves for a T1-weighted spin echo pulse sequence (180° pulse not shown) over two repetition periods and for three different tissues. The short TR leads to different amounts of recovery of the z-magnetisation for the three tissues, leading to T1-based contrast. The short TE minimises differences due to differences in T2 relaxation. T1-weighted images are characterised by bright fat and low signal intensity from static fluid.

Figure 16

T2-weighted spin echo. T1 and T2 relaxation curves for a T2-weighted spin echo pulse sequence (180° pulse not shown) for three different tissues. The long TR minimises differences due to differences in T1 relaxation. The long TE leads to different amounts of decay of the xy-magnetisation for the three tissues, leading to T2-based contrast. T2-weighted images are characterised by bright fluid and low signal intensity from muscle.

Figure 17

'Proton density'-weighted spin echo. T1 and T2 relaxation curves for a 'proton density'-weighted spin echo pulse sequence (180° pulse not shown) for three different tissues. The long TR minimises differences due to differences in T1 relaxation, while the short TE minimises differences due to differences in T2 relaxation, leading to T2-based contrast. 'Proton density'-weighted images are characterised by high signal intensity from most tissues and low tissue contrast.

Figure 18

Black blood contrast from spin echo pulse sequences. Black blood appearance using spin echo pulse sequences is caused by the motion of blood through the image slice between the 90° and 180° pulses. The 90° pulse causes resonance in all the tissue within the slice, however a spin echo signal is only produced when the same tissue and blood also receive the 180° refocusing pulse. Blood that moves out of the slice during the time between the 90° and 180° pulses doe not produce a spin echo, resulting in a signal void as seen in the major vessels of the black blood spin echo image example.

Figure 19

Use of low flip angles with gradient echo pulse sequences. Gradient echo sequences can use a variable (low) flip angle for the excitation pulse which allows much shorter TR values to be used without losing too much signal. When a 90° rf pulse is used (top row), the short TR allows very little recovery between rf pulses. The z-magnetisation quickly reduces, resulting in a low signal amplitude when it is transferred into the xy plane. The use of a low flip angle (in this case, 30°, bottom row), allows the z-magnetisation to remain much closer to its equilibrium value. This, when transferred into the xy plane, results in a much larger signal in comparison.

Figure 20

Bright blood contrast from gradient echo pulse sequences. Gradient echo pulse sequences often use very short repetition times to enable fast imaging. This results in limited recovery of the tissue magnetisation between pulses. Tissue that remains within the slice therefore has a reduced signal. Blood that flows through the image slice is constantly being replaced by fully magnetised blood which is able to generate a much higher signal when the excitation pulse is applied, resulting in a bright blood appearance. Flow-related enhancement can clearly be seen in the ascending and descending aorta on the bright blood spoiled gradient echo image example. Note that there is less flow-related enhancement within the main pulmonary artery and atria as the blood is not flowing through the image slice and is therefore partially saturated.

Figure 21

ECG synchronisation of imaging pulse sequences. Cardiac synchronisation is achieved by obtaining an ECG signal from the patient using MR-compatible ECG electrodes and leads. A software algorithm is then used to detect the QRS complex and generate a synchronisation pulse. This initiates the pulse sequence controller to produce rf and gradient pulse waveforms that are amplified to drive the rf transmitter and gradient coils. This is then repeated, with each cardiac cycle triggering a new repetition of the pulse sequence.

Figure 22

Accelerated spin echo imaging with turbo or fast spin echo. The conventional spin echo pulse sequence (left) applies a single 180° pulse following the 90° pulse to generate a single spin echo, filling only one line of k-space each R-R interval. The turbo or fast spin echo pulse sequence (right) applies multiple 180° pulses following the 90° pulse to generate multiple spin echoes. Multiple lines of k-space are filled within each R-R interval by applying a phase encoding gradient with a different amplitude to each echo. In this diagram each phase encoding gradient is colour coded to identify which corresponding line of k-space is filled. The phase encoding applied to each echo is removed by applying an equal and opposite re-winder gradients after each echo is sampled. In this example, four 180° pulses are applied to generate four spin echoes (echo train length or turbofactor = 4). This provides a four-fold acceleration in scan time.

