Lecture 3: MRI...How a gyrating hydrogen proton changed the world

While the world is being scared to bits with the invasion of our peace by corona virus, a discussion on MRI could be a valuable distraction. The last time we discussed, we looked at a few things in quantum physics. It is very important that we understand the basic behaviour of atoms and this will help us understand their role in forming the images generated during an MR scan. I managed to explain that hydrogen as a proton is an active MR nuclei and that if you put these active nuclei in an external magnetic field and apply a radiofrequency pulse, there could be interactions. These interactions are a prerequisite for image formation in MRI. Please note that an external magnetic field (in an MRI discussion) simply means the magnetic field that the MRI scanner produces. In this post, I have 2 main objective

1.       To explain how hydrogen is selectively utilized in MRI away from other active MRI nuclei in the body. Remember I mentioned that other active nuclei are (or could be) present in the body and can also interact with the external magnetic field and radiofrequency in likewise manner.

2.       To explain how the hydrogen active MR nuclei interacts with the external magnetic field and radio frequency.

Now let us look at what it is about hydrogen that makes it very important and useful in MRI. Aside the physical properties of hydrogen that makes it an active MR nuclei, hydrogen is very abundant in the body and is found in both water(H₂O) and fat (COOH). And as I explained earlier in my first post, every tissue in the human can literally either be water or fat. This is so say that the tissues either predominately contains water or fat. For the purpose of this discussion, it is enough to just know that every tissue in the human body will contain hydrogen either in the form of water or fat or a mix of both. This also applies to diseases where there are significant changes in the water and/ or fat composition or content and this is mostly the basis of diagnoses. You might be wondering how MRI differentiates between hydrogen proton (active MR nuclei) in water and fat in making images. To be able to explain how hydrogen active MR nuclei are selectively used in MRI, I will have to use what is called “Larmor Equation”. Please forgive me in advance but this discussion will get technical at some point but I promise to keep it very simple. Just as simple as I can.

ω = γB_o

where

ω is the Larmor frequency in MHz,

γ is the gyromagnetic ratio in MHz/tesla

B_o is the strength of the external magnetic field in tesla

This equation is very important if not the most important in MRI. You will understand this equation when we discus the interaction of active MR nuclei with external magnetic field. But I mentioned it now just to pick out the gyromagnetic ratio. Gyromagnetic ratio is the only factor that uniquely separate hydrogen MR active nuclei from other and you will soon learn why. Now what is this ratio? Gyromagnetic ratio is of a particle or atom (in this case hydrogen) is the ratio of its magnetic moment to its angular momentum. Now this is getting very technical but let me explain it in simple terms. Remember we talked about how hydrogen protons possess a charge and motion (called spin) and hence have a magnetic field or simply exist as magnets. Now magnetic moment is simply how strong the magnets of the hydrogen proton are (measured in Tesla) and angular momentum is how fast the proton(s) are moving in a known circular axis/path (measured in radians per sec or MegaHertz). If you divide the angular momentum with the magnetic moment, you will get gyromagnetic ratio measured in radians per second per Tesla or MegaHertz per Tesla . Gyromagnetic ratio are different for different active MR nuclei and Hydrogen has a unique gyromagnetic ratio (42.58 MHz/T) that no other active MR nuclei can have. This will make more sense when I explain the interaction of active MR nuclei with magnetic field and radiofrequency.

