Comparative Analysis of 3 Machine Learning Methods for Identifying Minimal Predictors of Patellofemoral Instability Risk Factors

Abstract

Background:

Magnetic resonance imaging (MRI) assessments are considered important for predicting patellar dislocation. Risk factors for patellar dislocation have not yet been clearly identified.

Purpose:

To identify patellofemoral instability anatomic risk factors using MRI and enhance the area under the curve (AUC) through optimized machine learning (ML) methods.

Study Design:

Case-control study; Level of evidence, 3.

Methods:

An age- and sex-matched control group of 121 patients was selected. The assessed patellofemoral morphological parameters included trochlear depth, sulcus angle, trochlear facet asymmetry, lateral trochlear inclination, Wiberg index, lateral patellar facet angle, Wiberg angle, patellar tilt, and trochlear medialization. Differences between groups were analyzed based on the MRI parameters. In addition, ML models were created and optimized using these measured parameters to investigate their diagnostic potential. Logistic regression analysis (LRA), support vector machine (SVM), and light gradient boosting machine (LGBM) were employed as machine learning techniques.

Results:

Sex differences were found in trochlear depth, trochlear groove medialization, lateral patellar facet angle, and Wiberg angle, whereas no sex differences were observed in the other measured parameters. Significant differences between the control and dislocation groups were found for all patellofemoral morphological parameters, except for trochlear facet asymmetry. A significant difference was observed in the patellar height parameter between the 2 groups. Among the measured patellofemoral parameters, patellar tilt showed the highest AUC (0.8). Of the optimized ML models, the LGBM demonstrated the highest AUC at 0.873. When the number of variables used in the SVM model, which employed the fewest variables, was applied to both LGBM and LRA, the SVM model achieved the highest AUC at 0.858.

Conclusion:

Patellar tilt and trochlear depth exhibited the strongest correlation with patellar dislocation. The optimized ML techniques showed improved AUC values compared with those of existing models. However, while a higher AUC can be achieved by using more variables, this approach has proven to be inefficient. Therefore, for practical clinical applications, it is important to focus on using the minimum number of variables in optimized ML models.

Keywords

light gradient boosting machine logistic regression analysis machine learning patellofemoral instability support vector machine

Patellar instability is one of the most common causes of anterior knee pain in young adult patients.^1,14 Several studies have demonstrated a correlation between anatomic features of the patellofemoral joint and patellar instability, which can lead to anterior knee pain and eventually patellofemoral joint arthritis.^{2,4,5,9,10,23} Trochlear dysplasia and tibial tubercle-trochlear groove distance are particularly well-known risk factors for patellar instability.⁴ Once a patellar dislocation occurs, recurrent patellar dislocation is very common.^8,12 Recurrent patellar dislocation often leads to the gradual development of focal cartilage lesions in the patellofemoral joint, increasing the risk for developing patellofemoral joint arthritis at a younger age.²

Predicting the likelihood of patellar instability or recurrence is important, and previous studies have identified various combined risk factors for this condition.^19,20,31 However, the biomechanics of the patellofemoral joint, which affect patellar stability, involve complex interactions among numerous contributing factors.^13,24,31 Furthermore, research on anatomic factors affecting well-known factors, such as trochlear dysplasia and tibial tubercle-trochlear groove distance, remains limited.¹³

Recently, machine learning (ML) algorithms have been increasingly applied in orthopaedics to extract essential information from large datasets, particularly radiologic images.^25,29 These applications of ML demonstrated remarkable performance in diagnosis, decision-making, and predicting critical events.²⁹ ML algorithms, in particular, are effective at analyzing complex anatomic structures such as the patellofemoral joint.²¹

Recently, Kwak et al¹⁸ identified risk factors for acute patellar lateral dislocation using magnetic resonance imaging (MRI) measurements and achieved clinically relevant performance with an interpretable, model-based, optimized ML method in pediatric patients.¹⁸ Therefore, applying ML algorithms to radiologic images is a potentially useful approach for analyzing patellofemoral anatomic structures that affect patellar instability.

This study aimed to develop reproducible ML to assess patellofemoral morphology and anatomic factors associated with recurrent patellar dislocation using MRI and to identify patients at risk of recurrent patellar dislocation through optimized ML methods. Moreover, we aimed to develop and compare 3 optimized ML models to determine which method achieves the highest area under the curve (AUC) with the fewest variables for predicting patellar dislocation in adults. We hypothesized that applying optimized ML would effectively predict the risk of recurrent patellar dislocation in young adult patients with fewer variables.

