A convolutional neural network-based method for the generation of super-resolution 3D models from clinical CT images

Background and objective: The accurate evaluation of bone mechanical properties is essential for predicting fracture risk based on clinical computed tomography (CT) images. However, blurring and noise in clinical CT images can compromise the accuracy of these predictions, leading to incorrect diagnoses. Although previous studies have explored enhancing trabecular bone CT images to super-resolution (SR), none of these studies have examined the possibility of using clinical CT images from different instruments, typically of lower resolution, as a basis for analysis. Additionally, previous studies rely on 2D SR images, which may not be sufficient for accurate mechanical property evaluation, due to the complex nature of the 3D trabecular bone structures. The objective of this study was to address these limitations. Methods: A workflow was developed that utilizes convolutional neural networks to generate SR 3D models across different clinical CT instruments. The morphological and finite-element-derived mechanical properties of these SR models were compared with ground truth models obtained from micro-CT scans. Results: A significant improvement in analysis accuracy was demonstrated, where the new SR models increased the accuracy by up to 700 % compared with the low-resolution data, i


Introduction
The increased rate of bone fragility fractures in the elderly population has become an increasing concern with our aging societies [1,2].This demographic group has a much higher incidence of fractures than younger individuals, largely due to age-dependent decreases in bone mass and deterioration of bone structure.Current clinical guidelines rely on areal bone mineral density (aBMD) estimations derived from Dual Energy X-ray scans (DXA) as a surrogate measure for fracture risk.However, the sensitivity of aBMD in terms of classifying fracture risk ranges from low to moderate [1,3,4].Two of the main drawbacks of using DXA scanners for assessing fracture risk are the low resolution of the image data and the lack of a 3D representation of the skeleton.The low resolution does not allow visualization of the bone architecture, which has been shown to explain a large portion of the measured variance in ultimate strength of bone specimens tested ex vivo [2].
Micro-CT instruments have been utilized to scan small bone specimens at a resolution down to 1 μm [5].While these images provide an accurate representation of the trabecular structure, the use of micro-CT scanning on living human beings is not feasible due to the high radiation dose.Advancements in CT imaging in recent years has enabled the use of higher resolution scans (HR-CT) for limited regions of peripheral bones [6].These techniques generate CT images with a voxel size of 60-125 μm [6][7][8][9] albeit at a modest signal-to-noise ratio.This is close to the thickness of an individual trabecula radius, being about (or slightly less than) 100 μm [10,11].However, the HR-CT models may still result in morphological bias compared to ground truth (GT) trabecular bone structures [9,12,13].These findings suggest that the current resolution is not sufficient to accurately distinguish the trabecular bone structure from the background, and the presence of noise induces further bias.Additionally, a long scanning time increases the likelihood of motion artifacts occurring.
To fully utilize the HR-CT data, there is a need to develop computational postprocessing methods to optimize the image quality, which would allow for accurate quantification of bone architecture.Neural networks (NN) have developed rapidly in the last few decades, especially in the biomedical engineering field [14,15].The use of NN-based SR algorithms for enhancing image quality was reported in recent years [16][17][18][19][20][21][22][23].These algorithms have been utilized to refine optical microscopy [19] and CT-images [16,17,[21][22][23], generating higher-resolution (HR) images from relatively lower-resolution (LR) data.Recent SR NN-based studies have used the technique on CT images of trabecular bone [16,22,23].However, most of them have targeted quality enhancement in 2D, making it difficult to transform the results into 3D morphological parameters or derived mechanical properties.A recently published study worked on 3D SR enhancement, however the LR data utilized were based on down-sampled micro-CT images [21], which does not necessarily reflect the level of quality present in image data acquired directly by clinical CT scanners.
This study presents a workflow that utilizes the enhanced deep super-resolution network (EDSR) [20], to improve the resolution of LR (HR-CT) images of trabecular bone structures, imaged with different scanners.The GT image data that was utilized for model training and validation was acquired using a micro-CT scanner.Mechanical properties were predicted by finite element analysis.Morphological and mechanical properties of 3D SR models were evaluated and compared to the results of corresponding GT models.We hypothesized that NN-based algorithms can effectively generate three-dimensional SR trabecular bone structures from clinical CT data, exhibiting a high degree of agreement with the GT models for morphological and derived mechanical properties.

