Using Video-Fluoroscopy and Multibody Modelling to Unveil the Influence of a Gradually Reducing Femoral Radius on Ligament Elongation Patterns Following Posterior Cruciate-Retaining Total Knee Arthroplasty

Abstract

Stability in total knee arthroplasties (TKAs) is mainly provided by soft tissue structures and the implant geometry. Paradoxical anterior translation could be decreased with a gradually reducing femoral radius compared to a dual-radii design. However, the influence of the sagittal curvature of the femoral condyles on knee ligaments remains unclear. This study quantified the length change patterns of the medial and lateral collateral ligaments (MCL and LCL) and posterior cruciate ligament (PCL) in 15 subjects with a gradually reducing radius and 15 subjects with a dual-radii TKA. Kinematics obtained from video-fluoroscopy were used to drive personalised multibody knee models. The ligament lengths were analysed throughout complete cycles of level gait, stair descent, and sit-to-stand-to-sit activity. Regardless of the implant design, our results indicated flexion-dependent elongation patterns in all ligament bundles. Importantly, however, subjects with the dual-radii implant design exhibited higher ligament strains during the mid-flexion phase compared to those with gradually reducing designs. Our findings, therefore, emphasise the importance of the impact of subtle changes in implant geometry on the loading patterns of the knee soft tissues, which need to be acknowledged by implant manufacturers and orthopaedic surgeons.

1. Introduction

Total knee arthroplasty (TKA) is one of the most successful joint replacement surgeries [1,2]. However, a significant number of patients remain dissatisfied with the surgery outcomes. Only half of patients report satisfaction with their ability to resume routine daily activities after joint replacement [3], and even lower satisfaction rates are reported in regard to returning to sport [4]. Among several factors, abnormal kinematics (defined as deviations from the natural movement patterns of a healthy knee joint) and postoperative knee instability are major reasons for patient dissatisfaction after TKA [5,6].

TKA procedures can lead to different kinematics compared to those of intact knees [7,8,9,10]. Unnatural knee kinematics, such as the paradoxical femoral anterior motion associated with cruciate-retaining (CR) TKAs [11,12,13,14,15], may originate from differences between the articular geometries of the implants compared with the natural knee [16,17]. A previous modelling study emphasised the influence of condylar geometry on AP translation during a simulated squat movement [18]. They suggested that paradoxical anterior motion is caused by the dual-radii femoral condyle design, since it occurs at the transition from the distal to the posterior radius. This finding was further supported by several other studies reporting less sudden anterior translation in gradually reducing radius implants [12,13,14,15]. In addition to TKA design, improper ligament balancing has been consistently mentioned as a factor that may contribute to abnormal knee kinematics and postoperative joint instability [19,20]. In particular, excessive laxity of the posterior cruciate ligament (PCL) has been linked to suboptimal kinematic outcomes and joint instability, while a tight PCL may lead to overloading of the polyethylene inlay, potentially shortening the lifespan of the implant [19,21,22,23,24]. In the context of cruciate-retaining total knee arthroplasties (CR-TKAs), it is crucial to uphold a harmonious interplay between the implant’s articular geometry and ligament strain patterns. This balance ensures the proper functionality of the posterior cruciate ligament (PCL), essential for controlling anteroposterior translation, while also preventing potential issues related to ligament over-tensioning that could adversely affect the overall performance of TKAs [6]. However, there is a limited understanding of the intricate relationship between implant design, ligament strain patterns, and their collective impact on TKA biomechanics.

Technical difficulties and ethical considerations hinder proper assessments of ligament laxity/tension in vivo. As a result, the majority of our knowledge about ligament strain patterns after TKA comes from in vitro cadaveric investigations, where the cadaveric specimen is mounted onto a mechanical rig and the ligament strain/force during loaded or unloaded knee flexion is measured by implantable sensors. Using such an approach, Berger and co-workers [25] investigated the relationship between implant conformity and collateral ligament strains. They noted that augmenting implant constraints has the potential to decrease the strain on the medial collateral ligament (MCL), consequently reducing frontal plane laxity in the knee. However, owing to challenges associated with its anatomical position, they refrained from measuring PCL strain. Furthermore, in vitro cadaveric test setups are typically limited in their ability to simulate dynamic functional activities. Recent advances in combining video-fluoroscopy and multibody modelling of the knee appear to overcome these limitations by estimating ligament strain patterns based on the relative movement of the ligament attachment sites during complete cycles of dynamic activities [26,27,28]. This technique has been employed to evaluate the elongation patterns of the native knee ligaments [27,28,29], as well as ligament strain patterns post-TKA [27,30]. However, the impact of implant design on the functionality of knee ligaments remains to be fully understood.