Methods

Study Population

This study was approved by the institutional review board (IRB) of our institution (4-2022-0366). Informed consent requirements were waived owing to the retrospective design. After IRB approval, we collected and reviewed MRI data from 194 patients >20 years who were diagnosed with acute patellar dislocation between January 2010 and April 2022. Patients who visited the outpatient clinic because of knee pain after minor trauma, such as a sprain, and had acute patellar dislocation confirmed on MRI were included in the study. Patients were excluded if they had any of the following: a history of knee dislocation or traumatic injury; previous knee surgery; fractures; tumorous conditions affecting knee morphology; or unsuitable MRI scan slices for measurement. After applying these criteria, 124 patients were included in this study. A total of 200 control patients were selected using stratified random sampling with proportional allocation from our MRI database. Strata were divided based on sex and age, with sex classified as male or female, and age group categories: 20-29, 30-39, 40-49, 50-59, and 60-69 years. Each stratum was then randomly selected using proportional allocation. The same exclusion criteria applied to patients with patellar dislocation were also applied to patients in the control group. Ultimately, data from 121 control patients were collected and compared.

Measurements of Patellofemoral and Patellar Height Anatomy

MRI was performed on a 1.5- or 3-T MR system (Achieva or AchievaTX Ellition, Philips Healthcare, Best; MR 750, GE Healthcare; Trio, Siemens Healthcare) using a dedicated multiphased array knee coil. The patients were transferred to the MRI unit and examined in the supine position.

The patellofemoral joint was assessed using sagittal and axial views, while patellar height was measured exclusively using the sagittal view. For sagittal measurements, we used the sagittal slice that displayed the maximum patellar length. For axial measurements, we selected the slice where the cartilage covered the entire trochlear area, including both the trochlea and the anterior aspect of the femoral condyle. In addition, the axial slice showing the most posterior aspect of the femoral condyles was employed to establish the posterior baseline and landmarks for condylar height measurements. To assess interobserver variability, the MRI scans were remeasured by 2 observers >4 weeks after the initial measurements. The patellofemoral morphological parameters assessed included trochlear depth,^1,2,5,10 sulcus angle,^1,2,4,5,10 trochlear facet asymmetry,² lateral trochlear inclination,^1,2,5 trochlear medialization,⁵ Wiberg index,^4,5 lateral patellar facet angle,¹⁰ Wiberg angle,⁵ patellar tilt,^5,9,10,14 and the Insall-Salvati ratio (IS).^4,10 The measurement methodologies for each parameter are summarized in Table 1 and Figure 1.

Table 1

Description of Morphological Parameters ^a

Morphological Parameter	Description
Trochlear depth	The line tangential to the posterior condyle is labeled as “p.” The distance from line “p” to the apex of the medial facet is referred to as “a,” the distance to the apex of the lateral facet is referred to as “c,” and the distance to the femoral sulcus is denoted as “b” (Figure 1A). The trochlear depth is calculated as (a + c)/2 - b.
Sulcus angle	The sulcus angle is specified as the angle formed by the 2 lines tangent to the medial trochlear facet and the lateral trochlear facet (Figure 1B).
Trochlear facet asymmetry	The distance from the apex of the medial facet to the femoral sulcus is denoted as “e,” and the distance from the apex of the lateral facet to the femoral sulcus is denoted as “d” (Figure 1C). Trochlear facet asymmetry is expressed as (e/d) × 100%.
Lateral trochlear inclination	The line tangential to the posterior condyle is labeled as “p,” and the line tangent to the lateral facet is labeled as “f.” The inclination of the lateral trochlear facet is specified as the angle between lines “p” and “f” (Figure 1D).
Trochlear groove medialization	A line tangential to the posterior condyle is labeled as “p.” A line perpendicular to line “p” and touching the medial condyle is labeled as “g,” a line perpendicular to line “p” and touching the lateral condyle as “i,” and a line perpendicular to line “p” and passing through the femoral sulcus as “h” (Figure 1E). If we designate the distance between “g” and “i” as TW and the distance between “h” and “g” as MW, then the trochlear groove is expressed as (MW/TW) × 100%.
Wiberg index	The patellar width is determined by the length AB, utilizing the medial edge A and lateral edge B. The patellar thickness is determined by the length CD, utilizing the front polar point C and back polar point D. Let E represent the intersection point of AB and CD. The Wiberg index is expressed as AE/AB (Figure 1F).
Lateral patellar facet angle	The angle of the lateral patellar facet is specified as the angle between the line connecting the medial edge and the lateral edge of the patella and the line tangent to the lateral patellar facet (Figure 1G).
Wiberg angle	The Wiberg angle is specified as the angle formed by the line tangent to the medial patellar facet and the line tangent to the lateral patellar facet (Figure 1H).
Patellar tilt	Patellar tilt is specified as the angle between the line connecting the medial edge and the lateral edge of the patella and the line touching the posterior condyle (Figure 1I).
IS	The patellar tendon’s length is represented as N_IS, and the patellar length is represented as D_IS. The IS ratio is expressed as N_IS/D_IS (Figure 2J).

