Collimator optimization and collimator-detector response compensation in myocardial perfusion SPECT using the ideal observer with and without model mismatch and an anthropomorphic model observer

Abstract

The collimator is the primary factor that determines the spatial resolution and noise tradeoff in myocardial perfusion SPECT images. In this paper, the goal was to find the collimator that optimizes the image quality in terms of a perfusion defect detection task. Since the optimal collimator could depend on the level of approximation of the collimator-detector response (CDR) compensation modeled in reconstruction, we performed this optimization for the cases of modeling the full CDR (including geometric, septal penetration and septal scatter responses), the geometric CDR, or no model of the CDR. We evaluated the performance on the detection task using three model observers. Two observers operated on data in the projection domain: the Ideal Observer (IO) and IO with Model-Mismatch (IO-MM). The third observer was an anthropomorphic Channelized Hotelling Observer (CHO), which operated on reconstructed images. The projection-domain observers have the advantage that they are computationally less intensive. The IO has perfect knowledge of the image formation process, i.e. it has a perfect model of the CDR. The IO-MM takes into account the mismatch between the true (complete and accurate) model and an approximate model, e.g. one that might be used in reconstruction. We evaluated the utility of these projection domain observers in optimizing instrumentation parameters. We investigated a family of 8 parallel-hole collimators, spanning a wide range of resolution and sensitivity tradeoffs, using a population of simulated projection (for the IO and IO-MM) and reconstructed (for the CHO) images that included background variability. We simulated anterolateral and inferior perfusion defects with variable extents and severities. The area under the ROC curve was estimated from the IO, IO-MM, and CHO test statistics and served as the figure-of-merit. The optimal collimator for the IO had a resolution of 9-11 mm FWHM at 10 cm, which is poorer resolution than typical collimators used for MPS. When the IO-MM and CHO used a geometric or no model of the CDR, the optimal collimator shifted toward higher resolution than that obtained using the IO and the CHO with full CDR modeling. With the optimal collimator, the IO-MM and CHO using geometric modeling gave similar performance to full CDR modeling. Collimators with poorer resolution were optimal when CDR modeling was used. The agreement of rankings between the IO-MM and CHO confirmed that the IO-MM is useful for optimization tasks when model mismatch is present due to its substantially reduced computational burden compared to the CHO.

Figure 1

Sample short axis images showing hearts with defects present in the anterolateral (top) and inferior (bottom) myocardium with extents of 5%, 10% and 25% from left to right. For illustrative purposes, defects shown have 100% severity.

Figure 2

Plot of the resolution-sensitivity tradeoff for the collimators investigated in this study. The resolution is the total system (geometric + intrinsic) FWHM resolution at 10 cm from the collimator face and the geometric sensitivity is relative to that of the GE-LEHR collimator (C₂). On the right, the corresponding hole diameter and the septal thickness of the different collimators are reported.

Figure 3

Noise-free (top) and noisy (bottom) projection images obtained using collimators C₁ to C₈ (from left to right). From left-to-right note the decreasing noise and sharpness of the images, as expected. Images were displayed using a logarithmic map to better show the low activity organs.

Figure 4

Sample noise-free projection images using the collimators C₁ to C₈ (from left to right) when modeling the full CDR (top), the GRF only (middle) and no CDR modeling (bottom). Images were displayed using a logarithmic map to better show the low activity organs.

Figure 5

Sample transaxial images containing the center of mass of the heart centroid for different phantoms and the corresponding attenuation maps (rows 1 and 2). Rows 3 to 5 show the corresponding reconstructed image slices using collimator C₂ and ASF, ASG and ASN compensation methods after 36 updates.

Figure 6

Performances of the IO and IO-MM observers as represented by the AUC for the different collimators and CDR modeling methods.

Figure 7

ROC curves for the optimal collimators for three different CDR modeling methods.

Figure 8

Observers’ performances for the different defect locations.

Figure 9

Observers’ performances for the different defect extent-severity combinations.

Figure 10

2D contour plots of the AUC values as a function of the iteration number and the Butterworth filter cutoff frequency for the different compensation methods using the optimal collimators.

Figure 11

Sample short axis of defect-free images corresponding to the optimal reconstruction parameters for collimators C₁ to C₈ (from left to right) reconstructed using compensation methods ASF (top), ASG (middle) and ASN (bottom).

Figure 12

Plot of AUC values for the different collimators and CDR compensation methods using optimal reconstruction parameters.