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Medical Engineering & Physics 33 (2011) 1303– 1308

Contents lists available at ScienceDirect

Medical Engineering & Physics

jou rna l h omepa g e: www.elsev ier .com/ locate /medengphy

ollateral ligament length change patterns after joint line elevation may notxplain midflexion instability following TKA

hristian König, Georg Matziolis, Alexey Sharenkov, William R. Taylor, Carsten Perka,eorg N. Duda, Markus O. Heller ∗

ulius Wolff Institute and Center for Musculoskeletal Surgery, Charité – Universitätsmedizin Berlin, Center for Sports Science and Sports Medicine Berlin, Philippstr. 13, Haus 11, 10115erlin, Germany

r t i c l e i n f o

rticle history:eceived 27 February 2010eceived in revised form 15 June 2011ccepted 18 June 2011

eywords:nee

a b s t r a c t

Midflexion instability (MFI) after TKA is a phenomenon often described as varus–valgus instabilitybetween 30◦ and 45◦ knee flexion. The exact mechanisms causing MFI remain unclear, but elevationof the joint line (JLE) may be one possible cause. In an in silico approach using 4 subject specific muscu-loskeletal models, the length change patterns of the collateral ligaments during knee flexion (relative tothe extended knee) were calculated for the anatomically reconstructed joints as well as for JLEs of 5 and10 mm. Analysis of the distance between the ligaments’ attachment sites (DA) in midflexion revealed a

KAoint linetabilityollateral ligamentsidflexion instability

relative decrease in DA magnitude after JLE for both collateral ligaments in comparison to the anatom-ically reconstructed knee. This finding suggests that JLE could contribute to MFI. However, the anteriorligament regions also experienced a DA increase (MCL) or only a slight DA decrease (LCL) for each JLEsimulated. From this perspective, the anterior ligament portions are unlikely to slacken in midflexionand JLE is unlikely to contribute greatly to MFI. In conclusion, our findings did not support the idea thatJLE is a major contributor to midflexion instability for this particular ultra-congruent implant design.

. Introduction

Careful balancing of the soft-tissue stabilizers is essential forhe success of total knee arthroplasty (TKA) [1–3]. In particularn non- or semi-constrained implants, the lateral collateral liga-

ent (LCL) and the medial collateral ligament (MCL) ensure thenee’s varus/valgus stability while the MCL also resists externalotations and anterior–posterior translations [4,5]. Even thoughap and ligament balancing techniques have been established toreate a stable joint in extension and flexion [1,3,6–8], joint sta-ility related problems account for a significant proportion of TKAevisions [9–15].

Of particular concern here is the varus–valgus instability of thenee in flexion angles between 30 and 45◦, also referred to as mid-exion instability (MFI) [16]. Even knees that have been carefullyalanced in extension and at 90◦ flexion can exhibit MFI. While thexact mechanisms leading to MFI are not fully understood, eleva-ion of the joint line (JLE) after TKA has been suggested as a potential

ontributor to MFI [16,17]. An approach towards a better under-tanding of MFI can be derived from the work of Amis and Zavras18], where it was found that the location of the ligaments’ femoral

∗ Corresponding author. Tel.: +49 30 2093 46128; fax: +49 30 2093 46001.E-mail address: markus.heller@charite.de (M.O. Heller).

350-4533/$ – see front matter © 2011 IPEM. Published by Elsevier Ltd. All rights reserveoi:10.1016/j.medengphy.2011.06.008

© 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

attachment sites relative to the knee flexion axis significantly influ-ences the length change patterns of the cruciate ligaments duringflexion. Since JLE alters the knee’s flexion axis relative to the loca-tion of the collateral ligaments’ femoral attachment sites, it is likelythat JLE can induce altered lengthening or shortening characteris-tics of the collateral ligaments at different flexion angles [19,20].The function of the collateral ligaments, which is critical for pro-viding varus–valgus stability of the knee during flexion, might thusbe compromised at certain points of the flexion/extension cycle.

Computer modelling opens up the possibility to systematicallystudy the influence of selected parameters. By studying multi-ple subjects using patient-specific models, a robust response asto whether JLE results in a substantially larger distance decreasebetween the femoral and tibial collateral ligament attachmentsites in midflexion could be obtained and compared to provide anunderstanding of the support provided by the passive soft tissuestructures at different knee flexion angles.

