In vivo kinematics and ligamentous function of the knee during weight-bearing flexion – an investigation on mid-range flexion of the knee

Abstract

Purpose:

To investigate the in-vivo femoral condyle motion and synergistic function of the ACL/PCL along the weightbearing knee flexion.

Methods:

Twenty-two healthy human knees were imaged using a combined MRI and dual fluoroscopic imaging technique during a single-legged lunge (0°-120°). The medial and lateral femoral condyle translation and rotation (measured using geometric center axis-GCA), and the length changes of the ACL/PCL were analyzed at: low (0°-30°), mid-range (30°-90°) and high (90°-120°) flexion of the knee.

Results:

At low flexion (0°-30°), the strains of the ACL and the posterior-medial bundle of the PCL decreased. The medial condyle showed anterior translation and lateral condyle posterior translation, accompanied with a sharp increase in external GCA rotation (internal tibial rotation). As the knee continued flexion in mid-range (30°-90°), both ACL and PCL were slack (with negative strain values). The medial condyle moved anteriorly before 60° of flexion and then posteriorly, accompanied with a slow increase of GCA rotation. As the knee flexed in high flexion (90°-120°), only the PCL had increasingly strains. Both medial and lateral condyles moved posteriorly with a rather constant GCA rotation.

Conclusions:

The ACL and PCL were shown to play a reciprocal and synergistic role during knee flexion. Mid-range reciprocal anterior-posterior femoral translation or laxity corresponds to minimal constraints of the ACL and PCL, and may represent a natural motion character of normal knees. The data could be used as a valuable reference when managing the mid-range “instability” and enhancing high flexion capability of the knee after TKAs.

Level of Evidence:

Level IV

Introduction

Numerous studies have reported data on ACL and PCL functions using in-vitro experimental measurements [15, 23, 32]. In-situ forces of the ACL and PCL were measured at different flexion angles when the knee was subjected to an anterior or posterior tibial load [23, 32]. There are also studies that have investigated the knee kinematics by dissection of the ACL and PCL using cadaveric knees [11, 15]. These data have provided fundamental knowledges for the development of total knee arthroplasties (TKAs) [14, 45]. For example, posterior-cruciate retaining (CR) and substituting (PS) prostheses have been developed to reproduce the PCL function [39, 40, 46]. Bicruciate-retaining (BCR) and bicruciate-substituting (BCS) knee prostheses have been developed to reproduce both ACL and PCL functions [24, 32]. However, despite widely reported clinical successes in the treatment of severe knee diseases, follow-up studies indicated existence of residual pain of the knee, decreased range of motion (ROM), stiffness, and wear and loosening of the prosthesis [18]. Up to 36% of clinically successful patients were reported to experience mid-range flexion “instability” (paradoxical motion at mid-range of flexion) which could make patients feel a “non-natural” knee after surgery [44]. Either CR or PS TKAs could only achieve, on average, a maximal knee flexion around 120° [40].

To improve TKA biomechanics function, there are studies that investigated the PCL or cam-post contact forces using cadaveric knee specimens after TKAs [1, 39]. There are also studies that investigated the PCL function and cam-post contact timing during in-vivo functional weightbearing flexion of the knee [1, 7, 30, 39, 47]. For example, the PCL function has been investigated in a CR TKA during in-vivo weight-bearing flexion of the knee [8, 45]. The cam-post contact timing in PS TKAs has been examined during in-vivo knee motion [30, 39, 47]. Recent studies also compared the kinematics of BCR or BCS TKAs with those of normal knees. However, the mechanisms that could be associated with the “abnormal” mid-range motion [25, 26] as well as the limited high flexion [6] of the knee after TKAs are still not well understood.

