MRI, a deep body photography : Chapter 2

As I was saying in my previous article, the nucleus with nonzero spin when placed in a magnetic field will align either along the field or opposite it. And based on this orientations, it is said to be at certain magnetic potential energy. So now since atoms live by certain code, they can only stay at these energy levels. If you hit the lower energy nucleus with a photon to provide it with energy enough to get to the top floor, then it absorbs the photon and gets to that floor. This is what is called Nuclear Magnetic Resonance.

So a nucleus interacts with certain frequencies, so what good does it do?
In our daily life, we see things around us because the matter around us is able to absorb or reflect the electromagnetic radiation or simply LIGHT that our eyes can see. So if we wish to see anything, what do we do? We take a torch and blow the light. This light is partially reflected and absorbed by surrounding things. If the reflected light falls n you eyes, you see them.

This is what the people do here in MRI or NMR spectroscopy or in X-ray or whatever. They take out their special torches, special as in every torch has its own working frequency range. The x-ray torch in x-ray region and the MRI in radio frequency region. Yeah! radio frequency is what the region is called because our daily radio transmission is done in this wavelength region.

There is a lot to take in now. Consider a nucleus with spin 1/2. it has two levels as in the following figure.

nucleus is a tiny magnet, remember. So when a spin half magnet placed in external field it got two energy levels.

What if we had a nucleus with some spin S. how many levels will it have? It’s a magnet right. Then two levels, one orientation along the field and the other opposite to it.
But, no. You are wrong if you think so. Instead the number of energy levels are equal to “2S+1”. Strange right! the inner tenants i.e., protons and neutrons can change their alignment to come up with all those levels. Somehow the spin value is same but, the levels are many and discrete. So the transitions take place at many frequencies.

So does that mean the nucleus transitions take place at certain frequencies for a fixed magnetic field? Yes, if the effective field the nucleus is experiencing is fixed then the transition or resonance frequencies are fixed.

Saw the word “EFFECTIVE there”? This is the time I told you about the factors that affect the Resonance.

Imagine yourself walking under a tree. Now imagine walking under a tree. Does the amount of rain you are hit with remain same? No. It’s a bad example, but what I want to say is the surroundings play an important role too.

Do you remember how magnets behave when you bring it near another one. They align in opposite directions. Exactly the same scenario, here, surrounding molecules or atoms are full of electrons. These electrons are again magnets. When placed in the external field these electrons align themselves so that their effective magnetization is opposing the external field. Thus net magnetization experienced by the Target nucleus is less than the value of external field. We know the transition energies are proportional to the external field. Now since the effective field is less than the field we thought it is experiencing, the transition frequencies are less. if you wish it to absorb the previously known frequencies which are absorbed by the free nucleus, you have to increase the external field value. This effect of surroundings on the Resonance is called Diamagnetic effect. So if the target nucleus is nearby a electronegative molecule or atom, that means more electrons nearby, thus more shielding from external field is done. If you see the frequencies less than the expected values, that means our target is nearby some molecule shielding it.

An opposite effect also occurs, called paramagnetic effect, where the electrons in p-orbitals deshield against the external field.

Now imagine having two or three similar nucleus together. Now the number of levels again increase. Remember how Deuterium has net spin greater than Tritium. Inner tenants arrange themselves opposite to each other. So whenever you take two similar beings of quantum realm, they do this stuff, grouping together and establishing more floors. Consider the following molecule.

In the methylene position, there are two hydrogens, so they join hands and give rise to following levels….

See three levels, both aligning opposite to the field, both aligning opposite to each other and then both aligning along the field.
Similarly in the methyl position, there are 3 hydrogens. So what they do is the following:

See four different levels. This effect of called Spin-spin coupling, since a group of similar spins couple to give this. By absorbing these frequencies in the spectrum one can say at which position the hydrogen is placed.

Doesn’t the methyl positioned hydrogens involved with the methylene positioned ones? Oh yes! they do. why not. Such an effect is called Nuclear Overhauser effect. Guess what! by studying these frequencies, one can study the 3-d arrangement, since this is the study of surrounding lattice.

I think I am done with the important effects on NM resonance. I still didn’t began to explain how the MRI works. But as I said, books were written on this topic. I am just trying to cover the basic basics one must know to understand the working of MRI.

How can one use the knowledge of NMR to study the inner tissues? First let’s us understand how NMR spectroscopy is done. What is spectroscopy? It is the study of matter based on its interaction with the matter. Everyday we see the structures around us, based on how visible light is interacting with the structured matter. Well, it is Spectroscopy. You look at a chain some girl is wearing. You will get to know whether it’s gold or silver based on the light it reflected. This is also spectroscopy. I would like to mention all the possible interactions of matter with electromagnetic radiation or simply light.

First sort of interaction that mankind must of known is reflection, which can be said as elastic scattering of photons. So a mirror reflects most of the visible light.

The other interactions are absorption, emission, and refraction, then transmission, inelastic scattering such as compton and raman scattering. Do you think of any other form of interaction. I think i know two other cases. take a particle and its antiparticle. Bring them together. Boom! they annihilate each other giving out energy, in the form of photons of course. Now just watch the above phenomenon reversing the time. There is photon, which gave out two particles, I mean a particle and an antiparticle.

It would be cool if I show you the feynman diagrams and illustrate all the interactions of light and matter. But I am a idiot. I just want to publish more articles, I will write one on Feynman diagrams.

So a spectroscopy study means to consider any one of the phenomena and to study the material or sample based on such phenomena inside it. Absorption spectroscopy is to illuminate a sample with light and to collect the transmitted part. The scattering in these samples are considered to be negligible or not necessary in some cases. So the spectrum of absorption is taken and we study what particular frequencies are absorbed and to what extent. This is used to study few phenomenon like SPR.

In our case of NMR spectroscopy, we have a radio frequency emitter, a strong magnet and a receiver. So we either fix the frequency or fix the magnetic field and change the other. One must be fixed. And we see how the sample under study is responding like at what field values is the absorption high or at what frequencies it is high. Since we know from the theoretical studies and experimental confirmations the expected values of most of the nuclei, this spectroscopy helps to detect the presence of all the known nuclei. There is a most important part to this spectroscopy which also plays an important part in the MRI scanning called FID. This is based on relaxation processes.

With this I would like to end this article. One more article is minimum requirement to explain the MRI working. Thank for your patience.

Originally published at on November 11, 2016.

All I know is that I can think and that I exist. What I think defines me in a way. So I am a Thinker, Physicist and Philosopher.