Читать книгу Essential Concepts in MRI - Yang Xia - Страница 27

The earliest NMR experiments ran in a continuous-wave (CW) mode, where the spectrometer is tuned to observe the component of M, which is 90˚ out of phase to the rotating field B₁, the so-called absorption mode signal. (Earlier in Section 2.7, we set both B₁(t) and u in the direction of x′, and v in the direction of y′ in the rotating frame.) During an experiment, the magnetic field B₀ is swept slowly through the resonance frequency. As each chemically identical spin group comes into resonance, it undergoes nuclear induction and a voltage is induced in the pick-up coil (cf. the three peaks of ethanol in Figure 1.4). This approach is called the CW method, where the signal of the specimen is recorded continuously on an oscilloscope. Provided that this field sweep is done sufficiently slow, the absorption mode signal at each frequency corresponds to the steady state value of v when M has come to rest in the rotating coordinate system. Hence it is also called the slow passage experiment. Since neither the resonance frequency nor the number of the equivalent groups in a specimen is known, doing an NMR experiment using the CW method could take a long time.

By examining the Bloch equation in the rotating frame [Eq. (2.23)], the following observations can be made:

1 When we are far from the resonance (i.e., |ω0 – ω| is large), we have u = v = 0 and Mz = M0. The non-zero values of u and v appear only in a small interval around ω0, that is, when there is a resonance.

2 Where T1T2(γB1)2 ≪ 1 (i.e., the rf power applied is sufficiently low so that the saturation does not occur), v can be simplified as (2.24)By comparing Eq. (2.24) with the line-shape functions in Table 2.3, we see that v is a Lorentzian centered at ω0 with a line width at half maximum of 1/(πT2). Hence, in principle, the FWHM of the resonant peak can be used to determine the T2 relaxation time.

3 When T1T2(γB1)2 is not sufficiently smaller than 1, we can have these situations:when T1T2(γB1)2 < 1, the spins are below saturation, and the signal ∝ γB1T2when T1T2(γB1)2 = 1, spins are saturated, where both signal and SNR reach the maximumwhen T1T2(γB1)2 > 1, the Signal starts to drop.

4 Only the transverse component of the precessing M induces an observable signal in the receiver coil. The transverse component can be written as (2.25a) (2.25b)

where the complex i indicates a 90˚ phase shift (i = −1); v (which is in the direction of y′) is called the absorption spectrum, where the signal is proportional to the power absorbed from the EM field; and u (which is in the direction of x′) is called the dispersion spectrum (which is a common term in optics). Note that the signal is proportional to B₁ not B₁² [10].