IS, Insall-Salvati ratio.

Figure 1.

Schematic representation of the (A) trochlear depth, (B) sulcus angle, (C) trochlear facet asymmetry, (D) lateral trochlear inclination, (E) trochlear groove medialization, (F) Wiberg index, (G) lateral patellar facet angle, (H) Wiberg angle, (I) patellar tilt, and (J) IS. IS, Insall-Salvati ratio.

Statistical Analysis

Statistical analysis was conducted using R software Version 3.6.3 (R Foundation). The Student t test was employed to compare parameters between the control and dislocation groups, while the chi-square test was used to compare the proportions of pathology between these groups. To assess both inter- and intraobserver reliability, the intraclass correlation coefficient was calculated. Receiver-operating characteristic (ROC) curves were employed to determine the cutoff value with the highest sum of sensitivity and specificity. The performance of the ROC curves was assessed by the AUC, with higher AUC values categorized as follows: excellent (0.90-1), good (0.80-0.90), fair (0.70-0.80), poor (0.60-0.70), and failure to discriminate (0.50-0.60).

Machine Learning

Using the measured parameters, we developed ML models to investigate their diagnostic potential. We employed logistic regression analysis (LRA), support vector machine (SVM), and light gradient boosting machine (LGBM) as ML techniques. To identify parameter combinations that maximize the AUC, we used a genetic algorithm, treating each parameter as a binary gene. K-fold cross-validation was used to calculate the AUC for each iteration of the genetic algorithm. We selected the combination with the fewest parameters among the 3 models that showed optimal results. Subsequently, we assessed the performance of the remaining 2 models with the same number of parameters and compared the performance of all 3 models based on these results.

Results

Measurement Morphology Results

Radiologic measurements showed excellent reliability, with interobserver reliability ranging from 0.82 to 0.93 and intraobserver reliability ranging from 0.87 to 0.98. Of the 245 total patients, 128 were women and 117 were men.

Sex differences were observed in several measurements. The mean trochlear depth was 3.3 ± 1.6 mm in the female group and 3.7 ± 1.9 mm in the male group. The mean trochlear groove medialization was 40.4 ± 3.4 and 45 ± 3.5 in the female and male groups, respectively (P < .05). The mean facet angle was 24.1°± 4.2° in the female group and 22.2°± 4.6° in the male group (P < .05). The mean Wiberg angle was 134.8°± 8.6° in the female group and 140.4°± 8.1° in the male group (P < .05). However, no sex differences were found in other variables (Table 2).

