### FRCR Physics Notes

#### FRCR physics notes contents

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# T1 and T2 signal

Transverse magnetisation and creation of signal

The MR signal is created by the precession of the nuclei in the xy plane in-phase, which creates a net magnetisation. This magnetisation precesses at the Larmor frequency inducing an electric voltage in the receiving coils. This electric signal is a sinusoidal wave of the same frequency as the net nuclei precession.

The signal is greatest during and immediately after the brief 90° RF pulse has been switched off. Then, the transverse magnetisation (Mxy) decays to zero and the longitudinal magnetisation (Mz) recovers to 100%. This consists of two different and independent mechanisms:

1. Spin-Lattice Relaxation

2. Spin-Spin Relaxation

#### Note

It is important to note that these two processes are occurring at the same time but are completely independent i.e. the Mz of T1 recovers along a different time course to the Mxy of T2.

## 1. Spin-lattice relaxation

As the nuclei precess in the transverse plane they are jostled by the surrounding molecules (i.e. the surrounding lattice) and they give up their energy to these molecules. As they do so they return to the longitudinal magnetisation (Mz) exponentially. This is called Spin-Lattice or Longitudinal Relaxation. The rate at which this happens is governed by the time constant T1.

• T1 is the time it takes for Mz to recover to 63% of its maximum value.
• T1 depends on the surrounding molecules and lattice.

*** T1 is always longer than T2 (except water in which T1 = T2) ***

Note: The 90° RF pulse will pull all the Mz signal to 90° i.e. to the Mxy plane. This means if we have a large Mz signal then apply a 90° RF pulse, it becomes an Mxy signal of the same magnitude. We will ignore this for the moment as we are only focusing on the Mz signal which is zero, but we will come back to it when we look at weighted imaging.

#### Effects on T1

Fat and protein: short T1. The molecules are large with low innate energy. This makes them very effective at absorbing energy causing a quick loss of Mxy and, therefore, quick recovery of Mz and a short T1.

Water: long T1. The molecules are small and move quickly making them inefficient at jostling the nuclei and absorbing energy. This causes a long T1.

Bone / calcium / metal: very long T1. The macromolecules are fixed and rigid and are the least effective at removing energy from the precessing nuclei.

*** Fast food (fat causes short T1) and long drink of water (water causes long T1) ***

## 2. Spin-spin relaxation

Once the RF pulse is stopped, the magnetic properties of each nuclei alter the local magnetic field and cause some to precess faster and some slower (remember, the precessional, or Larmor frequency, is determined by the strength of the magnetic field).

Gradually the nuclei lose their coherence and the net transverse magnetisation reduces to zero. The rate it does so is exponential and called the “Free Induction Decay“.

The rate at which the transverse magnetisation is lost is determined by the magnetic interaction between the spins and is called the spin-spin or transverse decay. The time constant of this fall-off is called the T2.

• T2 is the time it takes for the transverse magnetisation to decay to 37% of its value (i.e. loses 63% of its maximum signal)
• T2 depends on the local magnetic field.

#### Effects on T2

Bone / calcium / metal: short T2. The local variation of magnetic field is greatest in solids and macromolecules that are rigid.

Fat: Short T2.

Water: Very long T2. The lighter molecules are in rapid thermal motion that smoothes out the local field producing a longer T2.

### T2* or free induction decay

What has just been described is the exponential curve of transverse decay in the ideal world. However, when we measure it in the real world we find that the transverse decay is much quicker; the signal reduces to zero faster than expected. This is called the T2* curve.

This is due to the effect of the local and external magnetic field inhomogeneities. Although the B0 magnetic field is largely the same throughout it is not exactly homogeneous and the tissue and other materials within the magnetic field will also affect the magnetic field. This variation causes the nuclei to dephase quicker.

The spin-echo sequence explained next deletes the effect of local field inhomogeneities so that only the tissue characteristic T2 effect is recorded.

## T1 and T2 values

Relaxation times of different tissues in a magnetic field of 1 Tesla:

 T1 (ms) T2 (ms) FatKidneyWhite matterGrey matterCSFWaterBone, teeth 25055065080020003000Very long 8060901001503000Very short

### Σ  Summary

• T1 recovery
• Due to spin-lattice relaxation
• Recovery of longitudinal magnetisation (Mz)
• T1 time constant is time it takes to recover 63% of maximum Mz
• T2 decay
• Due to spin-spin decay
• Decay of transverse magnetisation (Mxy)
• T2 time constant is time it takes to decay to 37% of maximum Mxy
• T2* / Free Induction Decay
• T2 decay due to superimposed magnetic field inhomogeneities
• T2* shorter than T2
• T1 vs T2
• Water: long T1, very long T2
• Fat: short T1, short T2
• T1 is always longer than T2 except in pure water in which T1=T2