How long (in seconds) after the gradient Gx changes sign will the gradient echo occur and why?

Consider the imaging problem in Problem 13.3. Assume the effective spin density within the cube is constant and equal to 1.

(a) Refer to Figure P13.1 and sketch the 2-D function f(x, y) that you will image. Also sketch |F(u, 0)|.

You use the gradient echo pulse sequence shown in Figure P13.9 to image the slice with gradient Gx = 0.5 G/mm and Gy = 0.

(b) Find the duration (in seconds) of the x-gradient preceding the readout gradient in order to collect data in the range −0.4 cm−1 ≤ u ≤ 0.4 cm−1.

(c) How long (in seconds) after the gradient Gx changes sign will the gradient echo occur and why?

(d) After reconstructing the data collected during the acquisition, will we able to get a perfect reconstruction of g(, 0◦), where g(, θ) is the Radon transform of f(x, y)? Explain

Figure P13.9

Figure P13.9 Pulse sequence for Problem 13.27.

Problem 13.3

You intend to image one slice (z = 5 cm,  z = 1 cm) of an off-centered cube having width 10 cm as shown in Figure P13.1. You are given Gz = 1 G/mm and − = γ 4.258 kHz/G.

Figure P13.1 See Problem 13.3.

(a) Find the bandwidth (in Hz) of the RF waveform needed to perform the slice selection.

(b) Give a mathematical expression for the RF waveform B1(t) (in the rotating frame) that is needed to perform the slice selection.

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….