Data acquisition and image registration
Clinical HR-CT images of cubic bone samples (12-15 mm side length) were obtained in previous studies from the trabecular compartment of 14 human donor radii, using different clinical HR-CT instruments (Table 1) [9,12,13].Scanners used were: SkyScan 1176 (Bruker micro-CT, Kontich, Belgium), NewTom 5 G (QR Verona, Verona, Italy), 3D Accuitomo 80 (J.Morita MFg., Kyoto, Japan), Multitom Rax (Siemens Healthineers GmbH, Forchheim, Germany), XtremeCT (Scanco Medical AG, Brüttisellen, Switzerland), Somatom Force (Siemens Healthineers, Erlangen, Germany), and Verity (Planmed, Helsinki, Finland).The resolution of the different HR-CT scanners can be found in Table 1.The clinical HR-CT images represent the LR datasets in this study and the micro-CT images were utilized as the GT datasets.The registration process of the clinical CT data to the micro-CT references was conducted manually using a two-step approach in MeVisLab (MeVis Medical Solutions AG, Bremen, Germany) [12].

Neural network
The EDSR model was adapted from a previous study on convolutional neural network (CNN) for SR [20], where the work was focused on SR tasks on RGB images with a large diversity of content, e.g.animals, buildings, etc., with no application to medical imaging SR tasks.The code used was adapted from the torchsr (v1.0.3)Python library (3.7.4) [24], which was built on PyTorch [25].The code was modified to suit single layer CT images, where only the grayscale (luminance) of the images was used.
The performance of the EDSR model was evaluated by identifying the optimum parameters and hyperparameters of the EDSR model for the Accuitomo dataset, i.e. the upscaling factor (×2, ×4), number of residual block layers (r), number of feature channels (f), patch size, initial learning rate, learning rate decay steps, loss function, and the optimizer [25].The number of residual block layers and feature channels influence the model size, i.e. the number of parameters included in the model.A larger patch size may provide more information for the training, however, at the cost of training time.Initial learning rate, learning rate decay steps, and optimizer influenced the optimization path.The loss function was used to evaluate the SR images' differences to the GT images.For the validation, the parameters' peak signal-to noise ratio (PSNR) and structural similarity (SSIM) were used to evaluate image quality [26,27].The r16f128×4 model showed the highest performance with a low training time and was selected for further training with all datasets.The hyperparameters utilized in this case were: initial learning rate of 1E-4, learning rate decay step of 1000, l1 loss, and the use of the Adam optimizer [28].
The performance of the EDSR models in this study was compared to state-of-the-art SR algorithms, that demonstrated good performance in the recent NTIRE 2023 challenge on efficient super resolution [29], the spatially-adaptive feature modulation (SAFM) [30] algorithm and the multi-level dispersion residual network (MDRN) [31] algorithm.The evaluation involved comparing the SR images generated by the EDSR models and these algorithms, using metrics such as the PSNR and SSIM.

Neural network training
Following the image acquisition and registration, the GT images were paired to the corresponding LR images.Since the GT images were not always divisible by the upscale factor, they were resized to ensure divisibility using bicubic interpolation to obtain a LR representation of the GT images.Given that the GT images had a voxel size of 8.67 μm, where neighbouring layer images were often very similar, we selected every 4th (×2) or every 2nd (×4) layer for the LR and GT image pairs to avoid overfitting and to reduce training time.This approach ensured that the number of training images was the same for both the ×2 and ×4 models.Furthermore, the CT images from different datasets were mixed with every 10th image selected, and the new mixed dataset was used for training as an additional model.A schematic representation of the workflow is illustrated in Fig. 1.
LR and GT image pairs were available for 14 bone samples.For the mixed dataset, the number of LR GT image pairs was 3006, and the number of validation pairs was 156.All training images were augmented by random rotation or flipping to mitigate overfitting caused by image similarity.The ESDR SR models were trained on 32 threads on a computer cluster (Euler, ETH-Zurich), with each model training taking 2-5 days to complete.The SAFM and MDRN models were trained on an AMD RX 6900 XT GPU, with each model training taking approximately one day to complete.

