An imaging phantom was designed and manufactured to quantify the error in reconstructing cartilage thickness (CNA Precision Machine, Ogden, UT) (). The phantom body was constructed using nylon (Natural Cast Nylon, Professional Plastics Inc., Fullerton, CA). Nine chambers were drilled into the phantom body (). Each chamber was composed of a central nylon cylinder encased by cylindrical sleeves of aluminum and polycarbonate (Standard Polycarbonate, Professional Plastics Inc., Fullerton, CA). The central nylon cylinder simulated trabecular bone, the cylindrical sleeve of aluminum represented cortical bone, and the outer cylindrical sleeve simulated cartilage (, middle). All aluminum cylinders were machined to a wall thickness of 1.00 mm to represent cortical bone with constant thickness. The polycarbonate cylindrical sleeves were machined to wall thickness values of 0.25, 0.50, 0.75, 1.00, 2.00, and 4.00 mm (Phantom Chambers 1-6, , top). An outer polycarbonate four-prong spacer was press-fit into each of the chambers between the outer layer of simulated cartilage and adjacent nylon phantom body (, middle). The spacer held the central cylinders securely in place and provided a “joint space” that could be filled with contrast agent. The joint space in phantom chambers 1-6 (, top) was held constant at 2.0 mm. A varying joint space (0.25, 0.50, and 1.00 mm) with constant simulated cartilage thickness of 2.00 mm was used in the remaining three compartments (Phantom Chambers 7-9, , top). Finally, nylon threaded caps were used to seal the fluid in the chambers. A micrometer with accuracy of ±0.01 mm was used by the manufacturer to determine the wall thickness tolerance of the aluminum and polycarbonate cylindrical sleeves, representing cortical bone and cartilage, respectively. The tolerance was reported to be within ± 0.07 mm.
Figure 1 Top- schematic of phantom used to assess the detection limits of MDCT in the transverse plane. The longitudinal (L) imaging plane is also shown. Simulated cartilage thicknesses of 4.0, 2.0, 1.0, 0.75, 0.5, and 0.25 mm with constant joint space of 2.0 (more ...)
Nylon, polycarbonate and aluminum were chosen because their x-ray attenuation values are similar to trabecular bone, cartilage and cortical bone, respectively (25
). The size of the phantom (250×250 mm) was representative of a typical field of view (FOV) for imaging human diarthrodial joints. The outer diameter of each compartment (outer boundary of simulated cartilage) was kept constant at 52 mm while the diameter of the aluminum sleeve and central nylon cylinder were adjusted between 38–46 mm to accommodate differences in cartilage thickness and joint spacing. This range of cylinder diameters is similar to that reported in the literature for human femoral and humeral heads (29
). The range of cartilage thickness (0.25– 4.00 mm) was chosen to represent the range reported in the literature for human articular cartilage (32
CT Imaging Protocol
All phantom scans were performed with a Siemens SOMATOM® Sensation 64 CT Scanner (Siemens Medical Solutions USA, Malvern, PA). This scanner makes use of a periodic motion of the focal spot in the longitudinal direction to double the number of simultaneously acquired slices with the goal of attaining improved spatial resolution and elimination of spiral artifacts regardless of spiral pitch. Constant scanning parameters for our study were: 120 kVp, 512×512 matrix, 300 mm FOV, and 1 mm slice thickness. A total of 6 contrast enhanced scans and 4 non-enhanced scans were performed. The imaging protocol detailed below was performed on three separate days to assess the reproducibility of the CT scanner and segmentation procedure.
Contrast Enhanced Scans
Contrast agent (Omnipaque 350 mgI/ML, GE Healthcare, Princeton, NJ) was mixed with 1% lidocaine HCL (Hospira Inc., Lake Forest, IL) in separate concentrations of 25, 50, and 75%. The phantom was scanned using a tube current of 200 mAs for each of the three concentrations (n = 3 scans) in the “transverse” or frontal plane (, top). The laser guide was used to align the CT slice axis perpendicular to the phantom chambers longitudinal axes, thereby minimizing volumetric averaging between slices. Additional transverse scans were conducted with tube currents of 150 and 250 mAs using the phantom filled with 50% contrast agent (n = 2 scans). A scan with tube current of 200 mAs was performed on the phantom filled with 50% contrast agent parallel to the phantom chambers “longitudinal” axes (, top) to intentionally introduce volumetric averaging.
