Three-dimensional knee model: constrained by isometric ligament bundles and experimentally obtained tibio-femoral contacts

The purpose of this study is to investigate the effect of anterior portion of anterior cruciate ligament, posterior cruciate ligament, anterior and deep portions of medial collateral ligament and the tibio-femoral articular contacts on passive knee motion. A well-accepted reference model for a normal tibio-femoral joint is reconstructed from the literature. The proposed three-dimensional dynamic tibio-femoral model includes the isometric fascicles, ligament bundles and irregularly shaped medial-lateral contact surfaces. With the approach we aim to analyze bone shape and ligament related abnormalities of knee kinematics. The rotations, translations and the contact forces during passive knee flexion were compared against a reference model and the results were found in close accordance. This study demonstrated that isometric ligament bundles play an important role in understanding the femur shape from contact points on tibia. Femoral condyles are not necessarily spherical. The surgical treatments should consider both ligament bundle lengths and contact surface geometries to achieve a problem free knee kinematics after a knee surgery.     

A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics

Combining musculoskeletal simulations with anatomical joint models capable of predicting cartilage contact mechanics would provide a valuable tool for studying the relationships between muscle force and cartilage loading. As a step towards producing multibody musculoskeletal models that include representation of cartilage tissue mechanics, this research developed a subject-specific multibody knee model that represented the tibia plateau cartilage as discrete rigid bodies that interacted with the femur through deformable contacts. Parameters for the compliant contact law were derived using three methods: (1) simplified Hertzian contact theory, (2) simplified elastic foundation contact theory and (3) parameter optimisation from a finite element (FE) solution. The contact parameters and contact friction were evaluated during a simulated walk in a virtual dynamic knee simulator, and the resulting kinematics were compared with measured in vitro kinematics. The effects on predicted contact pressures and cartilage–bone interface shear forces during the simulated walk were also evaluated. The compliant contact stiffness parameters had a statistically significant effect on predicted contact pressures as well as all tibio-femoral motions except flexion–extension. The contact friction was not statistically significant to contact pressures, but was statistically significant to medial–lateral translation and all rotations except flexion–extension. The magnitude of kinematic differences between model formulations was relatively small, but contact pressure predictions were sensitive to model formulation. The developed multibody knee model was computationally efficient and had a computation time 283 times faster than a FE simulation using the same geometries and boundary conditions.     

How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint

In an effort to prevent degeneration of articular cartilage associated with meniscectomies, both meniscal allografts and synthetic replacements are subjects of current interest and investigation. The objectives of the current study were to (1) determine whether a transversely isotropic, linearly elastic, homogeneous material model of the meniscal tissue is necessary to achieve a normal contact pressure distribution on the tibial plateau, (2) determine which material and boundary condition (attachments) parameters affect the contact pressure distribution most strongly, and (3) set tolerances on these parameters to restore the contact pressure distribution to within a specified error. To satisfy these objectives, a finite element model of the tibio-femoral joint of a human cadaveric knee (including both menisci) was used to study the contact pressure distribution on the tibial plateau. To validate the model, the contact pressure distribution on the tibial plateau was measured experimentally in the same knee used to create the model. Within physiologically reasonable bounds on five material parameters and four attachment parameters associated with a meniscal replacement, an optimization was performed under 1200 N of compressive load on the set of nine parameters to minimize the difference between the experimental and model results. The error between the experimental and model contact variables was minimized to 5.4%. The contact pressure distribution of the tibial plateau was sensitive to the circumferential modulus, axial/radial modulus, and horn stiffness, but relatively insensitive to the remaining six parameters. Consequently, both the circumferential and axial/radial moduli are important determinants of the contact pressure distribution, and hence should be matched in the design and/or selection of meniscal replacements. In addition, during surgical implantation of a meniscal replacement, the horns should be attached with high stiffness bone plugs, and the attachments of the transverse ligament and deep medial collateral ligament should be restored to minimize changes in the contact pressure distribution, and thereby possibly prevent the degradation of articular cartilage.     

