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….

## 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 G_{x} = 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 G_{x} 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 G_{z} = 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 B_{1}(t) (in the rotating frame) that is needed to perform the slice selection.