The aim of this study is to estimate the elongation patterns of the PCL and the collateral ligaments in cruciate-retaining dual-radii and gradually reducing radius TKAs during dynamic activities using a combined video-fluoroscopy and multibody modelling approach. Having observed variations in kinematics [12], we hypothesise that the ligament elongation patterns differ between the two implant designs.

2. Methods

2.1. Subjects

Two cohorts of subjects that had undergone unilateral CR fixed-bearing TKA were included in this study. The first group (GRAD) consisted of 15 subjects (8 m/7 f, aged 69.2 ± 8.6 years, body mass index (BMI) 27.9 ± 3.4 kg/m², Knee Injury and Osteoarthritis Outcome Score (KOOS) 88.5 ± 8.7) possessing a gradually reducing femoral radius implant (Attune, DePuy Synthes, Johnson and Johnson). The second group (DUAL) included 15 subjects (11 m/4 f, aged 68.5 ± 9.3 years, BMI 26.5 ± 3.7 kg/m², KOOS 92.0 ± 4.9) with a dual-radii femoral component (Sigma, DePuy Synthes, Johnson and Johnson). No statistically significant differences in BMI, age, or KOOS were observed between the two groups. The project was approved by the local ethics committee (KEK-ZH-Nr.: 2014-0468).

2.2. Kinematics

Six-degree-of-freedom (6 DoF) tibiofemoral kinematics during level walking, stair descending, sitting down on a chair, and standing up from a chair were captured by a moving single-plane fluoroscope [31]. In addition, whole-body kinematics were captured using 22 infrared cameras (Vicon MX system; Oxford Metrics Group, UK). The marker set used for capturing thigh and shank motion consisted of 5 skin markers on each segment (Figure 1). These markers were placed on key anatomical landmarks, including the epicondyles, malleoli, trochanter, tibial tuberosity, and the quadriceps tendon attachment on the patella. Additional markers were positioned on the thigh (midway between the trochanter and lateral epicondyle) and on the shank (midway between the lateral epicondyle and lateral malleolus), with another marker placed on the tibial, 4 cm superior to the ankle joint. Every activity was repeated at least 5 times, leading to a total of 579 repetitions. A subsequent 2D/3D registration algorithm was used to fit the positions of the CAD models of the tibial and femoral component geometries to the video-fluoroscopic images [32]. Detailed descriptions of the setup and 2D/3D registered tibiofemoral kinematics were previously reported by List and co-workers [12].

2.3. TKA Modelling

A previously developed multibody model [26] was used to create 30 models representing the subjects’ anthropometry (Figure 1). Within the OpenSim modelling environment, skin marker positions captured during the standing trials were used to scale the generic tibial and femoral bone geometries in the proximo-distal (PD) direction [33]. To validate this scaling method, the estimated bone lengths from the OpenSim linear scaling were compared to subject-specific bone lengths derived from frontal X-ray images of the lower limbs. Here, these subject-specific bone lengths were measured by calculating the distance between the proximal and distal joint centres. The knee centre was defined as the midpoint between the medial and lateral epicondyles, the ankle centre as the midpoint between the medial and lateral malleoli, and the hip centre as the centre of the femoral head. Specifically, for the six subjects with available X-ray images, the corresponding estimation errors were calculated and reported as percentages of bone length. Additionally, subject-specific implant dimensions were used to scale the bones in the medio-lateral (ML) and antero-posterior (AP) directions.

