# Nuclear Magnetic Resonance

1. May 2, 2005

### broegger

Hi,

I'm taking a course on medical imaging (mainly MRI), and I'm having trouble understanding NMR. Can anyone explain what this is all about in plain language? Here is what I make of it: Odd-numbered nuclei possesses a total spin of magnitude 1/2 and an associated magnetic moment (why is that, is there a classical analogue?), normally the nuclei is distributed nearly equally between spin-up and spin-down states, but this can be inverted by applying a time-varying RF-field (variying with the Larmor-frequency, why?). When the nuclei returns to their equilibrium states they emit radio waves, which can be measured and by analyzing the time from irradiation to emmision one can somehow infer something about the chemical enviroment of the nuclei in question (i.e. the type of tissue in the case of MRI). But how is this done and what is it precisely we are measuring?

Also, I don't understand why the largest RF-signal is generated by a 90° pulse, since the energyshift for 180° pulse is bigger?

Thanks.

Last edited: May 2, 2005
2. May 2, 2005

### ZapperZ

Staff Emeritus
What you are asking is practically the WHOLE course on Pulse NMR. I'm not sure one person, in one thread, is capable of explaining all you wanted to know in that question.

If you are able to, I highly recommend you get E. Fukushima's excellent text "Experimental Pulsed NMR: A Nuts and Bolts Approach". This is a bit more approachable than Slichter's classic text.

Zz.

3. May 2, 2005

### Claude Bile

This website is an excellent introduction to NMR, very digestible and lots of animated diagrams.

www.cis.rit.edu/htbooks/nmr/

Claude.

4. May 2, 2005

### Gokul43201

Staff Emeritus
Here's a very basic intro to what happens in an NMR measurement :

The nucleii of your sample have spins (and associated magnetic moments), which in the absence of an applied external field will all point in different directions. There is no classical analog to the intrinsic spin. When an external magnetic field H is applied, two things happen :

1. There is a split in the energy levels of the nucleons, giving rise to an energy difference $\Delta E ~~\alpha ~~\gamma H$ that is proportional to the field strength, H (just like the Zeeman splitting that you see for electrons); and

2. The majority of the spins line up along the direction of the applied field (the bigger the field and lower the temperature, the greater will be the fraction that lines up along the field). This is the same as saying that the majority of the nucleons occupy the lower energy state. The higher energy state corresponds to the spin lining up in the opposite direction to the field.

When the sample is illuminated with radiation of the right energy (close to the energy difference between the levels), it becomes possible to excite the nucleus from the lower energy state to the higher one, through the absorption of a photon. So, when the radiation energy (and hence frequency) matches the energy difference, the sample absorbs a large number of photons from the incident beam, and hence the detected intensity drops. This drop in intensity tells you what energy difference exists between the spin up and spin down states. And this energy is a characteristic of the material.

The matching of the radiation energy with the energy difference can be done in two common ways :

1. Continuously vary the energy, E, of the incoming photons by using an EM source whose frequency can be varied; keep the energy difference constant by fixing the applied magnetic field, B

2. Continuously vary the energy difference between the up and down states by changing the applied magnetic field, B; keep the energy E, (and hence frequency) of the EM excitation constant.

When the energies are matched, some large number of spins are now in the high energy state, and turning off the EM field will cause them to fall back into the low energy state. As they fall back, they emit radiation of energy = E(diff). This tells you what the energy difference is and hence, what the gyromagnetic ratio, $\gamma$ is. This number changes from one element to another. Also, the rate at which the spins fall back (decay) into the low energy state tells you about the strength of various interactions that are trying to keep the spin stuck in the high energy state, even in the absence of an applied EM field. So, studying the time constant of decay tells you about the environment of the nucleus of interest.

5. May 3, 2005

### da_willem

There is a clasical analogue, but you shouldn't take it too seriously as most physicists believe the magnetic moment and spin of a particle are 'intrinsic' and not the result of any rotational motion. Classically a charged object that rotates (spins) also constitutes a magnetic moment proportional to it's angular momentum (it's 'spin'). Think of a spinning charged object as a bunch of current carrying loops, wich as is well known, have a magnetic moment...

6. May 3, 2005

### broegger

Thank you all very much, especially Gokul for the excellent explanation. Also, thanks for link, Claude, very helpful.

I have one more question regarding MRI: How is position information obtained in an MRI scan, i.e. how can we know extract from the NMR-information where the different types of tissue is located?

7. May 3, 2005

### imabug

That is what the gradient fields are for.

For position information in MRI, you need three gradient fields (spatially varying magnetic fields, typically on the order of 10 mT/m). They're commonly referred to as the slice select (z-axis), phase (x-axis) and frequency (y-axis) encoding gradients.

The gradients change the local magnetic field strength the nuclei are exposed to, and therefore the frequency of the RF the nuclei give off (given by the Larmor equation) as they relax back to the equilibrium state. Given the frequency and knowledge of the gradient fields, you can localize where each particular frequency comes from.

There is a book called Magnetic Resonance Imaging: Principles, Methods and Techniques by Perry Sprawls (ISBN 0944838979) that provides a very readable introduction to MRI. It's targeted towards radiology residents and technologists, so everything is presented at a fairly low level.