Leg length discrepancy (LLD) is an orthopedic problem that frequently causes musculoskeletal disorders in children, such as gait deviations, scoliosis, low back pain, osteoarthritis, and postural control (1). Particularly, children with an LLD greater than 5 mm could have an increased risk of hip, knee, or back problems (2,3). Therefore, accurate and reliable LLD measurement is crucial for planning appropriate treatment (4-6).
Radiography of bilateral lower limbs is considered a standard approach to measuring LLD (1,7,8). Pediatric radiologists used to manually measure the LLD on radiographs from the upper edge of the femoral head to the distal tibia; however, while cognitively simple, this task is labor-intensive. A previous study (9) demonstrated that radiology technologists can be rapidly trained to measure LLD as precisely as can a board-certified pediatric radiologist. Therefore, the delegation of this time-consuming task to artificial intelligence (AI)-powered assistants is becoming increasingly important.
Deep learning (DL) is a powerful tool and, due to its successful application in a range of settings, it is expected that DL will be able to perform the simple but labor-intensive measurement component of radiologic examinations (10,11). In prior studies, DL was adopted for the automated and rapid measurement of LLD, including leg segmentation-based measurement (12) and anatomical landmark localization-based measurement (13). In these studies, both approaches employed convolutional neural networks (CNNs) from different perspectives and achieved promising accuracy. However, these studies were only performed on children from a preschool stage and of a relatively small cohort. Children with LLD, particularly, infants and toddlers, pose challenges in completing clinical routines.
Children will experience many remarkable changes in terms of both the structure and alignment of legs during their development (14). For instance, approximately 90% of cases of capital femoral epiphysis can be observed on radiographs as early as 200 days after birth (15). Sugawara et al. (16) and Garn et al. (17) reported that the 50th percentile of age at the appearance of the femoral head was 6 months in children with normal flexion and 8 months in children who had developmental dysplasia of the hip. Ossification of the trochanteric apophysis begins at approximately 4 years of age in both girls and boys, but that of the distal femoral epiphysis can occur prior to birth (18). Furthermore, the knee joint space of infants is demonstrated on radiographs to be wider than that observed in older children on radiographs due to the relatively small ossification center of the distal femoral epiphysis and proximal tibial epiphysis, as well as the surrounding epiphyseal cartilage, which is not visible on X-ray plain film. Figure 1 demonstrates a series of radiographs covering children at different stages.
Upon the success of a previous study (12), the present study adopted the leg segmentation-based strategy for automated LLD measurement. First, a cascaded CNN (referred to as “cascaded LLDNet”) was devised for the accurate pediatric leg segmentation. Second, a comprehensive assessment was performed; however, the limited spatial overlap was insufficient for evaluating the improper segmentation for LLD measurement. Our hypothesis was that the cascaded LLDNet could achieve promising pediatric leg segmentation and LLD measurement based on a comprehensive assessment of a large and comprehensive radiographic dataset comprising children at all stages, from infancy to adolescence, and with a wide range of diagnoses. We present the following article in accordance with the TRIPOD reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-22-282/rc).
The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). The study was approved by institutional ethics board of Xiamen Children’s Hospital, and individual consent for this retrospective analysis was waived. A total of 976 children who underwent full-length radiography of their lower limbs from the hips to the ankles filmed under anteroposterior single exposure were identified between January 2020 and December 2020 from the database of a local children’s hospital. The inclusion criteria were as follows: (I) adequate technical quality of radiograph; and (II) imaging field of view (FOV) that covered the entire bilateral femurs and tibias. The exclusion criteria were as follows: imaging FOV that did not include the entire bilateral femurs and tibias. We had 3 patients with internal fixation devices, and those patients were excluded. One radiograph did not include the distal tibias bilaterally in the imaging FOV, and thus it was excluded. Ultimately, there were 4 radiographs excluded based on the exclusion criteria (4/976, 0.41%), and 972 children were included in our study (520 children between 0–2 years and 456 children older than 2 years). The radiographs with leg deformities or skeletal dysplasias were not excluded because we wanted to establish a dataset with a broad spectrum of clinically common diseases.
The full-length radiography was acquired by 2 imaging acquisition systems, the DigitalDiagnost 3 digital radiography (DR) scanning unit (Philips Healthcare, Andover, MA, USA) and the SONIALVISION Plus multipurpose digital radiography/fluoroscopy (R/F) system (Shimadzu Corporation, Kyoto, Japan). For children under 2 years, we used the DR scanning unit because the FOV was sufficiently large to scan the entirety of the lower limbs in a single exposure. For older children over 2 years, we used the multipurpose R/F system perform full-length radiography of both lower limbs. This system determined the acquisition start point and end point under fluoroscopy, which was followed by acquisition of the images and then stitching of the images to generate full-length radiographs with a postprocessing workstation.
