Applying exponential data consistency conditions to non-homogeneous attenuation

Exponential data consistency conditions (eDCCs) have shown feasibility for motion correction and attenuation map alignment in SPECT. The eDCCs require all the activity to be contained within a convex region of homogeneous attenuation. In a non-homogeneous attenuation, activity outside the convex region can violate this assumption, introducing an additional source of inconsistency and inhibiting eDCC-based methods. We present the mathematical foundations of the sine-amplitude approach for coping with activity outside the region of constant attenuation and validate it using SPECT computer simulations.

The sine-amplitude method uses the time-varying aspect of the cardiac signal in ECG-gated SPECT studies to extract a component of the measured data that satisfies the eDCCs, even if the overall activity does not. Four noise-free activity distributions were simulated: a time-varying point source inside the heart, the point source with static liver activity, time-varying left-ventricle (LV) activity, and the LV with static liver activity. The liver activity violated the eDCC constraints. The method was evaluated with different levels of Poisson noise and liver activity. Consistency between exponential projections was assessed using the mean normalized difference (MND) over single- and multi-slice axial ranges.

In noise-free simulations, the liver activity outside the region of constant attenuation increased the LV activity single-slice MND from 2×10^-7to 6×10^-2. For the eleven-slice range, the presence of liver increased the LV activity MND from 2×10^-7to 5×10^-2.The sine-amplitude method reduced the LV single-slice MND to 1×10^-7and the eleven-slice MND to 8×10^-8. With noisy data, the sine-amplitude method improved the average MND values for all tested liver levels when the total heart counts were 2.1 to 53 times a typical clinical acquisition, depending on the axial range.

For time-varying SPECT data, the sine-amplitude approach can broaden the applicability of exponential data consistency conditions in non-homogeneous attenuation.