Determine the time tmax at which the absolute signal difference |φ(5) − φ(−5)| is maximum .

A planar scintigraphy imaging system (assume a 2-D system) is set up with the collimator as shown in Figure P8.5.

Figure P8.5 System setup for Problem 8.15.

Three compartments P, Q, and R mimick three different tissues, and have attenuations μP = 0, μQ = 0, and μR = 0.1 mm−1, respectively. Assume δ ≈ 0 mm. N0 atoms of radionuclide A ( = 3 hours) were put uniformly in compartment P, and  atoms of radionuclide B (= 6 hours) were put uniformly in compartment Q.

(a) Compute the projection φ(x) [units of photons s−1 cm−1] at 1) time t = 0 and 2) time t = .

(b) Determine the time tmax at which the absolute signal difference |φ(5) − φ(−5)| is maximum .

(c) What is the collimator efficiency and resolution?

(d) What is the absolute signal difference at time t = 3 hours incorporating collimator efficiency.

(e) What is the width of compartment P in the final image? (Assume the system resolution is dominated by the collimator resolution.)

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