Consider the two-dimensional cross section shown in Figure P9.6 consisting of three separate compartments R₁, R₂, and R₃.

Figure P9.6 Object geometry for Problem 9.9.

(a) Suppose a solution containing a 511 keV gamma ray emitting radionuclide with concentration 0.3 mCi/cm³ fills only R₂; R₁ and R₃ contain nonradioactive solutions. Let the linear attenuation coefficients (at 511 keV) in the three regions be μ₁ = 0.2 cm−1, μ₂ = 0.3 cm−1, and μ₃ = 0.1 cm−1, respectively. Suppose we image the radioactivity usinga (2-D) SPECT scanner outside the object. Compute the projected radioactivities gSPECT(, 90◦) and gSPECT(, 270◦).

(b) Now assume the radionuclide in (a) is replaced by a positron emitting radionuclide with the same concentration. Assume the linear attenuation coefficients in the three regions are the same. This time the body is imaged using a (2-D) PET scanner. Compute gPET(, 90◦) and gPET(, 270◦).

(c) Explain how to compensate for attenuation in a PET scanner in order to reconstruct an accurate image of the radionuclide concentration. Can you do the same for a SPECT scanner?