Now let’s look at the interaction of hydrogen active MR nuclei with external magnetic field. Remember we already described the hydrogen atom as an active MR nuclei spinning in their axis and existing as individual magnets. Magnetic moment is a term used to describe the strength of those magnets. The magnetic moments of the active MR nuclei are positioned randomly when outside of the magnetic field. But once inside the magnetic field, the magnetic moments of the protons (active MR nuclei)align with the external magnetic field.  We mentioned earlier that because protons which have a positive charge spin (move around in a circular path), they behave like magnets and how strong these magnets are, is described as magnetic moments.  Remember there are many hydrogen protons in the human body and Its logical to assume that these protons spin at different velocities and if the magnetic moments resulting from those spins are dependent on velocity, this means that the magnetic moments of the protons have different energies. When aligning with the external magnetic field, the magnetic moments with energies that are higher than the external magnetic field are the high energy spin-down or antiparallel nuclei and the ones with lower energy are the low  energy spin-up or parallel nuclei. Conventionally, there are fewer high energy spin down nuclei than low energy spin up nuclei and when you minus the spin down nuclei from the spin up nuclei you get a net magnetic moment called net magnetic vector (NMV). The NMV is an important quantity in MRI. Please remember how we arrived at it. You probably have been told that a 3Tesla MRI scanner is better that a 1.5Tesla scanner. The reason is simple. A 3Tesla will mean that there are a lot fewer high energy spin down magnetic moments aligning antiparallel to the 3Tesla external magnetic field than the low energy spin up magnetic moments. Don’t forget, a magnetic moment is high energy if its energy is more than that of the external field. This means a higher field strength (3 Tesla) will have lesser high energy antiparallel magnetic moments than a 1.5 Tesla scanner. And logically, if you have fewer antiparallel magnetic moments and more parallel magnetic moments, you will have a higher net magnetic vector when you minus the antiparallel from the parallel. A higher NMV gives more signals than a lower NMV and you will learn why and how as we progress.

Another phenomenon that happens as a result of interaction of active MR nuclei with external magnetic field is precession. Remember we said the active MR nuclei spin around their axes. In addition to this spinning, when put in an external magnetic field, the nuclei also spin or precess around the axis of the external magnetic field. This extra spin is called precession and it’s a very important phenomenon in MRI. So there is now two spinning movements; one around the axis of the nucleus and the other (precession) around the axis of the external magnetic field

Let’s look at this equation  again

ω = γB_o

And remember that ω is the Larmor frequency in MHz; γ is the gyromagnetic ratio in MHz/tesla  and B_o is the strength of the external magnetic field in tesla. The equation implies that the frequency at which the protons (active MR nuclei) precess is proportional to the external magnetic field strength and the gyromagnetic ratio. We already said gyromagnetic ratio is a constant quantity unique to each proton and this means that a stronger magnetic field will make the protons precess faster. You will learn the significance of this as you progress in MRI  

Larmor frequency can also be called precessional frequency and is a measure of how fast the nuclei spin around the external magnetic field. From the equation, the frequency is a product of the gyromagnetic ratio and external field strength. Throughout your encounter with MRI, you will hear a lot of mention of Larmor (precessional) frequency and the reason will become obvious as you progress but it is very important to note that while Larmor frequency can change depending on the magnetic field strength, the gyromagnetic ratio is a constant for different nuclei and is the basis for selectively using hydrogen nuclei in MRI.

To have an interaction with a radiofrequency, the radiofrequency must match the Larmor frequency of hydrogen. When this condition is met, another phenomenon called Resonance occurs. Depending on what the external magnetic field strength is, the Larmor frequency of hydrogen varies. This resonance is very important for an MR image to be formed. The Larmor frequency of hydrogen in a known external magnetic field strength can be calculated since the gyromagnetic ratio of hydrogen is a constant and unique only to hydrogen. This also means that using this specific Larmor frequency, only the net magnetic vector of hydrogen is utilized.

Let recap all we have learnt so far. For images to form in MRI, there must be an interaction between the magnetic moments of the hydrogen protons (active MR nuclei) and the external magnetic field and a radiofrequency pulse. The external magnetic field creates an energy level difference resulting to a net magnetic vector and precession. On applying a radiofrequency matching the Larmor frequency of hydrogen resonance occurs. Resonance is so important in MRI that it deserves a dedicated lecture. And hence, I will leave this discussion here with a promise to talk about resonance and how the images in MRI are formed in my next post.

I hope you have enjoyed reading this. If you have any questions or contributions or suggestions, please leave a comment in the comment box.