Despite that many studies have examined the ligamentous function and knee kinematics during various knee motions [11, 46], few data has been reported on how the ACL and PCL synergistically function with the changes of knee kinematics/laxity throughout the flexion arc [3, 37]. The quantitative data and relationship on the normal knee kinematics and corresponding ligament constraints along the functional flexion arc is not clearly delineated in literature and this knowledge is critical for improvement of contemporary TKAs that are aimed to reproduce the ligamentous function and normal knee kinematics to enhance the patient satisfaction [12-14, 45]. In this study, our objectives are to investigate 1) the in-vivo femoral condyle translation in the anterior-posterior direction and axial rotation and 2) the synergistic function of the ACL and PCL along the weightbearing flexion arc. It was hypothesized that 1) dynamic functional patterns of the ACL and PCL are consistent with the dynamic variation of knee kinematics and 2) the ligaments provide minimal restraints to the knee during mid-range flexion. To test these hypotheses, the ligament elongation and the knee condyle motion patterns were determined in living healthy human subjects during the full range of weightbearing flexion motion.

Materials and methods

This study included 22 healthy knees in 22 subjects (16 men and 6 women, age 33 ± 13 years; body mass index: 25.5 ± 3.5 kg/m²; 9 left and 13 right; no previous abnormal condition of the knee or lower limb). All participants who met the inclusion and exclusion criteria were enrolled through our institutional email broadcast network. Standard examination was performed on the knee, including the Lachman and anterior drawer test. Participants with increased laxity were excluded. Other exclusion criteria included knee pain, previous knee injury, and previous surgery to the studied lower limb. The magnetic resonance imaging (MRI) scan of the knee of each participant was assessed for potential meniscal tears, chondral defects, and ligamentous injuries. If present, the participant would be excluded from further analysis.

The MRI and dual fluoroscopic imaging techniques were used for the measurement of knee kinematics [22]. Each knee was imaged using a 3.0-Tesla MRI scanner (Siemens, Erlangen, Germany) with a fat-suppressed 3D spoiled gradient recalled sequence. Sagittal images with 1 mm thickness were captured in a 180 mm × 180 mm field of view and a resolution of 512 × 512 pixels. These images were used to construct three-dimensional (3D) surface models of the femur, tibia, and fibula (Fig. 1) in a solid modeling software (Rhinoceros; Robert McNeel and Associates, Seattle, WA).

Figure 1.

Two views of a typical 3D knee model at different flexion angles, including the geometric center axis (GCA) of femur (nave blue) and the tibial coordinate system (red). The model included femur, tibia, ACL and PCL. The ACL and PCL were both divided into two functional bundles: anterior-medical (AM) (yellow) and posterior-lateral (PL) (pink) bundles for the ACL, anterior-lateral (AL) (blue) and posterior-medial (PM) (green) bundles for the PCL.

After MR scanning, each subject performed a single-legged lunge and the knee was imaged at approximately 0°, 30°, 60°, 75°, 90°, 105°, and 120° of flexion using the fluoroscopes (BV Pulsera; Philips, Bothell, WA). The orthogonal fluoroscopic images and the 3D bony models of the femur, tibia, and fibula were imported into a virtual space in the solid modeling software that replicated the dual fluoroscopic image system. The outline of each bone was extracted from the fluoroscopic images. The projections of the 3D femur, tibia, and fibula models were matched to their corresponding outlines on the fluoroscopic images to reproduce the 3D positions of the model in space. The relative positions of the models were used to represent the 6DOF tibiofemoral positions at each selected flexion angle. This system had a reported error of < 0.1 mm and 0.3° in measuring tibiofemoral joint translation and rotation, respectively [22].

To determine the in vivo end-to-end distances of 3D wrapping paths of the ACL and PCL during motion, the anatomic tibial and femoral footprints of the ACL and PCL were determined based on the sagittal and coronal plane MR images with the guidance of anatomical descriptions[33, 34]. The ligament footprints were directly mapped onto the MRI-based 3D knee model. Since it was difficult to clearly distinguish the different functional bundles of the ligaments on their MRI images, they were divided into different bundles according to the anatomic studies.

To quantitatively describe the femoral condyle motion, a coordinate system on the tibial plateau was established (Figs. 1 and 2). The tibial long axis was parallel to the posterior wall of the tibial shaft. The medial-lateral axis was defined as a line connecting the centroids of the two circles fit to the medial and lateral tibial plateau surfaces. The anterior-posterior axis was perpendicular to the other two axes. The femoral long axis was defined along the femoral shaft. The knee flexion was measured between the long axes of the tibia and femur in the sagittal plane.