Table 2

Comparison of Morphological Parameters Between Female and Male Participants

Parameter	All Participants (N = 245)	Women (n = 128)	Men (n = 117)	P
	Mean ± SD (Range)	Mean ± SD (Range)	Mean ± SD (Range)
Trochlear depth, mm	3.5 ± 1.7 (–1.6 to 11.8)	3.3 ± 1.6 (–1 to 6.6)	3.7 ± 1.9 (–1.6 to 11.8)	.039
Sulcus angle, deg	156.4 ± 10.8 (118.1 to 195)	156.4 ± 10.9 (136.4 to 190)	156.3 ± 10.7 (118.1 to 195)	.9518
Trochlear facet asymmetry, %	61.2 ± 15.5 (27.5 to 147.7)	62.1 ± 17.1 (27.5 to 147.7)	60.1 ± 13.4 (36 to 108.6)	.3111
Lateral trochlear inclination, deg	12.6 ± 5.7 (0.2 to 42.7)	12.6 ± 5.5 (0.2 to 23.2)	12.6 ± 6 (0.6 to 42.7)	.9904
Trochlear groove medialization, %	42.6 ± 4.1 (32.3 to 53.3)	40.4 ± 3.4 (32.8 to 49.3)	45 ± 3.5 (32.3 to 53.3)	<.001
Wiberg index	0.5 ± 0.1 (0.3 to 0.7)	0.5 ± 0.1 (0.3 to 0.7)	0.5 ± 0.1 (0.3 to 0.7)	.4405
Lateral patellar facet angle, deg	23.2 ± 4.5 (10 to 43.7)	24.1 ± 4.2 (11 to 34.8)	22.2 ± 4.6 (10 to 43.7)	<.001
Wiberg angle, deg	137.4 ± 8.8 (92.1 to 162.3)	134.8 ± 8.6 (92.1 to 154.4)	140.4 ± 8.1 (115.8 to 162.3)	<.001
Patella tilt, deg	14.4 ± 10.1 (–33.2 to 65.2)	14.7 ± 9.8 (–33.2 to 47.1)	14.1 ± 10.5 (0.3 to 65.2)	.6238
Insall-Salvati ratio	1.1 ± 0.2 (0.7,2.1)	1.1 ± 0.2 (0.7 to 1.7)	1.1 ± 0.2 (0.7 to 2.1)	.4528

Significant differences were observed between the control and dislocation groups in 9 of the measured patellofemoral parameters, except for trochlear facet asymmetry. The mean trochlear depth was 2.7 ± 1.8 mm in the dislocation group and 4.3 ± 1.3 mm in the control group (P < .05). Using a threshold of 3.7 mm, 77% of the dislocation group and 23% of the control group had a pathologic trochlear depth. The mean sulcus angles in the dislocation and control groups were 160.5°± 11.9° and 152.4°± 7.8°, respectively (P < .05). The mean trochlear facet asymmetry was 59.7% ± 17.7% in the dislocation group and 62.6% ± 12.8% in the control group, with no significant difference between the groups. In the dislocation and control groups, the mean lateral trochlear inclination angles were 10.7°± 6.1° and 14.4°± 4.7°, respectively (P < .05). The mean trochlear groove medialization was 41.8 ± 4.2 in the dislocation group and 43.4 ± 3.9 in the control group (P < .05) (Tables 3 and 4).

Table 3

Comparison of Morphological Parameters Between Control and Dislocation Participants

Parameter	All participants (N = 245)	Control Group (n = 121)	Dislocation Group (n = 124)	P
	Mean ± SD (Range)	Mean ± SD (Range)	Mean ± SD (Range)
Trochlear depth, mm	3.5 ± 1.7 (–1.6 to 11.8)	4.3 ± 1.3 (–0.7 to 7.4)	2.7 ± 1.8 (–1.6 to 11.8)	<.001
Sulcus angle, deg	156.4 ± 10.8 (118.1 to 195)	152.4 ± 7.8 (137.1 to 186.6)	160.5 ± 11.9 (118.1 to 195)	<.001
Trochlear facet asymmetry, %	61.2 ± 15.5 (27.5 to 147.7)	62.6 ± 12.8 (37.2 to 93.9)	59.7 ± 17.7 (27.5 to 147.7)	.1341
Lateral trochlear inclination, deg	12.6 ± 5.7 (0.2 to 42.7)	14.4 ± 4.7 (2.6 to 23.1)	10.7 ± 6.1 (0.2 to 42.7)	<.001
Trochlear groove medialization, %	42.6 ± 4.1 (32.3 to 53.3)	43.4 ± 3.9 (34.5 to 53.3)	41.8 ± 4.2 (32.3 to 52.8)	.0029
Wiberg index	0.5 ± 0.1 (0.3 to 0.7)	0.47 ± 0.06 (0.30 to 0.64)	0.51 ± 0.09 (0.30 to 0.70)	<.001
Lateral patellar facet angle, deg	23.2 ± 4.5 (10 to 43.7)	24 ± 3.6 (15.6 to 34.8)	22.4 ± 5.1 (10 to 43.7)	<.001
Wiberg angle, deg	137.4 ± 8.8 (92.1 to 162.3)	138.6 ± 7.2 (117.3 to 151.8)	136.2 ± 10.1 (92.1 to 162.3)	.0352
Patella tilt, deg	14.4 ± 10.1 (–33.2 to 65.2)	9.8 ± 6.2 (0.3 to 39.1)	19.2 ± 11.1 (–33.2 to 65.2)	<.001
Insall-Salvati ratio	1.1 ± 0.2 (0.7 to 2.1)	1.01 ± 0.17 (0.66 to 1.48)	1.15 ± 0.22 (0.69 to 2.11)	<.001

