A three-dimensional morphometrical study of the distal human femur.

The objective of this paper is to present a method to describe the three-dimensional variations of the geometry of the three portions forming the distal part of the human femur: the medial and lateral femoral condyles and the intercondylar fossa. The contours of equally spaced sagittal slices were digitized on the distal femur to determine its surface topography. Data collection was performed using a digitizer system which utilizes low-frequency, magnetic field technology to determine the position and orientation of a magnetic field sensor in relation to a specified reference frame. The generalized reduced gradient optimization method was used to reconstruct the profile of each slice utilizing two primitives: straight-line segments and circular arcs. The profile of each slice within the medial femoral condyle was reconstructed using two circular arcs: posterior and distal. The profile of each slice within the lateral femoral condyle was reconstructed using three circular arcs: posterior, distal and anterior. Finally, the profile of each slice within the intercondylar fossa was reconstructed using two circular arcs: proximal-posterior and anterior, and a distal-posterior straight-line segment tangent to the proximal-posterior circular arc. Combining the data describing the profiles of the different slices forming the distal femur, the posterior portions of each of the medial and lateral femoral condyles were modelled using parts of spheres having an average radius of 20 mm. The anterior portion of the lateral condyle was approximated to a right cylinder having its circular base parallel to the sagittal plane with an average radius of 26 mm. The anterior portion of the intercondylar fossa was modelled using an oblique cylinder having its circular base parallel to the sagittal plane with an average radius of 22 mm. Furthermore, it is suggested that the distal portion of the lateral femoral condyle could be modelled using parts of two oblique cones while the distal portion of the medial femoral condyle could be modelled using a part of a single oblique cone, all cones having their circular bases parallel to the sagittal plane. It is also suggested that the posterior portion of the intercondylar fossa could be modelled using two oblique cones: a proximal cone having its base parallel to the sagittal plane and a distal cone having its base parallel to the frontal plane.     

A spatial model of the knee for the preoperative planning of knee surgery

A model on the spatial mechanical behaviour of the passive knee is presented. The femoral articular surfaces were represented by generalized, sagittally elliptical, toroidal surfaces. The medial and lateral tibial articular surfaces were represented by a dished spherical surface and the lower hemihyperbolic region of a torus respectively. Anatomical articular cartilage, knee ligaments and the posterior capsule were represented by spring-like deformable elements with non-linear load versus deflection characteristics. All the forces that act on the femur relative to the tibia were represented by three orthogonal forces and three associated moments. Spatial, articulation-dependent femorotibial kinematic constraint equations of the passive knee were formulated in an analytically explicit manner, based on the natural coordinates of the articular surfaces. The constraint equations were solved algebraically in closed form. Equations were derived that describe spatial femoro-tibial motion, ligament length, ligament strain, ligament-based elastic potential energy and the quasi-static equilibrium of the passive knee. Software was written, simulations on the motion characteristics and load versus deflection characteristics of the knee were carried out and graphical results were presented. The simulation of planar flexion/extension was almost spontaneous. The time taken to simulate spatial six-degree-of-freedom femoro-tibial motion was less than 2.5 min. The models were found to be capable of representing real-life passive knees to a high degree of satisfaction. It has been demonstrated that the models can provide knee surgeons with additional information on major aspects of the preoperative planning of knee surgery. The models can be used to enhance the preoperative planning of ligament reconstruction, articular surfaces related surgery, osteotomy and patellar tendon transfer surgery.     

A new approach to C2 continuous piecewise bicubic representation of the articular surfaces of diarthrodial joints

Based on the force-deflection equation for a beam subjected to lateral point loads, a C2 continuous piecewise bicubic mathematical representation was proposed to model complicated geometrical surfaces, e.g. the articular surfaces of human joints. The method was then extended so that it could be used for mathematical modelling of incomplete nets of data points, as well as smoothing of noisy and/or filtering of erroneous data points. Mathematical techniques were also developed to calculate the required unknown parameters explicitly, with no need to solve the system of equations simultaneously. The performance of the proposed method was evaluated on a number of surface modelling problems, including two known analytical surfaces and the human femoral and patellar articular surfaces. The results indicate that the proposed method is precise, flexible, and easy to apply and has several advantages over the conventional smoothing methods, i.e. the B-spline approach.     