We hypothesised that JLE and the subsequent change in theposition of the femoral collateral ligament attachment sites relativeto the femoral articulating surface alters the length change patternsof the collateral ligaments during knee flexion, specifically in mid-

flexion. The aim of this study was therefore to analyze the lengthchange patterns of the collateral ligaments during knee flexion forsituations of JLE after TKA in order to assess whether JLE can indeedcontribute to midflexion instability.

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Fig. 2. The medial and lateral collateral ligaments were each modelled by 5 portionsto better characterize their functional behaviour throughout flexion. To this end, thefemoral origin and tibial attachment sites of the medial (left) and the lateral (right)

ig. 1. The medial and lateral collateral ligaments (here displayed together with theruciate ligaments) were modelled using high resolution cross sectional images ofhe Visible Human (VH) dataset.

. Methods

.1. Musculoskeletal model

The computer model that formed the basis for this study waserived from the Visible Human (VH) CT dataset [21] and literatureata [22], and contained bony structures, muscles and simplifiedepresentations of the ligament insertion sites of the lower limb23].

To determine the length change patterns of the collateraligaments during knee flexion the musculoskeletal model wasomplemented with a more detailed description of the collat-ral ligaments. The high resolution colour images (resolution.32 mm × 0.32 mm × 1 mm) of the same VH dataset that was usedo create the reference musculoskeletal model were employed toocalize the collateral ligaments [24–29]. This allowed the 3D mod-lling of the medial and lateral collateral ligaments (Fig. 1) using

3D visualisation and volume modelling Software (Amira, Visagemaging, Berlin, Germany). In the combined 3D models of the tibia,emur and the collateral ligaments, the bony attachment sites ofhe medial and lateral collateral ligaments were each modelledn five portions to better characterize their functional behaviourhroughout knee flexion. The origin and insertion of each portionere identified with landmarks to allow calculation of the relative

hange in length of the ligaments (Fig. 2) [24–30]. For the MCL,dditional static wrapping points were defined at the proximalibia.

This more detailed reference model was then adapted to matchhe anatomy of four participating subjects using linear scaling23,31]. As a result of adapting the reference models’ femur and tibiasing subject specific scaling parameters, variation in the inser-ions of the knee ligaments across the four subjects was capturedn the models. Subsequently, a virtual total knee arthroplasty using

n ultra-congruent, fixed bearing and cruciate sacrificing implantesign (Columbus UC, Aesculap AG, Tuttlingen, Germany) was per-ormed on the same four musculoskeletal models [32]. Althoughhe bone sizes of the four subjects varied somewhat as a result of

collateral ligaments were identified using landmarks. For the MCL, static wrappingpoints were introduced at the proximal tibia. The current study focussed on theanalyses of the most anterior and posterior ligament regions (thick lines).

the subject specific scaling factors, a single implant size was foundto be adequate for all four subjects when the virtual implantationwas performed and verified by an experienced surgeon.

2.2. Variation of the joint line

JLE can result from a number of different clinical conditions,including, in the case of distal femoral bone loss, a too small tib-ial resection, the use of a too high inlay, or combinations thereof.For the current study, it was assumed that the tibial cut wasadequate and JLE was a result of modifying the proximal–distalposition of the femoral component and the height of the inlay [32].According to the manufacturer’s recommendation, the femoralcomponent was downsized with increased JLE. Thus the com-ponent’s anterior–posterior dimension was reduced by the sameamount that the JL was elevated, in order to avoid tightening ofthe flexion gap that would otherwise result from JLE. In this study,JLE of 5 mm and 10 mm was simulated. The leg length remainedunchanged in all simulations.

2.3. Kinematic adaptation

The tibio-femoral kinematics of the four subjects were adaptedto the postoperative situation by using a kinematic model thatreflected the geometry of the ultra-congruent prosthesis’ articu-lating surfaces [32]. In agreement with the geometric design ofthe femoral component that possesses three different radii, thismodel used three knee flexion angle dependent axes of rotation todescribe the relative positions of the components throughout therange of knee flexion. Since the axis of rotation of these radii didnot coincide, anterior–posterior, as well as superior–inferior trans-lation was captured in the kinematic model (albeit as secondaryeffects) according to the prescribed relative motion of the kneearound the three radii of the femoral component.

2.4. Collateral ligament length change

To assess the length change patterns in the anterior and poste-rior regions of both the MCL and LCL, the distances between pairs oflandmarks that represent the extremes of the individual ligament

insertion sites (anterior, posterior) were analyzed in both collateralligaments [30,33].

