NMR Spectroscopy

jumpguy

Hey everyone, I'm a bit muddled trying to understand the principles of NMR spectroscopy (with the eventual goal of properly understanding how MRI works in detail...) I come here to see if I'm correct in saying the following...

I'm trying to figure out what's going on at T1 and T2*. T1 is the rate of return of the nucleus to thermal equilibrium i.e when the free induction decay curve thing becomes flat (no emf induced). Is it true to say T1 can only be measured in the homogeneous magnetic field?

T2* is the rate of decay due to an inhomogeneous field. In T2* the nuclei are spinning out of step due to the inhomogeneous magnetic field and causing destructive interference (in the overall magnetic flux rate of change) and hence reducing the EMF produced rapidly. More rapidly than in T1.

T2 is the rate of degradation of the spin echos due to forces which are due to the nature of the material and not due to the inhomogeneous magnetic field (as that's been compensated for), right?

Also, since T2* depends on an inhomogeneous magnetic field, does that mean the value of T2* is stochastic, as no magnetic field is inhomogeneous in the exact same way as the next? One magnetic field may be more inhomogeneous than the next... Or do they have a standard inhomogeneous magnetic field in NMR spectroscopy?

I'd be very grateful for some help in grasping these ideas!

harmoxe

Hi jumpguy,
I'm not an expert on either NMR or MRI, but I know a little bit about magnetic resonance. I hope it helps.

jumpguy wrote: »

I'm trying to figure out what's going on at T1 and T2*. T1 is the rate of return of the nucleus to thermal equilibrium i.e when the free induction decay curve thing becomes flat (no emf induced). Is it true to say T1 can only be measured in the homogeneous magnetic field?

T1 is the relaxation rate to equilibrium, or more precise the relaxation rate between the two spin eigenstate states (parallel or anti-parallel to the external field).
In a homogeneous magnetic field, I a normal spin echo will measure T2, the homogeneous broadening. T2 and T1 are usually related.

It can be useful to think about this is the semi-classical picture of spin precession. If the external field is applied in the vertical direction (for example), then the spins in your sample are torqued into the horizontal plane by the first pulse. Here they will happily precess around the external field forever. Three things can now happen:
1) The external field can be inhomogenous and the spins in different areas will precess at different rates, dephasing at a rate T2*; this is the process that can be reversed by using a second pulse to flip all spins 180 degrees.
2) There can be random fields along the field direction of the field (usually thermal in origin); these also cause dephasing of the spins in the plane (T2), but this is not undone with the 180 deg pulse.
3) There the random fields perpendicular to the external field, this will cause to spins to gradually align themselves with the external field in a time T1. The time T1 depends on the strength of the random field compared to the external field.
The second and third processes are obviously related, but when the random fields are much smaller than the external field, T2 will be much shorter than T1.

T2* is the rate of decay due to an inhomogeneous field. In T2* the nuclei are spinning out of step due to the inhomogeneous magnetic field and causing destructive interference (in the overall magnetic flux rate of change) and hence reducing the EMF produced rapidly. More rapidly than in T1.

Yes, exactly. There is also control of T1 (via the external field) and T2* as the inhomogeneity is also chosen.

T2 is the rate of degradation of the spin echos due to forces which are due to the nature of the material and not due to the inhomogeneous magnetic field (as that's been compensated for), right?

Yes you are correct. There are also tricks to minimise T2 such as magic angle spinning, but that not really MRI. I've also heard of the magic-sandwich spin echo where you can correct for T2.

Also, since T2* depends on an inhomogeneous magnetic field, does that mean the value of T2* is stochastic, as no magnetic field is inhomogeneous in the exact same way as the next? One magnetic field may be more inhomogeneous than the next... Or do they have a standard inhomogeneous magnetic field in NMR spectroscopy?

No. The inhomogeneity is typically designed to be much larger than the intrinsic inhomogeneity of the external field. For example a small field gradient allied on top of the regular field.

jumpguy

harmoxe wrote: »

If the external field is applied in the vertical direction (for example), then the spins in your sample are torqued into the horizontal plane by the first pulse. Here they will happily precess around the external field forever.

