Origin of the MR signal

The primary origin of the MR signal used to generate images is either from water or fat within the patient's tissue; specifically it is from the hydrogen nuclei (consisting of a single proton) contained within free water or lipid molecules Hydrogen is one of a number of elements, including 31P, 23Na, 13C, whose nuclei exhibit magnetic resonance properties but the high intrinsic sensitivity and natural abundance in the form of water and lipid molecules makes it particularly favourable for imaging. Hydrogen nuclei, (single protons) possess an intrinsic property known as nuclear spin that gives rise to a small magnetic field for each proton, known as a magnetic moment. Normally the magnetic moments (spins) are randomly oriented but in the presence of the externally applied Bo field, they tend to align either toward or against the externally applied magnetic field. An equilibrium state is quickly attained where there is a small excess of spins aligned with the field (typically just a few per million) as this is the more energetically favourable direction of alignment. The excess of proton magnetic moments combines to form a net magnetic field or net magnetisation. This is often given the symbol M and at equilibrium it is aligned along the positive z axis (along Bo) with the value, Mo. It is often shown as an arrow or vector (Figure 2a).

Figure 2

Net Magnetisation, rf pulses and flip angle. a) At equilibrium, the net magnetisation, Mo is at equilibrium, aligned along the a axis. b). When an rf pulse is applied, Mo 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, Mz and Mxy. The rotating Mxy component generates the detectable MR signal. c) The maximum detectable signal amplitude after a single rf pulse occurs when Mo lies entirely in the plane of the x and y axes as this gives the largest Mxy 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.

The size of this net magnetisation is one of the key determinants of the maximum signal intensity that can be generated and used to form images. The greater the applied magnetic field strength, Bo, the greater the excess of protons aligned with the magnetic field and the greater the size of the net magnetisation.

In order to generate a MR signal from the net magnetisation, the radiofrequency (rf) magnetic field described earlier is generated by the integral rf transmitter coil and used to deliver energy to the population of protons. This field is applied at a particular frequency, known as the Larmor frequency, ωo that is determined by the equation:

This equation is known as the Larmor equation. The constant γ is called the gyromagnetic ratio and has a value of 42.6 MHz/Tesla for the proton. The Larmor frequency is therefore proportional to the strength of the magnetic field and for 1.5 Tesla, the Larmor frequency is approximately 64 MHz. This is also known as the resonant frequency, as the protons only absorb energy (or resonate) at this characteristic frequency. The rf field is normally applied as a short pulse, known as an rf pulse.

Radiofrequency pulses and flip angle

Before the rf pulse is switched on the net magnetisation, Mo, is at equilibrium, aligned along the z-axis in the same direction as Bo (Figure 2a). When the rf pulse is switched on, the net magnetisation begins to move away from its alignment with the Bo field and rotate around it. The speed of this rotational motion, known as precession, is also at the Larmor frequency. The Larmor frequency is therefore also sometimes referred to as the frequency of precession. The movement of the net magnetisation away from alignment with Bo is caused by a much slower rotation about the much smaller applied rf field, B1. This oscillating field, B1 is applied as a rotating field at right angles to Bo in the plane of the x and y axes. As it rotates at the same frequency as the Larmor frequency, it appears as an additional static field to the rotating net magnetisation vector. The net magnetisation therefore rotates about both the Bo and the B1 fields. As a result of these two rotations, the net magnetisation follows a spiral path from its alignment with the Bo field (z-axis) towards a rotational motion in the plane of the x and y axes.

Remember that the net magnetisation is the result of the sum of many individual magnetic moments. So long as they rotate together (a condition known as coherence) they will produce a net magnetisation that is rotating. The greater the amount of energy applied by the rf pulse, the greater the angle that the net magnetisation makes with the Bo field (the z axis). This depends upon both the amplitude and duration of the pulse. The rf pulse is switched off once the angle of precession has reached a prescribed value. This is known as the flip angle of the rf pulse (Figure 2b).

Once the rf pulse has caused the net magnetisation to make an angle with the z-axis, it can be split into two components (Figure 2b). One component is parallel to the z-axis. This is known as the z-component of the magnetisation, Mz, also know as the longitudinal component. The other component lies at right angles to the z axis within the plane of the x and y axes and is known as the x-y component of the net magnetisation, Mxy, or the transverse component. The transverse component rotates at the Larmor frequency within the xy plane and as it rotates, it generates its own small, oscillating magnetic field which is detected as an MR signal by the rf receiver coil. Radiofrequency pulses are commonly classified by both their flip angle and by their effect.

