The Three-Dimensional Morphology of the Patellofemoral Joint and the Normal Predicted Value of Tibial Tuberosity-Trochlear Groove Distance In Chinese Population

Our objective was to obtain normal patellofemoral measurements so as to provide a reference for prosthetic design. Besides, the absolute values and indices of TT-TG distances are still controversial in clinical application. A better method to enable precise clinical applications is still needed. 78 knees of 78 subjects without knee pathologies were included in this cross-sectional study. A CT scan was obtained from all subjects and three-dimensional knee models were constructed using Mimics and SolidWorks software. We measured and analyzed 19 parameters including TT-TG distance and dimensions and shapes of patella, femur, tibia, and trochlea. LASSO regression was used to predict the normal TT-TG distances. Results: The dimensional indexes, TT-TG distance, and femoral aspect ratio of the males were signicantly larger than those of females (all P values <0.05). However, after controlling the bias from age, height, and weight, there were no signicant differences in TT-TG distances, PAL, and anterior-posterior dimensions between genders (all P values >0.05). The Pearson correlation coecients between the AFO and other indexes were consistently below 0.3, indicating a none or weak relationship. Similar results were observed for the SA and the Wiberg index. Using LASSO regression, we obtained four parameters to predict TT-TG distance (R 2 =0.5612, P<0.01) to achieve the optimal accuracy and convenience.


Introduction
Although total knee arthroplasty (TKA) has proven to be a successful surgical procedure for alleviating pain and improving function in patients with knee osteoarthritis, patient satisfaction rates after TKA vary between 75% and 89% [39]. Anterior knee pain is a major reason for the dissatisfactions, which may be caused by a variety of abnormalities, including patellofemoral pathologies [44]. More and more researchers have observed mismatches of the patellofemoral joints after TKA. Matz et al. reported that the probabilities of changes in anterior femoral offset, anteroposterior size of the femur and anterior patellar offset after TKA were 40%, 60%, and 71%, respectively, compared with those before TKA [34].
Kalichman et al. suggested that increased trochlear angles were associated with exacerbated functional impairments [30]. Moreover, Jan et al. highlighted that the patellofemoral geometry was of great importance in TKA, but was often overlooked [29]. Finally, most of the endoprosthetic designs of the knees are based on the anatomical data of Caucasians, and less relevant for Asians and may result in component mismatches [33,51].
In the last few decades, researchers reported the shape differences of knees between ethnicity and gender. An extensive study from Mahfouz et al. analyzed 1000 normal adult knees to identify differences in three-dimensional knee morphology among Caucasian, African American, and East Asian populations, which calculating 11 femoral and 9 tibial measurements [33]. Asseln et al. comprehensively analyzed 412 pathological knees following TKA using 33 femoral and 21 tibial features to investigate gender differences and they indicated that large inter-individual variations should also be important for speci c implant design despite gender differences [3]. Yue et al. investigated the morphologic measurements of femur and tibia in healthy Chinese and white subjects and described the differences in knee anthropometry between gender and ethnicity [51]. Although most of the literatures a rmed gender differences between knee morphology, several literatures suggested no gender differences regarding anterior condylar anatomy and posterior condylar offset [15,49]. Meanwhile, relative fewer studies on gender differences of patellofemoral morphology were investigated and most of them analyzed the patella, but not the anterior and posterior condylar of the femur or entire patellofemoral joint [31,35,40].
In conclusion, the sexual dimorphism of the entire patellofemoral morphology is still controversial.
The tibial tubercle-trochlear groove (TT-TG) distance is a well-established reliable index that evaluates tibial tubercle lateralization and patellofemoral instability. Increased TT-TG distance is generally implicated as a risk factor for patellofemoral instability and used as an important criterion to make decisions in surgical procedures [27,46]. The TT-TG value of > 15 mm is recommended as abnormal, and the value of > 20 mm is the threshold for performing tibial tubercle osteotomy [12,37]. However, this absolute value does not respect the anatomic differences between gender and ethnicity, and it was hypothesized that TT-TG distance is highly correlated to the knee size [13,25,38]. Hernigou et al. indicated that the normal TT-TG distances varied as the knee sizes and predicted the normal TT-TG value of Greek using the femoral width and tibial width for the rst time. However, the mediolateral width of the femur and tibia might not be the best parameters to describe the knee sizes, and similar parameters also included the height and weight of the patient [23]. Thus, it is still needed to analyze appropriate parameters to predict the normal TT-TG distance and to create the reference criterion in Chinese. Therefore, our objectives were (a) to obtain normal patellofemoral measurements and identify gender differences to provide a reference for prosthetic design; (b) to determine the normal predicted TT-TG value to enable precise clinical diagnoses and prediction of medial transfer of the tibial tuberosity.

