Resources: - [thePIRL YouTube](https://www.youtube.com/@thepirl903) - [How MRI Works - Part 1 - NMR Basics](https://www.youtube.com/watch?v=TQegSF4ZiIQ) - [How MRI Works - Part 2 - The Spin Echo](https://www.youtube.com/watch?v=M7yh0To6Wbs) - [How MRI Works - Part 3 - Fourier Transform and K-Space](https://www.youtube.com/watch?v=R_4GuyJTzMo) - [How MRI Works - Part 4 - The Gradient Recalled Echo (GRE)](https://www.youtube.com/watch?v=vapJRr6gAds) - [MRI4ALL Paper](https://onlinelibrary.wiley.com/doi/10.1002/jmri.29771) - [MRI4ALL Github](https://github.com/mri4all) - [50 mT Halbach MRI paper](https://pubmed.ncbi.nlm.nih.gov/32627235/) - [Ultra low field MRI study review paper](https://www.sciencedirect.com/science/article/pii/S2666956026000073) - [Tabletop MRI paper](https://www.sciencedirect.com/science/article/abs/pii/S1090780719302642) - [Laron Principles of MRI](https://larsonlab.github.io/MRI-education-resources/Introduction.html) ### How an MRI Works 1. $B_{0}$ Magnetic field aligns quantum spin of hydrogen atoms (protons) 2. RF coils send an RF wave (~100 MHz) at resonance to tip nuclei out of alignment 3. Nuclei precess giving off an RF signal for time T2 1. The magnetic field follows a gradient so the signal frequency variesx with position for imaging 4. Nuclei realigns with the field over time T1 The **Larmor Equation** describes the magnetic precession frequency of a proton which is placed in a time-varying magnetic field at resonance. $ \omega = \gamma \vec{B} $ $\omega =$ precession frequency $\gamma =$ gyromagnetic ratio of nucleus $\vec{B} =$ magnetic field The sum of precessions of the $N$ particles creates a changing magnetic field which creates a measurable voltage in the RF coils accord to Lenz's Law $\epsilon = -\frac{ \partial \Phi }{ \partial t }$. Magnetic resonance can be visualized with [CompassMR](https://www.drcmr.dk/CompassMR/) - Resonance example: $B_{0}=5 \text{ mT}$, $B_{1}=1\text{ mT}$, $B_{1}\text{ freq} = 0.6 \text{ Hz}$ - Resonance frequency depends on field strength - Disturbing the magnet in a static field causes it to precess back into alignment This gives us an equation for the signal voltage: $ S(t) = \underbrace{N \sin(\theta)\gamma \vec{B} }_{ A }\cos(\omega t)e^{-t/T_{2}} $ $N =$ number of particles with spin $\theta =$ flip angle (angle of spin with respect to magnetic field) $\omega =$ precession frequency $\gamma =$ gryomagnetic ratio $\vec{B} =$ magnetic field $T_{2} =$ time constant of Free Induction Decay (FID) Trick: let $\omega\to_{0}$ ("transition to the rotating frame") | Tissue | $T_{2}$ | | ------------ | -------- | | Bone | 1 ms | | Lung | 0.1-2 ms | | Spinal fluid | 160 ms | | Water | 1000 ms | ## Physics ### Questions - Why do certain atomic nuclei absorb and re-emit RF energy when placed in a magnetic field? - How does the magnetic field align nuclei? - Why does the RF pulse tip nuclei? - What causes the differences in T2 and T1 relaxation between elements? - T2 relaxation comes from spins becoming dephased from each other ### MRI Construction ### Magnet Creates a uniform B0 field through the middle ### Gradient Coils Alters B field in x, y, and z ### RF Coils