The effect of patellofemoral pain syndrome on patellofemoral joint kinematics under upright weight-bearing conditions

Patellofemoral pain (PFP) is commonly caused by abnormal pressure on the knee due to excessive load while standing, squatting, or going up or down stairs. To better understand the pathophysiology of PFP, we conducted a noninvasive patellar tracking study using a C-arm computed tomography (CT) scanner to assess the non-weight-bearing condition at 0° knee flexion (NWB0°) in supine, weight-bearing at 0° (WB0°) when upright, and at 30° (WB30°) in a squat. Three-dimensional (3D) CT images were obtained from patients with PFP (12 women, 6 men; mean age, 31 ± 9 years; mean weight, 68 ± 9 kg) and control subjects (8 women, 10 men; mean age, 39 ± 15 years; mean weight, 71 ± 13 kg). Six 3D-landmarks on the patella and femur were used to establish a joint coordinate system (JCS) and kinematic degrees of freedom (DoF) values on the JCS were obtained: patellar tilt (PT, °), patellar flexion (PF, °), patellar rotation (PR, °), patellar lateral-medial shift (PTx, mm), patellar proximal-distal shift (PTy, mm), and patellar anterior-posterior shift (PTz, mm). Tests for statistical significance (p < 0.05) showed that the PF during WB30°, the PTy during NWB0°, and the PTz during NWB0°, WB0°, and WB30° showed clear differences between the patients with PFP and healthy controls. In particular, the PF during WB30° (17.62°, extension) and the PTz during WB0° (72.5‬0 mm, posterior) had the largest rotational and translational differences (JCS Δ = patients with PFP—controls), respectively. The JCS coordinates with statistically significant difference can serve as key biomarkers of patellar motion when evaluating a patient suspected of having PFP. The proposed method could reveal diagnostic biomarkers for accurately identifying PFP patients and be an effective addition to clinical diagnosis before surgery and to help plan rehabilitation strategies.


Introduction
Approximately 25% of patients presenting with knee pain to musculoskeletal clinics are diagnosed with patellofemoral pain (PFP) [1]. Although extensively studied, the precise cause of PFP has not yet been entirely resolved because of the complexity of the interactions of

Study cohort
This study was approved by Stanford Institutional Review Board (IRB file #20144). All patient data were acquired and used only after written informed consent was obtained. Under the IRB-approved protocol, the study cohort included two groups: a PFP group consisting of 12 females and 6 males (mean age, 31 ± 9 years; mean weight, 68 ± 9 kg) who were treated for more than 6 months, but achieved no symptom improvement, and a control group consisting of 8 females and 10 males (mean age, 39 ± 15 years; mean weight, 71 ± 13 kg) with no symptoms of PFP. Included subjects in the PFP group suffered persistent anterior knee pain for at least three months up to 11 years and reported reproducible pain during at least two of the following physical activities: squatting, stair ascent/descent, kneeling, prolonged sitting, or isometric quadriceps contraction. The measurement conditions for patellar tracking were NWB0˚(supine), WB0˚(upright), and WB30˚(squat). Prior to testing, all study participants received an explanation of the study aims and agreed to participate.

CT image acquisition
Knee joint alignment under the conditions of WB0˚and WB30˚was measured on 3D volumetric images acquired with a cone-beam-based C-arm CT imaging system (Artis Zeego; Siemens Healthineers, Forchheim, Germany) as shown in Fig 1. Overexposure correction was applied to obtain saturation-free images by attenuating the X-ray beam on the periphery of an object [27]. The measurement parameters were as follows: photon energy, 80-125 KeV; resolution, 1240 × 960 pixels after 2 × 2 binning; and field-of-view, 300 × 400 mm 2 . The distance between the X-ray source and the patient was 980 mm and that between the patient and the detector was 218 mm. Measurements were acquired with the X-ray source and detector rotating around the patient in circular trajectory (π + fan angle). In total, 248 and 496 images were acquired in the upright (WB) and supine (NWB) positions, respectively. Two-dimensional projection images were reconstructed into a volumetric CT image using a filtered-backprojection method [28][29][30] implemented in our in-house reconstruction package, named CONRAD (Radiological Sciences Laboratory, Stanford University, Stanford, CA, USA) [31,32]. A pipeline for the CONRAD software framework for cone-beam imaging is shown in Fig 2.