Radiofrequency pulses that generate an MR signal by delivering energy to the hydrogen spin population, causing the magnetisation to move away from its equilibrium position are known as excitation pulses. The 90° rf excitation pulse delivers just enough energy to rotate the net magnetisation through 90° (Figure 2c). This transfers all of the net magnetisation from the z-axis into the xy (transverse) plane, leaving no component of magnetisation along the z-axis immediately after the pulse. The system of protons is then said to be 'saturated' and the 90° rf pulse is therefore sometimes referred to as a saturation pulse. When applied once, a 90° rf pulse produces the largest possible transverse magnetisation and MR signal. This pulse is used to initially generate the signal for spin echo-based pulse sequences.

Low flip angle rf excitation pulses rotate the net magnetisation through a pre-defined angle of less than 90° (Figure 2b). A low flip is represented by the symbol α or can be assigned a specific value, e.g. 30°. Only a proportion of the net magnetisation is transferred from the z axis into the xy plane, with some remaining along the z axis. While a low flip angle rf pulse produces an intrinsically lower signal than the 90° excitation pulse described above, it can be repeated more rapidly as some of the magnetisation remains along the z-axis immediately after the pulse. This excitation pulse is used to generate the signal in gradient echo pulse sequences to control the amount of magnetisation that is transferred between the z-axis and the xy plane for fast imaging applications.

The 180° refocusing pulse is used in spin echo pulse sequences after the 90° excitation pulse, where the net magnetisation has already been transferred into the x-y plane. It flips the direction of the magnetisation in the x-y plane through 180° as it rotates at the Larmor frequency (Figure 2d). This pulse is used in spin echo-based techniques to reverse the loss of coherence caused by magnetic field inhomogeneities (described in the next section).

The 180° pulses are also used to prepare the net magnetisation before the application of an excitation pulse. These are known as inversion pulses and are used in inversion recovery or dark-blood pulse sequences. They are applied when the net magnetisation is at or close to equilibrium and invert the excess population of proton magnetic moments from being aligned to anti-aligned with the Bo field (Figure 2e). Because the resultant magnetisation lies only along the z axis this pulse does not result in a detectable signal. It is used to prepare the z-magnetisation in inversion recovery pulse sequences and in black blood preparation schemes. This type of pulse is therefore also often referred to as a magnetisation preparation pulse.

MR signal characteristics - T1, T2 and T2* relaxation

Immediately after the rf pulse the spin system starts to return back to its original state, at equilibrium. This process is known as relaxation. There are two distinct relaxation processes that relate to the two components of the Net Magnetisation, the longitudinal (z) and transverse (xy) components. The first relaxation process, longitudinal relaxation, commonly referred to as T1 relaxation is responsible for the recovery of the z component along the longitudinal (z) axis to its original value at equilibrium. The second relaxation process, transverse relaxation, is responsible for the decay of the xy component as it rotates about the z axis, causing a corresponding decay of the observed MR signal. Longitudinal and transverse relaxation both occur at the same time, however, transverse relaxation is typically a much faster process for human tissue. The signal decays away long before the spin system returns to its equilibrium state.

T1 relaxation is an exponential process with a time constant T1. For example, if a 90° pulse (a saturation pulse) is applied at equilibrium, the z-magnetisation is saturated (reduced to zero) immediately after the pulse, but then recovers along the z-axis towards its equilibrium value, initially rapidly, slowing down as it approaches its equilibrium value (Figure 3). The shorter the T1 time constant is, the faster the relaxation process and the return to equilibrium. Recovery of the z-magnetisation after a 90° rf pulse is sometimes referred to as saturation recovery.

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, Mz is reduced to zero, but then recovers gradually back to its equilibrium value if no further rf pulses are applied. The recovery of Mz 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.