The phantom was scanned without fluid to estimate the error in cartilage thickness reconstruction for disarticulated, dissected cadaveric joints. Non-enhanced scans were performed in the transverse plane using tube currents of 150, 200, and 250 mAs (n = 3 scans). A final non-enhanced scan was performed with a tube current of 200 mAs parallel to the phantom chambers longitudinal axes to intentionally introduce volumetric averaging between successive slices.
Image Segmentation, Surface Reconstruction, and Measurement of Thickness
Phantom image data were transferred to a Linux workstation for post-processing. Image data were re-sampled post-CT using 0.5 mm slice intervals for the contrast enhanced and non-enhanced longitudinal scans to assess changes in reconstruction errors between an anisotropic spatial resolution (0.586×1.0×0.586 mm) and near isotropic resolution (0.586×0.5×0.586 mm). Thinner post-scan reconstructions in the transverse plane would have been ambiguous since the curvature of the phantom chambers did not change as slices were taken through this direction.
Separate splines for the outer surface of the aluminum cylinder, representing cortical bone, and the boundary between the polycarbonate cylinder and air (non-enhanced scan) or contrast agent (contrast enhanced scan), representing the outer layer of simulated cartilage, were extracted from the image data. Both automatic and semi-automatic thresholding techniques were employed using commercial segmentation software (Amira 4.1, Mercury Computer Systems, Chelmsford, MA).
Each dataset was automatically thresholded using a masking technique available in Amira 4.1, which allows the user to highlight pixels over a range of defined intensities. For datasets with contrast agent included, the mask was adjusted incrementally until all of the pixels representing nylon (the bulk of the phantom body) were excluded. Thus, pixels with intensities greater than this value were masked as contrast agent and simulated cortical bone whereas values less were defined as simulated cartilage. The same masking procedure was used for the non-enhanced scan datasets to define the simulated cortical bone boundary; however, the boundary between simulated cartilage and air was defined by reversing the mask such that all pixels representing the nylon body of the phantom were included. As mentioned above, the masking procedure was performed for each CT dataset separately to ensure that the appropriate threshold range was chosen independently of alterations in tube current, contrast agent concentration, spatial resolution or scanner direction. Following masking of all of the datasets it was later determined that inter-scan threshold values varied by less than 5%.
Due to CT volumetric averaging it was necessary to utilize a semi-automatic thresholding technique for datasets where contrast agent was included. However, this procedure was only required for phantom chambers with simulated cartilage thickness of 0.5 and 0.25 mm (chambers 5 and 6, , top); simulated cartilage thicker than this was effectively segmented by the automatic method, regardless of contrast agent concentration, tube current, spatial resolution or scanner direction. For the 0.5 and 0.25 mm chambers the baseline automatic threshold value was first used to define a general segmentation spline. Next, regions where pixels blended together were separated using a paintbrush tool available in Amira 4.1 such that the resulting spline followed the general boundary between simulated cartilage and contrast agent. Although volumetric averaging was present, the intensity gradient between contrast agent and simulated cartilage was strong enough to allow for easy visual separation. To ensure uniformity, all of the semi-automatic segmentations were performed by the senior author, A.E.A.
Splines were stacked upon one another and triangulated using the Marching Cubes algorithm (34
) to form surfaces that represented the outer surfaces of simulated cortical bone and cartilage. To preserve the native splines of the CT image data, the resulting polygonal surfaces were not altered via decimation or smoothing. A published algorithm was used to assign thickness to each of the nodes defining the simulated cartilage surface (35
). The algorithm has been tested for accuracy using concentric cylinders with known thickness. Reported errors were less than 2% (35
Thickness values were analyzed to determine the reconstruction errors and detection limit of MDCT and to investigate the influence of tube current, joint spacing, contrast agent concentration, and imaging plane. The overall thickness error for each phantom chamber was assessed using the root mean squared (RMS) error criteria:
where the summation is over the number of surface nodes n
is a constant thickness that was assessed by direct manufacturer measurement of the phantom. The mean residual error was calculated to determine the directionality of the error:
Descriptive statistics were calculated using statistical software (SPSS 11.5 for Windows 2002, SPSS Inc. Chicago, IL). Specifically, RMS and mean residual errors were averaged for the three days that CT scans were conducted. The resulting means were plotted (SigmaPlot 8.0, Systat Software Inc., San Jose, CA) with standard deviation error bars to indicate the inter-scan variation in reconstruction error.