A total of 97 computed tomography scans (CT) were collected retrospectively from three different facilities (University of Zürich, Switzerland, and University of Wisconsin, United States, University of Florida, United States). Inclusion criteria was the presence of at least the femur, patella, and proximal part of the tibia. Exclusion criteria was the presence of any pathologic abnormalities seen in the clinic or on the CT by experts, such as osteoarthritis, HD, MPL, osteochondrosis or previous surgery. This study included CT scans of both cadaveric limbs and live dogs.

All hindlimbs were scanned with 0.8-mm slice thickness with 512×512 matrix, pixel size ranging between 0.1927 mm and 0.473 mm (University of Florida—Model Toshiba, University Zürich—Brilliance CT, Philips AG, Zurich, Switzerland, and University of Wisconin-Model GE Medical Systems) The images were manually segmented using an open-source software (3D Slicer). Initial segmentation was performed using a threshold value of 350, followed by performing a smoothing using a built-in function for closing (fill holes) with kernel size of 3.0 mm. Each bone (femur, patella, tibia, and fabella) was segmented separately to create an individual model.

The models were meshed using the engineering software Geomagic WRAP (Geomagic, Inc., Research Triangle Park, NC) to obtain 3D models of reduced size and uniformly sampled vertices (target edge length 2 mm). Complete bones and partial models (proximal distal part of the femur and proximal part of the tibia) are created for evaluations. All femur models were cut to isolate the region of interest with uniform length. Due to large variation of length and size, the length of the partial femur model was normalized to be two times the length of the condyles (partial distal model) and femoral head (partial proximal model). The length was measured to be the diameter of a sphere fitted in the condyles and the diameter of a sphere fitted in the femoral head. The partial proximal tibia model was cut at the most distal part of the tibial tuberosity (34–37).

The models were aligned to an anatomical coordinate system based on anatomic landmarks, similar to previous joint kinematics studies (38). The origin was centered on the point equally distant to the center of the two condyles. Where the center was determined by registering a sphere to the geometry of the femoral condyle. The Y-axis was set to be parallel to the anatomical axis of the femur in a proximal-distal direction, with a positive direction going proximal. The Z-axis was set to be in a latero-medial direction, with the positive direction going medial. The X-axis was then calculated to be perpendicular to the other two axes. For each group and set of bones (left and right femur, tibia and patella, and the different groups), reference/template models were created. The template models were created from the median bone model, remeshed to have uniform vertices of 2 mm (39). All the training models were registered to the template model using the nearest neighbor algorithm (MATLAB and Statistics Toolbox Release R2020a, The MathWorks, Inc., Natick, MA.) to unify the number of faces and vertices.

Once all the training models were registered and aligned to the template model, PCA was performed. This operation generated the results as the shape variation and Modes for individual bones. A Mode was defined as the modification of the mean model due to the variation of only one component of the PCA. This allowed individual analysis of each component. The Modes were numbered 1 to 5 based on the magnitude of variation that was detected in the bones. For analysis, the data for the femur were divided between body weight groups, breed, and bones (Table 1). The specific bone regions analyzed were the femoral condyle, femoral head, and the tibial plateau. A realignment of the femur model was performed with Geomagic WRAP to obtain more detailed results in some cases, such as for interpretation of the Mode 2. Observation of the models at different alignment was used to obtain more insight in localization of the deformity in the different Modes. They were aligned based on the shape of their extremities (for example: the second Mode of the complete femur). A total of 33 SSMs (mean, ±3 standard deviations) representing the first 5 Modes from the PCA were generated for visual evaluations (Figures 1–6) (25, 29).

The second Mode showed a strong varus/valgus deformation of the femur, confirming previous studies that showed strong (up to 4°) variation in normal dogs (9, 40, 41). This result was found in both chondrodystrophic and retriever groups suggesting that varus-valgus is an important anatomical parameter, irrespective of breed. To get further insight on the location of the deformation we realigned the models based on the two extremities and at the mid-diaphysis to observe the curvature of the bone. This study discovered that there is effectively some curvature of the femoral shaft, although it is less than expected. The condyles are also not superimposing, which could also be interpreted as a difference in femoral condyle size.

We found that Modes 3, 4 and 5 were influenced by several factors, which made them more difficult to interpret. It is also important to realize that collectively these 3 Modes accounted only for 0.62% of variation. The best interpretation of the third Mode is a combination of three different components: width of the condyles, femoral head size and craniocaudal thickness of the whole femur. Mode 4 also shows 2 components: procurvation and torsion of the femoral head. Mode 5 could also have thickness and malignment components.

The magnitude of the deformation dependent on Modes 3, 4 and 5 is small compared to the Mode 1 and 2. This is expected because the majority of the variations are from Mode 1. This suggests that when the size factor is eliminated, the normal femur is very similar across different breads. Even though for Groups 2 through Group 6, categorized by weight class and specific breeds, the variability between individual dogs is still dominated by the size/scale factor. This can be identified by the changes in the length of the femur. Group 4 shows the most similar bone length (see Table 1) resulting in less variability in size between Models from large dogs. This reduction of size variability is reflected with the lower percentage represented by Mode 1 compared to other groups. For Group 5, typical specificities of the chondrodystrophic breeds can be seen on the mean model, such as a smaller major trochanter, thicker condyles, or femoral head, and stronger procurvation, which can also be seen on the variant Modes.

