Last updated: 2024-01-02

Introduction

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 profile of brain activity or function over time. MRI uses nuclear magnetic resonance (NMR) to image hydrogen nuclei (protons) which are very abundant in tissue. The human body is composed of 60% water, each molecule of which has two hydrogen atoms.

The video found at this URL may be instructive.

Polarization is the first step of MRI: spins are aligned or polarized using a strong magnetic field

In order to conduct magnetic resonance imaging in the usual clinical setting, a subject is placed in the strong magnetic field of an MRI scanner, usually of 1.5-3 Tesla, which is five orders of magnitude greater than the Earth’s magnetic field of approximately 50μT. The magnetic field of the scanner, termed B0, exerts a torque or force on the proton spins which tends to align them 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 longitudinal axis z), 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, MRIquestions.com (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 usual clinical setting using a strong magnetic field.

Detection is the second step of MRI: spin excitation via energy absorption followed by spin relaxation via energy emission and by signal acquisition

When spins, including 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 pulse 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 the protons respond (resound) initially by absorption of the provided energy and by proton spin excitation. Also, the perpendicular RF pulse, via its magnetic component, termed B1, will flip or tip the spins and by extension the longitudinal Mz magnetization to a certain angle. By selecting an appropriate pulse duration, the longitudinal magnetization Mz is tipped by 90° and is transformed to a transverse magnetization Mxy (Fig. 2, first subfigure on the left, red arrow). A pulse with a duration which enables a 90° tip/flip is called a 90° or π/2 pulse.

The transverse magnetization 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, MRIquestions.com (ref).

Shortly after, the RF is stopped, resulting in the ending of the energy absorption phase of the spins or in other words in the completion of the spin excitation phase. An energy emission phase (relaxation) is then triggered, as spins start emitting the energy they had 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 neighboring spins, by potential collisions with them, as well as by 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, similarly to what occurs following a collision, where a deceleration or a phase “lag” may be caused. Practically, they will start not being "in phase" or "in sync" 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 magnetization 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 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. 

A table with the T1 and T2 for different tissues is provided in Figure 4, which is derived from this page of the site mriquestions.com. It is possible to create MRI images based on either T1 or T2; these are called respectively T1-weighted or T2-weighted images. 

Figure 4: Table with the T1 and T2 values for different tissues derived from this page of the site mriquestions.com

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 echoes

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, MRIquestions.com (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).

Magnetic resonance image formation (encoding)

The spatial location of pixels is determined using phase end frequency encoding

In an MRI exam, the entire examined body area will emit a radiofrequency signal. A main issue is how to determine the signal intensity for individual pixels in order to form an image. To this purpose, it is necessary to use a technique that encodes the spatial location of pixels by linking them to a coordinate system (x,y axes). This is possible using a procedure of spatial encoding. The standard MRI image formation technique used today is the two-dimensional Fourier transform technique (2D FT) (ref.) which enables spatial encoding. It consists of the sequential application of two magnetic field gradients, one along the y axis and one along the x axis, which are called respectively, the phase encoding gradient and the frequency encoding gradient (Figure 10). 

Figure 10: Frequency encoding and phase encoding. Image: Allen D. Elster, MRIquestions.com (ref).

Application of a "phase encoding gradient" along the y axis

Initially, a magnetic field gradient termed the "phase encoding gradient" is applied along the y axis. In this manner, we give a different magnetic push to the spins of each row. When the gradient is stopped, the spins will be on different positions on the unit circle (cf. first image from https://en.wikipedia.org/wiki/Unit_circle) and will therefore have acquired a different phase. In other words, a phase shift will have occurred. 

If we were to compare spins to clocks, similarly to the example in Figure 10, where all spins are initially showing 12 o’clock, then, following the application of the gradient and the magnetic push in the second row, the spins of that row will show 3 o’clock, meaning, they that will have acquired a phase shift of 45°. Following this reasoning, we can understand that we will have rows of spins with the same phase. If we determine the phase, we will know where the specific point is located on the y axis. This will be possible following a Fourier transform of the data (1st dimension), which will evaluate the phase.

The first video at this page and the animation at https://www.cis.rit.edu/htbooks/mri/chap-7/g2-3.htm illustrate the principle. (By pausing the video at the end, we can appreciate that the spins have acquired different phases.)

The phase shift (Φ) is proportional to the strength of the gradient (G), the time (t) that the gradient is applied, as well as the gyromagnetic ratio (γ). It is calculated from the equation (ref.): 

Φ = γ * G * t

Application of a "frequency encoding gradient" on the x axis

Following the application of the “phase encoding gradient”, a magnetic field gradient termed "frequency encoding gradient" is applied along the x axis (Fig. 10). This makes the spins precess at different velocities depending on the magnetic field strength at the specific point of the gradient on the x axis. We will therefore have columns of spins with the same frequency. The principle is illustrated by the second video at this page and the animation at https://www.cis.rit.edu/htbooks/mri/chap-7/g2-2.htm.

We then excite the spins and during relaxation we acquire the signal. We will obtain a signal that will be the sum of all the different amplitudes corresponding to the different frequencies. This is provided by the Fourier transform of the data in this second dimension (cf. two-dimensional Fourier transform). 

From the MRI/NMR signal to image formation

Frequency encoding requires only a few milliseconds of signal reading, while phase encoding necessitates repetition of the imaging sequence. For a classic spin echo sequence, one phase encoding step is performed during each repetition time (TR). Since repetition times can be up to 3 seconds, phase encoding is much longer. 

The 2D Fourier procedure will provide a matrix of magnetic resonance signal intensities. These will be associated with x and y locations. Where the signal is highest, the pixels will be displayed as white, while where the signal is lowest, the pixels will be displayed as black. For intermediate signal values, pixels will have a certain greyscale value.

The most important signal intensity parameter is the proton number (proton density). A large number of protons, as in the case of soft tissues for instance, will provide a strong net magnetization M (Mz rotated to Mxy) and therefore an intense signal. Another important parameter is the tissue relaxation time. Fat and muscle have similar proton density but fat has a more intense signal. This is due to the fact that fat has a shorter T1 and a longer T2. Longer T2 means more persistent magnetization in the xy plane and therefore increased signal due to the Mxy magnetization and shorter T1 means quick recovery of magnetization to the z axis and therefore increased signal due to Mz.

Additional references: 

http://mriquestions.com/what-is-phase-encoding.html

http://mriquestions.com/frequency-encoding.html

Magnetic Resonance Imaging - detailed description