Transverse relaxation can be understood by remembering that the net magnetisation is the result of the sum of the magnetic moments (spins) of a whole population of protons. Immediately after the rf pulse they rotate together in a coherent fashion, so that as they rotate they continuously point in the same direction as each other within the xy plane. The angle of the direction they point at any instant is known as the phase angle and the spins having similar phase angles are said at this initial stage to be 'in phase' (Figure 4). Over time, for reasons explained in a moment, the phase angles gradually spread out, there is a loss of coherence and the magnetic moments no longer rotate together and they are said to move 'out of phase'. The net sum of the magnetic moments is thus reduced, resulting in a reduction in the measured net (transverse) magnetisation. The signal that the receiver coil detects (if no further rf pulses or magnetic field gradients are applied) is therefore seen as an oscillating magnetic field that gradually decays (known as a Free Induction Decay or FID). There are two causes of this loss of coherence. Firstly, the presence of interactions between neighbouring protons causes a loss of phase coherence known as T2 relaxation.

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.

This arises from the fact that the rate of precession for an individual proton depends on the magnetic field it experiences at a particular instant. While the applied magnetic field Bo is constant, it is however possible for the magnetic moment of one proton to slightly modify the magnetic field experienced by a neighbouring proton. As the protons are constituents of atoms within molecules, they are moving rapidly and randomly and so such effects are transient and random. The net effect is for the Larmor frequency of the individual protons to fluctuate in a random fashion, leading to a loss of coherence across the population of protons. i.e. the spins gradually acquire different phase angles, pointing in different directions to one another and are said to move out of phase with one another (this is often referred to as de-phasing). The resultant decay of the transverse component of the magnetisation (Mxy) has an exponential form with a time constant, T2, hence this contribution to transverse relaxation is known as T2 relaxation (Figure 4). As it is caused by interactions between neighbouring proton spins it is also sometimes known as spin-spin relaxation. Due to the random nature of the spin-spin interactions, the signal decay caused by T2 relaxation is irreversible.

The second cause for the loss of coherence (de-phasing) relates to local static variations (inhomogeneities) in the applied magnetic field, Bo which are constant in time. If this field varies between different locations, then so does the Larmor frequency. Protons at different spatial locations will therefore rotate at different rates, causing further de-phasing so that the signal decays more rapidly. In this case, as the cause of the variation in Larmor frequency is fixed, the resultant de-phasing is potentially reversible. The combined effect of T2 relaxation and the effect of magnetic field non-uniformities is referred to as T2* relaxation and this determines the actual rate of decay observed when measuring an FID signal (Figure 4). T2* relaxation is also an exponential process with a time constant T2*.

Significance of the T1 value

T1 relaxation involves the release of energy from the proton spin population as it returns to its equilibrium state. The rate of relaxation is related to the rate at which energy is released to the surrounding molecular structure. This in turn is related to the size of the molecule that contains the hydrogen nuclei and in particular the rate of molecular motion, known as the tumbling rate of the particular molecule. As molecules tumble or rotate they give rise to a fluctuating magnetic field which is experienced by protons in adjacent molecules. When this fluctuating magnetic field is close to the Larmor frequency, energy exchange is more favourable. For example, lipid molecules are of a size that gives rise to a tumbling rate which is close to the Larmor frequency and therefore extremely favourable for energy exchange. Fat therefore has one of the fastest relaxation rates of all body tissues and therefore the shortest T1 relaxation time. Larger molecules have much slower tumbling rates that are unfavourable for energy exchange, giving rise to long relaxation times. For free water, its smaller molecular size has a much faster molecular tumbling rate which is also unfavourable for energy exchange and therefore it has a long T1 relaxation time. The tumbling rates of water molecules that are adjacent to large macromolecules can however be slowed down towards the Larmor frequency shortening the T1 value. Water- based tissues with a high macromolecular content (e.g. muscle) therefore tend to have shorter T1 values. Conversely, when the water content is increased, for example by an inflammatory process, the T1 value also increases.

Significance of the T2 value

T2 relaxation is related to the amount of spin-spin interaction that takes place. Free water contains small molecules that are relatively far apart and moving rapidly and therefore spin-spin interactions are less frequent and T2 relaxation is slow (leading to long T2 relaxation times). Water molecules bound to large molecules are slowed down and more likely in interact, leading to faster T2 relaxation and shorter T2 relaxation times. Water- based tissues with a high macromolecular content (e.g. muscle) tend to have shorter T2 values. Conversely, when the water content is increased, for example by an inflammatory process, the T2 value also increases. Lipid molecules are of an intermediate size and there are interactions between the hydrogen nuclei on the long carbon chains (an effect known as J-coupling) that cause a reduction of the T2 relaxation time constant to an intermediate value. Rapidly repeated rf pulses, such as those used in turbo or fast spin echo techniques, can have the effect of reducing J-coupling, resulting in an increased T2 relaxation time and higher signal intensity from fat [6].

