Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

FIGURE 14-5. A: The laboratory frame of reference uses stationary three-dimensionalCartesian coordinates. The magnetic moment precesses around the z-axis at the Larmorfrequency. B: The rotating frame of reference uses Cartesian coordinate axes thatrotate about the z-axis at the Larmor precessional frequency, and the other axes aredenoted x' and y'. When precessing at the Larmor frequency, the sample magneticmoment appears stationary.appear to be stationary when they rotate at the precessional frequency. If a slightlyhigher precessional frequency occurs, a slow clockwise rotation is observed. For aslightly lower precessional frequency, counterclockwise rotation is observed. Amerry-go-round exemplifies an analogy to the laboratory and rotating frames of reference.Externally, from the laboratory frame of reference, the merry-go-roundrotates at a specific angular frequency (e.g., 15 rotations per minute [rpm)). Individualsriding the horses are observed moving in a circular path around the axis ofrotation, and up-and-down on the horses. If the observer jumps onto the merry-goround,everyone on the ride now appears stationary (with the exception of the upand-downmotion of the horses)-this is the rotating frame of reference. Eventhough the horses are moving up and down, the ability to study them in the rotatingframe is significantly improved compared with the laboratory frame. If themerry-go-round consists of three concentric rings that rotate at 14, 15, and 16 rpmand the observer is on the 15-rpm section, all individuals on that particular ringwould appear stationary, but individuals on the 14-rpm ring would appear to berotating in one direction at a rate of 1 rpm, and individuals on the 16-rpm ringwould appear to be rotating in the other direction at a rate of 1 rpm. Both the laboratoryand the rotating frame of reference are useful in explaining various interactionsof the protons with externally applied static and rotating magnetic fields.The net magnetization vector, M, is described by three components. M z is thecomponent of the magnetic moment parallel to the applied magnetic field and isknown as longitudinal magnetization. At equilibrium, the longitudinal magnetizationis maximal and is denoted as Mo, the equilibrium magnetization, where Mo =MZ) with the amplitude determined by the excess number of protons that are in thelow-energy state (i.e., aligned with Bo). M xy is the component of the magneticmoment perpendicular to the applied magnetic field and is known as transversemagnetization. At equilibrium, the transverse magnetization is zero, because the vectorcomponents of the spins are randomly oriented about 360 degrees in the x-y