Direction-dependent localization errors in SPECT images
(a) Simulated activity ratios were 20:6:1 in heart, tumor, and other tissues. (b) Twelve tumor sites, labeled A–L, were in axial slice superior to heart.
(a) LEHR collimator hole geometry, length of 2.635 cm, and diameter of 0.140 cm, determine angles through which rays may pass directly to the detector. (b) Cones of 49 rays were used to simulate distance-dependent collimator spatial resolution. (c) shows agreement between simulated and measured line-source profiles at distances of 15–30 cm. Measurements were made with a Trionix Triad (Trionix Research Lab, Twinsburg, OH) scanner using LEHR collimation.
The conformal 180° detector trajectory is overlaid on the attenuation map. At the 60 detector views, a circle marks the collimator position. The detector width is indicated by gray bars at the right lateral and anterior views, where distances to the axis of rotation are 25.7 and 23.9 cm, respectively.
(a) An anisotropic localization error pattern is marked by filled diamonds. (b) Direction-dependent localization precision is indexed by . Note that is also shown above.
Representative images (nDRC and DRC) reconstructed using the same projection data are displayed as function of iteration number and degree of postreconstruction smoothing.
(a) nDRC and (b) DRC images were averaged over the 80-image ensemble at iteration number 10. Spherical tumors appear elliptical and vary in orientation and degree of eccentricity. Distortions are related to tumor position relative to the detector trajectory.
Mean localization error for tumor sites A–L is plotted as a function of smoothing, iteration number, reconstruction method, and cross correlation. Within each broad column and row, mean localization error is displayed as a function of iteration number (1–25) on the horizontal axis and smoothing (0–2.5 cm FWHM) on the vertical axis. Labeled axes are shown above the phantom, using tumor F, DRC-XC as an example. The combination of iteration number and smoothing with the best mean localization error is marked by a white crossed box.
Box plots summarize the ensemble localization errors of tumors A–L. Black horizontal bars denote medians, filled rectangles denote the interquartile range (IQR), whiskers denote the last data point within from the 25th and 75th percentiles, and filled markers denote the outliers. Marked by * is a box plot representing random chance.
The fraction of correct localizations is plotted as a function of radius from the true tumor location. Dashed lines represent the normalized cross correlation and solid lines represent the un-normalized cross correlation. DRC lines are lighter than nDRC counterparts. Localization by random chance is shown by a black curve.
Estimates of tumor positions from the image ensembles are plotted on the attenuation map. For reference, tumor diameters are marked by solid white lines and search region boundaries by dotted white lines. Correct localizations are centered exactly in these circles.
(a) The detector is highlighted at two views: One proximal to tumor and the other more distal and orthogonal. (b) Position estimates at site G show that more precise localization is associated with a more proximal detector view where spatial resolution was relatively good and attenuation less severe.
(a) Direction-dependent localization bias and precision are plotted as a function of for tumors A–F. Horizontal dashed lines mark ideal bias and precision. Also plotted are curves showing tumor-collimator proximity and the survival probability for photons from a tumor to escape the phantom without being attenuated. (b) shows results for tumors G–L. Direction-dependent localization bias curve is truncated at site I.
Mean localization errors are reported with optimal combinations of smoothing and iteration number.
Differences in ensemble localization errors were assessed using Wilcoxon signed-rank test. Bold indicates .
Average tumor-collimator distance and attenuation survival probability are reported for tumors A–L.
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