Subject demographics
Two readers who had many years' experience of radiography took the measurements and repeated the measurements after two weeks.

Statistical analysis
All statistical analyses were performed using R (version 3.5.1,R Foundation for Statistical Computing, Vienna, Austria), and p values less than 0.05 were considered signi cant. The intraclass correlation coe cient (ICC) was performed to determine intrarater and interrater reliability, and the intrarater and interrater reliabilities were good to excellent (all ICCs > 0.85, Table 1).  For normally distributed data, the two-sample Student's t-test was performed to determine the signi cance of the difference between the genders, otherwise, the Mann-Whitney U test was used. Next, multiple variable linear regression analysis was used to analyze the signi cant difference between the genders again after controlling the bias from age, height, and weight. The Pearson correlation coe cients were performed to explore the relationship among all parameters.
The LASSO (Least Absolute Shrinkage and Selection Operator) regression models were constructed to predict the normal TT-TG distances. Firstly, the boxplot was generated to determine the outliers from the distribution of TT-TG in males and females, respectively. After deleting the outliers, the remaining data were both normally distributed. The LASSO regression models were created using the "glmnet" package of R software. We selected the directly measured parameters above the moderate correlation coe cient with TT-TG distance to enter the model for coe cient progression. And sex also entered the initial model. The LASSO regression introduces λ as a tuning parameter on the basis of linear regression, which controls the overall strength of the penalty. The greater the penalty is, the fewer parameters are retained in the model. Then the independent variable that has a great in uence on the dependent variable is selected and a relatively simpli ed model can be obtained. We used the mean squared error (MSE) as the selection criterion to describe the performance of the model. 10-fold cross-validation was automatically performed to calculate the λ value and MSE for a varying number of independent variables. We used the λ at which the minimal MSE is achieved (lambda.min) and the largest λ at which the MSE is within one standard error of the minimal MSE (lambda.1se) to select the optimal model.

Results
Demographic data 78 knees were included in the study. The means and standard deviations for all parameters, as well as age, height, weight, and BMI, are shown in Table 2. Regarding the Wiberg classi cation as modi ed by Baumgartl and Ficat, type I, II and III accounted for 7.5% (n = 3), 90% (n = 36) and 2.5% (n = 1) in males; and for 10.5% (n = 4), 89.5% (n = 34) and 0 (n = 0) in females, respectively. No other type was found. This indicates that most of the selected patellas were stable.  P values represent the signi cant differences between genders applying the two-sample t-test for independent samples.
P' values represent the signi cant differences between genders after controlling the bias from age, height, weight using the multiple variable linear regression model.
Data are presented as mean ± SD.
NA represents no linear relationship or not meeting the condition for linear regression analysis.  P values represent the signi cant differences between genders applying the two-sample t-test for independent samples.
P' values represent the signi cant differences between genders after controlling the bias from age, height, weight using the multiple variable linear regression model.
Data are presented as mean ± SD.
NA represents no linear relationship or not meeting the condition for linear regression analysis.

Gender differences of patellofemoral measurements
When using two-sample t-test for independent samples for gender comparison, PT, PFT, PW, PLFW, PLL, PAL, fML, fAP, femoral aspect ratio, tML, tAP, TT-TG distances, AFO and PFO of males were signi cantly larger than those of females, and the differences were statistically signi cant (all P values < 0.05). After controlling the bias from age, height, and weight, there were no signi cant differences in TT-TG distances, PAL, and anterior-posterior dimensions including PT, PFT, fAP, and PFO between genders (all P values > 0.05). Meanwhile, PW, PLFW, PLL, fML, femoral aspect ratio, tML, tAP of males were still signi cantly larger than those of females (all P values < 0.05). No signi cant differences between males and females were identi ed for the Wiberg index, SA, LTI, MTI, and TA (all P values > 0.05).