In our study, some patients had no clinical diseases but were observed to have an abnormal appearance or trauma in both lower limbs [referred to as “children with no clinical disease (NCD) group”]. The other patients in the radiographic dataset carried a wide range of diagnoses [referred as “children with various clinical diseases (VCD) group”], including orthopedic hardware, Beckwith-Wiedemann syndrome, bow legs, cerebral palsy, developmental dysplasia of the hip, fibrous dysplasia, fibrous cortical defect, foot tumor, growth and intellectual disability, knock knees, Langerhans cell histiocytosis, neurofibromatosis type 1, osteochondroma, scoliosis, Shwachman-Diamond syndrome, hip synovitis, tethered cord syndrome, and venous malformation.
The demographic information is summarized in Table 1. There were no significant differences between the NCD and VCD groups regarding femoral length, tibial length, or full leg length (P>0.05, t-test), but the LLD was significantly different between the NCD and VCD groups (P<0.05, t-test). This demonstrated that clinical disease in the VCD group was associated with pediatric LLD.
|Age||Groups||Number (N=972)||Age (years)||Sex (M/F)||Femoral length (cm)||Tibial length (cm)||Full leg length (cm)||Full LLD (cm)|
|0–2 years||NCD group||292||1.39±0.37||143/149||18.2±1.9
|>2 years||NCD group||199||5.20±2.46||100/99||26.9±5.8
The NCD group includes children with no clinical disease, while the VCD group includes children with various clinical disease. No significant difference was observed in age, sex, femoral length, tibial length, or full leg length between the NCD and VCD groups, but a significant difference was observed in full LLD (chi-squared test for sex and t-test for others). Data are shown as mean ± SD and (ranges). NCD, children with no clinical disease; VCD, children with various clinical diseases; M, male; F, female; LLD, leg length discrepancy.
Since the present study adopted the leg segmentation–based strategy for automatic LLD measurement, the ground truth consisting of manual segmentation served as the standard masks and leg length measurement to validate the accuracy of the computer-aided approach.
Manual segmentation was performed by a senior attending pediatric radiologist with more than 5 years’ working experience using ITK-SNAP v3.8.0 software (http://www.itksnap.org/pmwiki/pmwiki.php). The leg length was measured according to the anatomical landmarks adopted by Zheng et al. (12).
DL-based measurement of LLD
The proposed leg segmentation-based strategy typically comprised 4 stages: segmentation of pediatric legs by a cascaded LLDNet, postprocessing of segmentation masks, identification of anatomical landmarks, and measurements of the distances between them.
In the first stage of pediatric leg segmentation, we established a cascaded LLDNet to perform bilateral segmentation of the femurs and tibias in each radiograph (Figure 2). Specifically, the CNN model cascaded 2 identical, U-shaped network structures (each referred to as an LLDNet), with the first LLDNet being able to generate a probability matrix for the bilateral femur and tibia, and the second LLDNet being fed the probability matrix to segment the bilateral femurs and tibia in each radiograph.
Each cascaded LLDNet was conducted under the popular framework of U-Net but was improved via adoption of residual blocks (Figure 3A). The benefits of employing residual blocks included learning more features and accelerating convergence. The first residual block was followed by a residual convolutional block attention module (Res-CBAM), as shown in Figure 3B. The Res-CBAM consisted of a convolutional layer, CBAM, batch normalization, and rectified linear unit, in which the CBAM integrated both spatial and channel attention mechanisms to enhance discriminating feature maps (19). Additionally, the attention gate structure, as seen in Figure 3C, was added to skip connections to alleviate the semantic gap and highlight the target area in segmentation.
To assess the generalization of the automatic measurement of leg length difference, a 5-fold cross-validation was adopted in our study. Specifically, the participants were split into a training set (60% of the data, 3 groups), a validation set (20% of the data, 1 group), and a testing set (20% of the data, 1 group) with even distribution of age and presence or absence of clinical disease. The procedure was performed 5 times to ensure each participant could be tested.
PyTorch deployed on the Nvidia GeForce Ray Tracing Texel eXtreme (RTX) 2080 graphics processing unit (GPU; NVIDIA Corp, Santa Clara, CA, USA) was used to train the CNN model in an end-to-end mode with the input images resized to 448×160 pixels, scaled to [0, 1], and normalized with a max–min standardized method. The Dice loss function DiceLoss=1–2|A∩B|⁄(|A|+|B|) was employed, where A and B were manual and automatic segmentations, and |∙| was the volume of the corresponding segmentation mask. The batch size was 5, and the training time was 100 epochs. The initial learning rate was 1×10−4 and decayed by 10% every 30 epochs.
