Where is this slice centered? What is the slice thickness?

Consider a constant magnetic field B0 = 1.5 T is applied to an object. The gyromagnetic ratio of the object is γ = 2π × 4, 258 (rad/s)/G. Suppose the following RF pulse is applied

where f = 4.258 × 104 Hz, A = 2 G/Hz, τp = 2 ms, and ν0 is the Larmor frequency.

(a) Find ν0. Write down an equation to calculate the tip angle.

(b) Assume τp is long enough so that B1(t) could be approximated as

What is the spectrum of B1(t)? Sketch it. Suppose a slice selection gradient is applied in z direction while B1(t) is applied and Gz = 2 G/cm.

(c) Where is this slice centered? What is the slice thickness?

(d) If you want to select another slice adjacent to the current slice (moving in the +z direction) with the same slice thickness, how should you change the RF pulse? Assume Gz stays the same.

(e) Right after the RF pulse in (d), what is the maximum phase difference of the spins inside the current slice? How does one rephase the spins?

(f) Suppose you want to sample k-space using a sampling trajectory that starts as shown in Figure P13.10. Assume that |Gx| = 2.5 G/cm and |Gy| = 1.5 G/cm. Sketch a pulse sequence to achieve this part of the trajectory. Indicate the acquired signal, the readout gradient, the phase-encoding gradient, and the slice selection gradient.

(g) For the sampling indicated in (e), if FOVx must be 50 cm, what is the smallest sampling rate fs?

find the cost of your paper

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….