Figure 23

Double inversion black-blood preparation scheme. The double-inversion black-blood preparation pulse scheme uses two 180° inversion rf pulses to make the suppression of the blood signal more effective. The first inversion pulse, A, is not slice selective and inverts the magnetisation of all the tissue within range of the rf transmitter coil. The second inversion pulse, B, is a slice selective pulse that restores the magnetisation of the tissue within the intended image slice. The net effect of pulses A and B is to invert the magnetisation of all the tissue outside the intended image slice (shown in grey). After a prescribed inversion recovery period, TI, chosen as the time taken for the blood magnetisation to reach zero, an excitation pulse, C, is applied to generate a signal that is dependent on the current value the z-magnetisation of tissue and blood within the slice. During that same period, the non-inverted blood within the slice (red) is likely to have been replaced by the blood from outside the slice that has been inverted (grey) resulting in a signal void within the vessel.

Figure 24

Black-blood anatomical imaging with turbo or fast spin echo. The Black Blood Preparation scheme is applied at the beginning of the cardiac cycle with the image acquisition in diastole. The exact duration of the Black Blood inversion, TI_Blood is calculated to provide the best blood suppression and depends on the heart rate and the number of heart beats between each trigger pulse (typically TI_Blood = 400-600 milliseconds). The turbo or fast spin echo pulse sequence enables one or two slices to be acquired within a single patient breath-hold. The six images to the right have been acquired using six separate breath-holds.

Figure 25

Cine gradient echo imaging: ECG triggering versus retrospective ECG gating. Cine imaging is achieved by acquiring data for a single slice location at multiple time points throughout the cardiac cycle. Multiple images are then reconstructed at the corresponding time points, known as cardiac phases. These images are then viewed as a movie to allow the visualisation of cardiac motion and blood flow patterns. ECG triggering (top) initiates the data acquisition of the first cardiac phase immediately after the R-wave and acquires a predetermined number of cardiac phases. The data acquisition must stop before the end of the cardiac cycle to allow detection of the next R-wave. This results in the last part of the cardiac cycle not being imaged. Retrospective ECG gating (bottom) acquires data continuously and records the temporal position of the acquired data relative to the R-wave. The acquisition continues until k-space is filled for a sufficient number of time points and the data is sorted into cardiac phases retrospectively. This approach allows data to be assigned accurately to the end of the cardiac cycle, ensuring the whole of the cardiac cycle is imaged.

Figure 26

Accelerated cine imaging with turbo or fast gradient echo. The conventional gradient echo pulse sequence (left) applies a single low flip angle rf pulse to generate a single gradient echo. One line of k-space is filled each R-R interval for each cardiac phase. The turbo or fast gradient echo pulse sequence (right) rapidly repeats the low flip angle rf pulse to generate multiple gradient echoes. Multiple lines of k-space are filled within each R-R interval by applying a different amplitude of phase encoding gradient to each echo. In this diagram each phase encoding gradient is colour coded corresponding to the line of k-space filled. In this example, four rf pulses are applied to generate four gradient echoes, a parameter setting known as turbofactor= 4 (Philips), no of segments = 4 (Siemens), no of views per segment = 4 (GE). This constitutes one 'shot'. The remaining lines of k-space are filled by acquiring multiple shots over successive heart beats. This provides a fourfold acceleration of the image acquisition time.

Figure 27

Bright blood functional cine imaging using retrospectively-gated turbo or fast gradient echo. Either spoiled gradient echo or balanced SSFP pulse sequences may be used for this application. The number of lines of k-space acquired in each cardiac phase (in this example = 4) determines the acquisition time for this sequence (typically within a single breath-hold period). Increasing the number of lines (the turbofactor, no of segments or no of views per segment) shortens the acquisition time but increases the time between heart phases (the heart phase interval or 'TR'), resulting in poorer temporal resolution. bSSFP pulse sequences can achieve a shorter TR, resulting in shorter breath-hold periods for the same spatial and temporal resolution. The image examples show an end diastolic phase (cardiac phase 1) for spoiled gradient echo (left) and bSSFP (right). Note that the blood signal has more flow dependence for the spoiled gradient echo technique with the LV blood pool (through plane flow) is much brighter than the right ventricle (in-plane flow), whereas for the bSSFP technique they are of equal brightness due to the intrinsic contrast between blood and myocardium based on the T2/T1 ratio. Similarly, the slow-moving blood adjacent to endocardial border is partially saturated in the spoiled gradient echo image, resulting in poorer definition of the endocardial border. This leads to systematic differences in volumetric measurements between the two methods, with the bSSFP techniques yielding larger volumes and smaller ventricular masses.