Patient-specific knee joint finite element model validation with high-accuracy kinematics from biplane dynamic Roentgen stereogrammetric analysis

Little is known about in vivo menisci loads and displacements in the knee during strenuous activities. A new method that combines high-speed kinematics measured with biplane dynamic Roentgen stereogrammetric analysis (DRSA) and a subject-specific finite element (FE) model for studying in vivo meniscal behavior is presented here. Further model calibration in a very controlled uniaxial low and high-rate compression loading condition is presented by comparing the model behavior against the measured high-accuracy menisci DRSA kinematics and direct tibio-femoral pressure measurement from a K-scan sensor. It is apparent that certain model aspects such as removing of the pressure sensor from the model can result in relatively large errors (14%) in contact parameters that are not reflected in the change of the measured meniscal kinematics. Changing mesh size to 1mm by 1mm elements increased the magnitude of all but one of the contact variables by up to 45%. This local validation using accurate localized patient-specific geometry and meniscal kinematics was needed to enhance model fidelity at the level of contact between menisci and cartilage.     

3D finite element model of meniscectomy: changes in joint contact behavior

The goal of this study is to quantify changes in knee joint contact behavior following varying degrees of the medial partial meniscectomy. A previously validated 3D finite element model was used to simulate 11 different meniscectomies. The accompanying changes in the contact pressure on the superior surface of the menisci and tibial plateau were quantified as was the axial strain in the menisci and articular cartilage. The percentage of medial meniscus removed was linearly correlated with maximum contact pressure, mean contact pressure, and contact area. The lateral hemi-joint was minimally affected by the simulated medial meniscectomies. The location of maximum strain and location of maximum contact pressure did not change with varying degrees of partial medial meniscectomy. When 60% of the medial meniscus was removed, contact pressures increased 65% on the remaining medial meniscus and 55% on the medial tibial plateau. These data will be helpful for assessing potential complications with the surgical treatment of meniscal tears. Additionally, these data provide insight into the role of mechanical loading in the etiology of post-meniscectomy osteoarthritis.     

A detailed and validated three dimensional dynamic model of the patellofemoral joint

A detailed 3D anatomical model of the patellofemoral joint was developed to study the tracking, force, contact and stability characteristics of the joint. The quadriceps was considered to include six components represented by 15 force vectors. The patellar tendon was modeled using four bundles of viscoelastic tensile elements. Each of the lateral and medial retinaculum was modeled by a three-bundle nonlinear spring. The femur and patella were considered as rigid bodies with their articular cartilage layers represented by an isotropic viscoelastic material. The geometrical and tracking data needed for model simulation, as well as validation of its results, were obtained from an in vivo experiment, involving MR imaging of a normal knee while performing isometric leg press against a constant 140 N force. The model was formulated within the framework of a rigid body spring model and solved using forth-order Runge-Kutta, for knee flexion angles between zero and 50 degrees. Results indicated a good agreement between the model predictions for patellar tracking and the experimental results with RMS deviations of about 2 mm for translations (less than 0.7 mm for patellar mediolateral shift), and 4 degrees for rotations (less than 3 degrees for patellar tilt). The contact pattern predicted by the model was also consistent with the results of the experiment and the literature. The joint contact force increased linearly with progressive knee flexion from 80 N to 210 N. The medial retinaculum experienced a peak force of 18 N at full extension that decreased with knee flexion and disappeared entirely at 20 degrees flexion. Analysis of the patellar time response to the quadriceps contraction suggested that the muscle activation most affected the patellar shift and tilt. These results are consistent with the recent observations in the literature concerning the significance of retinaculum and quadriceps in the patellar stability.     

A new in vivo technique for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint

Patello-femoral disorders are often caused by changes of patello-femoral and/or tibio-femoral kinematics. However, until now there has been no quantitative in vivo technique, that is able to obtain 3D kinematics and contact areas of all knee compartments simultaneously on a non-invasive basis. The aim of this study was therefore to develop and apply a technique which allows for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint during different knee flexion angles and under neuromuscular activation patterns. One knee of each of the 10 healthy volunteers was examined in an open MR system under flexing isometric muscle activity at 30 degrees and 90 degrees. Three-dimensional kinematics and contact areas of the patello-femoral and tibio-femoral joints were analyzed by 3D image postprocessing. The reproducibility of the imaging technique yielded a coefficient of variation of 4.6% for patello-femoral, 4.7% for femoro-tibial displacement and 8.6% for contact areas. During knee flexion (30-90 degrees ), patella tilt (opened to medial) decreased (8.8+/-3.4 degrees vs. 4.6+/-3.1 degrees, p<0.05), while lateral patellar shift increased significantly (1.6+/-2.3mm vs. 3.4+/-3.0mm, p<0.05). Furthermore, a significant posterior translation and external rotation of the femur relative to the tibia was observed. Patello-femoral contact areas increased significantly in size (134+/-60mm(2) vs. 205+/-96 mm(2)) during knee flexion. This technique shows a high reproducibility and provides physiologic in vivo data of 3D kinematics and contact areas of the patello-femoral and the tibio-femoral joint during knee flexion. This allows for advanced in vivo diagnostics, and may help to improve therapy of patello-femoral disorders in the future.     

Knee joint kinematics during walking influences the spatial cartilage thickness distribution in the knee

The regional adaptation of knee cartilage morphology to the kinematics of walking has been suggested as an important factor in the evaluation of the consequences of alteration in normal gait leading to osteoarthritis. The purpose of this study was to investigate the association of spatial cartilage thickness distributions of the femur and tibia in the knee to the knee kinematics during walking. Gait data and knee MR images were obtained from 17 healthy volunteers (age 33.2 ± 9.8 years). Cartilage thickness maps were created for the femoral and tibial cartilage. Locations of thickest cartilage in the medial and lateral compartments in the femur and tibia were identified using a numerical method. The flexion-extension (FE) angle associated with the cartilage contact regions on the femur, and the anterior-posterior (AP) translation and internal-external (IE) rotation associated with the cartilage contact regions on the tibia at the heel strike of walking were tested for correlation with the locations of thickest cartilage. The locations of the thickest cartilage had relatively large variation (SD, 8.9°) and was significantly associated with the FE angle at heel strike only in the medial femoral condyle (R(2)=0.41, p<0.01). The natural knee kinematics and contact surface shapes seem to affect the functional adaptation of knee articular cartilage morphology. The sensitivity of cartilage morphology to kinematics at the knee during walking suggests that regional cartilage thickness variations are influenced by both loading and the number of loading cycles. Thus walking is an important consideration in the analysis of the morphological variations of articular cartilage, since it is the dominant cyclic activity of daily living. The sensitivity of cartilage morphology to gait kinematics is also important in understanding the etiology and pathomechanics of osteoarthritis.     

A comparison of the influence of global functional loads vs. local contact anatomy on articular cartilage thickness at the knee

Cartilage contact geometry, along with joint loading, can play an important role in determining local articular cartilage tissue stress. Thus individual variations in cartilage thickness can be associated with both individual variations in joint loading associated with activities of daily living as well as individual differences in the anatomy of the contacting surfaces of the joint. The purpose of this study was to isolate the relationship between cartilage thickness predicted by individual variations in contact surface geometry based on the radii of the femur and tibia vs. cartilage thickness predicted by individual variations in joint loading. Knee magnetic resonance (MR) images and the peak knee adduction moments during walking were obtained from 11 young healthy male subjects (age 30.5+/-5.1 years). The cartilage thicknesses and surface radii of the femoral and tibial cartilage were measured in the weight-bearing regions of the medial and lateral compartments of three-dimensional models from the MR images. The ratio of contact pressure between the medial and lateral compartments was calculated from the radii of tibiofemoral contact surface geometries. The results showed that the medial to lateral pressure ratios were not correlated with the medial to lateral cartilage thickness ratios. However, in general, pressure was higher in the lateral than medial compartments and cartilage was thicker in the lateral than medial compartments. The peak knee adduction moment showed a significant positive linear correlation with medial to lateral thickness ratio in both femur (R(2)=0.43,P<0.01) and tibia (R(2)=0.32,P<0.01). The results of this study suggest that the dynamics of walking is an important factor to describe individual differences in cartilage thickness for normal subjects.     

Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis

Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.     

Tibio-femoral movement in the living knee. A study of weight bearing and non-weight bearing knee kinematics using 'interventional' MRI

The aim of this study was to image tibio-femoral movement during flexion in the living knee. Ten loaded male Caucasian knees were initially studied using MRI, and the relative tibio-femoral motions, through the full flexion arc in neutral tibial rotation, were measured. On knee flexion from hyperextension to 120 degrees , the lateral femoral condyle moved posteriorly 22 mm. From 120 degrees to full squatting there was another 10 mm of posterior translation, with the lateral femoral condyle appearing almost to sublux posteriorly. The medial femoral condyle demonstrated minimal posterior translation until 120 degrees . Thereafter, it moved 9 mm posteriorly to lie on the superior surface of the medial meniscal posterior horn. Thus, during flexion of the knee to 120 degrees , the femur rotated externally through an angle of 20 degrees . However, on flexion beyond 120 degrees , both femoral condyles moved posteriorly to a similar degree. The second part of this study investigated the effect of gender, side, load and longitudinal rotation. The pattern of relative tibio-femoral movement during knee flexion appears to be independent of gender and side. Femoral external rotation (or tibial internal rotation) occurs with knee flexion under loaded and unloaded conditions, but the magnitude of rotation is greater and occurs earlier on weight bearing. With flexion plus tibial internal rotation, the pattern of movement follows that in neutral. With flexion in tibial external rotation, the lateral femoral condyle adopts a more anterior position relative to the tibia and, particularly in the non-weight bearing knee, much of the femoral external rotation that occurs with flexion is reversed.     

Deformation of the distal femur: a contribution towards the pathogenesis of osteochondrosis dissecans in the knee joint.

Osteochondrosis dissecans (OD) is a process of subchondral bone necrosis occurring predominantly in young individuals at specific sites. The aetiology of this disease remains controversial with mechanical processes due to trauma and/or ischaemic factors being proposed. This study aims at explaining the aetiology of OD in the knee joint as a result of the particular deformation of the condyles. A finite element analysis of the distal third of the femur was performed. A three-dimensional model was developed based on computed tomography scans of a normal femur, consisting of cortical bone, cancellous bone and articular cartilage. This model was subjected to physiological loads at 0, 30, 60 and 90 degrees of knee flexion. A complex deformation was found within each condyle as well as between the two condyles. Both medial and lateral condyles are deformed in the medio-lateral direction and at the same time compressed between the patella and the tibia in the antero-posterior direction. This effect is highest at 60 degrees of knee flexion. In both planes, the medial condyle is distorted more than the lateral one. Strain concentration in the subchondral bone facing the patella varies with flexion, especially for angles exceeding 60 degrees. The deformation of the femur in the predominant locus of OD in the medial condyle exceeds that of the lateral condyle considerably. The analysis shows that repeated vigorous exercise including extreme knee flexion may produce rapidly changing strains which in turn could ultimately be responsible for local subchondral bone collapse.     

Partial medial meniscectomy and rotational differences at the knee during walking

Loss of meniscal function due to injury or partial meniscectomy is common and represents a significant risk factor for premature osteoarthritis. The menisci can influence the transverse plane movements (anterior–posterior (AP) translation and internal–external (IE) rotation) of the knee during walking. While walking is the most frequent activity of daily living, the kinematic differences at the knee during walking associated with the meniscal injury are not well understood. This study examined the influence of partial medial meniscectomy (PMM) on the kinematics and kinetics of the knee during the stance phase of gait by testing the differences in anterior–posterior translation, internal–external rotation, knee flexion range of movement, peak flexion/extension moments, and adduction moments between the PMM and healthy contralateral limbs. Ten patients (45±9 years old, height 1.75±0.06 m, weight 76.7±13.5 kg) who had undergone partial medial meniscectomy (33±100 months post-op) in one limb with a healthy contralateral limb were tested during normal walking. The contralateral limb was compared to a matched control group and no differences were found. The primary kinematic difference was a significantly greater external rotation (3.2°) of the tibia that existed through stance phase, with 8 of 10 subjects demonstrating the same pattern. The PMM subjects also exhibited significantly lower peak flexion and extension moments in their PMM limbs. The altered rotational position found likely results in changes of tibio-femoral contact during walking and could cause the type of degenerative changes found in the articular cartilage following meniscal injury.     

Can altered neuromuscular coordination restore soft tissue loading patterns in anterior cruciate ligament and menisci deficient knees during walking?

Injuries to the anterior cruciate ligament (ACL) and menisci commonly lead to early onset osteoarthritis. Treatments that can restore normative cartilage loading patterns may mitigate the risk of osteoarthritis, though it is unclear whether such a goal is achievable through conservative rehabilitation. We used musculoskeletal simulation to predict cartilage and ligament loading patterns during walking in intact, ACL deficient, menisci deficient, and ACL-menisci deficient knees. Stochastic simulations with varying coordination strategies were then used to test whether neuromuscular control could be modulated to restore normative knee mechanics in the pathologic conditions. During early stance, a 3 mm increase in anterior tibial translation was predicted in the ACL deficient knee. Mean cartilage contact pressure increased by 18% and 24% on the medial and lateral plateaus, respectively, in the menisci deficient knee. Variations in neuromuscular coordination were insufficient to restore normative cartilage contact patterns in either the ACL or menisci deficient knees. Elevated cartilage contact pressures in the pathologic knees were observed in regions where cartilage wear patterns have previously been reported. These results suggest that altered cartilage tissue loading during gait may contribute to region-specific degeneration patterns, and that varying neuromuscular coordination in isolation is unlikely to restore normative knee mechanics.     

Ligaments and articular contact guide passive knee flexion

The aim of this study was to test the hypothesis that the coupled features of passive knee flexion are guided by articular contact and by the isometric fascicles of the ACL, PCL and MCL. A three-dimensional mathematical model of the knee was developed, in which the articular surfaces in the lateral and medial compartments and the isometric fascicles in the ACL, PCL and MCL were represented as five constraints in a one degree-of-freedom parallel spatial mechanism. Mechanism analysis techniques were used to predict the path of motion of the tibia relative to the femur. Using a set of anatomical parameters obtained from a cadaver specimen, the model predicts coupled internal rotation and ab/adduction with flexion. These predictions correspond well to measurements of the cadaver specimen’s motion. The model also predicts posterior translation of contact on the tibia with flexion. Although this is a well-known feature of passive knee flexion, the model predicts more translation than has been reported from experiments in the literature. Modelling of uncertainty in the anatomical parameters demonstrated that the discrepancy between theoretical predictions and experimental measurement can be attributed to parameter sensitivity of the model. This study shows that the ligaments and articular surfaces work together to guide passive knee motion. A principal implication of the work is that both articular surface geometry and ligament geometry must be preserved or replicated by surgical reconstruction and replacement procedures to ensure normal knee kinematics and by extension, mechanics.     

Tibio-femoral joint contact in healthy and osteoarthritic knees during quasi-static squat: A bi-planar X-ray analysis

The aim of this study was to quantify the tibio-femoral contact point (CP) locations in healthy and osteoarthritic (OA) subjects during a weight-bearing squat using stand-alone biplanar X-ray images.Ten healthy and 9 severe OA subjects performed quasi-static squats. Bi-planar X-ray images were recorded at 0°, 15°, 30°, 45°, and 70° of knee flexion. A reconstruction/registration process was used to create 3D models of tibia, fibula, and femur from bi-planar X-rays and to measure their positions at each posture. A weighted centroid of proximity algorithm was used to calculate the tibio-femoral CP locations. The accuracy of the reconstruction/registration process in measuring the quasi-static kinematics and the contact parameters was evaluated in a validation study.The quasi-static kinematics data revealed that in OA knees, adduction angles were greater (p<0.01), and the femur was located more medially relative to the tibia (p<0.01). Similarly, the average CP locations on the medial and lateral tibial plateaus of the OA patients were shifted (6.5±0.7 mm; p<0.01) and (9.6±3.1 mm; p<0.01) medially compared to the healthy group. From 0° to 70° flexion, CPs moved 8.1±5.3 mm and 8.9±5.3 mm posteriorly on the medial and lateral plateaus of healthy knees; while in OA joints CPs moved 10.1±8.4 mm and 3.6±2.8 mm posteriorly. The average minimum tibio-femoral bone-to-bone distances of the OA joints were lower in both compartments (p<0.01).The CPs in the OA joints were located more medially and displayed a higher ratio of medial to lateral posterior translations compared to healthy joints.     

3-D anatomically based dynamic modeling of the human knee to include tibio-femoral and patello-femoral joints

An anatomical dynamic model consisting of three body segments, femur, tibia and patella, has been developed in order to determine the three-dimensional dynamic response of the human knee. Deformable contact was allowed at all articular surfaces, which were mathematically represented using Coons' bicubic surface patches. Nonlinear elastic springs were used to model all ligamentous structures. Two joint coordinate systems were employed to describe the six-degrees-of-freedom tibio-femoral (TF) and patello-femoral (PF) joint motions using twelve kinematic parameters. Two versions of the model were developed to account for wrapping and nonwrapping of the quadriceps tendon around the femur. Model equations consist of twelve nonlinear second-order ordinary differential equations coupled with nonlinear algebraic constraint equations resulting in a Differential-Algebraic Equations (DAE) system that was solved using the Differential/Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory. Model calculations were performed to simulate the knee extension exercise by applying non-linear forcing functions to the quadriceps tendon. Under the conditions tested, both "screw home mechanism" and patellar flexion lagging were predicted. Throughout the entire range of motion, the medial component of the TF contact force was found to be larger than the lateral one while the lateral component of the PF contact force was found to be larger than the medial one. The anterior and posterior fibers of both anterior and posterior cruciate ligaments, ACL and PCL, respectively, had opposite force patterns: the posterior fibers were most taut at full extension while the anterior fibers were most taut near 90 degrees of flexion. The ACL was found to carry a larger total force than the PCL at full extension, while the PCL carried a larger total force than the ACL in the range of 75 degrees to 90 degrees of flexion.     

In vivo tibiofemoral cartilage deformation during the stance phase of gait

The knowledge of articular cartilage contact biomechanics in the knee joint is important for understanding the joint function and cartilage pathology. However, the in vivo tibiofemoral articular cartilage contact biomechanics during gait remains unknown. The objective of this study was to determine the in vivo tibiofemoral cartilage contact biomechanics during the stance phase of treadmill gait. Eight healthy knees were magnetic resonance (MR) scanned and imaged with a dual fluoroscopic system during gait on a treadmill. The tibia, femur and associated cartilage were constructed from the MR images and combined with the dual fluoroscopic images to determine in vivo cartilage contact deformation during the stance phase of gait. Throughout the stance phase of gait, the magnitude of peak compartmental contact deformation ranged between 7% and 23% of the resting cartilage thickness and occurred at regions with thicker cartilage. Its excursions in the anteroposterior direction were greater in the medial tibiofemoral compartment as compared to those in the lateral compartment. The contact areas throughout the stance phase were greater in the medial compartment than in the lateral compartment. The information on in vivo tibiofemoral cartilage contact biomechanics during gait could be used to provide physiological boundaries for in vitro testing of cartilage. Also, the data on location and magnitude of deformation among non-diseased knees during gait could identify where loading and later injury might occur in diseased knees.     

A three-dimensional finite element analysis of the upper tibia

A three-dimensional finite element model of the proximal tibia has been developed to provide a base line for further modeling of prosthetic resurfaced tibiae. The geometry for the model was developed by digitizing coronal and transverse sections made with the milling machine, from one fresh tibia of average size. The load is equally distributed between the medial and lateral compartments over contact areas that were reported in the literature. An indentation test has been used to measure the stiffness and the ultimate strength of cancellous bone in four cadaver tibiae. These values provided the statistical basis for characterising the inhomogeneous distribution of the cancellous bone properties in the proximal tibia. All materials in the model were assumed to be linearly elastic and isotropic. Mechanical properties for the cortical bone and cartilage have been taken from the literature. Results have been compared with strain gage tests and with a two-dimensional axisymmetric finite element model both from the literature. Qualitative comparison between trabecular alignment, and the direction of the principal compressive stresses in the cancellous bone, showed a good relationship. Maximum stresses in the cancellous bone and cortical bone, under a load which occurs near stance phase during normal gait, show safety factors of approximately eight and twelve, respectively. The load sharing between the cancellous bone and the cortical bone has been plotted for the first 40 mm distally from the tibial eminence.