Nuclear magnetic resonance

Introduction

Magnetic resonance imaging (MRI) uses a physical phenomenon called nuclear magnetic resonance (NMR), which has been described in the literature since 1940 (Bloch 1940, Purcell 1946, both 1952 Nobel Prize in Physics). From the beginning, applications appeared mainly in chemistry using MR spectroscopy (MRS). NMR imaging appears after 1970, and for better public acceptance, the word nuclear (or nuclear) has been deleted from the title and MRI has been adopted.

The image is created by non-trivial processing of measured responses to radiofrequency pulses, but because the result depends on unknown parameters, the resulting grayscale in the image cannot be considered as an absolute number (similar to Hounsfield's CT unit), but only relative to grayscale from surrounding tissues. MRI displays soft tissues well. MRI does not use ionizing radiation, so it is considered safer and less stressful than CT.

The atomic nucleus consists of neutrons and protons that constantly rotate around their own axis in a motion called spin. Protons are positively charged particles, and each moving charged particle creates a magnetic field and exhibits a magnetic moment. The magnetic moment, or magnetic dipole moment, is a vector physical quantity characterizing a magnetic dipole. The magnetic dipole moment is denoted by m and its unit is the ampere square meter A.m2. The magnetic dipole moment is determined by the relation m = IS, where I is the electric current passing through the dipole loop and S is the oriented area bounded by the dipole loop. For a specific basic idea of magnetic moment, consider only an electron. Its magnetic moment can be illustrated in this way: We will consider the simplest atom - a hydrogen atom that is at rest.

In the electrostatic field of a positively charged nucleus, a negatively charged electron will move along closed trajectories (orbits). The electron is electrically charged and therefore forms a current loop equivalent to a magnetic dipole when considered to move along a closed trajectory. This creates a magnetic field that is very weak, but will still interacts with the electron. This way, the magnetic moment of the electron can be intuitively understood. For other objects (protons, nuclei, atoms), the basic idea of ​​the interpretation of a magnetic moment is similar.

The quantity is called the magnetic moment. If we compare this concept with mechanics, we must necessarily conclude that this quantity will describe a rotating object. Given that there is a quantity of spin, which is also related to rotation in the basic approximation, we can conclude that the magnetic moment (of an electron, nucleus, atom) is also related to spin (of the electron, nucleus, atom).

Atomic nuclei with an even nucleon number do not behinteract magnetically with their surroundings (they do not have spin), because their magnetic moments are canceled out and cannot be used for MR imaging. Atomic nuclei with an odd nucleon number retain their magnetic moment. A common and well-known representative of this group is the hydrogen atom 1H, which has one proton and a relatively large magnetic moment. There is more than 60% of water in the body and 1H is therefore the most suitable object for MR imaging. Other representatives are 13C, 19F, 23Na, 31P.

Atomic nucleus in a magnetic field

If we insert the nucleus into a strong magnetic field, the rotational axes of the protons are arranged parallel to the lines of force of the external magnetic field. A larger number of them are in a position where their magnetic moment is oriented in agreement (in parallel) with the vector of the external magnetic field and a smaller number of protons are oriented in the opposite way (by 180 °, antiparallel). The antiparallel arrangement of protons is more energy-intensive and therefore less than half of them is oriented in this direction.

NMR principle

The principle of NMR is that if the rotating core is placed in a constant magnetic field B0, the magnetic moments (axes of rotation) are compared with the external magnetic field and the axis of the core will rotate slightly around the direction of the applied field B0. This movement occurs with each change in the applied magnetic field, until the core stabilizes in a given position. If the external field ceases to act, the core returns to its original rest position. If a second perpendicular (transverse) BT field is added, the nucleus will start rotating again. To keep the nuclei in constant motion, a high-frequency magnetic field is used, which simultaneously rotates in the XY plane. By choosing the size of the first static magnetic field B0 and choosing the size for the transverse magnetic field BT, it is possible to determine very precisely which nuclei will resonate. By resonance, the magnetic moment m of the nucleus is tilted by 90 ° into the XY plane and the axis then rotates according to the transverse field. If the transverse field is disconnected, the nucleus still rotates in the XY plane. By bringing a coil close to the rotating magnetic moment, a voltage is induced in it, which is then measured. Simply put, the magnitude of the measured tension depends on the position and type of tissue.