In the second stage of the postprocessing of segmentation masks, a maximum connected component analysis was performed to detect the pediatric legs in the segmentation label images. Specifically, given the 4 segmentation labels of left femur, left tibia, right femur, and right tibia in an image (referred to as a “4-label image”), we generated 4 new separate images, in which each image only contained on1e label (referred to as a “1-label image”). Then, the maximum connected region was recognized and reserved in each 1-label image, after which it was remerged into a 4-label image, which was treated as the final pediatric leg segmentation map.
In the third stage of the identification of anatomical landmarks, the same 3 landmarks used in a previous study (12) were determined for each limb: the apex of the femoral head (AFH; defined as the uppermost point of the femoral head, and if the femoral head of an infant less than 6 months old was not ossified completely, the ossified upper femoral apex was used to replace the AFH for measurement), the convexity of the medial femoral condyle (CMFC; defined as the bony protrusion on the inside edge of the bottom of the femur bone), and the center of the tibial plafond (CTP; defined as the center of the distal end of the tibia). The full leg length was defined as the sum of the femoral and tibial bone lengths, and the LLD was defined as the difference between the right and left full leg lengths. The femoral length was defined as the vertical distance between the AFH and the CMFC, and the tibial length was defined as the vertical distance between the CMFC and the CTP (Figure 4).
In the fourth stage of the measurement of the distance between landmarks, the length of the femurs, tibias, and full legs were calculated between corresponding anatomical landmarks (Figure 2D). Specifically, the femoral and tibial lengths were defined as the vertical distances between the AFH and CMFC and between the CMFC and TP, respectively. The full limb length was the sum of the femoral and tibial lengths. LLD was defined as the difference in the length between the right and left limbs.
Comprehensive assessment and statistical analysis
The comprehensive assessment in this study included the evaluation of the following: (I) the accuracy of the segmentation of pediatric legs based on 9 indices and (II) the consistency of the measurement of leg length between DL and ground truth based on 5 indices. Using the comprehensive indices above, we compared the proposed cascaded LLDNet with alternative DL models, including ResUNet (12), TransUNet (20), and the single LLDNet to demonstrate the superiority of the cascaded LLDNet.
To assess the accuracy of the segmentation of the pediatric leg, 9 indices were employed (21), including Dice, Jaccard, precision, recall, mean distance (MD), Harsdorff distance (HD), HD95, average symmetric surface distance (ASSD), and root mean square deviation (RMSD). The above metrics comprehensively measured the segmentation in terms of similarity (Dice, Jaccard, precision, and recall) and stability (MD, HD, HD95, ASSD, and RMSD). Additionally, the paired Wilcoxon signed-rank test (MATLABR2018b; MathWorks, Natick, MA, USA) was also employed to statistically compare the accuracy of the segmentation between different DL models. A value of P<0.05 indicated a significant improvement of the proposed cascaded LLDNet over alternative DL models in terms of the 9 indices. Given manual segmentation A and automatic segmentation B, the above 9 indices were defined as follows:
HD95 is similar to HD, expect that 5% data points with the largest distance are removed before the calculation, as follows:
To assess the consistency of the measurement of leg length between DL and ground truth, 5 indices, including the Pearson correlation coefficient (PCC), mean squared error (MSE), mean absolute error (MAE), maximum absolute error (MaxAE), and concordance correlation coefficient (CCC), were employed. Given the ground truth y and the predicted measurement by DL, the MSE and MAE were defined as follows:
Additionally, the Bland-Altman plot was adopted to visualize the differences in the measurements of leg length between the manual and automatic measurements. The mean bias and the coefficient of repeatability (RPC) from the Bland-Altman analysis were calculated. Given the 2 measurements, y2 and y1, the RPC was defined as follows:
Since an LLD >5 mm could be associated with an increased risk of osteoarthritis of the knee or hip, the sensitivity and specificity defined below were also calculated to evaluate automatic LLD measurement:
Comparison of segmentation with alternative DL models
The comparison of segmentation between the proposed cascaded LLDNet and the alternative DL models of ResUNet (12), TransUNet (20), and the single LLDNet is summarized in Table 2. Experimental results demonstrated that the cascaded LLDNet achieved the best segmentation accuracy in terms of similarity and stability indices. The visualized comparison of the segmentation results is also displayed in Figure 5, which further demonstrates that the cascaded LLDNet could greatly decrease segmentation errors.
|Deep learning model||Similarity indices||Stability indices|
|The maximum percentage improvement||↑0.5%||↑1.0%||↑1.0%||↓18%||↓47%||↓13%||↓19%||↓22%|
The ResUNet, TransUNet, single LLDNet, and proposed cascaded LLDNet were compared. *, the cascaded LLDNet significantly improved the performance according to paired Wilcoxon signed-rank test. SD, standard deviation; MD, mean distance; HD, Hausdorff distance; ASSD, average symmetric surface distance; RMSD, root mean square deviation; LLD, leg length discrepancy.