Pearson correlation coe cient analysis
As was shown in Fig. 6, the height, weight, the dimension of the patella, the dimension of the femur, the dimension of the tibia, and TT-TG distance were moderately-highly positively correlated with each other LASSO regression to predict normal TT-TG distance LASSO regression model was constructed to analyze the prediction of the normal values of TT-TG distances. 14 indexes were selected into the model. Coe cient progression was shown in Fig. 7. Taking lambda.min as a reference, 12 indexes were included and only PW and PLL were excluded (R 2 = 0.7064, P < 0.01), which was not convenient to clinical application. Thus we took lambda.1se as a reference, and the height, fML, tML, and tAP were included in the nal model (R 2 = 0.5612, P < 0.01). The formula is de ned as: The height is expressed in cm, while the fML, tML, and tAP in mm. In this study, only data with the height ranging from 160 to 185 cm, fML ranging from 67. 51

Discussion
In the past few decades, TKA has achieved great development, but there is a high rate of dissatisfaction, often due to patellofemoral pathologies. In addition to surgical techniques, inappropriate prosthetic design often results in mismatches of the patellofemoral joints [10,28]. It has been reported in the literature that even a millimeter-level error in TKA can lead to serious consequence [43]. In this study, we made comprehensive measurements of patellofemoral joints as a whole, obtained gender differences, and exploratively found some morphological characteristics, which provided a reference for prosthetic design. Meanwhile, we used LASSO regression model to predict the normal values of TT-TG distances so as to enable precise clinical diagnoses and predict medial transfer of the tibial tuberosity accurately.
Many studies have reported on the measurements of patella thickness. The comparisons of patellar thickness with those measured in other studies are shown in Table 3. We used student's t test to determine the signi cant differences between present results and those reported in other literatures. The result indicated that the patella thickness of Chinese tended to be smaller than that of the Caucasians, while comparable to that of the Korean and greater than that of the Indian [4,9,26,35,40,50]. This nding is consistent with the results from previous studies [31,35,50]. The re-establishment of original thickness and adequate residual bone thickness is considered as key surgery guidelines in TKA [22]. However, due to the mismatch of the patellar implants, the surgeons had to choose between the reestablishment of original thickness and adequate residual bone thickness. By choosing the former, the low residual bone thickness likely causes fracture and instability; by choosing the latter, the increased thickness of patella causes overstu ng of the patellofemoral joint and leads to anterior knee pain [1,41].
Although several studies have shown that adverse clinical outcomes were not likely to occur if the overall and residual bone thickness of patella was maintained in a reasonable range (postoperative thickness within 3 mm of the original thickness of the patella, and residual thickness between 10 and 15 mm), the changes of the patella might affect the patellofemoral contact pressures, thus leading to complications of the patellofemoral joint [31]. Therefore, the patellar prostheses with more available choices should be designed according to patellar characteristics.
We explained many gender differences from this study. The result showed that the dimensional indexes of the males were generally larger than those of females, which was consistent with previous studies [33,40]. In terms of the shape, the patella and the femur of the females were thicker than those of males in the anterior-posterior direction for the same medial-lateral dimensions, which was consistent with the relatively small femoral aspect ratio in females. Therefore, the shape of the distal femur of the males was more " at" compared to females, while females had a narrower distal femur than males. These results were comparable to those reported in previous studies [5,19,33,51]. We found that the Wiberg index and the shape of the trochlear exhibited no dimorphisms between gender. Gillespie et al reported that no signi cant difference between gender was found in the medial and lateral ange, which was similar to our results [19]. Based on these features, gender-speci c prostheses should be designed in consideration of gender characteristics. However, more and more studies focused on not only gender differences but individual differences [3,5]. Taking this issue into account, we exploratory analyzed the correlation coe cient between all parameters.
This study found that AFO, SA and the Wiberg index all varied greatly among individuals. These three indexes are the primary description of the patellofemoral shape and thickness. To avoid overstu ng and notching of patellofemoral compartment, the AFO should be treated appropriately. Matz et al reported that the probabilities of changes in AFO after TKA were 40% compared with those before TKA [34].
