Metal-backed versus all-polyethylene unicompartmental knee arthroplasty

Mechanical testing

Full details of the experimental methods can be found in the previous study.¹⁵ A total of ten fourth-generation composite Sawbone tibias (model #3401, density Pcf(g/cc) 102 (1.64); Pacific Research Laboratories, Vashon, Washington) were implanted with Sigma Partial (DePuy, Johnson & Johnson Professional Inc, Raynham, Massachusetts) fixed-bearing, non-conforming cemented medial UKA tibial components: five AP, five MB. These synthetic bones are a composite of rigid polyurethane foam (Young’s modulus E = 0.155 GPa) simulating cancellous bone and short fibre-filled epoxy composite (E = 16.7 GPa) simulating cortical bone. They have < 10% interspecimen variability and material properties, and mechanical behaviour similar to those of human cadaveric bone.¹⁸ The geometry of third and fourth generation tibias is identical.

The proximal tibia was coated with matt white paint and a black speckle pattern applied. Then two charge-coupled DIC cameras (Limess, Messtechnik und Software GmbH, Krefeld, Germany) were positioned to view the anteromedial tibia. Implants were loaded using a servohydraulic machine (Losenhausen Maschinenbau, Düsseldorf, Germany) in 500 N increments to a 2500 N medial load. Cameras were calibrated and images taken at 500 N increments. Images were 60 mm wide, giving a resultion of 0.0375 mm/pixel. Strain in the vertical direction was measured at ⩾ 80 consecutive points along an anteromedial line. DIC analysis was performed using Istra 4D 3.1 software (Dantec Dynamics, Skovlunde, Denmark). AE was measured by two Pancom Pico-z piezoelectric AE sensors (125 kHz to 750 kHz; Pancom, Huntingdon, United Kingdom) and IL40S preamplifiers (Mistras Group Ltd, Princeton Junction, New Jersey). AE recording was continuous and activity > 45 dB amplitude registered as a ‘hit’. Computer analysis was performed using AEWin 3.5 software (Physical Acoustics, Princeton Junction, New Jersey).

Finite element model creation and validation

A computer-aided design (CAD) model of a third-generation left composite tibia was obtained from the public domain¹⁹ and imported into ABAQUS CAE Version 6.12 (Simulia, Dassault Systemes, Waltham, Massachusetts) as cortical and cancellous parts. Anatomical axes were defined in coronal and sagittal planes. The proximal tibia was cut perpendicular to the coronal anatomical axis at 6 mm depth with 6° of posterior slope. The tibia was cut distally at 200 mm below the intercondylar eminence to reduce computational effort.

CAD models of tibial components (size 3 MB tibia, 8 mm tibial insert and a size 3 8 mm AP tibia) and 1.5 mm cement mantles were created using Autodesk Inventor 2012 (Autodesk Inc., San Rafael, California) based on implant measurements taken with a digital calliper sensitive to 1/100 mm. These were imported into ABAQUS CAE Version 6.12 and assembled creating two models (Fig. 1):

• a composite tibia with a cemented 8 mm AP tibial component;

• a composite tibia with a cemented MB tibial component and 8 mm polyethylene insert.

Fig. 1

FEMs with 8 mm all-polyethylene implant (left) and 8 mm metal-backed implant (right). Datum planes indicate anatomical axes used as reference for implantation.

All materials were assumed to be isotropic, homogenous and linearly elastic. Material properties are shown in Table I. Linear tetrahedral meshes with mean internodal distances of 1.5 mm to 2 mm were used. Mesh resolution was based on a 2% convergence criterion for the displacement magnitudes in the proximal tibia (Table I).^20,21 Cement was bonded to bone and tibial insert to metal baseplate using tie constraints. A coefficient of friction of 0.25 was used between implant and cement.²⁰ The distal tibia was fully constrained. Proximally, the tibia was constrained against medial/lateral and anterior/posterior translations at a node representing the anterior cruciate ligament footprint to prevent non-physiological bending.

