MRI Physics – The Atom – Deconstructing MRI Physics Test Review.

MRI Physics – The Atom

 

MRI Physics – The Atom

While a complete understanding of the Periodic Table of the Elements is useful, and a fundamental building block of many scientific fields, for our purposes as MRI Technologists we can hone our studies to focus on the basic properties that all elements share, and more importantly how these properties relate to magnetism and the particular Atom of interest in MRI, hydrogen-1 (protium), atomic symbol (H).

While there are three isotopes of hydrogen, hydrogen-1 or protium is by far the most naturally abundant comprising 99.985% of all hydrogen isotopes, and is the isotope relevant to MRI. From this point forward we will simply use “hydrogen” in place of hydrogen-1 (protium) to save space and your sanity.

 

Hydrogen is of such importance in MRI due to its relative abundance in the body, found in both water and fat and due to Hydrogen’s magnetic susceptibility due to its isotopic quality. Before delving further into these concepts, however, we must first understand the Hydrogen atom itself and the fundamental properties of atoms.

 

All atoms are made up of sub atomic particles that include, protons, neutrons, and electrons. Protons and neutrons comprise the nucleus (which can be thought of as a central core), while electrons inhabit an outer electron shell, which surrounds the nucleus.

Protons have a net positive charge, which can be remembered due to the fact that both proton and positive begin with the letter P.

Neutrons have no net charge, which can be remembered due to neutrons being neutral.

Electrons have a net negative charge; an easy memory device would be to remind yourself that electrocution would be a very negative experience.

 

Hydrogen is an atom with a single proton, no neutrons, and a single electron.  This results in an atom with an atomic number, which is simply the number of protons in an atom, of 1. The atomic weight of Hydrogen, which is defined by the average number of protons and neutrons within an atom, is 1.00794 AMU or atomic mass units. Electrons are excluded from atomic weight due to their relative lack of size, and while protons and neutrons are similar in mass they are both individually around 1,840 times as massive as an individual electron.

In having one proton but no neutron, hydrogen is an Isotope, which is an atom with an unbalanced or unequal number of protons to neutrons.  In having one positively charged proton, and one negatively charged electron, however, hydrogen does have a balanced charge and as such is not an Ion. An Ion is an atom with an unequal number of protons to electrons.

 

 Spin

 

The subatomic particles mentioned, protons, neutrons, and electrons are not motionless within the atom itself or within your body. These particles spin in three distinct ways within the atom in the absence of an external magnetic field.

  1. The protons and neutrons, which form the nucleus, spin together as the nucleus on its own axis.
  2. The electrons, as they are their own entity, spin on their own axis.
  3. The electrons also spin “around” the nucleus.

In non-isotopic atoms, in which there are an equal number of protons to neutrons, the spin of the nucleus is canceled out. Hydrogen, however, having an unequal number of protons to neutrons, is an isotope and as such has spin. This spin creates a magnetic moment vector with a north and south-pole within the atom and is the reason hydrogen is a viable option in MRI. Simply put, the spin within the nucleus causes hydrogen to act as a tiny magnet itself.

 

Without the presence of an external magnet the protons which comprise the hydrogen nuclei are spinning randomly and without uniform orientation to one another. When introduced to an external magnetic field, however, the orientation of the all nuclei switches course, and either align themselves toward or against the external magnetic field. There is logical due to the proton’s spin causing the nucleus to be a tiny magnet itself and would behave the way any magnet would in the presence of another magnetic force. There are many interchangeable terms to describe the orientation of the nuclei in this state, and while it is unfortunate that there are numerous terms to describe the same basic principle, all of the terms are relatively self-explanatory once the concepts become more clear.

 

Imagine the external magnetic field as a lazy river, and you, laying in your inner tube, are the nucleus. By simply allowing yourself to be taken by the lazy river you are expending very little energy. Similarly, the nuclei that simply align themselves with or toward the external magnetic field are considered in a low-energy state. Conversely, if you decided to swim against the lazy river’s current, you would expend significant energy fighting the current. Similarly, nuclei that align themselves against the external magnetic field are considered high-energy nuclei.

 

Now the interchangeable terms come into play.  Nuclei that are low energy are also referred to as parallel or spinup nuclei.  One visual device would be to imagine the lazy river pointed north or up, and in going parallel with the current your direction is north. Nuclei that are high energy, on the other hand, are referred to as Anti-Parallel or spin-down. Using the same visual device as above all three of these terms are easily memorable, and the concept itself is easily understandable.

 

Continuing with our analogy, there will naturally be more people inclined to take the low-energy route and allow the lazy river to continue pulling them in the direction of the current than those who will fight against the current and use up their energy. The same is true with atomic nuclei, and more nuclei are in a low-energy state than in a high-energy state when exposed to an external magnetic field. This excess of low energy nuclei is referred to as a net magnetization vector and will be discussed in depth throughout the text. One important detail to note is that this excess of “lazy” low energy nuclei is directly affected by the strength of the magnet. As the current in our metaphorical lazy river increases speed and strength, fewer people will be inclined to attempt to swim against it. Similarly, fewer nuclei are able to reach a high-energy state when the strength of the external magnetic field is increased. A real world example of this would be increasing magnetic field strength from 1.5 Tesla to 3 Tesla. With the increase in field strength, fewer nuclei will achieve a high-energy state and more nuclei will be in the low-energy, parallel, spin-up state.

