2.1.

Scanned Test Samples

Figure 1 shows the five test samples scanned for this study. They were manufactured in titanium-alloy (Ti6Al4V ELI-0406, Renishaw plc, United Kingdom, particle size 15 to $45\mu \mathrm{m}$) using an LPBF 3D-printer for metal alloys (AM400, Renishaw plc, Wotton-under-Edge, United Kingdom) at the Additive Design in Surgical Solutions facility (ADEISS) in London, Canada.

Fig. 1

Test samples scanned in this project. (a) Titanium-alloy, gyroid-based, and cylindrical samples with porosity fractions of 60%, 70%, 80%, and 90%. (b) Titanium-alloy, resolution, and conspicuity phantom. The internal features of this resolution phantom are shown in Fig. 2.

Four objects were designed as cylinders, 17 mm in diameter and 40 mm in length, with nominal internal porosities of 60%, 70%, 80%, and 90%. The internal porosity of these cylindrical test objects was achieved by modifying the thickness of a ${6\text{-}\mathrm{mm}}^3$, sheet-based gyroid unit. The computer-assisted design (CAD) for these test objects was performed in Blender (Version 2.79, blender.org, Amsterdam, The Netherlands).

The other test sample was designed as a truncated cone, 17 mm high, with a 25-mm-diameter base and a 10-mm diameter top. Internally, it incorporated several series of deliberately prescribed voids of various widths, corresponding to a range of line-pairs (1.6 to $10{\mathrm{mm}}^{-1}$), which extended from the top of the truncated cone to its base, along its longitudinal (i.e., central) axis. It also incorporated a series of voids of various widths, centrally located, to determine void conspicuity. This resolution phantom was designed to evaluate the ability of the CT reconstructions to resolve known internal features of various sizes within the object as the cumulative x-ray path-length through the metal increases. Figure 2 shows the detailed schematics of this titanium-alloy resolution and conspicuity phantom.

Fig. 2

Detailed schematics of the titanium-alloy, resolution, and conspicuity phantom. (a) Perspective view of the 3D-rendering of the CAD with a transparency filter. (b) Central, trans-coronal, synthetic slice of the phantom’s CAD. (c) Central, trans-axial, synthetic slice of the phantom’s CAD, showing the details of the internal voids. The bar patterns are described in lp ${\mathrm{mm}}^{-1}$. All other measurements are shown in mm. (d) Central, trans-sagittal synthetic slice of the phantom’s CAD.

2.2.

Dual-Exposure Data Acquisition

Four image acquisition protocols with increasing integration times were designed to image the titanium-alloy, 3D-printed samples for this study. The micro-CT scanner (eXplore Locus RS x-ray, GE Healthcare; London, Canada) operated at a peak tube potential of 80 kV and a fixed tube current of $400\mu \mathrm{A}$. The first protocol had an integration time of 261.3 ms, which was optimized for the 12-bit x-ray detector, so in an unattenuated region of the field-of-view the intensity values for each pixel did not exceed the maximum value of the detector [i.e., intensity $<2^{12}=4096$ analog-to-digital units (ADU)] of the eXplore Locus RS scanner. Unfortunately, it also meant that, during data acquisition, the pixels obscured by highly attenuating regions on the image were underexposed. The integration time of the other three protocols was designed to have nominally 4, 8, and 16 ($2^2,2^3$, and $2^4$, respectively) times the exposure of the first protocol. For simplicity, in this paper, we will refer to these protocols using the exposure value (EV) bracketing convention that is common to HDR optical photography. Here, EV0 represents the nonsaturated, short acquisition that is optimized for the 12-bit detector, and EVn represents acquisitions with exposures that are nominally “$2^n$” times the EV0 exposure. Table 1 summarizes the acquisition parameters for each EV protocol at 80 kV and $400\mu \mathrm{A}$.

Table 1

Dual-exposure HDR protocols for the eXplore Locus RS x-ray scanner.