At first, in the anatomically reconstructed knee, the distancebetween the attachment sites (DA) was computed for all four sub-

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ects during knee flexion from 0◦ to 90◦, using an increment of 15◦.ere, by keeping the leg length constant also the reference DA atxtension remained unaltered for all JL conditions. Then the rel-tive change in this distance in reference to the extended knee0◦ position) was calculated. These calculations were repeated forll modifications of the JL as described previously, resulting in aimulation of 12 cases in total (4 subjects, 3 conditions each). Fur-hermore, at every analyzed flexion angle, the DA changes thatccurred during flexion with an elevated JL were compared to theA changes in the anatomically reconstructed knee.

. Results

.1. Anatomical reconstruction

If the JL was anatomically reconstructed, the distance betweenhe femoral and tibial attachments in the anterior MCL increasedy 13.5 ± 0.4% compared to its reference length at extension whenexing the knee from 0◦ to 90◦ (Fig. 3). During the same knee flexionycle the MCL’s posterior regions experienced a distance decreaseelative to their reference length at full extension of 8.1 ± 1.1%. Inhe anterior region of the LCL the DA remained approximately con-tant, while the posterior LCL experienced a 14.6 ± 2.2% decreasen distance compared to its reference length at full extension whenhe knee was flexed to 90◦.

.2. DA changes after JLE in midflexion

In midflexion, JLE generally resulted in a reduced DA in the ante-ior and posterior regions of both collateral ligaments relative tohe anatomically reconstructed knee joint: while the DA increase

uring flexion (expressed relative to its reference length at fullxtension) in the anterior MCL of the anatomically reconstructedoint was 7.9 ± 0.4% at 45◦ knee flexion, the DA at 10 mm JLE was.9 ± 0.3%, indicating a 4.0 ± 0.1% DA decrease relative to the ref-

ig. 3. Length change patterns of the anterior (left) and posterior (right) regions of the mnee flexion. The dashed curve represents the anatomical reconstruction of the joint lin0 mm respectively.

Physics 33 (2011) 1303– 1308 1305

erence implantation. This relative decrease was somewhat largerthan the relative DA decrease observed as a result of JLE at 90◦

knee flexion (2.0 ± 0.2% at 5 mm and 2.8 ± 0.5% at 10 mm JLE). Inthe posterior MCL, the relative DA decrease caused by JLE was alsomore pronounced in midflexion than at higher flexion angles, com-pared to the anatomical reconstruction. For a JLE of 10 mm, a DAdecrease of 4.2 ± 0.1% was observed at 45◦ flexion, while at 90◦ flex-ion this reduced to 1.0 ± 0.9%. In the anterior LCL, a JLE of 10 mmdecreased the DA in midflexion by 2.6 ± 0.1% at 45◦ flexion com-pared to the anatomical reconstruction. In midflexion, there was aslight DA decrease in the posterior regions of the LCL compared tothe anatomical reconstruction (1.9 ± 0.03% at 5 mm and 3.0 ± 0.1%at 10 mm JLE (both at 45◦ flexion)).

3.3. DA changes after JLE in relation to the conditions of theextended knee

Despite the fact that with JLE the DA in the anterior MCL wasreduced in midflexion when compared to its DA in the anatomi-cally reconstructed condition, the DA during knee flexion did notfall below the reference DA obtained for the fully extended knee.For a JLE of 10 mm, the DA in the anterior LCL in midflexion fellslightly below the reference DA in extension (−2.1 ± 0.6% at 30◦

and −1.0 ± 1.1% at 45◦ flexion), while the DA for 5 mm JLE was−0.9 ± 0.6% at 30◦ and remained virtually unchanged compared tothe conditions in extension for a flexion angle of 45◦. In the pos-terior regions of the MCL and the LCL, the DA in midflexion wasalways found to be below the reference DA of the extended knee.This was true for the anatomically reconstructed knee as well as forthe conditions after JLE.

4. Discussion

Even though gap and ligament balancing techniques are estab-lished steps in TKA for creating a stable joint in both static and

edial (top) and lateral (bottom) collateral ligaments from full extension to 90◦ ofe, while the light gray and the gray curves represent joint line elevations of 5 and

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ynamic conditions [1,3,6–8], stability related problems are still aajor reason for a TKA revision [9–11]. It has been speculated that

n elevated joint line (JL) might contribute to midflexion instabil-ty [16,17]. However, little is known regarding effects of JLE on theollateral ligaments, which are key passive stabilizers of the knee,pecifically in midflexion.