Table 4

Anatomic Patellofemoral Instability Risk Factors ^a

Parameter	Control Group (n = 124)	Dislocation Group (n = 121)
Parameter	Pathology/Non-Pathology	Pathology/Non-Pathology	Sensitivity	Specificity	OR (95% CI)	P
Trochlear depth <3.7, AUC = 0.79	28/96	93/28	0.769	0.774	11.4(6.3-20.7)	<.001
Sulcus angle >156.6, AUC = 0.74	29/95	83/38	0.686	0.766	7.2(4.1-12.6)	<.001
Trochlear facet asymmetry <53.7, AUC = 0.59	42/82	63/58	0.521	0.661	2.1(1.3-3.6)	.006
Lateral trochlear inclination <11.6, AUC = 0.7	33/91	71/50	0.587	0.734	3.9(2.3-6.7)	<.001
Trochlear groove medialization <41.2, AUC = 0.6	32/92	52/69	0.43	0.742	2.2(1.3-3.7)	.007
Wiberg index >0.51, AUC = 0.62	29/95	68/53	0.562	0.766	4.2(2.4-7.3)	<.001
Lateral patellar facet angle <19.7, AUC = 0.59	12/112	36/85	0.298	0.903	3.9(1.9-8.1)	<.001
Wiberg angle >130.7, AUC = 0.58	13/111	33/88	0.273	0.895	3.2(1.6-6.4)	<.001
Patellar tilt >12.9, AUC = 0.8	33/91	93/28	0.769	0.734	9.2(5.1-16.4)	<.001
IS >1.15, AUC = 0.68	27/97	65/56	0.537	0.782	4.2(2.4-7.3)	<.001

AUC, area under the curve; IS, Insall-Salvati ratio; OR, odds ratio.

The mean Wiberg index was 0.51 ± 0.09 in the dislocation group and 0.47 ± 0.06 in the control group (P < .05). The mean lateral patellar facet angle was 22.4°± 5.1° in the dislocation group and 24°± 3.6° in the control group (P < .05). In the dislocation and control groups, the mean Wiberg angles were 136.2°± 10.1° and 138.6°± 7.2°, respectively (P < .05). The mean patellar tilt was 19.2°± 11.1° in the dislocation group and 9.8°± 6.2° in the control group (P < .05). Using a threshold of 12.9°, 77% of the dislocation group and 27% of the control group exhibited a pathologic patellar tilt. In addition, the mean patellar height, measured by the IS ratio, was higher in the dislocation group than in the control group (1.15 ± 0.22 vs 1.10 ± 0.17, respectively; P < .05) (Tables 3 and 4).

Assessment of Diagnostic Tests Considering Anatomic Factors of Patellar Instability

Among the instability factors, the highest AUC values were observed for patellar tilt (0.8), trochlear depth (0.79), and sulcus angle (0.74). Conversely, the lowest AUC values were observed for the Wiberg angle (0.58), lateral patellar facet angle (0.59), and trochlear facet asymmetry (0.59) (Table 4). Using all these factors, we developed optimized ML models, including LRA, SVM, and LGBM. The AUCs for these models were 0.849, 0.832, and 0.859, respectively (Table 5).

Table 5

Comparison of AUC and Optimized AUC Across Different ML Models ^a

	LRA	SVM	LGBM
AUC (95% CI)	0.849 (0.832-0.867)	0.832 (0.824-0.853)	0.859 (0.841-0.878)
Optimized AUC (95% CI)	0.858 (0.840-0.875)	0.858 (0.844-0.873)	0.873 (0.854-0.891)
No. of parameters	7	3	8

AUC, area under the curve; LGBM, light gradient boosting machine; LRA, logistic regression analysis; ML, machine learning; SVM, support vector machine.