The integration times prescribed into the scanner’s control interface differed from the true integration times. X-ray exposure times were measured with a custom sensor timer circuit, comprised of a phototransistor (APDS-9930) in contact with a small phosphor scintillator (Lanex regular); timing was achieved with an interrupt-driven microprocessor (Arduino Uno). It was empirically observed that true integration times were, on average, 65 ms longer than the nominal prescribed times in the protocol. Therefore, the prescribed integration times for EV0, EV2, EV3, and EV4 were revised to be 200, 981, 2026, and 4116 ms, respectively.

For each protocol, the objects were placed in the field-of-view of the scanner using a custom-made holder to circumvent the rehoming of the specimen loading bed of the eXplore Locus RS scanner. This precaution was implemented because it was determined that the linear bed mechanism was not able to return to the initial scanning position with sufficient accuracy, which resulted in registration errors when combining projection images for HDR radiography.

Each protocol, starting at EV0, collected a total of 200 projection images at 1-deg angular increments. For each subsequent EV protocol, the projection images were inspected to ensure that the EVn images were not completely saturated and that they included at least 50% of the sample’s valid data. Dark-field images, required for offset correction, for each protocol were acquired in a way that matched that of each EV condition. Finally, only one bright-field image was acquired using the EV0 protocol, and this bright-field image was scaled appropriately for use with each HDR-CT reconstruction.

2.3.

Dual-Exposure HDR Projection Data Postprocessing

HDR projection images were generated by combining pairs of EV0 and EVn data. Dark noise in each image of the pair was corrected using dark fields (i.e., images acquired with no x-rays on) acquired with their respective EV0 and EVn integration times. This was necessary to address the time-dependent aspect of dark-noise intensity. Next, the EV0 image was multiplied by a scaling factor (EVnf) to increase signal values it to match EVn. The scaling factor was calculated on a per-projection basis using the following equation:

The final step was to combine the dark-noise-corrected and intensity-matched EV0 (IM EV0) projection images with the corresponding set of dark-noise-corrected EVn projections, using only valid data optimized from each. From visual inspection of thresholded EVn projections, it was determined that the EVn data were valid below 95% of the saturation value in those images. Similarly, for the intensity-matched EV0 projections, it was determined that regions in the EV0 images below the 75% saturation value were underexposed due to photon starvation at the detector and should thus be discarded. Thus, the pixels in EV0 image above the 75% saturation value were considered valid. For pixels values between these two thresholds ($t_{95}$ and $t_{75}$), where both EV0 and EVn contained valid data, their intensities ($I_{x,y}$) were assigned using a weighted average using the following equation:

This ${\sin }^2+{\cos }^2$ functional combination was chosen to minimize image stitching artifacts between the two data sets and to reduce the likelihood of discontinuity artifacts in the CT reconstructions, which have been described in the literature as a common limitation of HDR-CT.^9,15 Figure 3(a) shows the location of the threshold boundaries in an EV0 projection image of the titanium-alloy resolution phantom, and Fig. 3(b) shows the same boundaries in a EV4 projection image.

Fig. 3

Projection images used to generate HDR data showing the location of the 95% saturation and 75% saturation threshold boundaries. (a) Projection image of the titanium-alloy, resolution phantom acquired using the EV0 protocol. (b) Projection image of the titanium-alloy, resolution phantom acquired using the EV4 protocol.

The final postprocessing step, before CT reconstruction, involved the implementation of a combined, wavelet-Fourier, ring-artifact removal filter, following the protocol described by Münch et al.¹⁶ This additional processing step was required to compensate for the reduced efficacy of the gain-and-offset correction achieved using the intensity-matched bright-field only.

2.4.

CT Reconstruction and Data Analysis

The 200 projection images collected with the EV0 protocol and each of the HDR pairs (EV0 and EVn) was used to perform CT reconstructions using a limited-view (i.e., 200 deg angular range), Parker-weighted, Feldkamp, Davis, and Kress, filtered-backprojection algorithm.¹⁷ The voxel spacing of the reconstruction matrix was $90\times 90\times 90\mu \mathrm{m}$. Prior to CT reconstruction, the projection images for the cylindrical samples were corrected for beam-hardening using the protocol described by Edey et al.¹⁸ Note that it was not possible to implement this correction in the reconstruction of the resolution phantom, because the phantom diameter exceeded the thickness of the calibration object used for the beam-hardening correction. Furthermore, the correction parameters were different for each HDR image set, which made it difficult to compare the improvements in conspicuity with increasing penetration depth in this phantom that were due to HDR-CT alone.

