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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.

spaceholder redUsing 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).