Figure 2.

Femoral condyle motions were determined using the projection of the GCA on tibial plateau surface, including the anterior-posterior translation of the medial and lateral condyles, the internal-external rotation of the GCA along the tibial long axis. External rotation of the GCA (internal rotation of the tibia) was defined as positive.

To describe the condylar motions, the geometric center axis (GCA) was selected. Two co-axis cylinders were constructed using the posterior geometries of the medial and lateral femoral condyles. The axis of the cylinders was defined as the GCA axis. The two vertical cross sections of the cylinders in sagittal planes of the knees were located at the largest radius of both posterior femoral condyles and the centers of the two circular cross sections were selected to represent the centers of the medial and lateral condyles (Fig. 1) [5, 29]. These center points were projected on the tibial plateau surface to determine the medial and lateral femoral condyle translations using the tibial coordinate system, and the angles of between the GCA axis and the medial-lateral axis of the tibial plateau were defined as rotations of the GCA (Fig. 2).

The ACL and PCL were both divided into functional bundles (Fig. 1): anterior-medical (AM) and posterior-lateral (PL) bundles for the ACL, anterior-lateral (AL) and posterior-medial (PM) bundles for the PCL [4, 17]. This technique has been described in previous studies from our laboratory to measure ligament kinematics [17]. A mathematical optimization was implemented to find the shortest 3D wrapping path of each ligament bundle around the bones. The lengths of each bundle were determined at each selected flexion angle of the knee. Following the methods by Taylor et al. [41] (measuring the relative strain of the ACL), the ligament length changes were normalized to a reference to represent a normalized length change (also termed strain in this paper). The strain was calculated using the engineering strain formula: ε=(l-l₀)/l₀ ×100%, where l represents the instantaneous length of the ligament, l₀ was a reference length and ε was the strain representing the normalized length change.

It has been reported that the cruciate ligament function in about 5% strain levels during normal functional daily activities [31, 35]. Since a real reference length was not known for each ligament, the ACL and PCL were assumed to carry 5% strain at full extension and 120° of flexion, respectively in this study. The ligament strains at other flexion angles were calculated accordingly. A positive strain showed elongation (stretching) of the ligament and negative strain showed shortening (relaxing) of the ligament.

This study was approved by the institutional review board of the Massachusetts General Hospital (Partners Human Research Committees, protocol #: 2003P000337 / PHS). Written consent was obtained from each subject prior to participating in this study.

Statistical analysis

Femoral condyle positions in the anterior-posterior direction, the femoral condyle rotation represented by the GCA rotation, and the elongation and strain of each ligament at each flexion angle were presented using a mean value and a standard deviation. A repeated measure one-way analysis of variance (ANOVA) and a post Turkey’s post-hoc analysis was used to analyze the differences at each flexion range. Independent variable was the range of knee flexion angles. The dependent variables were defined as femoral condylar position changes in the anterior-posterior translations, GCA rotations and ligament length/strain. Specifically, the data were analyzed in 3 ranges: low flexion (0°- 30°), mid-range flexion (30°- 90°) and high flexion (90°- 120°). Analyses were performed using the SPSS Statistics 23.0 and a p value of < 0.05 was considered to be significant.

A post-hoc power analysis indicated that 15 subjects would provide over 95% power to detect the kinematics changes (shown in Table 1) at low flexion angles.

Table 1.

Anteroposterior motion and internal-external rotation of the medial and lateral condyles at each flexion range. P-values compared the motions at the two ends of each flexion range.

Flexion Range	0° - 30°		30° - 60°		60° - 90°		90° - 120°
	Difference	P value	Difference	P value	Difference	P value	Difference	P value
Medial AP	2.2 ± 1.8	0.002	0.9 ± 1.5	n.s.	−0.6 ± 2.2	n.s.	−2.3 ± 2.3	0.001
Lateral AP	−4.0 ± 3.4	0.000	−1.4 ± 2.3	n.s.	−2.1 ± 1.9	0.026	−1.9 ± 3.6	n.s.
IE Rotation	8.8 ± 4.2	0.000	2.7 ± 2.9	n.s.	2.1 ± 3.5	n.s.	1.3 ± 4.8	n.s.