Improvements in conspicuity with increasing penetration depth were assessed using the titanium-alloy resolution and conspicuity phantom shown in Fig. 2. Conspicuity was qualitatively evaluated using a trans-coronal CT slice plane perpendicular to the prismatic voids located inside the central region of the phantom—similar to the synthetic slice shown in Fig. 2(b). Visualization window and level were optimized by visual inspection to depict the best contrast for the EV0 reconstruction, which was compared with the HDR pairs.

The cylindrical test samples were used to evaluate the HDR-CT technique for highly porous geometries. These reconstructions were visually inspected in trans-sagittal CT slices to visualize any discontinuity artifacts caused by the HDR stitching. These slices were also interrogated using a line-profile across the walls of the gyroid unit to evaluate improvements in image quality and SNR between the conventional-DR and the HDR volumes.

3.1.

Generation of HDR Projection Images

HDR projection images were successfully generated for all test samples, with the exception of the 90% porous cylinder, due to the high degree of overexposure of the projection images for protocols with integration times longer than that of EV0. Table 2 provides a summary of the EV0 and EVn pairs used to generate HDR-CT reconstructions for each test sample. The 12-bit DR (4096 ADU) of the detector was effectively extended to 14.18 (18,514 ADU), 15.24 (38,625 ADU), and 16.29 bits (80,118 ADU) for EV2, EV3, and EV4, respectively.

Table 2

Summary of HDR-CT protocol-pairs per test sample.

The intensity of the pixels (${\mathrm{HDR}}_{x,y}$) of an HDR EV0 and EVn projection image pair was assigned following three conditions:

Figure 4 shows angle-dependent variations in the factors used to match EV0 intensity values for the 60% porous cylinder and the resolution and conspicuity phantom to each corresponding EVn on a per-projection basis. These scaling factors showed the same variability between samples, and the variability trend described a specific signature for each object.

Fig. 4

Scaling factors [Eq. (1)] for matching the intensity of EV0 projection images to EVn as a function of projection angle for the 60% porosity cylinder for: (a) the EV0, EV2 HDR pair and (b) the EV0, EV3 HDR pair, and for the resolution and conspicuity phantom for: (c) the EV0, EV2 HDR pair; (d) the EV0, EV3 HDR pair; and (e) the EV0, EV4 HDR pair.

The EV0 and EVn combination strategy, in projection images, demonstrated the ability to remove any visually obvious stitching artifacts. Figure 5 shows the results of this procedure for one of the projection images of the resolution and conspicuity phantom, obtained using the EV0 and EV4 protocols. This figure shows that the EV0 data have been appropriately scaled to closely match the intensity values of EV4 below the 75% saturation threshold ($t_{75}$). Furthermore, the intensity-matched EV0 (IM EV0) data over the 95% saturation threshold ($t_{95}$) properly extrapolate the intensity values of EV4 for the region in EV4 where pixels reach the saturation point. The HDR intensity values in between the $t_{75}$ and $t_{95}$ thresholds were calculated using the previously described ${\sin }^2+{\cos }^2=1$ identity [Eq. (2)]. Figure 5(c) shows the effectiveness of this strategy in the combination of the two datasets, mainly due to the behavior of the identity near the thresholds, which ensured that the combined pixel values were properly weighted between the IM EV0 and the EV4 data. Specifically, the intensity value of a combined HDR pixel was heavily weighted toward EV0 near the $t_{95}$ threshold and heavily weighted toward EV4 near the $t_{75}$ threshold, with a smooth transition.

Fig. 5

HDR strategy for the combination of EV0 with EVn projection images. (a) Dark-corrected, EV0 projection image of the resolution and conspicuity phantom, scaled to match the intensity values of EV4 (i.e., intensity-matched, IM EV0). Due to a long ray path through the metal in the central region of the phantom, pixels were underexposed in the EV0 image and were discarded from the final HDR projection image. (b) Corresponding, dark-corrected EV4 projection, showing regions with saturated pixels and valid data. (c) Line-profile through pixels marked by the red-dotted line in (a) and (b) showing the ${\sin }^2+{\cos }^2$, weighted-average combination strategy for pixels with intensity values between the 95% ($t_{95}$) and 75% ($t_{75}$) saturation thresholds.