To reduce the effect of the femoral length and to isolate the proximal and distal parts of the femur, all the femur models were cut. The only clear interpretation could be made from the first Mode of the femoral condyles SSM, which is the size factor. The rest of the Modes showed a mixture of different combined factors of condyle length, thickness, length of the femoral shaft above the patella grove, and malalignment. Previous studies investigated the femoral condyle size or other condyle variation as a morphological factor that may predispose to CCLD in dogs (42, 43) as well as humans (44, 45). Future studies could use SSM to compare these parameters in dogs with CCLD and normal dogs. For the femoral head SSM, size was the most dominant factor. Interestingly the second Mode represented the size of the femoral head independently of the major trochanter. Modes 3 to 5 represented some differences in alignment as well as a small difference in the anteversion angle of the femoral head. However, the relevance is to be questioned, as the differences are minor. It should be noted that no pathological deformation has been observed such as patellar groove depth differences typically seen in MPL disease, strong varus/valgus of the femoral shaft or deformation of the femoral head typically seen in hip dysplastic cases (18, 20). This indicates a good set of inclusion and exclusion criteria for our data sets.

The first 2 Modes from the complete tibia SSM are similar to the femur SSM, representing the size and a combination of varus/valgus variability. While the third Mode showed a combination of different factors, the fourth Mode showed a difference in the craniocaudal thickness of the tibial shaft. The fifth Mode represented a difference in the thickness of the tibia plateau and distal extremity. Interestingly, no Modes show a difference in the position of the tibial tuberosity in relation to the tibial shaft or a torsion like the femur. The lower variability in morphology of the tibia relative to the femur is consistent with previous studies that show that most variation is situated in the femur (46). The Modes from the PCA focused on the tibial plateau follow a similar pattern, with Mode 1 being the size factor. The only other clear factor was observed in Mode 4, procurvation. Other Modes did not show any clear identification of variability.

The first Mode of the PCA of the patella shows size as the most important factor. Interestingly the second Mode shows an elongation or a more sharply cornered proximal extremity of the patella. Modes three to five most likely represent malalignment.

It should be noted that while some Modes show certain deformations, they can also be interpreted in different ways depending on which Modes are considered. For example, an elongation-type deformation (with a variation on the shaft of the bone only and none on the thickness) can be interpreted as either elongation or as the thickness of the bone, as an elongated bone would be a narrower bone after size adjustment (as the main focus is the proportional variance). Another type of biased interpretation is best shown with the varus/valgus example. If a shaft is seen to be curved while aligned on the condyle, the curvature is not necessarily based on the condyle. It could be situated anywhere on the shaft. Only further analysis with realignment could address this problem.

While the current study does not report measurement of any length or angles, some comparisons can be made with the literature. When reviewing the measurements from different studies on geometrical bone morphology, they show high variability. Additionally, when comparing breeds, the different values overlap between small and large breeds and do not show a clear difference. For example, when looking at the anteversion angle of the femur, some studies found for small breeds angles between 20° and 27°, while on large dogs the values were between 16° and 25° (7, 10, 47–49). While precise angles were not measured in this study, variations on procurvation and torsion which both influence those angles were observed. Stronger procurvation on smaller breeds was observed when comparing different breeds.

Since the number of studies on the tibial angles is limited, the results show more correlation. Smaller breeds have a greater tibia plateau angle (30° vs. 25° in large breeds), Z angle (69.2° to 58.8°), distal tibial axis/proximal tibial axis angle (10.8° to 4.5°), greater relative tibial tuberosity width (0.86° to 0.74°).

We could not see that in our study since we found an overall similarity between breeds. However, the overlapping from those studies is great when looking at the range of the values. Nevertheless, we could show a great variability which could explain the differences seen in those studies. Differences in varus/valgus, procurvation and thickness were observed from the tibia SSM, which all influence those angles (50, 51).

To the best of our knowledge, this study is the first to present SSM for dogs’ hind limbs. This method of measurement considers the whole bone shape rather than single measurements, which is a crucial step toward a better understanding of the anatomy and further research on diseased bones. The different results in measurements in the literature reinforce the need for SSM. One of the tools of SSM is classification, the possibility of classifying if a stifle from a specific case is normal or pathologic bone, without having to rely on individual clinicians’ measurements. With the development of SSMs from bones without any clinical orthopeadic abnormalities, the process can be extended to diseased dogs to observe qualitative and quantitative changes in the Modes for certain diseases such as MPL or HD. This could allow the description of the pathologic changes and the correction needed without the need for manual analysis. Another useful application is using this SSM model to help with the surgery on certain bones by facilitating the finding of landmarks which are needed to perform the operation.

This study has several limitations. The most significant factor is the limited sample size. The complete set of femurs (n = 61) could be considered a large enough data set, but when divided into groups, the sample sizes for the individual groups are greatly reduced. PCA analysis is a powerful tool that can help represent variations of geometric morphology, but it does not identify a single factor for the significance of each Mode it generates. Therefore, each Mode must be visually analyzed and interpreted. While some of the Modes can be easily identified (Mode 1 for scale), other Modes can be more difficult to interpret due to the significantly smaller magnitude of shape variation presented. Other methods like independent component analysis can be used as an alternative, but they all have their strengths and weaknesses. Also, despite consistent methods of model preparation, errors from segmentation, pre-registration, and alignment cannot be eliminated. Lastly, due to the significant effect of the size variation, other clinically interesting variations of deformation could not be extensively identified. However, this could also be because the current training data sets were from dogs without any clinical orthopeadic abnormalities. And from the chondrodystrophic dog’s half of them were beagle which shows only a small amount of the typical differences seen in those breeds. Perhaps, when data from pathological cases are evaluated, these clinically interesting variations will be observed.