• Chapter 4 • Contents
  T1: Spin-Lattice Relaxation  T1 on the Microscopic Scale  Cross Relaxation T1 on the Macroscopic Scale  The Partial Saturation Sequence  The Inversion Recovery Sequence T2: Spin-Spin Relaxation T2 on the Macroscopic Scale  The Spin Echo Sequence Practical Measurements of T1 and T2  In vitro Determination  In vivo Determination  T1 (T2) Images and Weighted Images  Measurements in Medical Diagnosis  Rapid Relaxation Estimation Techniques   Biomarkers

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04-02 T1 on the Microscopic Scale

he relaxation times of pure substances, for instance water, can be easily ex­­plain­­ed. A living system, however, contains a large number of chemical com­po­nents, all of which contribute to the observed pro­ton mag­ne­tic re­so­nan­ce sig­nal. These com­po­nents possess different relaxation times. Thus, the analysis of the ob­ser­ved NMR signal in terms of the different subsystem pa­­ra­­me­­ters (con­­cen­­tra­­tion and relaxation times) is complex but very important.

For the sake of simplicity, we will deal with T1 only in two-component sys­tems. A si­mi­lar discussion is possible for T2.

For example, T1 of muscle tissue protons obtained at 0.1 Tesla is about 300-400 ms, but more than three quar­ters of the received proton signal stems from water pro­tons, which in the pure liquid show a T1 of several seconds.

Using an example from clinical routine, cerebrospinal fluid (CSF) has similar re­la­xa­tion times as water. Brain edema, which reflects pathologically high water con­tent in brain tissue, possesses relaxation times that are closer to brain tu­mors than to CSF (Figure 04-03).

What is the reason for this discrepancy?

This is best explained using the relaxation rate R1. R1 equals 1/T1. Several dif­fe­rent R1 com­po­nents can be added to each other to create a new R1 (cf. Chapter 12).

The T1 of a biological sample is a parameter reflecting the physical and che­mi­cal pro­per­ties in the environment of the observed nuclei. If the environment is not the same throughout the sample, then the obtained T1 will only reflect the mean pro­per­ties of the sample. In most tissues, one component, usually water, do­mi­na­tes the re­la­xa­tion be­ha­vior. In special cases, where two com­po­nents with sig­ni­fi­cant­ly dif­fe­rent T1 values are present in comparable amounts, a complex situation arises, which makes a quantitative interpretation difficult.

Let us consider two systems containing two different groups of protons, one mov­­ing fast, one moving slower. Both possess dif­fe­rent T1 relaxation times and thus dif­fe­rent R1 relaxation rates. We can compare them with the example in Fi­gu­re 04-06.

Here we have two containers, I and II, filled with water. Both of them have an out­let, but the outlet of Container II is larger than that of Container I (Figure 04-06a). The rate, R, at which water is leaving I and II can be ex­pres­sed in milli­liters per second, and the time needed to empty the containers is gi­ven by V/R, where V is the volume of the water (assuming that the water pres­sure is constant).

If we construct another container (Container III) with volume V and equip it with two outlets (Figure 04-06b), one similar to the outlet of Container I and one similar to the outlet of Container II, then the water in this container will leave at a rate which is the sum of the two outlet rates.

Figure 04-06:
The container example explains the use of relaxation rates instead of relaxation times in a complex system. (a) Two containers I and II with differently sized outlets; (b) one container with two differently sized outlets.

This reflects the relaxation time of a tissue composed like our example in Figure 04-03. Although we have two different components, we only measure one common re­la­xa­tion time for this tissue.

If the exchange rate between the two groups of protons is very slow or absent, we can identify two different contributions to the relaxation be­ha­vi­or. A physical rea­son for such a behavior can be found, for example, in samples containing both fat and mus­cle tissues. The fat cannot exchange protons with the water in the mus­cle tissue. In the case of slow proton exchange, the system will show double ex­po­nen­tial re­la­xa­tion. Other biological systems can show a single ex­po­nen­tial re­la­xa­tion be­havior, as if they were relaxing governed by a single re­la­xa­tion time.

It is possible to distinguish the data, provided that enough data points are avai­l­ab­le. How­ever, the accuracy actually needed for such measurements is often un­der­esti­mat­ed, in particular in whole-body imaging machines.

04-02-01 Cross Relaxation

Solids, such as proteins and membranes, have a wide range of re­so­nan­ce fre­quen­cies, which allows for energy exchange between different parts of the solid. The pro­cess of energy exchange in a solid is referred to as spin diffusion. Thus, if part of the solid relaxes more rapidly than the rest, it can en­han­ce the relaxation of the whole solid.

A similar process can occur between so­lids and bound wa­ter molecules, with the pre­sence of solids (such as proteins and membranes) in tissue acting to reduce the ob­serv­ed relaxation time for wa­ter. This process is described as off-resonance ir­ra­dia­tion and can be ex­ploi­ted to enhance contrast (mag­net­iza­tion trans­fer con­trast; cf. Chapter 11).