Patella tracking estimation
We set a reference of the joint coordinate system (JCS) as the knee joint of the left leg. Three anatomical landmarks along the x, y, and z axes of the patella and three of the femur were used to establish a JCS. As shown in Fig 3, points P_M (patella medial) and P_L (patella lateral) were the most medial and lateral points with the highest (+) and lowest (−) values on the X p axis. Point P_B (patella bottom) was the lowest point on the patella. Points F_EPL_L (femur lateral) and F_EPL_M (femur medial) were the most lateral and medial points with the highest (+) and lowest (−) values on the X F axis, and point F_GRV (femur groove) had the highest value on the Z p (+) axis. Based on these anatomical landmarks, coordinate axes were established on the patella [X P (+) axis, lateral; X P (−) axis, medial; Y P (+) axis, proximal; Y P (−) axis, distal; Z P (+) axis, anterior; and Z P (−) axis, posterior] and the femur [X F (+) axis, lateral; X F (−) axis, medial; Y F (+) axis, proximal; Y F (−) axis, distal; Z F (+) axis, anterior; and Z F (−) axis, posterior]. Six kinematic degrees of freedom (DoF) values, representing translational and rotational movements of the patella relative to the femur, were derived. According to Fig 4,patellar   tilt (PT,˚) between the Z P and Z F axis was (+ L) lateral and (− M) medial, patellar flexion (PF,˚) between the Y F and Y P axis was (+ F) flexion and (− E) extension, and patellar rotation (PR,˚) between the X P and X F axis was (+ C) clockwise and (− CC) counterclockwise. Patellar anterior-posterior shift (PT z , mm), a shift of the patellar coordinate system origin projected on the Z F axis, was (+ A) anterior and (− P2) posterior. Patellar proximal-distal shift (PT y , mm), the shift projected on the Y F axis, was (+ P1) proximal and (− D) distal. Patellar lateral-medial shift (PT x , mm), the shift projected on the X F axis, was (+ L) lateral and (− M) medial. The tracking points on the CT images are shown in Fig 5. Here, we describe the acquirement process for the 3 rotational DOF values for the JCS. For example, let's consider how to get the PF. The angle size between the Y F and Y P axes is the PF magnitude. Next, we determine the sign of the PF. The PF has a direction of rotation from the Y F axis (femur) to the Y P axis (patella). The rotation direction (Y F to Y P ) corresponds to one of two rotation directions (+ flexion, − extension) in Fig 6a. The sign in the corresponding direction becomes the sign of the PF value. The sign of the PF is + (flexion). We can determine the magnitude and sign of the PF. We can find the rest of the variables in the same way.
Next, we will describe the acquirement process of the 3 shifted DOF values for the JCS. For example, let's consider how to get Z F . We find a projection point (Cross_P2) of P o in the extension line of the Z F axis. The projection is the orthogonal condition. The distance between the projection point and F o is the PT z magnitude. We determine the sign of the PT z . The direction from F o to Cross_P2 (F o to Cross_P2) corresponds to one of two directions (+ anterior,posterior) in Fig 6b. The sign of the PT z is + (anterior). We can determine the magnitude and sign of the PT z . We can find the rest of the variables in the same way. The DoF values on JCS were computed by the codes implemented in MATLAB R2015b (MathWorks, Natick, MA, USA), as shown in Fig 6. Additionally, to identify the statistical differences between the subjects and the PFP patients, we have summarized the p-values from t-tests in Table 2 for the comparisons between the patients and the controls.

Statistical analysis
We evaluated the kinematic difference between the two groups (patients with patellofemoral pain and controls) using five statistical tests: 1. Unpaired t-test (Table 2), 2. One way analysis of variance (ANOVA) (S1 Table), 3. Wilcoxon rank sum (S1 Table), 4. Mann-Whitney test (S1 Table), and 5. Kolmogorov-Smirnov test (S1 Table). A p-value less than 0.05 was considered statistically significant and could differentiate the kinematics between the two groups. ANOVA was implemented using the Python program language; all other statistical methods were implemented using MATLAB.

Patella tracking parameter analysis
The mean kinematic DoF (± standard deviation, SD) values include patellar medial-lateral shift (PT x , mm), proximal-distal shift (PT y , mm), anterior-posterior shift (PT z , mm), tilt (PT, ), flexion (PF,˚), and rotation (PR,˚), respectively. The three conditions were NWB0˚, WB0˚, and WB30˚, respectively. The obtained DoF values are shown in Table 1 and Figs 7 and 8. As shown in Table 2, the statistical analysis based on the unpaired t-test resulted in five different JCS coordinates with significant differences (p < 0.05) between patients with PFP and control subjects. The statistically significant JCS coordinates included patellar anterior-posterior shift under all three loading conditions, patellar proximal-distal shift under NWB0˚, and patellar flexion under WB30˚. These statistically significant results generally corresponded well to the results based on the other four representative statistical methods, except for the