Furthermore, although the similarity indices achieved by the cascaded LLDNet were only slightly improved in quantity (0.5–1% percentage increase of indices; P<0.05; paired Wilcoxon signed-rank test), the stability indices improved dramatically between the different DL models under comparison (13–47% percentage decrease of indices: P<0.05, paired Wilcoxon signed-rank test), as shown in Table 2. The percentage improvement in terms of similarity and stability indices shown in Table 2 not only demonstrate the superiority of the cascaded LLDNet in segmenting pediatric legs, but also emphasize the necessity of the comprehensive assessment in the LLD study.
Comparison with radiology reports
Other than the evaluation of segmentation accuracy, the consistency in the measurement of leg length between DL and ground truth was also comprehensively assessed by the 5 metrics of PCC, MSE, MAE, MaxAE, and CCC. The 5 metrics were also compared between the proposed cascaded LLDNet with the alternative DL models of the ResUNet (12), TransUNet (20), and the single LLDNet (Table 3).
|Anatomical structure||Deep learning model||Pearson correlation coefficient||Mean squared error (cm)||Mean absolute error (cm)||Maximum absolute error (cm)||Concordance correlation coefficient|
|Full leg length||ResUNet||0.99*||0.50||0.22||8.91||0.99|
The ResUNet, TransUNet, single LLDNet, and proposed cascaded LLDNet were compared. *, significant correlation with P<0.05 between radiology reports and the automated measurements. LLD, leg length discrepancy.
Regarding the comparison of the measurement of the length of the femur, tibia, and full leg, as shown in Table 3, the proposed cascaded LLDNet achieved better performance in the measurement of consistency over alterative DL models under comparison. Regarding the LLD measurement, the cascaded LLDNet also obtained the best consistency with ground truth (PCC =0.94, P<0.05; MSE =0.02, MAE =0.09, MaxAE =1.85, CCC =0.94) over the other methods.
In addition, Figure 6 exhibits the incidence of different anatomic LLD magnitudes among the participants, where LLDs of 0–2 and 8–10 mm had the highest and lowest incidence in the population in our study, respectively. With respect to the incidence of different anatomic LLD magnitudes among the participants, the scatter plots (with PCC, CCC, MSE, MAE, and MaxAE) of the comparison between the radiology report and DL models (Figure 7), indicated that the best measurement consistency of femoral length, tibial length, leg length, and LLD was achieved by the cascaded LLDNet. The Bland-Altman plot (Figure 8) was also used to assess the agreement between the manual measurement and the leg length calculated by the cascaded LLDNet. Regarding the LLD difference between the manual and automatic measurements, the Bland-Altman analysis showed a mean bias ± SD of 0.003±0.15 cm and RPC of 0.29.
Using the results of the manual measurement of LLD as the gold standard, we computed the sensitivity and specificity of the automatic LLD measurements of all cases with LLD >5 mm and LLD >10 mm. The sensitivity and specificity established for LLD >5 mm were 0.792 and 0.962, respectively, while those for LLD >10 mm were 0.938 and 0.992, respectively.
In the present study, we developed a cascaded LLDNet for automatic LLD measurement and then comprehensively assessed its performance on a radiographic dataset covering children at all stages from infancy to adolescence and with a wide range of diagnoses. The LLDNet performed better in the LLD study in terms of similarity and stability compared to the other models (Table 2 and Figure 5). Experiments comprehensively employing a variety of metrics and statistical analyses demonstrated the superiority of the cascaded LLDNet in the LLD study over ResUNet (12), TransUNet (20), and the single LLDNet (Figure 3A).