3D morphological analysis
To construct 3D models and evaluate their morphological and mechanical properties, the 2D images were stacked in the third dimension, i.e. missing slices for the ×4 model were generated with bicubic interpolation, with three images interpolated between two SR images.
To compare the microstructure of LR, GT, and SR models, the 3D models from the different groups were segmented.As the segmentation methods may influence the morphology and mechanical properties [32], different algorithms were implemented and compared.The LR models were segmented with the Otsu and max entropy method [33,34], while the GT model was segmented with the Otsu method only.For the SR models, both Otsu and adaptive methods were used for segmentation for comparison [33,35,36].After segmentation, unconnected small volumes were identified with component labelling and deleted, as they could cause numerical instability in the downstream FE simulations.The segmentation was implemented using ImageJ, MATLAB (R2022b, MathWorks, Natick, USA), and CTAn (1.17.7.2, Bruker, Kontich, Belgium).Bone volume fraction (BVF), bone to surface volume ratio (BS/BV) and trabecular thickness (Tb.Th) were quantified with CTAn.

Finite element analysis
The segmented 3D models were meshed using a direct voxel-to-mesh conversion for a commercial FE solver (ABAQUS 2021, Dassault Systèmes, Vélizy-Villacoublay, France) [37].A built-in concrete damaged plasticity (CDP) material model was used for bone tissue.Modulus of elasticity was set to 16.45 GPa, which represents dense bone at 1.8 g/cm 3 [38], and a Poisson's ratio of 0.3.Other important CDP material properties are summarized in Table 2.
Uniaxial compression was simulated in three orthogonal directions (i.e.x-, y-, and z-direction as shown in Fig. 2).A displacement of 0.5 mm was applied on one surface of the bone samples, with displacement constrained in all directions on the opposite surface.The forcedisplacement curves were transformed to stress-strain curves by Fig. 1. 3D super-resolution workflow and the architecture of the EDSR model [20].LR CT images were used as input to the EDSR model which outputs SR images.Initially, the LR images underwent processing via a convolutional layer, subsequently followed by several residual blocks.These blocks were assembled utilizing convolutional layers paired with rectified linear unit (ReLU) activation layers [20].Ultimately, the up-sampling module was trained at the terminal segment of the network, employing varying upscale factors.The generated SR images were compared to ground truth images, and the EDSR internal parameters (e.g.weights and biases) were adjusted to minimize differences.Finally, the EDSR model was used to generate SR images from LR images of the test datasets, and the SR images subsequently stacked in 3D for morphological evaluation and FE model simulations.

Table 2
Material properties for bone tissue used in the FE simulations [38].

Property Compression Tension
Modulus of elasticity (GPa)   considering the cross-section area and height of the samples.The apparent modulus of elasticity was calculated using linear regression of the most linear part, i.e. between 30 % and 80 % of the ultimate stress.Ultimate stress was calculated as the maximum reaction force in the direction of the applied displacement divided by the nominal crosssectional area of the specimen.The FE comparison was only implemented for GT, LR Otsu, and SR mix adaptive models, since the best morphological performances were found in these groups.

Neural network training
The parametric studies revealed that models trained with an upscale factor 2 (×2) did not outperform those with an upscale factor 4 (×4), as shown in Fig. 3. Furthermore, we found that larger models (i.e. more NN model parameters) did not consistently yield better results compared to the simpler models.Similarly, the performance of SAFM×4 (with a PSNR of 15.95 and SSIM of 0.6471) and MDRN×4 (with a PSNR 15.91 and SSIM of 0.6628) models did not exhibit a notable enhancement in performance when compared to the EDSR model (r16f128×4 with a PSNR of 15.99 and SSIM of 0.6509).As a result, we selected the EDSR model with 16 block layers (r), 128 feature channels (f), and an upscale factor of 4 (×4) for subsequent training, taking into account both performance and training time.
Fig. 4 illustrates the performance of LR, SR, and an SR model trained with mixed data (from different CT datasets).Among the LR groups, the Somatom gave the lowest PSNR value (12.57dB), and the Accuitomo showed the highest (14.56 dB).The SR image trained on the Accuitomo dataset exhibited the best performance with the highest SSIM and PSNR values (PSNR 15.98 dB, SSIM 0.6577), while the Verity group showed the worst performance with the lowest PSNR and SSIM values (PSNR 12.82 dB, SSIM 0.6111).Fig. 5 illustrates the performance of LR, SR, and SR models of different trabecular bone samples.Among the LR groups, the bone sample 1 provided a lowest PSNR value (14.56 dB), and the bone sample 4 showed the highest (16.76 dB).The SR image of bone sample 3 trained on multi-datasets exhibited the best performance with the highest PSNR value (18.02 dB), while the bone sample 1 showed the worst (PSNR 15.11 dB).