Discussion
In this study, we hypothesized that patients with PFP will show different JCS coordinates in vivo under NWB and under physiologically relevant WB conditions compared to healthy control subjects. This hypothesis was supported by the findings presented in the current study. The data for the 18 patients confirmed that the PF during WB30˚, the PT y during NWB0˚, and the PT z during NWB0˚, WB0˚, and WB30˚were statistically different (p<0.05) between the patients with PFP and healthy controls. Of the five statistically significant JCS coordinates presented, two p-values (PF and PT z during WB30˚) were less than 0.01 and the other two (PT z during NWB0˚, WB0˚) were less than 0.001 ( Table 2). Given that p<0.001 is generally considered to indicate high statistical significance, the significant JCS coordinates presented in this study can serve as accurate biomarkers to diagnose knee conditions.
A study by Bruno et al. [33] reported that despite contraction of the quadriceps, there were obvious differences in the lateral translation of the patella relative to the femur during WB0˚in the upright position and NWB0˚in the supine position. Hence, we focused on patellar tracking during the following conditions: NWB0˚, WB0˚, and WB30˚.
Some reports have provided measurements during unrealistic conditions, such as PFP evaluation in the supine position only [34] or while leaning on the equipment during the loading task [23]. For example, in a study by Esfandiarpour et al. [19], the lunge test was performed with one leg supported on the ground, while the knee of the other leg was flexed at 90˚. The lunge, supine, and leaning tests differ from actual conditions that involve squatting or straightening to mimic movements performed in daily activities. Hence, the conditions used in several previous studies were controversial and not practical for the study of PFP. Therefore, clinically relevant weight-bearing conditions were employed in the present study (WB0˚and WB30˚) for the diagnosis of PFP.
Esfandiarpour et al. [19] reported that the PT values of the PFP patients during NWB0ẘ ere laterally tilted (− L) as compared with those of the control group due to the stabilization by the retinacula and ligaments, as well as the articular geometry. In the present study, the PT values during NWB0˚of the PFP and control groups (p<0.53) were +8.36˚± 7.3˚and +6.58± 8.11˚, respectively. On the other hand, the PT values of the PFP group during WB0( p<0.36) and WB30˚(p<0.72) showed abnormal lateral patellar tilt as compared with the control group. The PT values of the control group remained relatively constant. Regarding the difference between the PT values of the PFP and control groups, our results are generally consistent with the trends in value change compared to the referenced study [19]. However, our values are different from the referenced study's values. Draper et al. [23] reported that the PT x values of the PFP group were lower during WB0t han NWB0˚. In the cited study, patellar motion is generally generated by quadriceps contraction. The quadriceps contraction has a gap between the WB0˚(weight-bearing) and NWB0( non-weight-bearing). The quadriceps contraction during NWB0˚shows unbalanced activation by the vastus medialis obliquus. However, the quadriceps contraction during WB0d oesn't have unbalanced activation in the quadriceps. The quadriceps contraction during NWB0˚, due to unbalanced quadriceps motion, causes more lateral patella translation compare to that during WB0˚. Conversely, we have a different opinion than the authors of the cited study. Abnormal pressure on the patella surface by wrong alignment of the patella causes pain when the patella isn't precisely in the center of the groove of the femur. To avoid the pain, patients generally try to move the patella to a region with less pain. A laterally translated patella typically is not located in the center. Therefore, the patient unconsciously contracts muscles that makes it move in the opposite direction (medial translation) to alleviate the pain. The patella can move relative to the medial direction. The PT x values of the PFP group were higher during WB0˚than NWB0˚. Unlike the cited study, our PT x values of the PFP group were greater during WB0˚than NWB0˚(6.39 ± 4.64 vs. 4.73 ± 6.22 mm, respectively).
Additionally, our NWB0˚are different from those in the cited study. In our NWB0˚, the whole body is in contact with the ground. However, in the cited study's NWB0˚, the upper part of the body is in contact with the ground, but the legs are not. The patella indirectly receives the load from the lower leg. The cited study's condition is not actually NWB0˚. Our NWB0˚is a more suitable NWB condition than the cited study's NWB0˚.
Esfandiarpour et al. [19] also reported a difference in PR values between the PFP and control groups during NWB0˚and WB0˚of about 40˚, while in the present study, there was a difference in the cross-flexion angle of about 10˚between NWB0˚and WB0˚.
We focused on the resulting patellar flexion (PF,˚), patellar anterior-posterior shift (PT z , mm), and patellar proximal-distal shift (PT y , mm) values. First, as shown in Figs 8b, 9b and 9c, the PF, PT z , and PT y values during WB0˚to WB30˚were significantly changed in the control group. In contrast, those of the PFP group during WB0˚to WB30˚changed very little. Second, as shown in Fig 7b, there were differences in PF value gaps during NWB0˚vs. WB0˚with the greatest difference during WB30˚. Third, as shown in Fig 8b, the PT y values during NWB0å nd WB 0˚were reversed the PFP and control group. Fourth, as shown in Fig 8c, there were differences in PT z values during NWB0˚, WB0˚, and WB30˚between the PFP and control groups. Lastly, as shown in Fig 9, the largest differences were observed in the values of PF during WB30˚(− E: − 17.62˚) (p < 0.01) and PT z during WB0˚(− P2: − 72.50 mm) (p < 0.01) between the PFP patients and healthy subjects which suggests that PF during WB30˚and PT z during WB0˚can be used as diagnostic biomarkers for identifying patients with PFP.
Carlson et al. showed that a strongly contracted quadriceps reduce the bony constraint on the patella, causing the patella to deviate from normal tracking along the femoral groove [34]. Especially, in weight-bearing conditions, an activation imbalance of quadriceps causes the abnormal action of the patella in the PFP group [19]. Previous studies have speculated that the cause of the activation imbalance of quadriceps might be that the muscles in the PFP group adapted to reduce the concentrated joint stress and consequently reduce pain, increasing the area of patellofemoral contact [35,36]. Moreover, the patellofemoral joint contact area increases with PF [37] and PF is highly corrected with PT z . Our results showed that the largest differences in DoF values between the PFP and control group was observed in PF during WB30˚(− E: − 17.62˚) (p < 0.01) and PT z during WB0˚(− P2: − 72.50 mm) (p < 0.01), which suggests that the PFP group presumably adapted to avoid knee pain. To further understand the origin of knee pain, we suggest evaluation of the patellofemoral contact area between the patella and the femur on CT images.
There were several limitations to this study: (1) factors involved with patellar movement, such as joint morphology, knee muscle activity, and tendon function [23] were not considered; (2) PFP should be accurately distinguished from other types of anterior knee pain, such as patellar tendinopathy [35]; (3) other clinical causes of knee pain attributed to rheumatologic or neurologic pathologies should be ruled out [35]; (4) although patellar maltracking is sometimes related to the condition of the peripatellar fat pads [38], the effects of the peripatellar fat pads were not considered; and (5) we did not consider the function of the patellofemoral joint with more common causes of PFP such as when walking or using the stairs. However, Bruno et al. [33] reported that it is not always possible to apply more than 25% of the body weight with knee flexion of 90˚. (6) It is imperative to evaluate the entire kinetic chain in a comprehensive approach to the treatment of PFP [39]. We should keep in mind the dynamic relationships of the hip and ankle joints with the knee joints. These relationships are complex because the hip and ankle joints can affect the knee joints. For example, excessive rearfoot eversion is a factor correlated with the development and persistence of PFP in some cases. For patients with chronic PFP, psychological factors should be considered [40]. Therefore, future research should consider the combined effects of various factors under appropriate circumstances in PFP patients. We will plan to investigate the patellofemoral contact area between the patella and femur in a future study.