 

This net magnetization vector, or excess hydrogen nuclei that align parallel to the external magnet, aligns itself in this fashion only in the presence of an external magnetic field. As stated before, in the absence of an external magnetic field, hydrogen nuclei are not in cohesion with the other hydrogen nuclei of the body and spin independently and randomly. This nucleic spin is known as a magnetic moment; magnetic, due to the spin of hydrogen exerting a small magnetic field of its own.

 

In the absence of an external magnetic field these randomly aligned magnetic moments can be thought of as random patrons at the waterpark wandering around as they please. Such patrons can walk in infinite directions independent of the orientation or direction of the other patrons in the park. Such is the case with magnetic moments. In the presence of an external magnetic field, however, the excess magnetic moments, or excess low energy patrons in the lazy river allowing themselves to be pulled in the direction of the current (or magnet) are what compose the net magnetization vector described above.

 

In discussing spin and its importance within MRI there is one additional topic that must be discussed to truly understand the fundamentals of magnetism on an atomic level. That is the concept of Precession. Precession is the spin of the magnetic moment in the presence of an external magnetic field and creates a circular pathway around the external magnetic field. This can be easily visualized using your arm. Extend your arm straight out in front of your body and aim your fingertips at a particular object in space. This object can be thought of as the external magnetic field, and your arm as the magnetic moment. In slowly rotating your arm around the object, such as in an arm circle exercise, you are illustrating the general pathway that a precessing atom would take. It is important to note that this rotation or spin is not of the atom itself, but is of the magnetism generated by the proton in the hydrogen nuclei under the influence of an external magnetic field.

The speed of this precession is variable and is dependent on the strength of the external magnetic field and the gyromagnetic ratio of the atom at hand. The formula to calculate Precessional Frequency is known as the Larmor equation, and while this formula looks intimidating initially, upon closer examination you will find that is no more difficult than the simplest of algebra problems. The Larmor Equation is as follows.

ωo = Bo x λ

Where ωo is the precessional frequency

Bo is the strength of the external magnetic field

And λ is the gyromagnetic ratio

Again, these complex terms and symbols may seem initially intimidating but we will break this equation down into very easily understandable terms.

We will start with Precessional frequency ωo. This can be understood easily using our outstretched arm circle exercise described above. Precessional Frequency is simply how many times your arm circles in a given time frame. In Magnetic Resonance, we are describing how many times the magnetic moment of hydrogen spins around the external magnetic field in one second. This value is described with the unit of measurement MHz or Megahertz which is millions of spins per second.

Next is external magnetic field strength Bo. As MRI Technologists this is simply how powerful the external magnetic field of your machine is, which is measured in Tesla. Common high field system strengths are 1.5 T and 3.0 T.

Finally, we will discuss gyromagnetic ratio λ. Gyromagnetic ratio is a constant number that is associated with a given atom containing an MRI active nuclei. It illustrates the effect of magnetism over precessional frequency. As the external magnetic field increases in strength, for instance from 1.5T to 3.0T MRI Active nuclei will increase their speed of precession. Therefore Gyromagnetic ratio is expressed as spins per field strength or MHz/T (Megahertz per Tesla). While there are numerous MRI Active Nuclei with their own Gyromagnetic Ratio the registry will not be expecting you to have these numbers memorized and will provide you with each Gyromagnetic Ratio when appropriate, with one exception. Any Guesses?

HYDROGEN!

The Gyromagnetic Ratio of hydrogen is 42.57 MHz/T or 42,570,000 spins per second per Tesla.

Given this number and these principles test questions regarding the Larmor equation become simple.

In given any two numbers you can solve for the third using basic algebra. For instance, say you are given an external field strength of 3.0T and are asked to solve for the precessional frequency of Hydrogen, which we know has a gyromagnetic ratio of 42.57MHz/T. Using the above equation we would plug in our known figures.

ωo = Bo x λ

We know that the external magnetic field strength is 3.0T

ωo = 3.0T x λ

We also know that the gyromagnetic ratio of hydrogen is 42.57MHz/T

ωo = 3.0T x 42.57MHz/T

At this point, we have broken the equation down into a very simple algebra problem as promised. We simply multiply 3.0×42.57 to get 127.71 and simplify units. The Tesla denominator in the gyromagnetic ratio cancels out the Tesla numerator in the external magnetic field leaving us with only MHz. (If these mathematical terms are dense or too far in your distant memory we understand, simply knowing that the value you end up with for precessional frequency is MHz will suffice). In simplifying we end up with a precessional frequency ωo of 127.71 MHz.

What does this value tell us about the principles of magnetism and how is this information useful?

The Larmor equation illustrates very clearly that external magnetic field strength has a direct effect on precessional frequency. The precessional frequency at a given field strength is of great importance in MRI as Resonance relies on a disturbance, in MRI a radiofrequency pulse, unsettling MRI active nuclei at a similar frequency to that which they are precessing.

 

The above concepts are extremely dense, particularly to those who are unfamiliar to them. Before continuing on to the next section we strongly recommend that you review the above concepts and analogies until they become clear, as MRI Physics largely relies on scaffolding and your future comprehension of the topic largely relies on your understanding of these fundamental principles.

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