In Chapter 3 the concept of the radio-frequency magnetic field B₁ was introduced. In this detail section I will distinguish between a transmit B₁ magnetic field (B_1T) and receive B₁ magnetic field (B_1R) from an imaging coil. B_1T is the B₁ that you were introduced to in Chapter 3. The amount of transverse magnetization produced by a single B_1T pulse is proportional to the sine of the rotation angle (θ).

The NMR signal is not directly proportional to the sine of this rotation angle because the coil sensitivity comes into play. The sensitivity of the imaging coil is proportional to B_1R. So B_1R is the radio frequency magnetic field created by the sample. This portion of the book describes a method to measure the B_1T and B_1R magnetic fields from a spin-echo pulse sequence. The units on these calculated quantities are arbitrary.

For a single RF pulse of length t, and amplitude, B_1T, the signal can be shown to be proportional to

B_1R Sin(2π γ B_1T τ).

For a spin-echo pulse sequence, where the product of B_1T τ of the 180^o is twice that of the 90^o pulse, the signal is proportional to

B_1R Sin³(2π γ B_1T τ).

Therefore, it should be possible to determine spatial distribution of the relative B_1T and B_1R values in a magnetic resonance imaging coil knowing the signal at several B_1T settings near the prescribed rotation angles of the sequence.

To measure the relative B_1T and B_1R as a function of position within an imaging coil, the imaging coil must be connected to the imager and the following general procedure followed.

1. Place a signal-bearing phantom in the imaging coil. The signal bearing substance should have a relatively short T₁ so as to minimize the acquisition time.
2. Tune the coil so that it is matched to the impedance of the imager and resonates at the resonance frequency of the imager. (See the Imaging Coil section of Chapter 9 for more detail.)
3. Select a TR value approximately five times T₁. Set the other imaging parameters to produce an image of a slice with an appropriate in-plane resolution.
4. Determine the approximate power needed for an average rotation of the spins in the phantom by 90^o and record an image. (This power level will be defined as P₉₀.)
5. Record several additional images with the transmit power set at approximately 0.5 dB increments above and below P₉₀. You need to record enough points to fit a curve to the signal data. If you plot the signal from three arbitrary pixels in your images as a function of transmitter power you should see plots like this.
6. Convert the power (P) settings in dB used to record the images into arbitrary magnetic field (B) units using the relationship
   dB = 20 log (B). A plot of signal from the same three arbitrary pixels in the images as a function of B will look like this.
7. Fit the data points with a function of the form
   Signal = B_1R sin³(B_1T B). B_1T will be greater for pixels where B peaks at smaller values. B_1R is the scaling factor for the function, therefore, the greater the signal, the larger B_1R. This figure depicts the variation in B_1R for three different pixels with unequal B_1R values, but equal B_1T.

It should be emphasized that B_1T and B_1R are in arbitrary units. Calibrating B_1T is possible knowing properties of the pulse, but this is not necessary for most applications.

The animation window contains examples of B_1T and B_1R images for a slice through a spherical RF homogeneity phantom. The red line is a plot of the field through the center of the slice. The phantom is filled with one of three solutions: (1) 14 mM aqueous NiCl₂, (2) a reverse micelle solution of water, AOT (a surfactant), and decane, and (3) 154 mM Aqueous NaCl and 6 mM NiCl₂. These three solutions were chosen to point out a problem associated with the signal bearing substance in a phantom. The inverted parabolic shape of the 14 mM aqueous NiCl₂ filled phantom is due to the standing wave artifact. This artifact is observed when the wavelength of the RF in the phantom solution is twice the diameter of the phantom. The parabolic shape of the 154 mM Aqueous NaCl and 6 mM NiCl₂ filled phantom is due to the conductivity artifact associated with high electrical conductivity solutions. In this situation, the energy is concentrated on the surface of the conducting sphere. The shape of the field in the reverse micelle solution filled phantom more accurately represents the B_1T and B_1R fields in the imaging coil. The improved accuracy is because the standing wave and conductivity artifacts are minimized owing to the dielectric constant and conductivity of the reverse micelle solution.

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