Conclusion
This study proposed an innovative approach to accurately diagnose patellar motion such as patellar maltracking in PFP patients by using a clinical C-arm CT scanner capable of acquiring a volumetric CT image of patients under realistic weight-bearing (WB0˚and WB30˚) and supine, non-weight-bearing conditions (NWB0˚). When comparing the patients with PFP and control subjects, significant differences (p < 0.05) were observed for patellar proximal-distal shift (PT y ) during NWB0˚, patella flexion (PF) during WB30˚, and patella anterior-posterior shift (PT z ) during NWB0˚, WB0˚, and WB30˚on the CT scan. In particular, the rotational and translational differences (JCS Δ = patients with PFP-controls) in DoF values were clearly seen in the PF during WB30˚(−17.62˚, extension) (p < 0.001) and the PT z during WB0˚(−72.50 mm, posterior) (p = 0.007). We showed that the action was revealed by the PT y during NWB0˚, the PF during WB30˚, and the PT z during NWB0˚, WB0˚, and WB30˚, which could be used as diagnostic biomarkers for identifying patients with PFP. Our results provide new insights toward an improved understanding of patellofemoral joint movement during nonand weight-bearing conditions. The proposed method is an effective adjunct for clinical diagnosis before surgery and to help plan rehabilitation strategies.