3.2.

HDR-CT of Porous Cylindrical Samples

Figures 6 and 7 show trans-axial slices of the HDR reconstructed volumes using various combinations of EV0 and EVn scans. In all cases, the conventional-DR (i.e., single-exposure) reconstructions exhibit reduced image quality, mainly due to a reduced SNR within the titanium-alloy regions in the conventional-DR reconstruction. For the 60% porous cylinder, the differences in SNR between the EV0 EV2 and the EV0 EV3 HDR reconstructions were not as significant as the differences between the HDR and the conventional-DR volumes.

Fig. 6

Results of the CT reconstructions for the 60% titanium-alloy, porous cylinder. (a)–(c) A trans-axial slice through the data for the conventional-DR, the EV0 EV2 pair, and the EV0 EV3 pair, respectively. (d) A 3D-rendering of the data in a perspective view. (e) and (f) The voxel values through a line-profile following the red-dotted line in (a) to compare the differences in SNR between datasets.

Fig. 7

Results of the CT reconstructions for the 70% and 80% titanium-alloy, porous cylinders. (a) and (b) A trans-axial slice through the 70% porous cylinder for the conventional-DR and the EV0 EV3 pair, respectively. (d) and (e) A trans-axial slice through the 80% porous cylinder for the conventional-DR and the EV0 EV2 pair, respectively. (c) and (f) The voxel values through a line-profile following the red-dotted line in (a) and (d) to compare the differences in SNR between the respective datasets.

Figure 7 shows the SNR improvement for the 70% and 80% porous cylinders between the conventional-DR reconstructions and the HDR reconstructions with the longest integration times for each object. The improvements in SNR were more pronounced for the 70% porous cylinder, whereas for the 80% porous cylinder, the improvements in image quality were barely noticeable. These results indicate that for samples with low total x-ray path-lengths through solid metal HDR might not be necessary.

3.3.

HDR-CT of Resolution Phantom

The resolution and conspicuity phantom was specifically designed to evaluate the visualization of internal voids for varying total x-ray path-lengths through a block of solid titanium-alloy. This was assessed using a trans-coronal slice placed at the center of the phantom and perpendicular to the prismatic voids that ran through its longitudinal axis. The diameter of the phantom, at the void conspicuity limit for the nominal $30\text{-}\mu \mathrm{m}$ wide prism, was used as a reference to describe the total x-ray path-length limit for each CT reconstruction. The void conspicuity limit was reached at a diameter of 14.45 mm for the conventional-DR reconstruction. The EV0 EV2 HDR reconstruction improved this conspicuity limit up to 16.08 mm and the EV0 EV3 HDR up to 19.84 mm. For the EV0 EV4 reconstruction, further improvements to the void conspicuity limit would be challenging to assess. Unfortunately, the EV0 EV4 reconstruction suffered from artifacts caused by the increased dark-noise collected at this $16\times$ longer exposure. Figure 8(f) shows the improved CT number accuracy in a profile-line through the voxels located along the longitudinal axis of the phantom, and within one of the prismatic voids, which contributes to the observed improvements in void visualization for the HDR-CT reconstructions.

Fig. 8

CT reconstructions for the resolution and conspicuity phantom. (a), (b), (d), and (e) A trans-coronal slice through the reconstructed data for the conventional-DR, the EV0 EV2, the EV0 EV3, and EV0 EV4 pairs, respectively. The red arrows in these images describe the location of the void conspicuity limit for the 30- and the $300\text{-}\mu \mathrm{m}$-wide prismatic voids. The red horizontal lines mark the void conspicuity limit reached by the immediately shorter HDR reconstruction. The red circle in (e) shows the location of a discontinuity artifact for the EV0 EV4 dataset. (c) A 3D rendering of a perspective view of the EV0 EV3 HDR reconstruction with the top portion of the phantom clipped at the level marked in (a). (f) The intensity values of voxels in a profile-line located along the longitudinal axis of the phantom and within the $300\mu \mathrm{m}$ wide prismatic void.