Using a genetic algorithm to optimize the AUC, we observed a notable improvement across all 3 ML models compared with their preoptimized versions (Table 5). After optimization, the parameter selection was as follows: LRA with 7, SVM with 3, and LGBM with 8 parameters. Trochlear depth, facet angle, and patellar tilt were consistently identified across all 3 models. Among these, the LGBM model demonstrated the highest optimized AUC. Notably, the SVM model achieved the highest AUC when using only 3 out of 10 parameters. Further analysis was conducted on the LGBM and LRA models using 3 parameters. Among the various combinations of 3 parameters, the combinations yielding the highest results were identified. In the LRA model, the combination of trochlear depth, patellar tilt, and IS ratio resulted in the highest AUC of 0.848. Similarly, in the LGBM model, the combination of trochlear depth, Wiberg index, and patellar tilt yielded the highest AUC of 0.848.

Discussion

The most important finding of this study is that integrating anatomic analysis using MRI with optimized ML techniques significantly improved the AUC value. Specifically, when comparing the 3 ML methods, the optimized approach enhanced the AUC while using fewer variables: LRA reduced the number of variables by 3, SVM by 7, and LGBM by 2 compared with standard ML methods. Notably, the optimized SVM achieved an AUC of 0.858 using only 3 variables, while the optimized LGBM reached an AUC of 0.873, with 8 variables, indicating only a small difference.

To further validate this, we applied the ML models using only 3 variables to LRA and LGBM, but SVM still outperformed the others with the highest AUC. Therefore, the optimized SVM method stands out as the most efficient approach for predicting patellar dislocation, making it suitable for clinical application.

Optimized ML research starts with the accurate measurement of morphological parameters from MRI scans of the patellofemoral joint. A meta-analysis of previous studies found that measuring knee patellar height and groove angle from MRI images is reasonably reliable.²⁷ However, the reliability of other measurements lacked sufficient evidence.²⁷ Our study contributes to this field by demonstrating reliable intra- and interobserver consistency in anatomic MRI measurements. Previous studies suggested that variations in trochlear dysplasia may stem from measurements taken at different locations.

The trochlea of the patellofemoral joint begins to engage when the knee is flexed at approximately²⁶ 20°. Consequently, it is highly likely that the femoral trochlea will not be visible on the axial slice taken through the largest axis of the patella, particularly when the knee is fully extended.^7,30 The high reliability observed in our study may be attributed to taking the measurements through the superimposition of multiple slices.^18,33

Our analysis of sex differences in the patellofemoral joint revealed significant differences in trochlear depth, trochlear groove medialization, Wiberg angle, and facet angle, while no other parameter was significant. This finding aligns with that of a previous study, except for the difference observed in trochlear depth.¹¹ These differences can be attributed to individual morphometric traits, which are influenced not only by genetic, environmental, and cultural conditions but also by lifestyle, health, and functional status. These factors complicate the development of standardized measurements and the interpretation of common values.

The morphological features of the patellofemoral joint have been extensively studied to identify risk factors for various conditions, including patellofemoral joint cartilage damage,^15,28 radiographic features of patellofemoral osteoarthritis,¹⁶ pain and function,¹⁷ and patellar dislocation.^6,18 Our study found that trochlear depth and patellar tilt are the most important anatomic risk factors for patellar dislocation, which is consistent with recent research findings.⁶ Chen et al⁶ characterized patellofemoral morphology and identified major anatomic risk factors for recurrent patellar dislocation using computed tomography (CT) images. Their study showed that trochlear depth, the most frequently observed anatomic risk factor, exhibited the strongest relationship with recurrent patellar dislocation. Previous research also identified a significant relationship between patellar shape and patellar tilt under both static and dynamic conditions.²² Recently, Yamada et al³² found that patellar shift is moderately to strongly correlated with patellar tilt in 95% of patients with patellar dislocation. This finding aligns with our study, where patellar tilt exhibited the highest AUC of 80. When medial patellofemoral traction decreases or there is dysplasia of the vastus medialis obliquus, the patella tends to tilt and shift laterally.²² This results in increased force on the lateral facet of the patella and reduced stress on the medial facet. Consequently, the medial facet may develop hypoplasia, leading to an elevated Wiberg index.²² Our results support this mechanism, as the dislocation group exhibited a higher Wiberg index compared with the control group.

