T1, T2 and T2*

Chapter 3

We shall see:

•T1 Relaxation Time

•T2 Relaxation Time

•Dephasing

•Interactions between individual spins

•External magnetic field inhomogeneity

•The received signal

•Free Induction Decay (FID)

•Differences between T2 and T2*

T1 Relaxation Time

• The term relaxation means that the spins are relaxing back into their lowest energy state or back to the equilibrium state.

•

• T1 is called the longitudinal relaxation time because it refers to the time it takes for the spins to realign along the longitudinal (z) axis.

• T1 is also called the spin-lattice relaxation time because it refers to the time it takes for the spins to give the energy they obtained from the RF pulse back to the surrounding lattice in order to go back to their equilibrium state.

• After the RF pulse is turned off, two things will occur:

a) The spins will go back to the lowest energy state.

b) The spins will get out of phase with each other.

• Mz (t) = M0 (1 - e-t/T1)

T1 RECOVERY

T1 RECOVERY GRAPH

T2 Relaxation Time

• Rapid decay of the Mxy component after the RF pulse is turned off. As the longitudinal magnetization vector Mz recovers, the transverse vector Mxy decays at a rate characterized by T

• Mxy (t) = M0 e(-t)/T2

T2 RELAXATION

T2 GRAPH

T1 and T2

DEPHASING

• After the 90° RF pulse is turned off, all spins are in phase. They are all lined up in the same direction and spinning at the same frequency ω0. There are two phenomena that will make the spins get out of phase:

interactions between spins

external field inhomogeneities.

INTERACTIONS BETWEEN INDIVIDUAL SPINS

• When two spins are next to each other, the magnetic field of one proton affects the proton next to it. Assume one proton is aligned with the field and the other is against it.

• It is called a spin-spin interaction.

• This interaction is an inherent property of every tissue and is measured by T2.

EXTERNAL MAGNETIC FIELD INHOMOGENEITY

• This is the second phenomenon that makes spins get out of phase. No matter how good a system we have, no matter how stable the external magnetic field is, some variation in the homogeneity of the magnetic field still exists (usually measured in parts per million).

• The two causes of spin dephasing are: a) Spin-spin interactions (internal

inhomogeneities)

b) External magnetic field inhomogeneities

• These two phenomena together cause protons to spin at slightly different frequencies. Imagine that we have three protons:

a) One is precessing at the true Larmor frequency = ω0.

b) One, exposed to slightly higher magnetic fields, is precessing at a frequency slightly faster than the Larmor frequency = ω0+.

c) One, exposed to slightly weaker magnetic fields, is precessing at a frequency slightly slower than the Larmor frequency = ω0-.

• If we wait long enough, the three protons in the x-y plane will get completely out of phase. The net magnetic field within the x-y plane will then go to zero.

• Therefore, at time = 0, all spins are in phase, and their vector sum will be at maximum magnitude.

THE RECEIVED SIGNAL

• The RF coil (e.g., head or body coil) is often both a transmitter and a receiver. The signal is received at the same location at which it is transmitted.

• When the magnetic field of each spin (or each group of spins) is in the same direction as the RF coil receiver, a very large signal is induced in the RF receiver coil.

FREE INDUCTION DECAY (FID)

• It is the fast decay of signal after removal of RF pulse.

• After we turn off the RF pulse: a) The spins begin to precess freely.

b) The signal starts to decay with time.

c) The spins induce a current in the receiver coil.

• Mxy (t) = M0 e-t/T2* (cos ω0 t)

DIFFERENCES BETWEEN T2 AND T2*

• T2* decay depends on both a) External magnetic field

b) Spin-spin interactions

• If we have a perfect magnet that does not introduce any inhomogeneity, then T2* can be eliminated.but practically it is impossible.