Load was applied directly to the polyethylene articular surface. For validation purposes, the medial plateau only was loaded (this reflected the experimental setup where the aim was to detect only microdamage originating medially): distributed load, uniform weighting, applied at the central node over a radius of 6 mm (113.1 mm² area). This closely reflected the contact area found experimentally of 116 mm^2 15 and the contact point reported in kinematic studies.²² A 2500 N load was applied parallel to the tibial mechanical axis. Strain data (volume of cancellous bone elements experiencing minimum principal strain < -3000 µε and < -7000 µε or maximum principal strain > 3000 µε and > 7000 µε, and peak minimum and maximum principal strains) were recorded at each 500 N increment. In accordance with the commonly used convention in engineering, the negative sign denotes compression and positive tension.

To validate each FEM against AE mechanical testing data,¹⁵ the mean number of AE hits (sound waves of > 45 dB amplitude signifying microdamage events) on loading and unloading five specimens of each implant was correlated with FEM-predicted cancellous bone strain data. DIC-measured vertical strain was correlated with FEM-predicted cortical bone vertical strain.

Statistical analysis

This was performed using SPSS version 19.0 (SPSS Inc., Chicago, Illinois). Correlation between parametric variables was assessed using Pearson’s correlation coefficient. Linear regression analysis was used to explore significant correlations in continuous data with linear relationships. Autocorrelation was tested using the Durbin-Watson statistic (0, positive autocorrelation; 4, negative autocorrelation and 2, no autocorrelation) and residuals were determined to be normally distributed prior to linear regression analysis.

Additional FEM simulations

After validation, additional FEM simulations were undertaken. CAD files were manipulated to create AP tibial components and MB polyethylene inserts of 6 mm and 10 mm thicknesses by adding or removing 2 mm slices. To better represent physiological conditions, and eliminate bending from a unilateral load, a lateral plateau load was added as a distributed load at the central node with radius 6 mm. A 60:40 medial:lateral load division²³ was used and a 4170 N maximum total load (2500 N medial load) was incrementally applied. Maximum load was therefore approximately six times the patient’s body weight (82 kg (804 N) mean body weight for UKA in our unit)⁵ and reflects physiologic tibiofemoral loading.²⁴ Material properties, interactions, constraints and boundary conditions were unchanged. Numerical data were extracted for strain variables as before.

FEM validation

Compressive strain correlated with AE data more closely than tensile strain (Table II). The greatest correlation existed between the volume of cancellous bone elements with compressive strain < -3000 µε and the number of AE hits on loading (Table III, Fig. 2). Anteromedial cortical bone vertical strain, measured using DIC, correlated strongly with that predicted by the FEM (Pearson’s correlation AP 0.956, p = 0.01; MB 0.885, p = 0.01; all implants R = 0.838, R² = 0.702; standard error 0.45; Durbin-Watson 0.32) (Fig. 3).

Fig. 2

Scatter graphs for both implants showing the mean number of acoustic emission (AE) hits measured at each load compared with finite element model-predicted volume of cancellous bone elements with compressive (minimum principal) strain < -3000 µε (AP, all polyethylene; MB, metal backed).

Fig. 3

Scatter graphs showing digital image correlation (DIC) measured cortical bone vertical strain along an anteromedial line for 8 mm all-polyethylene (AP) and metal-backed (MB) implants (inset) and predicted finite element model (FEM) vertical strain data at nodes along the same line (inset).

Linear regression analysis of experimental AE data and predicted FEM data are shown in Table III. Regression equations for both implants fitted the data significantly well (analysis of variance (ANOVA) p < 0.005). That is, the dependent outcome variable (AE hits on loading) was significantly predicted by the regression model using the independent FEM variables of volume of elements with strain >3000 µε or < -3000 µε.

For the MB implant, regression equations fitted well for all FEM variables investigated (ANOVA p < 0.01). For the AP implant, regression equations fitted well (ANOVA p < 0.05) for volume of elements with compressive strain < -3000 µε. The equation for tensile strain > 3000 µε did not predict AE hits significantly well (ANOVA p = 0.099). This is to be expected in a model loaded in compression.

Linear regression analysis was based on discrete AE hit data and FEM-predicted strains. The strongest correlations existed for the MB implant (Table III) (p < 0.008 t-test). When data for both implants were combined, correlation was greatest between AE hits and FEM-predicted volume of elements with compressive strain < -3000 µε (Table III). AE-measured microdamage and FEM predicted strains were related with a confidence of > 95%.