Although some previous studies showed no signi cant differences between restoration of AFO and clinical outcomes, there was a trend toward improved outcomes [34,42]. Other studies showed that if the AFO increased after TKA and the there was a risk of overstu ng due to the mismatch of the prosthesis, the pressure of the patellofemoral joint would increase, and then there would be complications such as anterior knee pain and decreased knee motion [20]. If there was a risk of notching of the patellofemoral joint, it leaded to cause instability in knee exion [6]. Taking these issues into account, more and more studies analyzed the shape and variance of the distal femur. Lonner and Gillespie et al indicated that the overall variability of the anatomy of the distal femur should be taken into account but not gender difference [19,32]. According to the individual differences, Everhart et al proposed a binary classi cation system to describe the shape of the distal femur and ve binary categories were selected based on the aspect ratio, trochlear width, trochlear tilt, the ratio of medial and lateral trochlear width, and trochlear groove angle [14]. Besides, Varadarajan et al reported that the laterally oriented proximal part and medially oriented distal part formed the intact trochlear groove, and there was a turning point to distinguish these two part [48]. Moreover, Chen et al proposed a quaternary system based on the position of the turning point [8]. Due to the greatly individual variance of the distal femur, more studies on different shapes of the femoral components should be focused, and prosthetic implants with greater varieties in sizes and shapes of anterior femoral condyle needed to be designed.
The TT-TG distance had signi cant positive correlation with tubercle sulcus angle (TSA) and Q-angle, and was considered to be objective and reliable in the quanti cation of extensor mechanism malalignment and patellar instability [21,23]. In the previous studies, the measurement of the TT-TG distance was mainly used in image overlapping technology based on CT and MRI. However, several literatures have reported the inaccuracy of the current measurement [2,21], and we found that mild adduction or abduction of the lower extremity resulted in a greater change in this value. In this study, we took this issue into account, and used the online reslice of the mimics software to standardize the selection of images, so that the collected transverse picture was as perpendicular to the mechanical axis of the lower limb as possible, which greatly ensured the accuracy of measurement.
This study reported the average CT-based TT-TG distance to be 13  [37]. Hinckel et al reported that the MRIbased TT-TG distance was 3.1-3.6 mm smaller than CT-based TT-TG distance, which explained the inconsistency of the above results [24]. demonstrated the need for combining the TSA and the TT-TG distance to avoid overcorrection during medial tibial tubercle osteotomy [21]. Our result reported that the TT-TG distance had a positive correlation with height and the knee size, which was comparable to other literatures [11,16,23]. Moreover, several literatures described that application of the TT-TG indices (ratio of the TT-TG distance to the tibial maximal mediolateral axis) obtained more reliable and standardized results [7,16]. Hernigou et al used fML and tML to establish normal values of TT-TG distances in Greek. However, they also raised doubts about whether the two parameters were applied as the best predictors [23]. Taking these questions into account, the present study applied LASSO regression model to analyze the best predictors of the normal TT-TG distances. LASSO regression is a machine learning method that can shrink the coe cients of variables that do not contribute information to the model to zero and is well suited to feature selection for high-dimensional data [36]. Using this method, we obtained four parameters to predict normal TT-TG distance, namely height, fML, tML and tAP, to achieve the best accuracy and convenience. The prediction formula obtained by us provided a more accurate reference for clinical determination of patellar instability, rather than the absolute values or TT-TG indices. Meanwhile, the formula can play a guiding role in the more accurate localization of the tibial tubercle during the tibial tubercle osteotomy.
Insu ciency of the study Limitations of the present study include the relatively small sample size. With all measurements derived from knees with extension, there was no data from the knees with 30° of exion. Thus, the patellar tilt, patellar height, bisect offset, and other factors could not be obtained. We are continuing to study additional subjects and to acquire data from knees with a exion angle of 30°. Another limitation of the present study was that the formula for predicting TT-TG distance has not been clinically veri ed, and more studies on the clinical effectiveness of the formula need to be performed.

Conclusion
In summary, the dimensional indexes of the males were generally larger than those of females. In terms of the shape, the patella and the femur of the females were thicker than those of males in the anteriorposterior direction for the same medial-lateral dimensions. Moreover, the AFO, SA, and the Wiberg index all varied greatly among individuals. More attention should be paid to not only gender differences but individual differences. Besides, using LASSO regression, we obtained four parameters to predict normal TT-TG distance, namely height, fML, tML and tAP, to achieve the best accuracy and convenience. This study provided a reference for prosthetic design and a new method of predicting TT-TG distance to enable precise clinical diagnoses and guide the medial transfer of the tibial tuberosity accurately.    The Pearson correlation coe cients of all variables.

Figure 6
The Pearson correlation coe cients of all variables.  Coe cient progression with LASSO. The rst dotted line means that we used the λ at which the minimal mean squared error (MSE) is achieved (lambda.min) to select the optional model. The second dotted line means that we used the largest λ at which the MSE is within one standard error of the minimal MSE (lambda.1se) to select the optional model. The latter was selected as the nal model in this study.