Chapter 20, Problem 51RPP

BIO Magnetic resonance imaging In magnetic resonance imaging (MRI). a patient lies in a strong uniform constant magnetic field $\stackrel{\to }{B}$ oriented parallel to the body. Typical magnitudes of this field are between 1.0 T and 3.0 T The field is produced by a largo superconducting solenoid. The MRI measurements depend on the magnetic dipole moment $\stackrel{\to }{\mu }$ of a proton, the nucleus of a hydrogen atom. The proton magnetic dipoles can have only two orientations either with the field or against the field. The energy needed to reverse this orientation ("flip" the protons) from with the field to against the field is exactly $\Delta U=2\mu B$

(like the energy needed to turn a compass needle from north to south).

The pulse of an alternating magnetic field of frequency several tens of MHz irradiates the patient's body in the region to be imaged When this alternating field is tuned correctly so that its energy equals the $\Delta U=2\mu B$ needed to reverse the orientation of the protons from with the external $\stackrel{\to }{B}$ field to against it, a reasonable number of protons will flip. When the protons return to their initial orientation and a lower energy stale, they produce an alternating magnetic field with almost exactly the same frequency as that of the original radiation. This alternating magnetic field produced by the protons is detected and provides information about the spatial distribution of the concentration of protons as well as information about the structure of the material surrounding the protons in the region irradiated by the alternating magnetic field. The proton concentration as well as the protons' characteristic interactions with their surroundings differ in fat, muscle and bone tissue, and in healthy and diseased tissue.

The MRI imago of an internal body part is made by adjusting an auxiliary magnetic field which varies the external B field over the region being examined so that the probe field energy equals the flipping energy $\Delta U=2\mu B$ in only a thin slice of the body. A measurement is made at this slice. The external magnetic field is then adjusted to flip protons in a neighboring slice Continual shifts in the magnetic field and detection of proton concentrations at different slices produce a map of proton concentration in the body. The MRI image of the lower back in Figure 20.36 indicates an L45 disc that has partially collapsed— it has lost water and because it contains fewer protons, it produces a darker MRI image.

Which answer below is closest to the energy of the probe field needed to flip protons? The magnetic dipole moment of a proton is $\text{1}\text{.41 }\times {\text{ 10}}^{\text{-26}}\text{J/T}$.

$\begin{array}{l}\text{a}\text{. 4 J}\hfill \\ \text{b}\text{. 4 }\times {\text{ 10}}^{\text{-10}}\text{J}\hfill \\ \text{c}\text{. 4 }\times {\text{ 10}}^{\text{-25}}\text{J}\hfill \\ \text{d}\text{. 4 }\times {\text{ 10}}^{\text{-26}}\text{J}\hfill \\ \text{e}\text{. 4 }\times {\text{ 10}}^{\text{-27}}\text{J}\hfill \end{array}$