NOTE: AP: anterior-posterior translation; IE: internal-external GCA rotation. P value of < 0.05 was considered to be significant, n.s. represented p-values > 0.05 and non-significant,

Results

Femoral condyle translation and rotation during the knee flexion range

The medial femoral condyle moved anteriorly by 2.2 ± 1.8mm and 0.9 ± 1.5 mm during 0° - 30° (p < 0.05) and 30° - 60° (n.s.) of knee flexion range, and then posteriorly by 0.6 ± 2.2 mm and 2.3 ± 2.3 mm during 60° - 90° (n.s.), and 90° - 120° (p < 0.05) of knee flexion range, respectively (Fig. 3a, Table 1). Whereas the lateral femoral condyle moved always posteriorly by 4.0 ± 3.4 mm (p < 0.05), 1.4 ± 2.3 mm (n.s.), 2.1 ± 1.9 mm (p < 0.05), and 1.9 ± 3.6 mm (n.s.) during from full extension to 120° of flexion at a 30° increment. Anterior femoral translation reached maximal at 60° of flexion. During the mid-range flexion, the medial condyle exhibited the reciprocal anterior-posterior translation about 1.5 ± 3.1 mm between 30°-90° of flexion.

Figure 3.

a) Medial and lateral femoral condyle translation in anterior-posterior (AP) direction along the flexion arc. b) Internal-external (IE) femoral condyle rotation represented by the GCA rotation along the flexion arc.

The femoral condyle GCA showed consistent external rotation with the knee flexion (Fig. 3b). The external GCA rotation changed by 8.8° ± 4.2° from 0° to 30° of flexion (p < 0.05). The rotation changed by 2.7° ± 2.9° from 30° to 60° (n.s.), and by 2.1° ± 3.5° from 60° to 90° (n.s.). From 90° to 120°, the change of GCA rotation was only 1.3° ± 4.8° (n.s.).

Elongation and strain of cruciate ligaments along the flexion arc

The elongation and strain of the ACL, and PCL are shown in Figures 4 and 5. The AM and PL bundles of the ACL showed reduction in length throughout the flexion range (Fig. 4). The mean peak strain was set as 5% at 0° of flexion for both bundles (Fig. 5). At 30°, the strain of was 0.1 ± 3.9% for the AM, and −9.6 ± 5.2% for the PL bundles. Beyond 30°, both bundles demonstrated consistently increased negative strain values. The AL bundle of the PCL had a −16.8 ± 6.9% strain at full extension (Fig. 5). Its strain increased throughout the flexion range and became positive after about 90° of flexion. The PM bundle of the PCL had a positive strain of 2.3 ± 10.2% at full extension of the knee and the strain was reduced to negative value between about 10° and 90°. Beyond 90° of flexion, the strain became positive and kept increasing with flexion. During the mid-range flexion (30° - 90°), both ACL and PCL had negative strains that showed minimal restraints to the knee joint function (Fig. 5).

Figure 4.

Elongation of two bundles of the a) ACL and b) PCL along the flexion arc of the knee during the single-legged lunge motion.

Figure 5.

Relative elongation (strain) of the ACL and PCL bundles along the knee flexion arc. The strains were calculated by setting the peak strain value of 5% at full extension for the ACL bundles and at 120° of flexion for the PCL bundles. Positive values represent tension and negative values represent relaxation of the ligament bundle.

Discussion

The most important findings of this study were that both cruciate ligaments showed minimal constraining function and the medial condyle exhibited the physiological reciprocal anterior-posterior translation in the mid-range of flexion (30° - 90°) of the knee. ACL and PCL showed constraints to the knee mainly at low (0° - 30°) and high (90°- 120°) flexion angles, respectively. Therefore, the hypotheses, 1) dynamic function patterns of the ACL and PCL are consistent with the dynamic variation of knee kinematics, and 2) the ligaments provide minimal restraints to the knee during mid-range of flexion, were confirmed by the results.