The models had a 6 DoF joint defined between the tibial and femoral implant components positioned within their parent bones based on a mechanical alignment approach [34]. The ligaments were modelled as bundles of one-dimensional fibres, with 20 fibres dedicated to each of the PCL and MCL and 10 fibres to represent the LCL. Regarding the anatomic definition of knee ligament bundles [35,36], the MCL was further divided into anterior (MCLa), intermediate (MCLi), and posterior (MCLp) portions. The PCL was divided into antero-lateral (PCLal) and postero-medial (PCLpm) portions, each represented by 10 strands. Wrapping objects representing the bone surfaces were implemented to prevent penetration of the ligament fibres into the bone.

Knee joint kinematics obtained from video-fluoroscopy were used as inputs to drive the 6 DoF tibiofemoral joint within the multibody model. Elongations of the ligament fibres were calculated as changes in the ligament length ($l$) relative to the reference length ($l_0$) defined at heel strike during level walking (i.e., $(l-l_0)/l_0$). For each ligament bundle, an average elongation pattern was extracted from the length change patterns of the individual fibres within the bundle. The outcome patterns were presented either against the time normalised to the percentage of the gait cycle or against the corresponding knee flexion angle.

2.4. Statistical Analysis

Each subject’s ligament elongation patterns were averaged over data obtained from five activity repetitions. Similarly, the elongation patterns of all subjects within each implant group were averaged to represent the ligament behaviour within the knee replaced by the studied implant. A one-way ANOVA test based on statistical parametric mapping (SPM) was performed to assess the influence of the implant design and activity type on the elongation patterns of each ligament bundle [37]. ANOVA combined with statistical parametric mapping (SPM) is a common method used to analyse differences in time series data across multiple groups [38,39,40]. The level of significance was set to α = 0.05.

3. Results

3.1. Validation of the Scaling Technique

The femur and tibial lengths measured using skin marker locations during the standing trials were 446.5 ± 19.1 mm and 422.7 ± 20.1 mm, respectively. In comparison, analysis of subject-specific X-ray images indicated femur and tibial lengths of 431.6 ± 11.9 mm and 422.0 ± 16.0 mm. Thus, the scaling method demonstrated an estimation error of 3.7% for the femur length and 1.6% for the tibial length relative to the X-ray measurements (Table S1; Supplementary Information File).

3.2. Reference Lengths

The mean reference lengths of the MCL bundles ranged from 94.9 ± 5.3 mm (MCLp) to 103.1 ± 5.9 mm (MCLa) for the GRAD subjects and from 105.2 ± 3.2 mm (MCLp) to 114.9 ± 3.8 mm (MCLa) for the DUAL subjects. For the PCL bundles, the reference lengths were 39.4 ± 2.1 mm for the GRAD subjects and 41.4 ± 1.9 mm for the DUAL subjects for the anterior-lateral portion and 39.6 ± 2.5 mm for the GRAD subjects and 41.9 ± 2.2 mm for the DUAL subjects for the posterior-medial portion. The LCL reference length was 50.4 ± 3.2 mm for the GRAD subjects and 54.7 ± 2.3 mm for the DUAL subjects.

3.3. Level Gait

During the stance phase of level walking, for both implant designs, a small inter-subject variability was observed in the ligament elongation patterns, however, with transition to the swing phase, the inter-subject variability started to increase (Figure 2, Figures S1 and S2; Supplementary Information File). During the first half of the gait cycle (GC), the MCL bundles remained close to their reference lengths (with average length changes between -0.2 and 1.2% for the GRAD subjects and from 0 to 1.2% for the DUAL subjects), while the PCL and LCL bundles were slightly lax (with average length changes between −4.8 and 0.4% for the GRAD subjects and from −4.5 to 0% for the DUAL subjects) (Figure 2).

During the second half of the GC, the different bundles started to exhibit distinct elongation patterns (Figure 2); while the PCL and LCL bundles experienced a rapid slackening, the MCL bundles started elongating. Here, the PM portion of the PCL showed lower strains than the AL portion and a local minimum at around 70% of the GC in level gait (GRAD: −14.07 ± 3.4%, DUAL: −11.59 ± 3.76%), while the AL portion of the ligament reached its maximum elongation at around 80% GC (GRAD: 1.96 ± 2.88%, DUAL: 3.28 ± 2.69%, Figure 2).