Finite element analysis

Loading both plateaus altered the bone strain distribution for both implants: lateral strain shielding and medial metaphyseal flare strain concentrations (bending) were resolved.

Cancellous bone minimum principal strain

A greater volume of cancellous bone was strained below -3000 µε and -7000 µε in the 8 mm AP than the 8 mm MB model at every load (Fig. 4). At lower loads (1668 N and 2502 N), twice the volume of cancellous bone had a compressive strain of < -3000 µε in the AP than in the MB implant. At 4170 N, the volume of elements with compressive strain < -7000 με was three times greater in the AP implants (Fig. 4).

Fig.

Volume of cancellous bone elements with compressive (minimum principal) strain < -3000 µε (a) and < -7000 µε (b) for both metal-backed (MB) and all-polyethylene (AP) implants of 6 mm to 10 mm thickness.

Altering polyethylene thickness significantly affected the volume of overstrained cancellous bone in AP implants. At loads > 2502 N, reducing AP implant thickness from 10 mm to 6 mm increased the cancellous bone volume with compressive strain < -7000 µε by 1.5 to three times (Fig. 4). Altering MB insert thickness made little difference to the volume of bone overstrained (Figs 4 and 5). AP implants displayed 2.2 (10 mm) to 3.2 (6 mm) times the volume of cancellous bone compressively overstrained < -7000 µε compared with MB implants at 4170 N (Fig. 4).

Fig.

Volume of cancellous bone elements with tensile strain (maximum principal strain) > 3000 µε (a) and > 7000 µε (b) for both metal-backed (MB) and all-polyethylene (AP) implants of 6 mm to 10 mm thickness.

Strain contours demonstrated different patterns of minimum principal strain between implants (Figs 6 to 8). In the MB implant, high compressive strain was confined to the cut tibial surface, but extended much deeper under the AP implant (Figs 6 and 7). In the AP implant, minimum principal strain was concentrated anteromedially in association with the keel and peg (Fig. 7), and at the posteromedial rim of the tibia (Figs 7 and 8). Reducing AP implant polyethylene thickness increased peg and keel concentrations (Fig. 8). In the MB implant, strain concentrated laterally at the implant corner and at the keel, with relative shielding at the peg (Figs 7 and 8). Altering MB insert thickness had little effect (Fig. 8). Peak minimum principal and peak maximum principal strain occurred in elements just anterior to the implant keel in both implants.

Fig. 6

Mid-coronal oblique contours of the cancellous bone for each 8 mm implant at total load of 4170 N (medial load 2500 N). Strain > -50 µε appears pale grey, strain < -7000 µε appears black.

Fig. 7

Medial aspect contour of the outer surface of cancellous bone for each 8 mm implant. Strain > -50 µε appears pale grey, strain < -7000 µε appears black.

Fig. 8

Axial compressive (minimum principal) contours of the upper surface of cancellous bone for implants of different thickness at a 2502 N total load (1500 N medial load). Strain > -50 µε appears pale grey, strain < -7000 µε appears black.

Cancellous bone maximum principal strain

When loading in compression, tensile strains are the result of Poisson’s effect. Therefore, smaller volumes of cancellous bone experienced more excessive tensile than excessive compressive strains. The volume of cancellous bone with tensile strain > 3000 µε differed significantly between implants at loads ⩾ 2502 N (Fig. 5). Altering MB insert thickness made little difference to the volume of overstrained bone (Fig. 5). Reducing AP thickness from 10 mm to 6 mm increased the volume of cancellous bone with tensile strain > 3000 µε by 1.5 to 3.24 times at loads > 2502 N (Fig. 5). In 6 mm implants, the ratio of cancellous bone volumes with tensile strain > 3000 µε (AP:MB implants) was 5.7:1 at 2502 N and 2.4:1 at 4170 N. For 10 mm implants the ratios were 2.2:1 and 1.8:1, respectively.

The volume of cancellous bone with tensile strain > 7000 µε differed between implants at high loads. At 4170 N the volume of cancellous bone overstrained > 7000 µε increased exponentially in the 6 mm AP implant (Fig. 5). Deformation was greater in AP implants, with more bending in both coronal and sagittal planes.