The ACL has been reported to carry varying loads along the flexion path in-vitro when the cadaveric knee was subjected to an anterior tibial load [23]. The PCL has also been shown to carry maximal loads between 60° to 90° of flexion in in-vitro cadaveric knee tests [23]. These studies applied the same external loads, such as an anterior-posterior tibial load, to the knee at different flexion angles. However, when the knee specimen was subjected to a simulated muscle load, the ACL was shown to carry load only at low flexion angles [43]. Our data indicated that ACL function diminished beyond 30° of flexion. The PM bundle of the PCL showed function at close to full extension of the knee. Both bundles of the PCL showed increasing function only after 90° of flexion. Overall, both ACL and PCL had reduced function in mid-range of knee flexion (30° - 90°) in this study. The data on ACL and PCL function were consistent with previous in-vivo studies on ACL and PCL elongations during knee flexion [16]. To fully understand the function of the ACL and PCL, the ligament biomechanics should be investigated using both in-vitro measurements under simulated external loads and in-vivo measurements under physiological loading conditions.

At low flexion angles, our data showed that the medial femoral condyle translated anteriorly and lateral condyle posteriorly with flexion, accompanied by a sharp increasing of external femoral condyle rotation (~8° GCA external rotation/internal tibial rotation) [27]. This is consistent with the ACL function at low flexion angles. Literature has reported that both CR and PS TKAs showed more posterior femoral positions than the normal knees at low flexion angles [7, 28]. Sacrificing the ACL in the TKAs has been attributed to the kinematics change at low flexion angles [36]. Recently, there are studies reporting that both BCR and BCS TKAs, either retaining or substituting the ACL using an anterior cam-post mechanism, could only partially restore the femoral positions at low flexion angles [12, 14, 32]. For example, Kuroyanagi et al. [21] compared the knee kinematics data from different studies using similar methods and identical measurement techniques, and they showed that both medial and lateral condyles of the BCR TKA were more posteriorly positioned at full extension than the native knee, and with reduced internal tibial rotations. Grieco et al. [12] also showed similar findings for a BCS TKA at low flexion angles of the knee. The geometric alterations of the articular surfaces of the tibiofemoral joint as well as the cam-post contact mechanics could play a role in the observed abnormal kinematics of the TKAs at low flexion angles. Future investigation should examine how to improve tibiofemoral articulation and how to closely restore the normal ACL function at low flexion angles in a TKA to better restore anterior knee stability at low flexion angles.

In the mid-range of flexion, the medial femoral condyle moved reciprocally by ~1.5 mm, but the lateral femoral condyle moved constantly towards posterior direction with flexion. The GCA kept rotating by 4.8° ± 4.3° from 30° to 90°. Many previous researches showed similar observations on femoral condyle motions in the mid-range of flexion [8, 25]. For example, Kozanek et al.[20] showed a reciprocal motion of the medial femoral condyle motion during a step-up motion of the knee. Our data on diminished function of both ACL and PCL in the mid-range flexion indicates that the anterior-posterior motion of the knee may mainly be constrained by other surrounding tissues such as the menisci, muscle contractions, as well as articular cartilage geometries and deformation. These data showed that certain anterior-posterior laxity in mid-range flexion could be the kinematics characters of normal knees in response to in-vivo physiological loads. Therefore, retaining or substituting the ACL and PCL in TKAs may not affect the motion of the knee at mid-range of flexion [7]. Paradoxical femoral movements in TKA patients were reported to provoke dynamic instability of the knee [9]. In literature, there are studies showing that the dual cam-post mechanisms in BCS TKAs could not enhance the mid-range stability and axial rotation of the medial and lateral condyles [13, 38]. Early cam-post engagement was shown to increase posterior femoral rollback, but also cause tightness to the knee motion [2, 7]. Elimination of the mid-range laxity in TKAs may interfere with the natural knee motion and cause over-constraints to the knee. Future studies should investigate the physiological mechanisms of mid-range laxity of normal knees in response to various in-vivo loading conditions and if contemporary TKAs can reproduce normal knee laxity at mid-range of flexion and at the same time to avoid the patient’s feeling of mid-range “instability”.