Effects of ageing on the biomechanical properties of rat articular cartilage

Previous studies have demonstrated that male Sprague Dawley (SD) rats experience age-related bone loss with the same characteristics as that in ageing men. As articular cartilage, like bone, is a critical component of the health and function of the musculoskeletal system, the authors hypothesized that articular cartilage in the untreated male SD rats could be a suitable model for studying the age-related deterioration of articular cartilage in men. To test this hypothesis, male SD rats were killed at between 6 and 27 months. The right femur of each rat was removed. The effects of ageing on the structural integrity of the distal femoral articular cartilage were studied by biomechanical testing with a creep indentation apparatus. The aggregate modulus, Poisson's ratio, permeability, thickness, and percentage recovery of articular cartilage were determined using finite element/non-linear optimization modelling. No significant differences were observed in these biomechanical properties of the distal femoral articular cartilage as a function of age. Therefore, untreated male SD rats appear to be unsuitable for studying the age-related changes of articular cartilage as they occur in men. However, and more intriguingly, it is also possible that ageing does not affect the biomechanical properties of articular cartilage in the absence of cartilage pathology.     

Comparison of human and animal femoral head chondral properties and geometries

Investigations into tissue-preserving orthopaedic treatments should consider the tribology of articular cartilage; where simulations using animal joints are a predominant choice. However, very few studies have investigated the differences between human and animal cartilage. The aim of the present study was to characterise the differences in geometry and mechanical properties of human, porcine, bovine and ovine articular cartilage. Creep indentation was performed on osteochondral plugs taken from the superior region of femoral heads of all these species. Cartilage thickness was measured via the resistive force change of a needle descending through cartilage and bone. A biphasic finite element model was used to derive equilibrium elastic modulus and permeability. Results showed that human cartilage was significantly thicker than all other species tested. A positive correlation was found between femoral head diameter and cartilage thickness when comparing between species of quadrupeds. Human cartilage had the largest equilibrium elastic modulus, which was significant when comparing against porcine and bovine. However, porcine cartilage had significantly lower permeability. Significant differences in geometry and mechanical properties of articular cartilage were found between all species tested. It is necessary to consider these variations when choosing animal tissue to represent human.     

Dynamic analysis of an axially moving robot manipulator supported by bearings

In this study, a robot manipulator is modelled as a cantilever beam, which moves in an axial direction, has a lumped mass at the end, and is supported by intermediate springs. Considering the tip mass and intermediate springs in the modeling, we derive the equations of motion in which the rigid-body motion is coupled with the flexible motions, and then analyze the transverse vibrations of the beam. Furthermore, we study the tip mass effects on the natural frequencies and the corresponding mode shapes. The natural frequency loci veering is analyzed for variations in the tip mass and the spring position/stiffness. In addition, we investigate the exchange and localization of modes around these veering regions as well as the parameter effects on the mode shapes. Using a Short-time Fourier transform (STFT), the relationship between the dynamic characteristics and dynamic responses are described. It is found that the dynamic characteristics of the beam are dependent on the veering distance. It is also shown via dynamic responses that the mode exchanges occur when a veering distance is close.     

A technique for the measurement of patellar tracking during weight-bearing activities using ultrasound

A new fixation device, the femoral clamp, was developed in this study for the ultrasound measurement of patellar medio-lateral motion during sitting and squatting knee flexion/extension. Seventeen subjects, 6 males, 11 females, aged between 18 and 40 years were recruited for the test. Results showed that the patella moved medially then laterally from extension to flexion when sitting. Weight-bearing knee motion produced a more laterally tracked patella without the presence of the initial medial patellar translation. The tracking patterns of the patellae were similar regardless of knee movement direction. The patellar lateral position was greatly affected by the movement task (p < 0.0005), and was also influenced by gender for maximum medial position (p < 0.05). The reproducibility of the measurement was between 0.29 and 0.90 for the intra-rater and 0.34-0.75 for the inter-rater reliability. The accuracy of the ultrasound measurement was validated by interventional magnetic resonance (iMR) imaging of the patella and the mean error of the measurement was 1.4 +/- 3.2 mm. Although further research is needed to improve the accuracy and reliability of this method, it has demonstrated the feasibility of obtaining patellar tracking data during load-bearing activities.     

