Calibration-free device sizing using an inverse geometry x-ray system
Measuring vessel dimensions from coronary angiograms. In order to correctly select an interventional device to treat a stenosis, the physical dimensions of the vessel must be determined. The angioplasty balloon or stent should match the (a) diameter of the healthy vessel and (b) length of the lesion.
Tomographic blur of single-plane images and multiplane composite. (a) Schematic showing a vessel segment (gray) spanning several image planes (dotted lines). (b) In each of the single-plane images, the part of the vessel near the image plane is in focus, while portions above and below are blurred. (c) A set of single-plane images is combined into a multiplane composite, where all portions of the vessel appear in focus, similar to conventional fluoroscopy. Note that the curve in the vessel phantom wire is physical and is not an imaging artifact. For clarity, the system dimensions have been exaggerated.
Vessel profile model. (a) The unblurred vessel model assumes a circular cross section with the profile shown in the figure. (b) The LSF is estimated based on actual measurements or an imaging model. (c) The unblurred profile is convolved with the LSF to create a blurred vessel profile. (d) The blurred profile (solid line) is subtracted from the background (dashed line) to approximate the observed profile (circles).
ROIs for 3D vessel localization. (a) An intensity profile is extracted perpendicular to the centerline and two ROIs, and , are defined at either edge of the vessel along the profile. (b) The ROIs defined on the composite image are applied to the score image stack. The 3D localization algorithm is executed on each ROI score stack to produce a coordinate for each ROI, and . (c) The two coordinates from the ROI score stack correspond to opposite edges of the vessel. The two values are averaged to estimate , the coordinate of the 3D vessel centerline.
3D vessel edge localization. (a) The vessel edge ROI was applied to the score image stack to produce the ROI score stack . (b) , the maximum intensity projection of , was created. (c) A threshold equal to 80% of the maximum value in is applied to to create the binary mask of the vessel edge, . (d) The binary mask was applied to each image in the score image stack to create . A value equal to 40% of the maximum value in was subtracted from each image in . Negative values were set to zero and the values in each score image were summed. (e) The position of the vessel edge in the ROI was calculated as the weighted average of the score sums, which was equivalent to the center of mass of the shown distribution.
Pixel size vs plane position. The pixel size of single-plane images decreases monotonically as the position of the plane increases. (Inset) Pixel size is a function of the position of the image plane , the source-to-detector distance , the spacing between focal spot positions , and a constant . Image field-of-view decreases as the image plane moves toward the detector and the number of pixels in each plane is fixed (e.g., ).
Vessel phantom orientations. (a) To test the algorithm with different levels of vessel magnification, the phantoms were imaged parallel to the image plane from 16 cm above isocenter to 16 cm below [(b) and (c), respectively] in 2 cm increments. Note that the inverse geometry causes the magnification to increase as the object moves toward the detector. (d) To test the algorithm with foreshortened vessels, the vessel phantom plane was rotated about isocenter from 0° to 75° [(e) and (f), respectively] in 15° increments. The cross indicates isocenter. For clarity, the system dimensions have been exaggerated.
Diameter error for different vessel magnifications. The mean diameter error for each vessel phantom diameter was calculated for vessels parallel to the image plane but at different distances from the source, producing different magnifications in the composite images. Average diameter errors remained relatively constant, remaining for all diameters.
Measured diameter for different vessel magnifications. Plot (a) shows the measured diameter vs position for the 0.5, 1.0, and 2.1 mm diameter vessels. Plot (b) shows the measured diameter for 0.7, 1.4, and 2.8 mm diameter vessels. Dashed lines represent true diameter. Labels in right margin indicate the true diameter of each segment. Error bars represent ±1 SD.
Measured diameter error for different angulations. The average diameter error showed little to no dependence on the vessel orientation for low to moderate foreshortening (vessel angle ). Diameter errors generally increased for all vessel diameters when the vessels were severely foreshortened (vessel angle ).
Measured relative length for different vessel magnifications. The measured relative vessel length (measured vessel length/true vessel length) (gray) was calculated and averaged for all vessel segments at each position. Apparent length (black) is the relative length measurement expected using conventional methods, assuming the magnification calibration was performed only at isocenter. Error bars represent ±1 SD.
Measured relative length for different angulations. Relative vessel length (measured vessel length/true vessel length) (gray) was averaged for all vessel segments imaged at each orientation. The apparent vessel length (black) assumes a conventional magnification calibration and no compensation for the degree of vessel foreshortening. Error bars represent ±1 SD.
Diameter error with apparent foreshortening. Angle corresponds to angle between the vessel center axis and the image planes.
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