Thanks a lot, I understood most of your post. This bit has me confused though. If you apply the 90degree pulse, then would the nuclei not precess forever, but only for a time of T2 due to other random fields (which you said were mostly thermal in nature) before resuming back to thermal equilibrium? This is assuming the magnetic field is perfectly homogeneous.

Is T1, in simple terms, just the time it takes for the nuclei to line up in thermal equilbrium with the external magnetic field, and T2 the time taken for it to stop precessing after a 90degree pulse has been applied? The reason the spin echo is done is because we can't have a perfect magnetic field, and the spin echo technique accounts for that?

Or am I after going waaaay off the track now?

fox65

jumpguy wrote: »

Thanks a lot, I understood most of your post. This bit has me confused though. If you apply the 90degree pulse, then would the nuclei not precess forever, but only for a time of T2 due to other random fields (which you said were mostly thermal in nature) before resuming back to thermal equilibrium? This is assuming the magnetic field is perfectly homogeneous.

The phrase precess forever is a little misleading. Spins precess forever due to the effect behind the larmor frequency.

Following a 90Deg pulse. The spins are rotated into the horizontal and aligned. They will precess due to the larmor frequency. You will gradually you will loose the aligment and your enduced signal. Either the spins will return to their equilibrium state (via T1), or the spins will dephase (via T2 and T2*).

To expand on the T2 effect. Following the 90 Deg Pulse the spins are now aligned. They will now precess and gradually become randomly orientated in the horizontal axis. This random orientation will not enduce a signal. The time it takes for the enduced signal to decay is T2.

T2* arises due to imhomogenisation in the field and by interaction with other magnetic moments. This speeds up the T2 decay. This is a random process and can be corrected for using a subsequent 180deg pulses following the initial 90deg pulse. No magnetic field is perfectly homogenous and secondly other magnetic moments (ie other molecules) will generate field gradients.

jumpguy wrote: »

Is T1, in simple terms, just the time it takes for the nuclei to line up in thermal equilbrium with the external magnetic field, and T2 the time taken for it to stop precessing after a 90degree pulse has been applied? The reason the spin echo is done is because we can't have a perfect magnetic field, and the spin echo technique accounts for that?

Or am I after going waaaay off the track now?

Correct spin echo techniques correct for the random process behind T2* while allowing T2 to occur.

fox65

jumpguy wrote: »

Is it true to say T1 can only be measured in the homogeneous magnetic field?

This is not true. T1 can be measured in imhomogenous fields. For T1 measurement, typically one measures the growth of magnetisation in the horizontal plane. From this we can extract a T1. It takes a little more time to measure but can be done.

jumpguy wrote: »

One magnetic field may be more inhomogeneous than the next... Or do they have a standard inhomogeneous magnetic field in NMR spectroscopy?

I'd be very grateful for some help in grasping these ideas!

It can also depend from day to day. There is a process known as shimming. Within a NMR, there are small electro magnets which are controlled. The location of these are specific. These reduce the imhomegenaty of the field. Shimming is performed multiple times a day and will vary from day to day. Thus is is impossible to give every magnet a fixed imhomogenatity rating as such

jumpguy

fox65 wrote: »

Following a 90Deg pulse. The spins are rotated into the horizontal and aligned. They will precess due to the larmor frequency. You will gradually you will loose the aligment and your enduced signal. Either the spins will return to their equilibrium state (via T1), or the spins will dephase (via T2 and T2*).

Thanks a lot, your answers have been very helpful. I think I understand just what T1, T2 and T2* are now. Just a question though, after the 90degree pulse has been applied, you say the spins will either return to their equilibrium state OR just dephase. How do you know which event will occur?

fox65

It is a combination of both. both occur at the same time. but T2 is always shorter then T1, generally much shorter then T1 thus is the main process which causes the enduced signal to decay.

jumpguy

fox65 wrote: »

It is a combination of both. both occur at the same time. but T2 is always shorter then T1, generally much shorter then T1 thus is the main process which causes the enduced signal to decay.

Excellent, that is how I imagined it all along! The nuclei precessing less and then just returning to equilibrium.

Thank you! Now onto k-spaces... :pac: