Summary Statement

Simulated increases in body weight led to increased displacement, von Mises stress, and contact pressure in finite element models of the extended and flexed knee. Contact shifted to locations of typical medial osteoarthritis lesions in the extended knee models.

Background

Osteoarthritis (OA) is a degenerative, chronic disease of the articular cartilage that affects more than 150 million people [1]. In the knee, OA can begin as either isolated medial OA or isolated lateral OA. Previous research [2,3] shows medial OA and lateral OA have characteristic cartilage lesion locations and progression patterns as well as flexion angles associated with lesion development, indicating strong involvement of mechanical factors in disease initiation. Therefore, it is important to investigate these mechanical factors. Previous studies combined data sets (geometry, motion, load) from separate sources. The aim of the current work was to use a consistent multi-modal approach.

Iterative finite element (FE) models are used to simulate bone remodelling that takes place due to the surgical insertion of an implant or to simulate fracture healing. In such simulations element material properties are calculated after each iteration of solving the model. New material properties are calculated based on the results derived by the model during the last iteration. Once the FE model has gone through a number of such iterations it is often necessary to assess the remodelling that has taken place. The method widely used to do this is to analyse element Young's modulus plots taken at particular sections through the model. Although this method gives relevant information which is often helpful when comparing different implants, the information is rather abstract and is difficult to compare with patient data which is commonly in the form of radiographs.

The authors suggest a simple technique that can be used to generate synthetic radiograph images from FE models. These images allow relatively easy comparisons of FE derived information with patient radiographs. Another clear advantage of this technique is that clinicians (who are familiar with reading radiographs) are able to understand and interpret them readily.

To demonstrate the technique a three dimensional (3D) model of the proximal tibia implanted with an Oxford Unicompartmental Knee replacement was created based on CT data obtained from a cadaveric tibia. The model's initial element material properties were calculated from the same CT data set using a relationship between radiographic density and Young's modulus.

The model was subject to simplified loading conditions and solved over 365 iterations representing one year of in vivo remodelling. After each iteration the element material properties were recalculated based on previously published remodelling rules. Next, synthetic anteroposterior radiographs were generated by back calculating radiographic densities from material properties of the model after 365 iterations. A 3D rectangular grid of sampling points which encapsulated the model was defined. For each of the elements in the FE model radiographic densities were back calculated based on the same relationships used to calculate material properties from radiographic densities. The radiographic density of each element was assigned to all the sampling grid points within the element. The 3D array of radiographic densities was summed in the anteroposterior direction thereby creating a 2D array of radiographic densities. This 2D array was plotted giving an image analogous to anteroposterior patient radiographs. Similar to a patient radiograph denser material appeared lighter while less dense material appeared darker.

The resulting synthetic radiographs were compared to patient radiographs and found to have similar patterns of dark and light regions.

The synthetic radiographs were relatively easy to produce based on the FE model results, represented FE results in a manner easily comparable to patient radiographs, and represented FE results in a clinician friendly manner.

Introduction: A unique failure mode of hip resurfacing is femoral neck fracture. These tend to occur early after surgery during normal activities. One theory regarding fracture occurrence includes the introduction of stress magnifiers in the form of notches on the superior neck. The presence of a notch can arise from reaming or from removal of osteophytes during surgery. The aim of the present study was to investigate the effect of notching the femoral neck, following resurfacing by using a finite element (FE) model.

Methods: A physiological load case was simulated in the FE model of a femur, implanted with a cemented hip resurfacing system. Twelve implant alignments were modelled: an ideal implant alignment with no notch, and a 1 mm, 3 mm, 5 mm and 7 mm superior notch; 5° anteversion, 5° and 10° degrees retroversion; 5° and 10° degrees in varus and valgus. These models were compared to that of an intact femur for baseline analysis.

The intact femur geometry was derived from a CT dataset of a cadaveric femur and CT numbers were converted into a realistic distribution of material properties. The FE intact mesh was based on an experimentally validated mesh of a human femur. The femur was segmented into 22 neck sections.

The loading condition was modelled to represent an instant at 10% of gait where all muscle forces were included. The femoral neck regions were compared between the models to evaluate the effect of notch sizes on stress distribution. Maximum tensile stresses were compared to the ultimate tensile stress (UTS) of cortical and cancellous bone.

Results: As the notch size increased the peak and average 1st (tensile) and 3rd (compressive) principal stress increased along the superior portion of the femoral neck. For the 5 mm superior notch, the maximum 1st principal stress increased by 283% and 154% when compared to that of the ideally aligned implant and the intact femur respectively. The largest increase of tensile stress was observed when the implant was mal-aligned in 10° of varus; this resulted in a 768% increase in stress compared to the ideally implanted model.

Discussion: The introduction of a superior notch causes a stress concentration on the femoral neck. Although the stress concentration is pronounced, a notch on the superior aspect of the femoral neck may not lead to fracture following resurfacing; the UTS of cortical bone is 100MPa, and the UTS of cancellous bone is between 2MPa and 20MPa. Peak stresses in the model are well below the UTS of cortical bone, and for damage to accumulate in cancellous bone, energy absorption in the ‘honey-comb’ structure of trabecular bone must be considered. Varus mal-alignment resulted in the largest increase in tensile stress on the superior aspect of the neck, and has been associated with femoral neck fracture; this type of mal-alignment may be critical when considering femoral neck fractures.

Purpose: The aim of this research was to characterize the correlation of magnetic resonance image (MRI) measurements of femoral anteversion and tibial torsion with transverse plane kinematics from the gait analysis of ten healthy and nine cerebral palsy (CP) children.

Methods: The bone morphologies of nine spastic diplegic CP and ten healthy children were obtained by analysis of 3D MRIs. Location of anatomical landmarks along the femur and tibia were detected using medical imaging software. Each point was then defined with respect to bone-embedded femoral and tibial Cartesian coordinates, allowing 3D reorientation of the bone independent of the patient position within the scanner. Femoral anteversion was defined as the angle between the femoral neck and the transcondylar plane. Tibial torsion was defined as the angle between the transcondylar axis of the proximal tibia and the bi-malleolar axis.

Three-dimensional motion of the lower limbs was measured using gait analysis. Transverse plane kinematics, including hip rotation and foot progression angles were recorded.

Results: A moderate correlation was found between femoral anteversion, and maximum and average hip rotation in CP children (0.64 and 0.65). A high correlation was also seen between tibial torsion and maximum and average values of hip rotation for CP children (0.71 and 0.74). In healthy children, the only correlation observed was between femoral anteversion and average foot progression in stance (0.75).

Discussion: In healthy children, femoral anteversion appears to influence foot progression angle, implying that this can lead to an internally rotated gait. In CP children, the correlation between femoral anteversion and hip rotation is only moderate. The interaction between different joints is more complex and the rotation of joints is determined by multiple factors. This study showed that tibial torsion also plays a role in determining hip rotation during gait.

In finite element (FE) analysis of long bones it is now common practice to calculate the material properties based on CT data. Although a unique material property is calculated for each element, assigning each element an individual material property results in excessively large models. To avoid this, it is usual to group the elements based on their material properties and to assign each group a single material property (Zannoni 1998). No study has analysed the effect the number of material properties used in a long bone FE model has on the accuracy of the results.

The aim of this study was to evaluate the variation in the calculated mechanical environment as a function of the number of material properties used in an FE model.

An FE mesh of a cadaveric human tibia containing 47,696 ten-node tetrahedron elements and 75,583 nodes was created using CT scans. Material properties were calculated for each element of the mesh based on previous work (Rho 1995, 1996). Eleven FE models were created by varying the number of groups (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024) the elements were divided into. A single material property was assigned to each group. All models were subject to an axial point load of 300N applied on the medial condyle of the tibial plateau while the distal end was fixed. The variation in maximum and minimum principal strains and deflections, at 17 well distributed surface nodes and at 65 randomly distributed nodes within the bone were plotted against the number of element groups. The total strain energy was also plotted against the number of groups. The errors for strain, deflection, and total strain energy were calculated for each model assuming that the model using 1024 element groups was accurate.

The parameter to converge with the least number of element groups was the total strain energy. At 512 element groups the error was less than 0.001% (0.7% for the two material model). The next to converge were the displacements. Using 512 materials the maximum error in displacement at the surface nodes was 0.001% (4.7% for the 2 material model), while for the internal nodes the maximum error was 0.53% (36.7% for the 2 material model). The least convergence occurred for principal strains. The maximum errors when 512 materials were used were 1.06% (57.7% for the 2 material model) and 3.02% (104.5% for the 2 material model) for the surface and the internal nodes respectively.

This study demonstrates the relationship between the accuracy of calculated mechanical environment and the number of material properties assigned to the model. While this study will allow the analyst to make an informed decision on the number of material properties for modelling the human tibia it also helps examine the validity of previous studies which, usually due to limited resources, used fewer material properties.

Finite element (FE) analysis is widely used to calculate stresses and strains within human bone in order to improve implant designs. Although validated FE models of the human femur have been created (Lengsfeld et al., 1998), no equivalent yet exists for the tibia. The aim of this study was to create such an FE model, both with and without the tibial component of a knee replacement, and to validate it against experimental Results: A set of reference axes was marked on a cleaned, fresh frozen cadaveric human tibia. Seventeen triaxial stacked strain rosettes were attached along the bone, which was then subjected to nine axial loading conditions, two four-point bending loading conditions, and a torsional loading condition using a materials testing machine (MTS 858). Deflections and strain readings were recorded. Axial loading was repeated after implantation of a knee replacement (medial tibial component, Biomet Oxford Unicompartmental Phase 3). The intact tibia was CT scanned (GE HiSpeed CT/i) and the images used to create a 3D FE mesh. The CT data was also used to map 600 transversely isotropic material properties (Rho, 1996) to individual elements. All experiments were simulated on the FE model. Measured principal strains and displacements were compared to their corresponding FE values using regression analysis.

Experimental results were repeatable (mean coefficients of variation for intact and implanted tibia, 5.3% and 3.9%). They correlated well with those of the FE analysis (R squared = 0.98, 0.97, 0.97, and 0.99 for axial (intact), axial (implanted), bending, torsional loading). For each of the load cases the intersects of the regression lines were small in comparison to the maximum measured strains (< 1.5%). While the model was more rigid than the bone under torsional loading (slope =0.92), the opposite was true for axial (slope = 1.14 (intact) 1.24 (implanted)) and bending (slope = 1.06) loads. This is probably due to a discrepancy in the material properties of the model.

More than 100,000 anterior cruciate ligament reconstructions are performed annually in the USA. The hamstrings and the patellar tendons are the most frequently used graft tissues. Up to ten percent of these grafts are deemed to have failed, generating considerable discussion in the literature regarding the ideal graft choice. A three-dimensional computational model, taking into account both material and geometrical non-linearities, would be useful in predicting the performance of different graft tissues and fixations. Unfortunately, the mechanical characteristics and parameters needed for such a model are complex and largely unknown. The aim of this study is to develop a method for measuring the geometrical properties needed as input for a three-dimensional tendon model.

A laser-based, non-contact technique is used to generate a series of cross-sectional profiles along the length of the tendon. Unlike previously proposed methods, it is able to detect concavities and can be constructed using equipment commonly found in an engineering laboratory. A laser line generator (Stocker-Yale Lasiris SNF, Quebec, Canada) projects a horizontal line onto the sample. Images of the line are acquired with a digital video camera (Basler A631fc, Germany) as the tendon is rotated. These images are reassembled into 2-D slices using MatLab software. Multiple cross-sections can be combined to create three dimensional geometries.

The new method was validated on objects of known shape (circular and hexagonal cylinders). The cross-sectional area measurement was found to be accurate to within 2.5%. The method was repeatable to within 1.7%. Six bovine flexor tendons have been analysed; concavities were evident in four of these. This method could be adapted to determine the surface geometries of other long and slender objects.

Introduction: Restoration of predictable and normal knee kinematics after a TKR can improve the patient’s function. Traditional designs exhibit grossly abnormal kinematics with the femur subluxing posteriorly in extension and a paradoxical forward slide in flexion. In addition, the kinematics are very variable. Newer designs were intended to overcome these problems, owing to their ability to provide ‘guided motion’ of the components. The medial pivot knee uses a specifically designed articulating surface constraining the femoral component to externally rotate about an axis through the medial compartment.

This study assesses the functional in vivo kinematics of Advanced Medial Pivot (AMP) TKR and compares it to kinematics of the normal knee.

Methods: Thirteen patients with pre-operative diagnosis of primary osteoarthritis, who had undergone a knee replacement with the AMP knee at least one-year prior were recruited in this study. All had an excellent clinical outcome (as assessed by AKSS) and underwent fluoro-scopic analysis whilst performing a step up activity. Knee kinematics were assessed by analysing the movement of the femur relative to the tibia using the Patella Tendon Angle (PTA) through the range of knee flexion. This data was compared to that of thirteen normal knees.

Results: The PTA for the normal knee has a linear relationship with knee flexion. The PTA is 14 degrees in full extension and decreases to -10 degrees at 100 degrees knee flexion during a step-up exercise. Between extension and 60 degrees of knee flexion, no significant difference was found between the PTA for the normal knee and for the AMP. The PTA for AMP is significantly higher for values of knee flexion exceeding 60 degrees. The standard deviation for different values of knee flex-ion is similar to that seen in the normal knee.

Conclusions: In extension, the PTA is near normal but in flexion PTA is higher than normal suggesting that the femur is too anterior. The variability of the kinematics for AMP TKR is similar to that of the normal knee and is better than that of most other knee designs that we have studied in the past, indicating that it is a stable TKR.

Introduction: The cam-post mechanism of Posterior Stabilized Total Knee Arthroplasty (PS-TKA) should provide a constraint that limits anterior translation of the femur on the tibia in flexion and thereby ensure femoral roll-back with progressive knee flexion. In a previous fluoroscopic study we showed that the sagittal plane kinematics of a PCL substituting TKA (Scorpio PS) was abnormal in flexion, suggesting inefficiency of the cam-post mechanism. We also assessed the movement of the femur relative to the tibia using the Patella Tendon Angle (PTA) through the range of knee flexion (0 to 90 degrees). The aim of the current study was to investigate in greater detail why the cam-post mechanism was ineffective by assessing the contact point movement and the distance between the cam and post.

Method: Twelve patients with Scorpio PS TKA underwent fluoroscopic assessment of the knee during a step up exercise and a weight bearing deep knee bend. The image distortion was corrected using a global correction method and the data was analysed using a 3D model fitting technique. Having determined the component position, the minimum distance between cam and post were determined. The femoro-tibial contact positions of the medial and lateral condyles were determined relative to the mid-coronal plane of the tibial component. The PTA was calculated by measuring the angle subtended by patella tendon with the tibial axis and was plotted against knee flexion angle (KFA).

Results: The relationship between PTA and KFA was abnormal relative to the normal knee. Between extension and 60 degrees flexion there was forward movement of both medial (11 mm) and lateral (5 mm) femoral condyles. Thereafter, both condyles moved back (10 mm). The cam-post mechanism failed to engage in one case while in others it engaged between 70 to 100 degrees.

Conclusions: The 3D analysis has confirmed the preliminary findings of the previous study using the PTA and KFA relationship. Despite the cam engaging in flexion normal knee kinematics were not restored. The femoral roll-back is inadequate and starts to occur at least 20 degrees before the cam and post engage.

Finite element (FE) analysis is widely used to calculate stresses and strains within human bone in order to improve implant designs. Although validated FE models of the human femur have been created (Lengsfeld et al., 1998), no equivalent yet exists for the tibia. The aim of this study was to create such an FE model, both with and without the tibial component of a knee replacement, and to validate it against experimental results.

A set of reference axes was marked on a cleaned, fresh frozen cadaveric human tibia. Seventeen triaxial stacked strain rosettes were attached along the bone, which was then subjected to nine axial loading conditions, two four-point bending loading conditions, and a torsional loading condition using a materials testing machine (MTS 858). Deflections and strain readings were recorded. Axial loading was repeated after implantation of a knee replacement (medial tibial component, Biomet Oxford Unicompartmental Phase 3). The intact tibia was CT scanned (GE HiSpeed CT/i) and the images used to create a 3D FE mesh. The CT data was also used to map 600 transversely isotropic material properties (Rho, 1996) to individual elements. All experiments were simulated on the FE model. Measured principal strains and displacements were compared to their corresponding FE values using regression analysis.

Experimental results were repeatable (mean coeffi-cients of variation for intact and implanted tibia, 5.3% and 3.9%). They correlated well with those of the FE analysis (R squared = 0.98, 0.97, 0.97, and 0.99 for axial (intact), axial (implanted), bending, torsional loading). For each of the load cases the intersects of the regression lines were small in comparison to the maximum measured strains (< 1.5%). While the model was more rigid than the bone under torsional loading (slope =0.92), the opposite was true for axial (slope = 1.14 (intact) 1.24 (implanted)) and bending (slope = 1.06) loads. This is probably due to a discrepancy in the material properties of the model.

Patellofemoral pain is a significant problem for patients with Total Knee Replacements (TKRs). It is hypothesized that pain is related to high patellofemoral forces (PFF). The aim of this study is to validate a model to estimate PFF after TKR, using a combination of non-invasive measurement and theoretical modeling.

Experiments were performed on four cadaver knee specimens to compare the PFF and the quadriceps force (QF) estimated by a model, with those measured using force transducers. Each knee was tested in its initial state and after implantation of three Scorpio designs: Cruciate Retaining (CR), Posterior Stabilised (PS), and the Posterior Stabilised Mobile Bearing (PS+). Each knee was extended/flexed under a simulated quadriceps load with 3 kg hung from the distal tibia. Relative movement of the bones was measured using a Vicon 612 motion analysis system. A 6DOF force transducer was used to measure PFFs and a uni-axial transducer was used to measure QFs. A fluoroscope simultaneously captured images of the leg extension activity. Parameters measured from the images were used as inputs to the model.

The measured and estimated PFF and QF matched closely between 20o and 80o of knee flexion for the TKRs. At higher flexion angles, the model overestimated the PFF by a maximum of 23N (7.6% max) for the PFF and by 31N for the QF (10.3% max). The estimated and measured Patellar Flexion Angles (PFA) were within 3.5o throughout the flexion range.

The model accurately predicts sagittal plane patellar kinematics and kinetics, using only fluoroscopy and externally measured forces as inputs. However, the model has a limitation in assuming that the extending moment is only due to the quadriceps.

Award for the best student biomaterials paper (US$ 2,000); a proper certificate