Time over which the oscillating field (B1) is applied
The gyromagnetic ratio (measure of the strength of the nuclear magnetism) Each nucleus has a fixed value. For hydrogen: ⁄ MHz/tesla.
Angular pulse terms such as π pulse (180o pulse) or a π/2 pulse (90o pulse), refer to the angle through which magnetization is tipped by B1 (Figure 3-12).
Figure 3-12 – the Tipping process
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6
M
(t)/M
0 PolarizationTime / T1τ
B1
M θ M 𝜃 𝑜 M M 90o Pulse 𝜃 𝑜 M M 180o Pulse189
Relaxation Process:
When the B1 field is turned off, the net magnetization decreases and system gradually returns to
equilibrium. During this process, the protons gradually lose their extra energy and return to equilibrium by emitting radio waves and by transferring energy to surrounding molecules. The processes by which nuclei transfer energy to their surroundings to return to equilibrium state are called relaxation. The relaxation processes are exponential in time and are described by two time constants, T1 as the
longitudinal magnetic relaxation time constant and T2 as the transverse magnetic relaxation time
constant. These two constant values are seldom equal. Transverse relaxation is always faster than longitudinal relaxation; consequently, T2 is always less than or equal to T1. In general, for protons in
solids, T2 is much smaller than T1.
T1-Longitudinal relaxation time
As the protons absorbed energy from B1, lift up to the high-energy state during T1 relaxation, any given
spin can return to the ground state only by dissipating excess energy to the surrounding (lattice) (Figure 3-13). Therefore this process also called spin-lattice relaxation. During the T1 time the z-component of M
returns to 63% of its original value.
(1) (2) (3) (4)
Figure 3-13 – Net magnetization return to equilibrium by turning off the B1, (the arrow represent net magnetization)
T2-Transverse relaxation time
During T2 relaxation, no energy is exchanged from the nuclei to lattice. Exchange of energy happens
among nuclei. Therefore T2 also called spin-spin relaxation. Transfer relaxation corresponds to the loss
of phase coherence or randomization of spins in transverse direction (x-y) direction, which causes the loss of transfer magnetization. T2 refers to the time required for the transvers component Mxy to decay
to 37% of initial value. A 90o pulse B1 gives energy to the protons and M rotates entirely into the x-y
plane (Figure 3-14). Coherence now exists in this transverse plane at the end of the pulse. The protons are all synchronized and precess at the same frequency. A transfer of energy can occur between these protons. Spin-spin relaxation refers to this energy transfer from an exited proton to a nearby unexcited proton. This energy exchange produces a gradual loss of phase coherence to the spins. As the coherence gradually disappears, the value of Mxy decreases toward zero (Figure 3-14). This loss of coherence is a
consequence of T2. T2 relaxation is more efficient in large molecules since they reorientate more slowly
190
(1) (2) (3) (4)
Figure 3-14 – de-phasing (loss of phase coherence) during T2
When a wetting fluid fills a porous medium, such as a rock, both T2 and T1 are dramatically decreased,
and the relaxation mechanisms are different from those of the protons in either the solid or the fluid. There are many different properties of the fluid and porous media that could be measured or explained by using the relaxation process and (T1, T2) values.
Spin-Echo and CPMG pulse sequence
Once the 90o B1 pulse is turned off, the proton begin to de-phase or lose phase coherency in B0 (Figure
3-14). As the net magnetization in the transverse plane decreases, a receiver coil that measures the magnetization in the transverse direction could detect a decay signal in this situation. If the magnetic field was really homogeneous (the amplitude is not a function of x, y or z), the signal would decay with a time constant T2. However, since the B0 has some inhomogeneity, the signal actually decays faster with
the time constant T2*, which called Free Induction Decay (FID). The FID is very short, which is lasting a
few milliseconds. Consequently in the small time interval between the two pulses, very little T1, some T2
de-phasing and substantial T2* occurs. The de-phasing resulting from T2* occurs at a constant rate since it
arises from the spatial inhomogeneity of the magnetic field. T2 de-phasing on the other hand fluctuates
randomly since it results from the interaction among the nuclei themselves. This type of de-phasing provides valuable sample information.
In order to measure T2, the signals must be recombined. It can be done by applying an 180o pulse after
the 90o pulse (after
τ
ms) to re-phase the proton magnetization vectors in the transverse plan (Figure 3-15). In effect, the phase order of the transverse magnetization vectors is reversed, so that the slower vectors are ahead of the faster vectors. The faster vectors overtake the slower vectors, rephrasing occurs, and a signal is generated that is detectable in the receiver coil. This signal is called spin echo. The echo time (TE) defined as the time between the 90o pulse and the re-phasing completion, which is 2τ
.Applying 90o B1 pulse at time 0.
Mxy
191
De-phasing after turning off the B1
At time τ ms, a 180° B1 pulse is applied to reverse the phase angles and thus initiates re-phasing.
Re-phasing is complete, and a measurable signal (a spin echo) is generated at time 2τ ms.
Figure 3-15 – Spin-echo sequence
Only a single echo decay very quickly. One way for determining T2 from spin echo amplitudes is by
repeating the spin echo method several times with very time
τ
.In CPMG method a series of 180o pulse are applied at intervals