The PCL was shown to have increasing function after 90° of flexion. Both femoral condyles consistently moved posteriorly with flexion accompanied with a small change in GCA rotation (1.2° ± 4.8°). This kinematical observation is similar to previously reported data of the knee kinematics in deep flexion angles [1, 30]. In TKA kinematics research, Yue et al. [45] has shown that the PCL in a CR TKA function differently compared to that of normal knees and was overstretched by over 5% more than the PCL of normal knees at mid-range and high flexion angles. Dimitriou et al.[8] indicated that both femoral condyles of a CR TKA had less posterior translations than normal knees at high flexion, especially at lateral side. Komistek et al. [19] found no difference between PCL retention and excision with regards to the position and movement of the lateral and medial femoral condyles on the tibial component. Similar observations have been reported for BCR and BCS TKAs [28, 38, 42]. Tsai et al. [42] investigated AL and PM bundles of the PCL in a BCR TKA (Vanguard XP, Biomet) and showed significantly (p<0.05) larger PCL elongation in the BCR knee at 90° of flexion than that of the contralateral non-operated knee. Comparison of the Journey BCS and Genesis II PS TKAs (Smith & Nephew Inc.) found that both TKA could not reach high flexion range in vivo that the designs were intended to achieve at 2 years follow-up [38]. Several studies [28, 42] noted that both axial knee rotation and lateral rollback seen in native knees were not restored even by BCR implants. Decreased posterior femoral translations have been related to the reduced maximal flexion capability of the knee [30, 40]. The cam-post mechanism of PS TKAs was designed to substitute the PCL function to enhance posterior femoral translation. The knee function and kinematics were shown to be affected by the timing of the cam-post engagement [39, 47] . Arnout et al. [2] and Zingde et al. [47] found that early cam-post engagement is not beneficial, because it could not accurately reproduce normal PCL function as shown by the data of this study. An early engagement could cause tightness to the knee and could increase the abnormal tibial post wear. Suggs et al. [39] has shown that an early engagement of the cam-post correlates to a reduction of maximal flexion of the knee; while a later engagement of the posterior cam-post was associated to larger maximal flexion angles of the knee. These analyses indicate that how to reproduce normal PCL function and knee kinematics at high flexion and thus, maximize knee flexion capability warrants further investigations.

It should be noted that there were certain limitations in this study. The data of ligament strain cannot be directly related to the true ligament strain or tension, because the reference lengths of the ligaments (the zero-load length) are unknown. Therefore, the strain values of the ACL and PCL were normalized by assuming a peak strain of 5% [31, 35] at full extension and 120° of flexion, respectively. However, this measurement has been shown to be linearly related to the true strain variation [41]. The 5% maximal strain was chosen based on suggestions on ligament functions in normal knee activities by Noyes et al. [31]. Since only the relative ligament functions were studied, this assumption should not affect the conclusion of data. Next, data from only one activity, a single-legged lunge, was investigated, although the tested motion actually represents the most functional activities of the knee including both mid-and deep-range of flexion. Kinematics with more strenuous activities, such as running and jumping, should be studied in future. Finally, all data were measured from normal, healthy subjects. Therefore, only implications to TKA biomechanics were presented using the normal knee kinematics and function as objectives. Future studies should include investigations of TKA patients with various implants. However, the data could be used as a valuable reference when managing the “abnormal” mid-range motion as well as the limited high flexion of the knee after TKAs.

Conclusion

In summary, this study investigated the in-vivo femoral condyle motion and the synergistic function of the ACL and PCL along the weightbearing flexion arc of living normal knees. The data indicated that the ACL and PCL play a reciprocal and synergistic role for the dynamic variation of the knee joint laxity during the weightbearing flexion. Mid-range reciprocal anterior-posterior femoral translation or laxity corresponds to minimal restraints of both ACL and PCL, and may represent a natural motion character of normal knees. The data could be used as a valuable reference when managing the mid-range “instability” and enhancing high flexion capability of the knee after TKAs.