3D morphological analysis
Several segmented 3D structures are illustrated in Fig. 6.The LR max entropy method could generate 3D structures with low BVF error (e.g.bone sample 1).However, it also resulted in structures with low connectivity and missing trabeculae (e.g.bone sample 2-4).In contrast, the LR Otsu models tend to preserve the whole trabecular structure but generate denser structures compared to the GT.SR adaptive models produced lower (improved) BVF values than the LR Otsu models, while preserving the structural geometry.The SR Otsu model had a similar performance to the adaptive model, but lost connectivity when the BVF was low.
The performance of the SR models was also compared between different CT datasets.As shown in Fig. 7, when the quality of the original LR CT images was low (e.g. group Verity, Fig. 4), the generated 3D models (e.g. group Verity, Fig. 7) performed worse than 3D models based on higher quality LR scans.Mixing datasets from different scanners was found to improve the SR model results when applied to low quality CT images compared to when learning only from its own CT dataset, e.g. group NewTom and Verity, Fig. 7.

Finite element model prediction of mechanical properties
The SR model based on the Accuitomo 80 results, was found to accurately predict the force-displacement response of the specimens when loaded in compression in the x-, y-, and z-directions, respectively (Fig. 9a-c), whereas the FE models built based on the LR data substantially overestimated stiffness and strength (Fig. 9d-f).On average the LR models exhibited a 771 % higher modulus and 539 % higher strength than the GT models.In contrast, the SR models showed errors lower than 10 % on average (stiffness: − 9.65 %; strength: 9.34 %).The modulus in the z-direction was 16.3 % higher than the GT models, whereas in the xand y-directions the SR models underestimated the modulus by 14.5 % and 31 %, respectively (Fig. 9e).Similar results were found for the comparison of strength (Fig. 9f).