Recent research has increasingly used ML to analyze factors contributing to patellofemoral joint instability.²¹ Nagawa et al²¹ conducted a statistical shape analysis using 3-dimensional (3D) MRI to compare patellofemoral instability models with normal femur models and developed an ML-based prediction model. However, the clinical application of their approach is limited owing to the time-intensive process of creating 3D MRI models. Conversely, Kwak et al¹⁸ optimized ML techniques to identify risk factors for patellar dislocation in pediatric patients using fewer variables from MRI analysis. However, their study reviewed only 1 ML method. Notably, Nagawa et al²¹ and Kwak et al¹⁸ used different ML models. In this study, we trained ML models using a total of 10 parameters, including LRA, SVM, and LGBM. Considering that using all parameters may not yield the best performance, we applied a genetic algorithm to identify the optimal parameter combination. The combination yielding the highest AUC varied across the different models. Specifically, LRA achieved the highest AUC with 7 parameters, SVM with 3 parameters, and LGBM with 8 parameters. The maximum AUC was achieved with LGBM at 0.873, followed by LRA and SVM at 0.858. Despite using only 3 parameters, SVM demonstrated notably high AUC performance, suggesting that fewer parameters could be advantageous in terms of time and cost.

To further investigate the benefits of using the SVM with 3 parameters, additional analysis was conducted. We calculated the highest AUC for all combinations using only 3 parameters for both the LRA and LGBM models, with each model yielding a maximum AUC of 0.848. Thus, the SVM consistently demonstrated the highest AUC when limited to 3 parameters.

To date, no studies have specifically compared various ML models for predicting dislocation based on patellofemoral parameters. The Askenberger study used the LRA model with 4 parameters but did not include model comparisons or validation, making it more of a statistical analysis rather than a comprehensive ML approach.³ In contrast, our study demonstrates that employing a minimal, optimized SVM ML technique offers practical advantages and may facilitate easier application in clinical practice.

However, this study has some limitations. First, all measurements were taken with the knee in a static position, which may not fully capture dynamic patellofemoral mechanics. Second, limb alignment was not accounted for owing to the lack of CT and whole-lower-leg radiographs. The retrospective design limited data on lower limb alignment, femoral anteversion, and external tibial torsion, which are relevant to patellar instability. Furthermore, tibial rotation and knee flexion angle were not controlled during the MRI scans, although the study was conducted under consistent conditions. Third, the parameters, including the modified Insall-Salvati, Caton-Deschamps, Blackburne-Peel, and the tibial tuberosity to trochlear groove distance, could not be incorporated into the study. Although we attempted to measure these dimensions, it was not feasible to include them because of the retrospective nature of the study and the limitations of the imaging data. Nevertheless, our study holds significant clinical relevance, as it aims to investigate the applicability of ML in the diagnosis of patellar disorders. Fourth, we did not distinguish between first-time and recurrent patellar instability patients, and the retrospective nature of this study does not allow us to establish clear diagnostic criteria for patellar instability. Although we assumed that the recorded diagnoses were accurate, this assumption inherently carries a risk of bias. Fifth, the timing of imaging could have influenced the presence or absence of joint effusion, which in turn may have affected patellar tilt measurements. Because patellar tilt was a key distinguishing factor between the cohorts, variability in effusion status at the time of imaging could have introduced additional bias. Sixth, the threshold values for the parameters were determined from radiological measurements, and additional biomechanical and clinical evidence is needed to make these values clinically actionable. Finally, while 3 optimized ML methods were compared, future research should consider additional methods that might offer better performance and faster results.

Conclusion

A notable difference in morphological parameters was observed between the control and dislocation groups, with patellar tilt and trochlear depth exhibiting the strongest correlation with patellar dislocation. This study introduces a novel, clinically accessible approach to identifying risk factors for patellar dislocation using MRI measurements and optimized ML techniques. Compared with existing models, the optimized ML model demonstrated the ability to predict patellar dislocation with fewer variables. Although models with higher AUC values were achieved, using an excessive number of variables proved inefficient. For practical clinical applications, it is important to consider using a minimum number of variables in optimized ML models.

Footnotes

Final revision submitted March 6, 2025; accepted April 7, 2025.

The authors have declared that there are no conflicts of interest in the authorship and publication of this contribution. AOSSM checks author disclosures against the Open Payments Database (OPD). AOSSM has not conducted an independent investigation on the OPD and disclaims any liability or responsibility relating thereto.

Ethical approval for this study was obtained from Severance Hospital, Yonsei University, College of Medicine (4-2022-0366).

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