Nuclear Magnetic Resonance and MRI 

Last updated: 2025-02-05

Principle of nuclear magnetic resonance and MRI

The human body is composed of 60% water. A water molecule consists of one oxygen atom and two hydrogen atoms. Electrons are rotating around the hydrogen nuclei, each of which is a single proton, and also around the oxygen nucleus (Figure 1). The number of protons in the human body is approximately 10 to the 15th power (348.4 x 1015 protons) [*]. 

The hydrogen nucleus or proton could be considered as rotating around itself or spinning and thereby developing a magnetic property called "spin". As a result, it behaves similarly to a bar magnet or a compass. When nuclei are in a magnetic field, their spins precess around the magnetic field lines similarly to a spinning top toy as shown in Figure 1 (dotted line).

Figure 1: The human body consists of 60% water. The number of protons is approximately 10 to the 15th power (348.4 x 1015 protons) [*]. In the water molecule image on the left, the hydrogen nucleus spin, represented by a blue arrow, resembles a bar magnet which precesses at a certain frequency around the magnetic field of the Earth (BEarth). This frequency is the magnetic resonance frequency.

Precessing is similar to revolving, considering that the spin axis is tilted and revolves by writing a cone around the magnetic field lines (Figure 1 - dotted lines). The precessional frequency ω, also called Larmor frequency, is proportional to the magnetic field strength. It can be calculated by multiplying the latter with a constant called magnetogyric ratio γ, which in the case of the hydrogen nucleus is 43 MHz/T. As we are found in the magnetic field of the Earth, which has an average strength of 50 microtesla (0.5 Gauss), our hydrogen nuclei precess with a frequency of 2150 Hz (cycles per second) as calculated below.

ω = γ * Β ⇒ ω = 43 MHz/T * 0.000005 T ⇒ ω = 2150 Hz

(Note: In MRI, we may use a magnetic field of 1 Tesla. What is the precessional/Larmor frequency in this case?)

The precessional frequency or Larmor frequency represents the magnetic resonance frequency of the nucleus. Electromagnetic waves of this frequency will resonate magnetically with the nuclei. As a result, the energy of the wave will be absorbed by the nucleus, which will be energized and excited to a higher energetic level (Figure 2, left). Simultaneously, the magnetic component of the wave will tip the spins towards alignment with the wave, and most importantly, it will tend to synchronize them. When the electromagnetic wave is stopped, the spins will relax by emitting the energy they absorbed.  

Figure 2 : On the left, the principle of magnetic resonance. On the right, magnetic resonance image of the bladder with intense signal due to water-related content.

The above principle is used in magnetic resonance imaging, where the emitted energy is captured by a detector and creates an image. Areas with high water content, as for example the interior of the bladder (Figure 2, right), will have a strong signal, while the contour will have a faint signal. In general, differences in contrast allow us to obtain composite images depicting body structures.

It is noted that we distinguish two stages in the relaxation of the spins and their transition to their original thermal equilibrium. In the first stage, the spins will repel each other (cf. protons repel each other) and even collide with each other, thereby getting desynchronized and slowed down. This is called T2 relaxation. In the second stage, the spins will stop being on the position on which they were tipped by the electromagnetic wave and will start returning to their original position. This is called T1 relaxation. As different tissues have different time constants for T1 and T2, appropriate protocols are used in magnetic resonance imaging.

In order to have a maximal intensity signal in the clinical setting, we perform spin alignment prior to excitation using a strong magnetic field generated by the MRI scanner. In standard conditions, in the low magnetic field of the Earth, spins point mostly to random directions. Upon excitation they will behave similarly to small flashlights. It is in our interest that the spins are maximally aligned and synchronized so that they generate a combined strong ray of light that will be picked up by the detector (Figure 3). Although the excitation electromagnetic wave may tend to contribute to that direction, a prior alignment step using a strong magnet of approximately 1 Tesla is used in clinical MRI. Other modalities may include using a wave with circular polarization during excitation. Alignment and synchronization of spins mediates a strong signal (Figure 3).

Figure 3: Alignment and synchronization of spins mediates a strong signal

Further reading: It is suggested to continue with the section "Magnetic Resonance Imaging (MRI)".