Using four musculoskeletal models of the lower limb post TKA32], we have demonstrated for an ultra-congruent implant designhat in midflexion an elevation of the JL resulted in a reduced dis-ance between the attachment sites of the anterior and posterioregions in both collateral ligaments when compared to the anatom-cally reconstructed condition.

This finding alone would indeed suggest that JLE can contributeo MFI. Although smaller, the DA of the anterior MCL still exhibited

distance increase between the attachment sites during flexion,ence indicating support from the passive soft tissue structures atidflexion, even in the JLE condition. Thus, as in the intact kneehere the MCL is known to be taut in extension and becomesore tight during flexion [5,33,34], the MCL displayed the char-

cteristics of a tensed ligament in midflexion. The anterior LCL,hich is taut throughout flexion in the intact knee [5], was also

ffected by JLE and experienced a distance decrease in midflex-on compared to the anatomically reconstructed JL. In contrast tohe anterior MCL, however, the DA in the anterior LCL decreasedelow the DA level in the extended knee. In the worst case, thenterior LCL is only just taut in extension and not pre-tensionednd would therefore become slack with the maximum observed.1% DA decrease (10 mm JLE at 30◦). Such a condition would result

n a varus/valgus laxity of less than 1.5◦ when considering an aver-ge ligament length of 60 mm and a knee width of 55 mm. In the

ntact knee, the posterior fibres of the MCL and LCL slacken withncreasing flexion angles [4,5,26,33], a behaviour that was alsoredicted by our model for the anatomically reconstructed knee.

n JLE conditions this effect was intensified in midflexion. How-

ig. 4. Length change patterns of the collateral ligaments for the conditions of joint line ehange patterns for the anterior (left) and posterior (right) regions of the medial (top) andurve represents the anatomical reconstruction of the joint line, while the solid curve rverage value for maximum tensile strain of the collateral ligaments as reported in the lit

Physics 33 (2011) 1303– 1308

ever, it is rather unlikely that a further slackening of already slackposterior fibres would contribute to any form of instability. JLEtherefore did not seem to be a major contributor to midflexioninstability when using the Columbus ultra-congruent prosthesisdesign.

Nevertheless, while the observed alterations in collateral lig-ament length change patterns in cases of JLE are unlikely tocontribute greatly to midflexion instability, they may still havean impact on the overall ligament function and should there-fore be subject to further investigation. For example the generallydecreased DA in lower flexion angles and in the case of the MCLalso in deeper flexion, may imply that fewer regions of the liga-ment can contribute to load sharing, possibly increasing the riskof overloading within the remaining active structures. In addition,the observed distance increase in the anterior LCL at higher flex-ion angles even above the DA of the extended knee in which theseareas of the ligament are already taut, may be a possible cause forcomplications.

Further complications may also arise when the JL is moderatelyelevated but the femoral component is not properly downsized.Compared to the anatomically reconstructed joint at 90◦ with 5 mmJLE the DA increased in the anterior MCL by 4.7 ± 0.5% to a total of18.2 ± 0.5% and to a total of 9.9 ± 0.8% in the anterior LCL (Fig. 4).Considering that the collateral ligaments are taut in extension[4,5,26,28], it seems safe to assume that any further increase in DAwould be linked to an increase in the ligament strain. It is thereforereasonable to assume that the DA increase observed in this study,specifically in the anterior MCL, is indicative of a strain increase inthis area of the ligament. While the absolute ligament strain can-not be determined with the methods presented here, it is very well

possible that as a result of the DA increases of as much as 18%, JLEmay cause strains in the ligaments which are approaching the mag-nitude of the maximum tensile strain of ligaments, reported to bebetween 13 and 17% [35,36].

levation and no downsizing of the femoral component. The graphs show the length lateral (bottom) collateral ligaments from full extension to 90◦ flexion. The dashedepresents a joint line elevation of 5 mm. The horizontal dotted line represents anerature.

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Even though global pre-operative lower limb kinematics foralking, stair climbing and knee bend activities were originally

aptured for the same four subjects using a gait analysis system23], no detailed general postoperative in vivo kinematic patternsave been presented so far in the literature that allow for subjectpecific modelling of postoperative kinematics [37–40]. Althoughltra-congruent implant designs were introduced to providenhanced joint stability, little is known about the actual interac-ions of such designs with the collateral ligaments. Investigationsnto such an implant design that offers a high level of constraintould therefore provide new insights into the performance of suchesigns, but also enable a more robust approximation of the postop-rative kinematics than would have been possible by using a moreonventional, less constrained implant design.