From 30% to 50% of the GC, statistical analysis revealed significant differences in the LCL and MCL elongation patterns between the two implants, indicating slightly larger strains in the MCL and more slackening in the LCL of the knees with the DUAL implant (p < 0.012; Figure 2 and Figure 3). Moreover, within the last 10% of the GC, significant differences between the GRAD and DUAL implants were observed in the length change patterns of all ligaments (p < 0.022; Figure 2 and Figure 3).

Comparing the two implant designs, the flexion-dependent elongation patterns revealed higher strains in the anterior lateral PCL and LCL for the DUAL implant in comparison to the GRAD design for flexion angles above 18° and 26°, respectively (p < 0.013; Figure 4 and Figure 5).

3.4. Sit-to-Stand-to-Sit Activity

The sit-to-stand-to-sit activity was characterised by almost symmetrical ligament length change behaviour throughout the entire cycle. The LCL and MCLp elongated during the stand-up phase (LCL: from −15.8 ± 2.2% up to −1.5 ± 1.8% for GRAD and from −14.0 ± 2.3% up to −1.2 ± 2.4% for DUAL and MCLp: from −3.4 ± 1.2% up to 0.6 ± 0.5% for GRAD and from −4.0 ± 1.6% up to 0.3 ± 0.8% for DUAL), followed by a slackening during the sit-down period. Similar patterns could be seen for the PCL bundles, but with a rapid lengthening before knee extension and rapid shortening after knee flexion, resulting in a “W” shaped curve (Figure 6, Figures S3 and S4; Supplementary Information File). Conversely, the intermediate and anterior portions of the MCL slightly elongated before they continuously shortened and reached their minimum length at around the middle of the sit-to-stand-to-sit cycle (GRAD: 0.2 ± 1.1% for MCLi and 0.3 ± 1.0% for MCLa and DUAL: 0.1 ± 1.1% for MCLi and 0.2 ± 1.1% for MCLa).

The MCL bundles showed a bi-phasic pattern throughout the range of knee flexion (Figure 7). While the MCLa and MCLi indicated a considerable elongation during flexion for smaller flexion angles, the MCLp remained close to its reference length before all three bundles started slackening with higher flexion angles (Figure 7). The maximum elongation within the MCL was the largest for the anterior fibres (GRAD: 6.4 ± 1.2% and DUAL: 6.4 ± 1.0% for MCLa, GRAD: 3.0 ± 0.8 and DUAL: 3.1 ± 0.8% for MCLi, and GRAD: 0.9 ± 0.4% and DUAL: 0.6 ± 0.7% for MCLp).

The two implant designs showed significantly different elongation patterns in the PCL and LCL bundles, almost throughout the entire range of knee flexion, with, in general, less relative elongation for the GRAD design (p < 0.009; Figure 8 and Figure 9). However, significant differences in the MCL elongation between the implant designs were observed, mainly in the posterior fibres and at higher flexion angles (p = 0.043; above 68° for the pMCL). The GRAD design demonstrated a greater relative elongation compared to the DUAL design (Figure 6, Figure 7, Figure 8 and Figure 9).

3.5. Stair Descent

The elongation patterns of the LCL indicated consistent slackening of the ligament during the stance phase of the stair descent activity, followed by a quick lengthening in the swing phase (Figure 10, Figures S5 and S6; Supplementary Information File). The shortest LCL length occurred at push-off (65% GC), with 14.67 ± 2.02% shortening for subjects with the GRAD implant and 13.34 ± 1.16% for subjects with the DUAL implant. The MCL bundles underwent a rapid shortening before toe-off and a quick elongation after that, resulting in a local minimum at the transition from stance to swing. During the first half of the GC, the MCLa and MCLi lengths steadily increased (up to 5.1 ± 1.0% and 2.6 ± 0.7% for MCLa and MCLi in GRAD and up to 5.7 ± 1.3% and 3.3 ± 0.9% for MCLa and MCLi in DUAL), whereas the MCLp remained near isometric. The anterior and intermediate bundles of the MCL showed a considerable shortening during the second half of the swing phase (Figure 10, Figures S5 and S6; Supplementary Information File). Both PCL bundles started slackening at the beginning of the GC, followed by a lengthening within the second half of the stance phase. The anterolateral portion of the PCL reached maximum lengthenings of 6.0 ± 3.4% (GRAD) and 6.4 ± 2.9% (DUAL) at around 75% of the GC.

