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Chapter 4

04-01
The Spin-Lattice (T1) Relaxation Time

04-02
T1 on the
Microscopic Scale

04-03
T1 on the
Macroscopic Scale

Partial Saturation
Inversion Recovery
04-04
The Spin-Spin (T2) Relaxation Time

04-05
T2 on the
Macroscopic Scale

Spin Echo
04-06
Practical Measurements of T1 and T2

In vitro Determination
In vivo Determination
T1 (T2) Image and
  Weighted Images

Measurements in
  Medical Diagnosis

"Biomarkers"


Chapter Four
Relaxation Times
and Basic Pulse Sequences

04-01 T1: The Spin-Lattice Relaxation Time

xcitation of an equilibrium system always transfers the system to an un­stable state of high energy. The length of time the system will remain there depends on the local conditions (Figure 04-01).


Figure 04-01:
Spinning away into dreams: you may need relaxing times to understand re­la­xa­tion ti­mes. But how long will you stay in this po­si­tion of low energy when the wa­ves start hit­ting you?


For a system of spin nuclei in a magnetic field, an unstable situation is created by a "wave": the excitation pulse — the system is ‘pumped up’ with energy sup­plied by the RF pulse. At the molecular level, the return to equilibrium depends on the local magnetic and electric conditions at the excited nuclei.

In the same way, we need a resonance condition to exchange energy from the ex­ter­nal world to the spin system. The excited spin system needs to be exposed to elec­tro­mag­ne­tic fields oscillating with a frequency at or close to the Larmor fre­quen­cy of the nuclei before it can relax. The relaxation corresponds to the ex­cess nuclei, which were transferred to the upper energy level returning to the lower en­er­gy level (Figure 02-06 and Figure 04-02).


Figure 04-02:
(a) and (b): A ball is stuck on top of a small hill (unstable high state of energy).
(c) and (d): If two boys try to get it down by throwing rocks at it, on statistical grounds, it will take less time for two boys to achieve their goal compared with one boy.


If an isolated proton is left excited in absolute vacuum in the absence of any sort of electromagnetic fields, several years might be needed before the nucleus could, by itself, spontaneously return to the equilibrium state of low energy. How­ever, if the proton is surrounded by water, this process can be ‘stimulated’ by the surrounding nuclei and will then require only a few seconds.

Table 04-01 gives an overview of the different phenomena the system is or can be exposed to while returning to its equilibrium.




Table 04-01:

The different relaxation processes. For clinical purposes, T1 and T2 are the important relaxation times; T1-rho is of less importance.


The first process of returning to the equilibrium state from an excited state is call­ed the spin-lattice relaxation process or longitudinal relaxation process. It is cha­rac­te­ri­zed by the T1 relaxation time. The T1 relaxation time is the time re­qui­red for the system to recover to 63% of its equilibrium value after it has been ex­po­sed to a 90° pulse.

For a given kind of nucleus, T1 depends on several parameters:

spaceholder 600 type of nucleus;
spaceholder 600 resonance frequency (field strength);
spaceholder 600 temperature;
spaceholder 600 mobility of observed spins (microviscosity);
spaceholder 600 presence of large molecules;
spaceholder 600 presence of paramagnetic ions or molecules.

The presence of large molecules or of paramagnetic ions or molecules is of spe­ci­al interest.

In pure water, the process of reorientation (translational movement, rotation, etc.) of a single water molecule occurs very rapidly. Since each molecule has its own magnetic field, this rapid reorientation results in a fluctuating magnetic field at neighboring nuclei.

To promote relaxation, the frequency of the reorientation must be at, or close to, the resonance frequency in pure water. If the frequency of this reorientation is much higher than the Larmor frequency of the protons the relaxation is in­ef­fi­cient. However, if we add more slowly moving large molecules such as proteins to the water, the water molecules will interact with them. This interaction in­vol­ves tem­po­ra­ry attachment of the water to the proteins and subsequent release.

This temporary bonding radically reduces the frequency with which the water molecules reorientate themselves. Pure water, i.e., water in the bulk phase, mo­ves much faster than water close to macromolecules or membranes. The slower the molecular motion, the shorter the relaxation time T1 (and T2), shown in Fi­gu­re 04-03 as an increase in brightness.


Figure 04-03:
(a) The lower the molecular motion, the shor­ter the relaxation time T1 (in­crea­se in brightness). (b) T1-in­flu­en­ced image after a brain tumor ope­ra­tion. Fluid-filled areas are dark, ede­ma­tous areas are bright: bulk water moves faster, protein-bound water in brain edema slower (shorter T1).


To characterize the motion of a molecule, the correlation time (tc) is used. It mea­su­res the minimum time required for a molecule to re-orientate itself.

Because of the presence of protein surfaces, the T1 relaxation times of water in living tissue are always shorter than those obtained for pure water. Table 04- 02 lists some representative T1 values of normal tissues.




Table 04-02:

Some T1 values of some human tissues measured on an MR imaging system at 0.15 Tesla. The standard deviation of these values can be between 10 and 30%; in general, relaxation time values measured in vivo are not very reliable.


T1 values vary with magnetic field strength. This influences image contrast in MR imaging so that it is not possible to make direct quantitative comparisons between T1 values at different fields. Thus, it is necessary to always mention the field strength when quoting T1 values. T1 data of brain tissues at dif­fe­rent fields are shown in Figure 04-04 (more details can be found in Chap­ter 10).


Figure 04-04:
Change of T1 relaxation times of gray and white matter versus field strength. Temporal gray matter (tGM) is depicted green and parietal GM (pGM) is blue; frontal white matter (fWM) is depicted yellow, temporal WM (tWM) is red.


The data for this figure was acquired with a special NMR equipment dedicated to re­la­xo­me­try. This subdiscipline of NMR deals with the relaxation behavior of dif­fe­rent sub­stan­ces. With a field-cycling relaxometer, ex vivo or in vitro mea­su­re­ments of the relaxation behavior of tissue samples or contrast-enhancing com­pounds can be per­for­med at any field strength at high accuracy; thus identical samples can be examined un­der identical conditions. Field-cycling relaxometry showed that T1 increases non­uni­form­ly with field, leading to specific fingerprints of T1 increase for different tissues [⇒ Rinck 1988]. However, due to the complexity of the method, such fingerprints or biological markers have only scientific but no clinical diagostic relevance.


The explanation as to how the presence of paramagnetic ions or molecules can en­hance the relaxation rate of water is highly complex. Electrons produce a much stronger magnetic field than the nuclei, but when pairing of electrons oc­curs, there is only a weak net field.


Figure 04-05:
The boys of Figure 04-02 have invited an­other boy (called "Gadolinium'). His pre­sen­ce on top of the hill kicking the ball down sig­ni­fi­can­tly shortens the time the ball would stay in the unstable state.


Pa­ra­mag­ne­tic compounds influence excited spins in a similar way and shorten T1. They have unpaired electrons; their reorientation produces a very strong fluc­tu­at­ing magnetic field, resulting in a significant reduction in the relaxation time (Fi­gu­re 04-05).

Typical paramagnetic substances include Mn2+, Cu2+, Fe2+, Fe3+, Gd3+, as well as molecular oxygen and free radicals. In certain circumstances, the ability of pa­ra­mag­ne­tic compounds to alter relaxation rates can be utilized to change the con­trast in magnetic resonance images; for this purpose, for instance ga­do­li­ni­um and manganese complexes are used as magnetic resonance contrast agents (see Chap­ter 13).

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