Magnetic Resonance Imaging


A detailed description can be found starting at this page. A synopsis follows.





Magnetic resonance imaging (MRI) can be distinguished in structural MRI, which allows to obtain a structural image, and functional MRI (fMRI), which when applied for instance to the brain, provides a functional profile representing brain activity over time. MRI uses nuclear magnetic resonance (NMR) to image hydrogen nuclei (protons) which are very abundant in tissue (cf. present in water molecules).



Polarization is the first step of MRI: spin alignment or polarization using a strong magnetic field


In order to conduct magnetic resonance imaging, a subject is placed in the strong magnetic field of an MRI scanner, usually 1.5-3 Tesla, which is five orders of magnitude greater than the Earth’s magnetic field (approximately 50μT). A magnetic field exerts a torque or force on the proton spins that tends to align the spins with the direction of the field and which counteracts the thermal motion. In usual conditions of the Earth’s magnetic field and standard temperature, there is little net alignment. Under the strong magnetic field of the MRI scanner (conventionally on the z axis), the spins become gradually aligned or polarized. The progressive alignment of an increasing number of spins results in the growth of a longitudinal magnetization along the z axis, termed Mz magnetization (Fig. 1, red arrow).



Figure 1: Growth of Mz magnetization towards a maximum value Mo. Image: Allen D. Elster, (ref).


This represents the first step of MRI which consists of the process of polarization, given that spins become aligned or polarized. The polarization step is mediated in the clinical setting using a strong magnetic field.




Detection is the second step of MRI: irradiation with radiofrequency, energy absorption on resonance, energy emission, signal acquisition and conversion to image pixel brightness


When spins, such as proton spins, are in a magnetic field, they will precess or wobble around its magnetic field lines, similarly to a spinning toy top before it comes to an end of its motion due to the gravitational force or torque. Their frequency of precession, also termed Larmor frequency (ω), is proportional to the magnetic field strength (B) and is given by the equation ω= = γ * Β, where γ is the gyromagnetic ratio of the proton being equal to 42,57 MHz/T and B is the magnetic field strength.


Following spin alignment and generation of the longitudinal magnetization, the subject is irradiated with an electromagnetic frequency equal to the proton Larmor frequency at this magnetic field strength. For instance, for an MRI scanner of B=1 T, the proton Larmor frequency ω is:


ω = γ * Β => ω = 42,57 MHz/T * 1 T => ω = 42,57 MHz.


The direction of application of this radiofrequency is set to be perpendicular to the z axis.


Upon irradiation with the radiofrequency (RF) of 42,57 MHz which is equal to the proton Larmor frequency, magnetic resonance occurs. This means that that the protons respond (resound) by absorption of the provided energy and proton spin excitation. If we apply the RF pulse for a π/2 duration, the magnetic component of the RF will tilt (tip/flip) the spins by 90°, while at the same the spins will be precessing at 42,57 MHz (megacycles per second). As a result, the longitudinal magnetization Mz will be transformed to a transverse magnetization Mxy (Fig. 2, first subfigure on the left, red arrow). This will precess in the xy plane at the Larmor frequency upon the effect of the RF. Due to the prior spin polarization spins will be precessing in a synchronized manner demonstrating phase coherence. 




Figure 2: Decay of Mxy component of magnetization. Image: Allen D. Elster, (ref).



Shortly after, the RF is stopped, the energy absorption phase of the spins or the spin excitation phase is completed and an energy emission phase (relaxation) is triggered, as spins start emitting the energy they absorbed. In more detail, in the absence of the magnetic component of the RF which was sustaining precession of spins in a coherent way, individual spins will be influenced by the magnetic effect of neighbouring spins or potential collisions with them, as well as the inhomogeneities of the magnetic field. Due to these influences they will start dephasing, that is the phase of their rotational motion will be altered, as for instance, following a collision, a deceleration or a phase “lag” may be induced. Practically, they will start not being "in phase" with other spins. As a result, a progressively decreasing number of spins will precess with the same phase, in a coherent manner and the Mxy magnetisation will decay exponentially in the process termed T2 relaxation or "spin-spin relaxation" (Fig. 2) with T2 being a time constant for the process. This is accompanied by energy emission which constitutes the magnetic resonance signal called "free induction decay" (FID) signal (Figure 3). The signal is captured by a coil of the MRI scanner. 



If we considered hypothetically that during the emission phase the Mxy magnetization was sustained, then we could imagine that each precession of its vector near a coil would generate a voltage in the form of a sine wave with frequency identical to the Larmor frequency and a stable amplitude. However, due to the decay of the Mxy magnetization which consists of the decrease of the number of spins precessing with the same phase, a dampening will be introduced and the generated signal termed "Free Induction Decay" will be an exponentially damped sine wave (Fig. 3). 



Figure 3: Free-Induction Decay (FID)Wikipedia 



The emitted energy is captured by a coil and transformed computationally to a pixel brightness signal for an image. Different tissues have different proton contents and different T2 and therefore different brightness values. A long T2 corresponds to a persistent Mxy magnetization and therefore a bright signal from Mxy. Conversely, a short T2 corresponds to a faint signal. A MRI image will be a composite of different signal intensities representing different tissues. 


After completion of energy emission, the spins which are found in the xy plane, return (relax) to their original orientation in the z axis. This process is termed T1 relaxation or "spin-lattice relaxation" with T1 being a time constant for this process. Different tissues have different T1. A short T1 provides a quick recovery of the Mz magnetization to its original value and therefore a strong signal from Mz. A long T1 provides a long recovery of Mz magnetization and therefore a fainter signal from Mz. 


It is possible to create MRI images based on either T1 or T2 and these are called respectively T1-weighted or T2-weighted images. 


In conclusion, following the polarization phase, which constitutes the first step of MRI and which in the clinical setting is mediated using a strong magnetic field, the subsequent step is the detection phase. This phase includes excitation with a radiofrequency and energy absorption followed by energy emission providing a signal which is captured by a coil.



MRI pulse sequences and echos


MRI uses pulse sequences to mediate repeated spin excitation and relaxation accompanied by signal generation. Pulse sequences can mediate an off-on magnetization or a steady state magnetization which is termed steady state free precession (SSFP) and is linked to a steady state signal emission from the subject.


If the end of the 90° pulse and the decay of Mxy magnetization is followed by a 180° pulse, the spins will refocus again on the xy plane but in the opposite orientation and Mxy will regrow providing a new signal (or a signal repetition) termed spin echo (SE) (Fig.4). If the echo is the result of three pulses e.g. 90°-90°-90° it is called a stimulated echo (STE) (Fig.4). Additionally, it is possible to use magnetic field gradients in order to accelerate the FID and refocus the spins generating a gradient echo (GRE) (Fig.4).




Figure 4: FID and SE/STE start. Image: Allen D. Elster, (ref).



Steady state precession imaging is an MRI technique which uses steady state magnetization (SSFP). In general, SSFP sequences are based on gradient echo (GRE) sequences. They use dephasing and rephasing magnetic field gradients to refocus and record the FID (SSFP-FID sequences), the spin echo/stimulated spin echo (SSFP-SE/STE) or both (SSFP-Double and SSFP-Balanced sequences).