Previous research on this subject has only been carried out on children from a preschool stage (13) and in a relatively small cohort (12); however, children with LLD at infant and toddler stages represent a particular challenge in clinical routines. Children experience many remarkable changes in terms of both the structure and alignment of their legs during development (14), as displayed in Figure 1. Therefore, a unified solution using DL on a large and comprehensive radiographic dataset covering children at all stages, from infancy to adolescence, and with a wide range of diagnoses, is desirable. Therefore, the present study employed a large sample number of 972 cases of pediatric bilateral lower limb radiographs to develop a unified solution for the LLD study and to avoid statistical deviations. Although a variety of different types of samples were enrolled, the metrics (Table 3) achieved by the cascaded LLDNet demonstrated a better consistency compared to those reported in previous radiology studies (12) and (13) when measuring the full leg length and LLD.
A comprehensive assessment is essential in an LLD study. The previous study (12) which used the same-leg segmentation-based strategy, only adopted the spatial overlap of the Dice similarity coefficient to evaluate segmentation accuracy. However, the Dice values only changed slightly between different DL models, as displayed in Table 2, indicating an insufficient ability to assess the segmentation. Figure 5 further demonstrates the limitation of the Dice index in measuring different segmentations. Our present study employed a comprehensive assessment strategy, including Dice, Jaccard, Precision, Recall, MD, HD, HD95, ASSD, and RMSD in terms of both segmentation similarity and stability, and we could comprehensively evaluate the improvement of different segmentation models. For clarity, the maximum percentage improvement of the cascaded LLDNet over other DL methods is summarized in the last line of Table 2. Although there was only a slight improvement in the similarity indices (0.5–1% in percentage increase), a dramatic improvement in the stability indices was observed (13–47% percentage decrease), which demonstrates the necessity of a comprehensive assessment in LLD study.
Knutson et al. (22) reported that only 10% of the average population has exactly equal leg length, 90% of patients have at least a 1 mm LLD, approximately 50% of the population has a 4 mm LLD, and approximately 90% of the population has an LLD of 10 mm or less. There is evidence that an LLD of >5 mm may be associated with a high risk of hip, knee, or back problems (2,3). These patients tend to adapt to the LLD over a long period and temporarily experience a reprieve of symptoms because of the body’s compensatory ability, but the LLD gradually increases with age, which is especially obvious in children (23,24). Thus, in our study, we compared the sensitivity and specificity of automatic LLD measurements of LLD >5 mm in all of these cases, resulting in a sensitivity of 0.792 and a specificity of 0.962. For comparison, we also calculated the sensitivity and specificity of the automatic measurement of LLD >10 mm, achieving a higher sensitivity of 0.938 and specificity of 0.992 as compared to the sensitivity of 0.88 and specificity of 0.97 reported in a study (13).
Some limitations to our study should be noted. First, this research was not grouped by children’s age and did not evaluate the degree of ossification of each ossification center according to the different growth stages, which might have introduced errors in automatic segmentation. In our follow-up research, we will conduct a study of details more relevant to the age group of the children and further evaluate whether the different degrees of ossification in the ossification center affect the automatic segmentation and measurement results. Second, the data included in the present study were only collected from 2 locally limited devices, the DigitalDiagnost 3 and the SONIALVISION Plus, and did not include other machines and sites, such as the ultra-low dose X-ray imaging system (EOS), which performs full-length, lower-extremity radiographs of the upright position (13,25) and may generate more accurate results. However, the EOS imaging system was not equipped for use due to the limitation of the practical conditions of the study. As a result, we used 2 existing photography systems for acquiring full-length, lower-extremity radiographs of the supine position (patients with internal/external fixation devices were excluded). Thus, the effectiveness and robustness of our method should be further validated in future studies with external, multisite data for higher clinical applicability. Third, although the algorithm we used to measure the femur and tibia was accurate, slight errors are unavoidable. The calculation of the full leg length was based on the sum of the length of the femur and tibia, while the calculation of LLD was based on the result of the full leg length, which could have generated a quadratic error and results with a relatively low prediction accuracy of LLD. Finally, an independent remeasurement of leg length was not performed.
We conducted a comprehensive study of LLD in a large sample comprising a diversity of case types. The LLD study consisted of 4 stages of implementation: cascaded LLDNet for leg segmentation, postprocessing of segmentation masks, anatomical landmark identification, and leg length measurement. Experimental results demonstrated that, compared with other LLD studies, our method was able to achieve a superior performance based on a comprehensive evaluation in terms of similarity, stability, and consistency with radiology reports.
Funding: This work was supported by the National Natural Science Foundation of China (Nos. 61802330 and 61802331) and the Project of Xiamen Scientific and Technological Plan (No. 3502Z20209220).
Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-22-282/rc
Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-22-282/coif). The authors have no conflicts of interest to declare.
Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). The study was approved by institutional ethics board of Xiamen Children’s Hospital, and individual consent for this retrospective analysis was waived. There are no details on persons mentioned within the text.
Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.
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