MR echoes

Whilst the FID can be detected as a MR signal, for MR imaging it is more common to generate and measure the MR signal in the form of an echo. This is because the magnetic field gradients that are used to localise and encode the MR signals in space cause additional de-phasing which disrupts the FID. The two most common types of echo used for MR imaging are gradient echoes and spin echoes. The following sections describe how these echoes are generated.

Gradient echoes

Gradient echoes are generated by the controlled application of magnetic field gradients. Magnetic field gradients are used to produce a change in field strength and hence a corresponding change in Larmor frequency along a particular direction. When a magnetic field gradient is switched on it causes proton spins to lose coherence or de-phase rapidly along the direction of the gradient as they precess at different frequencies. This de-phasing causes the amplitude of the FID signal to rapidly drop to zero (Figure 5). The amount of de-phasing caused by one magnetic field gradient can however be reversed by applying a second magnetic field gradient along the same direction with a slope of equal amplitude but in the opposite direction. If the second gradient is applied for the same amount of time as the first gradient, the de-phasing caused by the first gradient is cancelled and the FID re-appears. It reaches a maximum amplitude at the point at which the spins de-phased by the first gradient have moved back into phase, or 're-phased'. If the second gradient then continues to be applied, the FID signal de-phases and disappears once more. The signal that is re-phased through the switching of the gradient direction is known as a gradient echo. The time from the point at which the transverse magnetisation (the FID) is generated by the rf pulse, to the point at which the gradient echo reaches it's maximum amplitude is known as the echo time (abbreviated TE). This can be controlled by varying the timing of the applied magnetic field gradients. If the echo time is chosen to be longer, more natural T2* de-phasing occurs and the maximum echo amplitude becomes smaller. In practice, the TE is set by the MR system operator (in milliseconds) as it determines, amongst other things, the influence of T2* on the image contrast.

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 1st positive magnetic field gradient causes rapid de-phasing of the transverse magnetisation, Mxy, and therefore the FID signal to zero amplitude. The application of the 2nd 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.

Spin echoes

Spin echoes are generated by the application of a 180° refocusing rf pulse after the 90° excitation pulse (Figure 6). While the de-phasing caused by T2 relaxation is a random, irreversible process, the additional de-phasing caused by the presence of static magnetic field inhomogeneities is potentially reversible. At a certain time after the initial generation of the FID signal, a proportion of the relative phase change for each proton spin is related to the local value of the applied magnetic field. The application of a 180° refocusing pulse rotates the spins through 180°, effectively changing the sign of the relative phase change within the xy plane. Where the previous relative phase change was positive due to a locally increased field, the 180° pulse causes it to become negative and visa versa. As the local field variations remain fixed, the spins still continue to have the same Larmor frequency, so a spin in an increased field continues to gain in phase, while a spin in a decrease field continues to lose phase. Because the sign of their phase shifts has been swapped halfway through by the 180° refocusing pulse, the spins all come back into phase causing the FID to increase in amplitude, reaching a maximum at the echo time, TE. For the spin de-phasing caused by the field non-uniformities to be completely reversed at time TE, the 180° pulse must be applied at time TE/2. The signal that re-appears (re-phases) through the application of the 180° rf refocusing pulse is known as a spin echo. After reaching a maximum amplitude at time TE, the signal again de-phases due to the T2* relaxation process. For the purposes of imaging, magnetic field gradients are also applied during the de-phasing period and during the measurement of the spin echo.

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.

Spin echo versus gradient echo

In general, because of the 180° refocusing pulse removes the de-phasing caused by magnetic field inhomogeneities, the amplitude of the spin echo signal is greater than the gradient echo signal. Imaging based on spin echo is also less affected by the presence of field inhomogeneities caused by metallic artefacts (e.g. sternal wires or metallic heart). Gradient echo imaging is however more affected by the presence of magnetic field inhomogeneities caused by iron and so is useful, for example, in the assessment of patients with increased iron deposition within the heart and liver.