The current study used a kinematic model that was limited toagittal plane motion, since preliminary fluoroscopic analyses per-ormed in our lab indicate that only little internal–external rotationccurs in vivo with such an ultra-congruent fixed bearing design.s a result, internal–external movement was considered secondary

or these analyses and therefore not included. Here, an isolatedxial rotation of 5◦ would result in a DA increase of approximatelynly 0.3% (assuming an average ligament length of 60 mm and anee width of 55 mm and an eccentric rotation axis). While thenee kinematics were thus generic to the implant rather than sub-ect specific, the individual scaling of the musculoskeletal modelseflected the anatomical variation in the relative position of theigament attachment sites with respect to the femoral componentcross the four subjects. Therefore, the models did include essentialubject-specific variations in those musculoskeletal structures thatere key for the current study.

Observing the distance between ligament attachment sites toharacterize the function of the ligaments [30,33] has the limita-ion that the zero strain conditions of the ligaments are difficulto obtain [4] and any initial strain within the ligament as wells the condition of a slack ligament is not considered. However,ince the extended knee, in which the collateral ligaments are tautr strained [4,5,26,28] is used as a reference in this study, anyssumptions on ligament strains would be rather under- than over-stimated. Furthermore, we did not directly compare the DA lengthhange patterns in the anatomically reconstructed compared tohe healthy unimplanted knee. While we can therefore not ruleut that the anatomical reconstruction resulted in MFI, the lengthhange patterns of the collateral ligaments during flexion (i.e. aftern ideal TKA that maintained the joint line) were found not toiffer substantially from those patterns for the intact knee: in par-icular, the distances in the anterior proportions of the ligamentttachments in midflexion never fell below the values in extension.ollowing the literature that suggests that the ligaments’ anteriorortions are taut in extension [34,41–44] and also during flexion5,33], these results suggest that the ligaments also stay taut afterhe implantation of the prosthesis. Although this does not provideirect proof, this reasoning strongly suggests that it is unlikely that

nstability in midflexion would be caused by the ideally implantedrosthesis.

Amis and co-worker [18] already emphasized the importancef the locations of the ligament attachment sites relative to theemoral flexion axes, since these are closely associated with theength change patterns of the ligaments. Implant designs with dif-erent condylar radii, different sizing of the implant and patientpecific variation in the location of ligament attachment zones mayurther alter the ligament length change patterns in midflexion andarrant further investigation. The influence of the dynamics of the

ibial wrapping points was not further analyzed in this study, sincehe main influence of JLE on the ligaments’ DA is the changing posi-ion of the femoral ligament attachments relative to the rotationxis of the femoral component.

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Physics 33 (2011) 1303– 1308 1307

In this study we assumed that a well balanced knee was achievedfor the reference implantation in all subjects, without requiringexcessive soft tissue management. Furthermore, in the specificcases of 5 and 10 mm JLE, the tightening of the flexion gap canbe exactly compensated by an equivalent reduction of the femoralcomponents’ anterior–posterior dimension through the implanta-tion of a smaller implant size. In real life, the amount of JLE wouldnot always exactly match the available implant sizes, and wouldthus very likely necessitate some additional soft tissue balancing.In practice, a surgeon would try to balance the soft tissues in bothextension and 90◦ flexion during TKA by appropriate release tech-niques. However, the possibilities to accurately simulate these finerdetails of the surgical release techniques in silico are certainly lim-ited. The conditions analyzed here therefore represent a ratherspecific situation for which no additional soft tissue balancing isrequired. However, by focusing the study on elevation levels thatcould be matched by appropriate changes in the anterior–posteriorfemoral implant dimension, the number of unknown parameterswas minimized. This facilitated the study of the influence of JLE onthe behaviour of the collateral ligaments under well controlled con-ditions, and was therefore considered an acceptable approximationof the clinical situation.

As hypothesised, JLE did alter the length change patterns ofthe collateral ligaments during knee flexion, but our findings didnot support the idea that JLE is a major contributor to midflexioninstability for the Columbus ultra-congruent implant design.

Acknowledgements

This study was supported by a grant of the German ResearchFoundation (DFG SFB 760) and the European Union 7th FrameworkProgramme (FP7/2007-2013 ICT-2009.5.2 MXL 248693).

Conflict of interest

No conflict of interest declared.

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