The elongation patterns differed significantly between the implant designs, with higher strains observed for the DUAL implant in comparison to the GRAD design. Significant differences were observed starting at 29° of knee flexion for the LCL, and within the mid-flexion range for the PCL and MCL (p < 0.007; MCLa: 33–56°, MCLi: 27–59°, MCLp: 26–56°, PCLal: 13–65°, and PCLpm: 25–54°), as illustrated in Figure 10, Figure 11, Figure 12 and Figure 13.

4. Discussion

Soft tissue structures and implant design play important roles in TKA functionality. In particular, it is known that the sagittal curvature of the femoral component influences TKA kinematics [12,14,15], however, the influence of this design parameter on the functions of knee ligaments is not yet completely understood. This study combined video-fluoroscopy and multibody modelling of the knee to estimate the elongation patterns of the PCL, MCL, and LCL and compare them between gradually reducing femoral radius and dual-radii femoral component implants. The results indicated that the dual-radii implant design induced slightly larger ligament strains compared to the gradually reducing design, especially at the mid-flexion range.

Clear phase distinction was observed in the elongation patterns of the collateral ligaments along the complete cycle of gait activities. The bundles showed relatively isometric behaviour during the first 60% of the GC, likely due to the small knee joint range of motion. With the transition to the swing phase, the ligaments experienced considerable length changes (relative to their reference lengths), associated with the knee exhibiting larger flexion angles. Similar flexion-dependent strain patterns were observed in the sit-to-stand tasks, indicating very small strains when the knee was close to full extension, but considerable length changes at large flexion angles (Figure 7). The MCL length increased with higher flexion angles and reached its maximum at a 40–60° flexion angle, independent of the performed task, however, the strain was non-uniformly distributed between the MCL bundles (based on their location in the AP direction). The MCL strain patterns of the two implant designs were generally consistent with those measured in the healthy knee [41] and TKA knees [26,27,42], indicating the role of the anterior fibres in post-TKA joint stability. Moreover, the present data show that the knee ligaments experience large elongations in the unloaded swing phases of level walking and stair descending, as was also reported in the previous literature [20,27,41]. These findings indicate the importance of assessing ligament function throughout the entire activity cycle.

The LCL continuously slackened with higher flexion angles during the studied activities, as has been consistently reported in the literature [26,27,43,44]. Among the three activities studied, the LCL was slackest during the sit-stand-sit activity, followed by stair descent and then level walking. As a major restraint to the lateral opening of the knee joint, the LCL remained constantly lax, since no remarkable valgus stress occurred during the studied tasks [45,46]. Increased slackening with higher flexion angles can further be explained by the posterior position of the femoral attachment site relative to the centre of the knee rotation on the lateral condyle. These findings correspond to recently reported observations that the knee flexion angle drives post-TKA ligament elongation [26,27].

Soft tissue balancing is important for achieving satisfactory outcomes after TKA. While ligament laxity can lead to knee instability, highly tensioned ligaments may impair the knee’s range of motion [47]. Furthermore, unbalanced soft tissues promote polyethylene wear rates, leading to early TKA failure [48,49]. Normal length change patterns, specifically mirroring the strain patterns of ligaments in the natural, healthy knee, are a prerequisite for the PCL in achieving optimal functionality in PCR-TKA, aligning with its intended design [50,51]. Our results for the two studied implants reveal a slackening of the ligament as the knee flexed, with the shortest lengths of the PCLal and PCLpm occurring at around a 30–40° knee flexion before the ligament started lengthening (Figure 7). These patterns generally align with the elongation patterns of the natural PCL bundles [52,53,54], but with slight differences, as the PCLal in the healthy knee starts lengthening from early knee flexion. Having both ligaments slack at early knee flexion angles may contribute to mid-flexion instability and paradoxical anterior femoral translation, as observed in some PCR-TKA implants [11,12,13,14,15,55,56]. Furthermore, our findings fall within the range of ligament strains reported in a prior study investigating PCL elongation in TKA [20], although they may differ from a few others showing continuous lengthening of the ligament with knee flexion starting from full extension [30,57]. The substantial variations in reported data from the literature may partially originate from differences in measurement techniques, but are mainly related to the diverse implant designs studied.

