Derive a more general formula for MZ (t). You can assume that the transverse magnetization has completely dephased before each RF pulse, that is, Mxy(TR) = 0.

The following equations from Example 12.4 give the components of M after an α pulse (assuming the system is in equilibrium just before the α pulse):

Suppose that we now excite the sample with a train of α pulses, separated by a time TR. The equilibrium condition is true when TR is long compared with T1 and we can assume that MZ just before the pulse is equal to

Mo. Derive a more general formula for MZ (t). You can assume that the transverse magnetization has completely dephased before each RF pulse, that is, Mxy(TR) = 0. (Hint: In this more general formula, MO will be replaced with the steady-state value of the longitudinal magnetization. Define MZ after the (n + 1)th pulse to be  , and MZ after the nth pulse to be  . Relate these two quantities with an equation. Derive another (very simple) equation from the steady-state condition. You now have enough information to solve the problem.)

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Explain why attenuation is not a big problem in PET.

Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

Give the mean and the variance of the reconstructed image, mean[ˆ f(x, y)] and var[ˆ f(x, y)].

Ignoring the inverse square law and attenuation, an approximate reconstruction for SPECT imaging is given by where c˜() =  {||W()} and W() is a rectangular windowing filter that cuts off at = 0…..

Find the numerical responses in each to an event in crystal C(4, 6).

Suppose a PET detector comprises four square PMTs (arranged as a 2 by 2 matrix) and a single BGO crystal with slits made in such a way that it is….