The giant magnet (MRI) — the name and the spin

Sometime around March last year, my mum slipped on ice and landed on her wrist. She was asked to take an X-ray to assess the damage, but after getting an initial X-ray, she was also recommended to do an MRI since it was a scaphoid fracture.¹ Scaphoid fractures are not diagnosed on an X ray and hence MRI would be the gold standard for detecting them.²I was watching her, as she was being reeled into this giant magnet (as my dad would say — Fig. 1). But how does this giant magnet pull-out images of what is inside you. The physics of Magnetic Resonance Imaging is perplexing, and I have decided to go down this rabbit hole and share what I have learnt with you.

Fig. 1: MR Scanner 1.5T source: https://www.sqhpl.com/mri-scanners.php

Before we start this journey, we need to know why MRI is named so and why it makes sense. MRI comes from the family of NMR, which stands for Nuclear Magnetic Resonance. Although there is nothing “nuclear-ly” risky about it, the involvement of the nucleus of an atom is where it gets its name. But a widespread fear of using nuclear caused it to be called MRI instead of NMRI. The magnetic refers to the many magnetic components including the giant magnet, and resonance is to match the frequency of radio waves (RF) to the frequency of the spinning nucleus. I know it’s a whole lot to digest, so let’s break this down.

Consider an atom. There are protons in the nucleus (hence the nuclear), and a shell of electrons around the nucleus(Fig 2a, 2b). Within the nucleus, the protons rotate about their axis carrying their charge with them. This rotation is what we call “spin”. As the proton spins, the charge also moves around the proton’s axis, causing a very small current. Undeniably, where there is an electric current, there is a magnetic field (contributing to our magnetic aspect)(Fig. 2c)

Fig. 2. a) An atom b) Structure of atom with proton and neutrons in the nucleus and a shell of electrons c) spin orientation without magnetic field d) spin orientation in the magnetic field Source: a) VectorStock b)https://www.expii.com/t/protons-structure-properties-8612 c,d)https://bio.groups.et.byu.net/mri_training_b_Alignment_in_Magnetic_Fields.phtml

When we put these spinning protons, in our giant magnet (let’s name this magnetic field it the B₀ field ), they either align themselves along the B₀ field in a parallel fashion or against the field, anti-parallel, depending on their energy level (Fig. 2d). It is much easier for the protons to align themselves parallel to the B₀field, but some are very stubborn and take up more energy to align against the B₀ field. There are almost the same number of parallelly aligned protons as the anti-parallel ones, with the number of parallelly aligned protons being slightly greater. The effect of the parallel and anti-parallel protons cancels each other and the difference results in a few parallelly aligned protons. These parallely aligned protons are the one that create the signal to be detected. This difference increases with strength of the B₀ field.

It might be worrying that the difference is too small for any signal to be detected, but this theory is for one cubic centimeter (voxel) of tissue in the human body. Given that our primary source of protons in the human body is from hydrogen, and hydrogen being the main component of water, fat and other tissues, there’s a lot of it. Plus, we have to also consider Avogadro Number (order of 10²³) of atoms per gram of tissue. So, it’s safe to say, we have a significant amount of magnetic field to measure.

Fig. 3: Precession of proton in magnetic field Source: https://www.drcmr.dk/mr

These protons however, do not stay still in the magnetic field. The protons move in cone shaped fashion, essentially spinning about the B₀ field. It would look like the protons are a spinning top which are about the fall down, but they keep spinning forever (Fig. 3). This motion is called precession. The frequency of precession is called Larmor frequency, and this is what we have to detect (hence the resonance).

The equation tying the magnetic field and the Larmor frequency is called the Larmor equation and is as follows:

where γ is called gyromagnetic ratio. γ varies by the type of nuclei, hence differs with the type of tissue. ω₀ is Larmor frequency of the protons and B₀ is the main magentic field. For hydrogen in the water molecule, γ is 2.68x10⁸ rad/s/Tesla. In Hz, γ/2π = 42.6MHz/Tesla. This means our protons, when placed in the B₀ field, precess at a rate in the radio frequency range. You will hear the term radio frequency or RF quite often from this point on, since it is an important aspect of pulling images out. Depending on the strength of the B₀ field, the Larmor frequency may fall in or under the FM broadcasting range.

Therefore, our goal is to tune in to the right station and listen to what these protons have to say. We will cover this topic in our future blogs. (Hint: we use Radio Frequency equipment)

Key Takeaways:

1) Protons spin about their axis, thereby carrying their charge with the spin. This moving charge causes magnetism, of a very small magnitude.

2) These magnetic protons align either parallel or anti-parallel to the B₀ field.

3) The difference between the number of parallel and antiparallel spins might be small, but considering per gram of tissue, it’s a significant number.

4) The protons “precess” around the main magnetic field (B₀ field) with Larmor frequency, ω₀, which depends on the main field strength and the type of tissue.

Thank you for reading. I intend to write a series of blogs explaining different concepts of Magnetic Resonance Imaging, since its easier to read it this way. As we go through the series, you will be able to tie everything together and hopefully get interested in MRI.
I learn new concepts in MRI, as I am writing this blog, so if there is any error, please do let me know.

Thanks to my mum, my dad, all my friends who took time to read this blog and my PI, Dr. Zhongliang Zu, who has something new to teach me everyday.

References:

1. Amrami, K. K. (2005, August 1). Radiology corner: Diagnosing radiographically occult scaphoid fractures-what’s the best second test? Journal of the American Society for Surgery of the Hand. Retrieved November 10, 2022, from https://www.jhandsurg.org/article/S1531-0914(05)00083-5/fulltext
2. Haacke, C. (1999). Magnetic Resonance Imaging: Physical principles and sequence design. Wiley-Liss.
3. Rhemrev, S. J., Ootes, D., Beeres, F. J. P., Meylaerts, S. A. G., & Schipper, I. B. (2011, February 4). Current methods of diagnosis and treatment of scaphoid fractures — International Journal of Emergency medicine. BioMed Central. Retrieved November 10, 2022, from https://intjem.biomedcentral.com/articles/10.1186/1865-1380-4-4
4. Schild, H. H. (1999). Mri made easy: (… well almost). Berlex Laboratories.