The most striking differences between the GRAD and the DUAL implants were related to the strain patterns of the AL and PM bundles of the PCL. Statistical analysis revealed significant differences in the elongation patterns between the implant designs, which were consistent for all studied activities. In general, subjects with DUAL implants exhibited consistently higher elongation than those with GRAD implants. Interestingly, with higher flexion angles (>70°), the lengthening patterns of the PCL bundles in both groups tended to align (Figure 7, Figure 9, Figure 12 and Figure 13), corresponding with the similar AP translation patterns of the two implants previously reported at these larger flexion angles [12]. The literature states that the shift from the larger anterior radius to the smaller posterior radius at around 30° flexion contributes to mid-flexion instability [13,14,15]. Our results showed statistically significant differences between the two implant designs in the elongation patterns of the PCLal at 30° flexion across all studied activities (Figure 4, Figure 5, Figure 7, Figure 9, Figure 12 and Figure 13). In particular, the larger strains observed in PCLal in the DUAL design, compared to the GRAD design, could potentially overload the ligament bundle, leading to abnormal anteroposterior translation. This abnormal motion can manifest as a sensation of instability, as the knee fails to maintain proper alignment during dynamic activities. It is also important to note that the ligament reference strains reported in this study are relative to the strain at full knee extension. In practice, ligament fibres may experience some degree of pre-strain after intraoperative soft tissue balancing, which could result in higher strain peaks during functional activities and, in extreme cases, ligament overloading. Therefore, special attention should be paid to the design of the sagittal curvature, particularly in PCR-TKA implants, to ensure more natural ligament lengthening patterns. This can prevent the risks of over-slackening or over-tensioning of the ligaments, which can lead to instability and compromised functionality in the replaced joint.

Some limitations of the current study should be considered while interpreting the results. First, the data used in this study were originally collected as part of a different research project, and as such, we did not conduct an a priori sample size calculation specific to this study. Moreover, subject-specific multibody models were created by scaling a generic model according to the skin marker positions obtained during the standing trial and the implant dimensions. As a result, the exact individual femoral and tibial anatomy could not be represented within our multibody modelling pipeline. Moreover, the generic model consisted of a mechanically aligned TKA. Although a mechanical alignment was targeted for the studied subjects, the exact subject-specific implant alignments may deviate from those represented by the model. However, our study was designed to mainly focus on inter-implant and inter-activity comparisons, rather than reporting the subject-specific ligament elongation patterns, thus, the general findings of the current study remain valid. Here, the impact of slight differences in ligament reference lengths, arising from variations in subjects’ anthropometry between the two groups, on the final strain patterns is expected to be minimal, as the ligament length changes were normalised to their respective reference lengths defined at heel strike during level walking. Moreover, the kinematics obtained by the means of single-plane video-fluoroscopy used as input motion data are limited by the out-of-plane inaccuracy. However, the effect of varying the input kinematics and TKA implantation on the ligament elongation was previously assessed by a sensitivity analysis, reporting only minor influences of medio-lateral translation on ligament elongation patterns [20,26]. In this project, the ligament bundles were modelled as one-dimensional curvilinear fibres connecting the femoral and tibial attachment sites. In vivo lengthening of ligament bundles may be considered as a more complex three-dimensional motion consisting of interfacial sliding and fibre twisting [58]. Finally, the small range of overlap between the flexion angles experienced by different subjects, especially in the stance phase of gait activities, precluded a complete analysis of inter-implant differences that may be highlighted at larger flexion angles.

In conclusion, we demonstrated that ligament elongation patterns and, more specifically, those of the PCL clearly differ between dual-radii and gradually reducing radius implants. In addition, this project underscores the significance of the MCL and PCL in attaining mid-flexion stability following PCR-TKA. It further emphasises the critical requirement for achieving an optimal balance between implant design and ligament length change patterns to ensure satisfactory outcomes after joint replacement. Future studies with larger cohorts and a variety of implant designs are needed to gain a deeper understanding of how implant geometry influences post-TKA ligament function.