Discussion
This study proposes a workflow that generates SR CT models from clinical CT images to acquire an accurate representation of trabecular structure using a CNN.The SR models were validated against ground truth models of morphology and FE model derived mechanical properties, demonstrating that CNNs can improve prediction accuracy.The results further demonstrate that augmenting training data with CT images from different instruments may enhance the SR performance, particularly for the low-quality images.
A previous study suggested that the EDSR×2 model [20] would outperform the ×4 model, i.e. a model with an upscale factor 4, but we did not find this to be the case (Fig. 3).One possible reason is that the LR dataset used in the previous study was downscaled from GT images, whereas our LR and GT datasets were obtained separately using clinicaland micro-resolution scanners.Therefore, we opted to use the ×4 EDSR model in our study, as it can significantly improve both training and testing time while reducing the memory required for the testing and 3D modelling process.
We did not observe significant improvements by enlarging the model size (Fig. 3).This may be due to the limited number of datasets available, as we only had around 1500 LR images for each LR dataset, but increasing the number of parameters might cause overfitting instead of enhancing the CNN performance.Furthermore, since neighbouring images can be similar, repeated images could be used for training multiple times by the CNN, exacerbating the issue.Nevertheless, we observed that even a small model (r16f64×4) can also provide a high prediction accuracy (PSNR 15.81 dB, SSIM 0.6443), which could be attributed to the relatively simpler SR model, as we only need to fit a grayscale, i.e. a single layer, whereas a typical RGB image has three layers.Furthermore, the primary object, trabecular bone, is always a two-phase structure (background and bone), which is much simpler than other complex features that can be present in other types of pictures, such as those of humans or buildings.
The variation in EDSR parameters led to different SSIM and PSNR  values (Fig. 3).Nonetheless, differences in image quality between the SR images were difficult to discern.Additionally, the SSIM and PSNR values showed different SR qualities for the same SR images.It should be noted that both SSIM and PSNR are sensitive to the grayscale values, which are often altered during the segmentation and binarization process.This suggests that none of these metrics is optimal for trabecular bone SR evaluation.Therefore, an ideal evaluation method for trabecular bone SR should consider the contrast between the bone structure and the background, rather than the absolute grey value.This limitation is further evidenced by Figs. 5 and 6, which demonstrate that a low SSIM value in 2D images does not necessarily result in large errors in 3D BVF.Despite the limitation of the parameters used to quantify the quality of SR images, we chose to use them for the 2D SR images since it is a wellaccepted measurement in the SR field [26,27].Furthermore, as illustrated in Fig. 3, we did not observe a superior performance in our trabecular bone SR outcomes compared with the recently developed NN models, the SAFM and MDRN.There could be two plausible explanations for this.First, the enhancement in SR performance has been marginal in recent years, even in the broader SR field, as reported in [29,30].Second, the impact of registration errors, noise originating from the clinical CT images, and other artifacts induced by the original training datasets may outweigh the differences in SR NNs.This trend is particularly pronounced in our SR tasks, given that the LR images employed were not downscaled from GT images using algorithms, for instance, through interpolation.Consequently, only one EDSR model was used for the subsequent tasks.
The differences in performance across different CT datasets can be observed in Fig. 4, for the SR results.Our findings indicate that the Accuitomo 80 dataset produced the best results in 2D, while the Verity dataset produced the worst.This can potentially be attributed to the pixel size of the CT images, with Accuitomo images having a pixel size of 80 μm, providing more detailed information than the Verity images with a pixel size of 125 μm.However, the noise is also a crucial factor influencing the SR performance.The NewTom dataset has a pixel size of 75 μm but showed relatively poor performance due to high levels of noise.
Segmentation is a critical process before morphological analysis, as it can significantly impact the regions considered as background or trabecular bone [32], which would influence the BVF as well as predicted mechanical properties.In this study, we employed different segmentation methods for LR images, namely the Otsu method which is commonly used [33], and the max entropy method, which has been used in micro-FE analysis in previous work [34].Our findings revealed that the max entropy method resulted in a 10-20 % reduction in BVF compared to the Otsu method (Fig. 6), i.e. towards an improved prediction.However, the connectivity between the trabeculae was also affected by the segmentation algorithm, and LR max entropy segmentation may lead to losses in connectivity, which may affect the predicted mechanical response.In contrast to the segmentation of LR CT images, when segmenting images for SR modelling it is preferred to broaden the threshold boundaries rather than using a smaller interval.This is because the LR CT images may leave small features of the trabecular bone structure undetected, giving an underestimation of the SR structural volume and connectivity.A slightly higher BVF could balance this effect.Therefore, we also evaluated an adaptive segmentation method in addition to the Otsu method.Indeed, the BVF increased by around 8 %  using the adaptive method, which resulted in an error as low as 0.04 % compared to the GT (Fig. 7).Comparing the SR models based on their own CT datasets, the mixture of CT images from different instruments may improve the results as well, especially for the low-quality CT images, e.g. group Verity (Fig. 7).Similar conclusions can be drawn for the morphological analysis (Fig. 8).Hence, the developed SR Mix model could give good results for clinical data across different CT instruments.
Several important morphological parameters were evaluated, namely the BVF, BS/BV, and Tb.Th, for the GT, LR data, and SR models.The BVF, in particular, is an important determinant of bone fracture risk [1].The BVF of LR Otsu models was much higher than the GT models (200±86 %, Fig. 8a).In contrast, the SR model could reduce the BVF error to below 20 % (17±23 %).This can be attributed to the high Tb.Th in the LR images (Fig. 8c), which was significantly reduced in the SR models compared to the LR models.The trabecular separation (Tb.Sp) was not measured here as we assume the position of trabeculae detected by clinical CT instruments to be similar to that of the GT, and hence the Tb.Th and Tb.Sp are correlated.Moreover, the LR and SR differed significantly in terms of BS/BV (Fig. 8b).In conclusion, the SR with adaptive segmentation gave the best overall performance for the morphological parameters (mean error≤50 %), while the LR performed much worse (mean error can be over 100 %).Compared to the previous studies with the same database (e.g.[13,39,40]), a significant improvement can be found in morphological parameters evaluation.The results from the SR CT model are comparable to those from the micro-CT GT models, even without applying a linear regression correction.Furthermore, this approach may also address the issue of biases in clinical CT models that linear regression cannot rectify, as discussed in [39].Furthermore, the prediction accuracy for morphological parameters is also comparable with SR studies that used micro-CT for their LR datasets [21].In contrast, this study employed clinical CT images, which could introduce additional noise, motion artifacts, and other challenges.
The comparison of stress-strain response derived from FE model results (Fig. 9a-c) revealed that the LR Otsu method tends to substantially overestimate modulus and strength, likely due to its tendency to overestimate BVF and Tb.Th (Fig. 8).In contrast, the mechanical evaluation of SR adaptive models showed good agreement with the GT models, even in the post-ultimate stress regime.Both stiffness and strength of the SR models demonstrated low average errors (modulus − 10±37 %; strength 9±56 %) compared to the GT models (Fig. 9d).This prediction accuracy is significantly higher than that in a previous study with the same bone models [13].However, the prediction of modulus and strength varied in different directions.Specifically, the SR models underestimated the mechanical properties in x-and y-directions, however, overestimated them in the z-direction (Fig. 9e, f).This could be attributed to the limitation of the stack algorithm in 3D.
One limitation of this study is the low number of samples available for training and testing.Although thousands of clinical CT images were acquired for each group, most of them provided redundant information, particularly the neighbouring layers.The low number of samples also led to the restriction of the EDSR model to 2D rather than 3D, i.e. the number of specimens was insufficient for direct 3D deep learning model training.Additionally, the restriction of a 2D model may also enlarge the influence of model registration error, compared to a direct 3D model.However, this is the first time SR trabecular bone models have been developed from different clinical CT datasets, demonstrating a superior extraction of morphological and mechanical properties compared to the native clinical CT images.
Another limitation pertains to the quality and accessibility of the clinical CT employed in this study.As shown in Table 1, the acquisition time was long, potentially increasing the risk of motion artifacts.Furthermore, it has been reported that the HR-pQCT is confined to small volumes of interest and specific body sites.These limitations inherent to CT instruments may pose challenges for clinical application at the current stage.
Potential future investigations could encompass the creation of NN architecture tailored explicitly for SR tasks related to trabecular bone (e. g. [21]), employing advanced CT techniques to shorten scanning duration and mitigate motion artifacts (e.g.PCCT [41,42]), and utilizing a greater number of trabecular bone samples to directly construct 3D SR NN models.These endeavours would contribute to enhancing the accuracy of SR models and reducing the computing time associated with NN.Additionally, another prospective study could involve employing NN to directly predict morphological parameters and mechanical properties of trabecular bone, which might further accelerate the analysis process and provide the possibility of large bone sample analysis considering the trabecular bone micro-structure.

