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 divided into an 8 by 8 matrix of individual detectors. Assume that the PMTs and the detectors cover the exact same square area and that each PMT is 2 in by 2 in in size. This geometry is shown in Figure P9.5. The response of a PMT to an event occurring in a particular subcrystal depends on the distance from the center of the PMT to the center of the subcrystal, r, as follows

where τ = 1 inch.

(a) Find a general expression for the response in PMT(i, j) to an event in crystal C(k, l).

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

(c) Ignoring the possibility of noise, develop a scheme to uniquely identify the crystal in which an event occurred.

(d) Characterize a worst-case scenario in which the smallest possible additive noise in one PMT’s signal causes an error in event localization

Figure P9.5 Detector geometry for Problem 9.6.

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 detector thicknesses for NaI(Tl) and BGO.

Both NaI(Tl) and BGO can be used as PET detectors. The linear attenuation coefficient of BGO at 511 keV is 0.964 cm−1 as opposed to 0.343 cm−1for NaI(Tl). BGO does not….