• ### Little talk abount MRI & Gradient Coils

Davide Ruzza03/21/2023 at 21:50 0 comments

dear fellows long time no see!

Before talking about the gradient coils (the point of the next log) I'm going to explain briefly and not in too much detail the theory behind MRI.

# Magnetic properties of Protons

Ok, let's start with some basic concepts. Protons (hydrogen atoms) have an intrinsic property called Spin. This gives the proton magnetic properties like a small magnet.

Now think of all the water molecules that are in our body, in a normal state where there is no magnetic field around, protons are randomly oriented resulting in a net zero magnetization. Suppose we apply some magnetic field like a big magnet, protons are going to align with it. Imagine it's like a little magnet on a table if we place nearby a strong magnet the first will align and attach to the latter.

Not all protons align with it or to be more clear it can be in two states: parallel where protons align in the same direction of the external field or antiparallel direction. The first one is preferred because it has a lower energy state than the antiparallel one. Think of two magnets with the same polarity, you need a lot of force to squeeze them together like you need 'higher energy', if we flip one of them they will automatically snap together (low energy).

For these reasons more protons will align in a parallel state, thus resulting in a net magnetization in the forward direction. if the population of parallel and antiparallel is 50%-50% their magnetization cancels out like adding and subtracting. The stronger the external magnetic field the higher will be the population of parallels with respect to antiparallels protons and the bigger will be the net magnetization. To achieve this, modern MRI produces a magnetic field in the order of 7-8 Tesla that is like 100k times stronger than that measured on the surface of the earth (65uT).

# Precession

Now that we have magnetized our body, the image comes from the non-uniform density of water in our different tissues (bones, skin, muscles, ... ). We need some way to measure this density and produce the image we need. To achieve this we need to use an antenna that produces a precise radiofrequency wave.

Why?

Well, when protons, that possess spin, are immersed inside a static magnetic field, exhibit a phenomenon called precession, it behaves like a gyroscope.

if we rotate the proton from the direction of the main magnetic field it starts to precess. This happens because the main magnetic field forces the proton to realign but the proton has an angular momentum from the spin that prevents the alignment. Consequently, an apparent rotation appears around the axis of the main magnetic field. Gyroscopes have an analogous behavior, you can check Prof. Walter Lewin from MIT in one of his lectures about angular momentum.

The frequency at which the proton precess depends on the magnetic field intensity and the gyromagnetic constant (intrinsic property which differs atom by atom), described by the Larmor equation:

# Our body as Radio Transmitter

Now the answer to the previous question: why do we need an antenna? well, the goal is to rotate 90deg away from the main direction which from now on I will call "z", we send an electromagnetic wave to the proton with the same frequency given from the Larmor equation. The EM wave gives a "push" at the right time while the proton precess ( I'm oversimplifying a lot here, maybe I'm going to explain this in more detail in another log )

After some time the proton has a rotation of 90deg respect to z so we stop transmitting. In this situation, the proton feels the torque from the magnetic field to realign in the z-direction. So the proton precess back and in doing so, another electromagnetic wave is generated but this time from the proton itself.

We receive this signal (with another antenna as we do for a radio or television). Where the tissue has higher density it produces bigger signal intensity because more protons...

• ### Preface

Davide Ruzza10/18/2022 at 21:54 0 comments

# Presentations

Hi, this is my first time documenting my work so I need time to get used to this kind of communication.

I present myself, my name is Davide and I come from Italy. I'm currently studying material engineer at the University of Napoli Federico II. My main subjects of course regard matter from large to the nanoscale, anyway my courses are based largely on physics (and chemistry).

Ok, now I know this project will take some time, and before publishing this first log I've already documented myself more or less on how an MRI works. So I have a general idea of how to proceed.

# A Review of an MRI

An MRI which stands for "Magnetic Resonance Imaging"  is a fascinating device that allows you to take a picture of a slice of your body. Maybe in another log ill explain in detail how it works. Still, the main function in a very simple fashion is to use a strong magnetic field (usually achieved with a superconductor ring) so all the electrons in our body "align" with it. we then send some signal with a specially tuned antenna, therefore we receive back another signal. The final step is to reconstruct the image with some fancy math that involves a Fourier transform. The image is grayscale, and every value corresponds to electron density (aka matter density) so we can discriminate all the different body tissues (skin, bone, brain, organs, fat, muscle, ...).

Obviously in reality an MRI is extremely more complex but we can section it, into individual and independent pieces:

• Main Magnetic Field: I can't afford a big superconductor ring that I must maintain at a temperature of 9.4 Kelvin (-272°C). There are two alternatives, put a current through a wire in a specific geometry or with permanent magnets in a special configuration (we need a homogeneous field over space so there is a specific way to do this). With the superconductor, we can produce a really strong magnetic field in the range of 7 T (Tesla) and even 11 T on recent MRIs. It sounds like a small value but as a reference, the average value of the magnetic field on Earth's surface is 60 milli micro Tesla. The alternatives can produce a field of 0.5-1 T so we call this specific type of MRI "Low Field" or "Ultra Low Field". The question is, why do we need a strong magnetic field? the answer is resolution, the stronger the field higher will be the resolution of our image.
• Auxiliary Magnetic Field: usually said gradient coil. When we align all the electrons with the main field we need to know where an atom is in real space. To do this we need a gradient coil that produces a varying magnetic field in space. For every value of this field, we can relate a position in space. Also, another function is to select a particular slice of our body.
• RF coil: radio frequency coil. It's a radio antenna that can send and receive within a specific narrow bandwidth. The frequency of this antenna depends on the strength of the Main Magnetic field, for a commercial MRI which provides a field of like 7-10 T the frequency of transmission and receive of the RF coil is in the order of 200-300MHz. Sometimes TX (transmission) and RX (receive) are separated in two different antennae so we can get the best tuning for the two of them.

In order to build a complete an functional MRI I need to build this 3 main parts. Of course, there is more to talk about this but in the future, I'm going to cover as much as I can in detail. In the next log I'm going to disscus how i'm going to measure the magnetic field that I will produce in future.