Larmor frequency

As already mentioned, protons perform a rotational motion around their axis, or spin. This creates a magnetic field in their surroundings and exhibits a magnetic moment. In addition, protons placed in a magnetic field also show precessional motion. This can be imagined as a movement on the mantle of an imaginary cone (an even more illustrative example can be the movement of a spinning top). The frequency of this movement is called the Larmor frequency. It depends on two factors:

• the intensity of the external magnetic field
• the type of atomic nucleus, expressed by the gyromagnetic ratio (a constant dependent only on the properties of the nucleus).

Example

For hydrogen 1H, the gyromatic ratio is = 42.58MHz / T (269.2T-1), ie. in the field B0 = 1.5T the hydrogen nuclei will have a precession motion frequency f0 = about 64MHz.

Resonance

On the one hand, the direction of the magnetic moment of each individual preceded proton changes over time, on the other hand, the protons move in different phases, ie they are tilted in different directions in a given time. This interrupts their effect on the total vector of magnetization of the tissue in a plane perpendicular to the direction of the magnetic field. The vector of the resulting tissue magnetization thus has a direction identical to the direction of the lines of force of the outer magnet and cannot be measured in this state. We can say that it is in eclipse by the external magnetic field.

In order to be able to measure the resonant frequency of protons, ie their spectrum, it is necessary to deviate the total magnetization vector from its equilibrium position and thus achieve the formation of a transverse tissue magnetization vector. As mentioned above, the size of the transverse vector is zero due to the chaotic motion of the particles. Changes can be achieved by supplying energy in the form of an electromagnetic pulse. In order for the electromagnetic waves to be absorbed by protons, it is necessary that the Larmor frequency of the particles be equal to the frequency of the transmitted pulse.

If this is the case, there is a magnetic resonance phenomenon, which has several consequences:

• protons begin to perform their precessional motion in phase,

• the difference between parallel and antiparallel (more energy-intensive) protons is reduced and thus the vector of longitudinal magnetization is reduced.

The result is the already mentioned transverse magnetization vector.

"The situation is aptly compared to a cruise ship with many passengers on board: as long as the passengers are distributed and randomly and fairly evenly on board, the ship sails straight. However, as soon as the passengers gather together and begin to walk around the deck railing, the ship will periodically tilt gradually in all directions. "

Relaxation times T1 and T2

After the end of the electromagnetic pulse, the protons are no longer supplied with energy and therefore return to their original, more energy-efficient, parallel position and their synchronous motion disappears. This process is called relaxation.

There is a gradual increase in the longitudinal magnetization vector, and the time taken for this vector to recover to 63% is called T1 (longitudinal relaxation, or spin-lattice relaxation). At the same time, however, the transverse magnetization vector is lost by the disappearance of the synchronous motion of the protons, which is a consequence of the interaction of the magnetic fields of the individual particles. The time taken for the transverse magnetization vector to fall to 37% of its value is called T2 (transverse relaxation, or spin-spin relaxation).

In absolute terms, relaxation times T1 are 2-10 times longer than relaxation times T2. In biological tissue, T1 values ​​range from 300–2000 ms, T2 30–150 ms. In practice, the decrease in the transverse component of tissue magnetization is influenced by even small changes in the inhomogeneity of the external magnetic field. The decline is thus much steeper.

Types of electromagnetic pulses used for MR

90 ° pulse - rotating the vector of tissue magnetization by 90 ° and the transverse vector is created. The time between pulses is called TR (time to repeat). The time TR between the individual pulses is shortened so that the tissues do not have time to regain the full value of the longitudinal magnetization vector. The received signal from the tissue then differs in how large the vector of their tissue magnetization is at the time of sending the new pulse.

the combination of 90 ° and 180 ° pulse - 90 ° causes an increase in the transverse magnetization vector and after its end the vector starts to decrease again. However, at the time denoted TE / 2, a 180 ° pulse is sent, which changes the orientation of the precessional motion of the protons by 180 °, and the originally faster preceded protons are slower behind the protons preceded and the decreasing transverse vector begins to increase. Over the next TE / 2 period, the proton motion is synchronized, resulting in re-maximization of the signal. After adding the TE / 2 times, we get the TE time - the echo time.