Conclusion
In conclusion, a modified enhanced deep SR network based on CNNs was successfully implemented to generate SR images using data from different clinical HR-CT scans.Our results demonstrate that the SR images outperform the LR (HR-CT) images for the determination of morphological parameters, as confirmed by a 3D comparison to GT micro-CT scans.The performance differences between different SR NN models were marginal.However, the SR quality was highly influenced by the original HR-CT image quality.The mixture of different CT image datasets may improve the SR model performance, especially for the lowquality CT images.The adaptive segmentation method can help the SR models to better match the connectivity and predicted mechanical response to that derived from ground truth image data.Finally, we believe that this study demonstrates that SR techniques could significantly enhance image quality of clinical image data and have a substantial impact on assessment of fracture risk in future clinical practice.

Fig. 2 .
Fig. 2.A schematic illustration of the coordinate system and boundary conditions applied in the FE simulations (loading in the z-direction case).
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Fig. 3 .
Fig. 3. Super-resolution models (EDSR, SAFM, MDRN) results for different parameters, as applied to dataset Accuitomo.The SR images generated by SAFM×4 and MDRN×4 models were highlighted by the orange box.The EDSR r16f128×4 model was utilized for further training (highlighted by the green dashed rectangle).

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.Zhou et al.

Fig. 4 .
Fig. 4. Super-resolution model (EDSR r16f128×4) results using different training sets.The SR models were trained individuals from different clinical CT instrument data (LR).In contrast, the SR mix model was trained based on a mixture of all the images from the different clinical CT instruments.

Fig. 5 .
Fig. 5. Super-resolution model (EDSR r16f128×4) result for different trabecular bone samples from the Accuitomo dataset, i.e. bone sample 1, 2, 3, and 4 from the validation group.The GT, lLR, SR, and super resolution image from mixed dataset (SRMix) structures are illustrated with the corresponding SSIM and PSNR values.

Fig. 7 .
Fig. 7. 3D SR results for a sample specimen based on input from different CT scanners with corresponding BVF values indicated (%).

Fig. 9 .
Fig. 9. Force-displacement curves from FE simulations of GT, LR, and SR models in the (a) x-, (b) y-, and (c) z-directions.Different colours represent different bone samples in the validation dataset.The modulus and strength error comparison between LR and SR is illustrated in (d) as average values, and the differences in different directions between GT and SR are shown in (e) and (f).

Table 1
Scanning parameters for the micro-CT scanner (GT) and the 6 different clinical scanners used in this study.
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