Finite element analysis of intramedullary devices: the effect of the gap between the implant and the bone

This paper examines the interaction interface between the implant and the bone for an intramedullary femoral nailing system using a finite element (FE) model and specifically considers the hypothesis that the local geometry at the interface is significant to the resulting localized contact stress between the medial and lateral aspect of nail and endosteum. Contact mechanics algorithms are used in the FE modelling technique that can be developed to deal with any form of intramedullary device for which contact at the bone-implant interface is important. Global stiffness data from the FE model are compared with available data from an experiment carried out on a construct of the bone and the device that uses intramedullary femoral nails. Acceptable agreement is obtained. The results demonstrate that the mechanical interface between the implant and the bone is significantly affected by the gap geometry and magnitude. In particular, larger gaps lead to greater concentrations of stress on the medial side, while the distribution of stress is more uniform at the lateral contacts. Furthermore, the results show that the gap can have a marked effect on the stresses that occur on the fracture plane.     

Development of artificial articular cartilage

Attempts have been made to develop an artificial articular cartilage on the basis of a new viewpoint of joint biomechanics in which the lubrication and load-bearing mechanisms of natural and artificial joints are compared. Polyvinyl alcohol hydrogel (PVA-H), 'a rubber-like gel', was investigated as an artificial articular cartilage and the mechanical properties of this gel were improved through a new synthetic process. In this article the biocompatibility and various mechanical properties of the new improved PVA-H is reported from the perspective of its usefulness as an artificial articular cartilage. As regards lubrication, the changes in thickness and fluid pressure of the gap formed between a glass plate and the specimen under loading were measured and it was found that PVA-H had a thicker fluid film under higher pressures than polyethylene (PE) did. The momentary stress transmitted through the specimen revealed that PVA-H had a lower peak stress and a longer duration of sustained stress than PE, suggesting a better damping effect. The wear factor of PVA-H was approximately five times that of PE. Histological studies of the articular cartilage and synovial membranes around PVA-H implanted for 8-52 weeks showed neither inflammation nor degenerative changes. The artificial articular cartilage made from PVA-H could be attached to the underlying bone using a composite osteochondral device made from titanium fibre mesh. In the second phase of this work, the damage to the tibial articular surface after replacement of the femoral surface in dogs was studied. Pairs of implants made of alumina, titanium or PVA-H on titanium fibre mesh were inserted into the femoral condyles. The two hard materials caused marked pathological changes in the articular cartilage and menisci, but the hydrogel composite replacement caused minimal damage. The composite osteochondral device became rapidly attached to host bone by ingrowth into the supporting mesh. The clinical implications of the possible use of this material in articular resurfacing and joint replacement are discussed.     

Static and dynamic pressure profiles of a patellar-tendon-bearing (PTB) socket

The purpose of this study was to evaluate the pressure distribution at the stump/socket interface in amputees wearing the patellar-tendon-bearing socket. A specially built strain gauged type pressure transducer was used for measuring this pressure distribution in four unilateral transtibial amputees. Pressure and gait parameters were measured simultaneously while they were standing and walking. Pressure profiles were compiled at 10, 25 and 50 per cent of gait cycle and compared with the pressure profiles predicted by Radcliffe in 1961. The subject's anterior-posterior pressure profiles were different from each other. However, at toe-off, each subject exhibited an increase in pressure at the patellar tendon. Their medial-lateral pressure profiles were similar: exhibiting high pressure at the medial proximal and lateral distal regions except for one subject who exhibited high pressure at the lateral proximal region instead. The subjects' pressure profiles did not resemble Radcliffe's anticipated pressure profiles. This was because ground reaction force was not the only factor affecting the resulting pressure profiles.     

Intraoperative knee anthropometrics: correlation with cartilage wear

Accurate knee morphology is of value in determining the correct sizing of prosthetic implants. Intraoperative measurement of key linear dimensional variables was carried out on 196 Caucasian knees (osteoarthritic patients: 68 male and 128 female). Of the 196 knees measured, 70 had extensive cartilage degeneration. Statistical analysis was carried out on this large sample size of data. Summary statistics and correlation coefficients between variables were determined and compared between subgroups. Male knees were on average larger than female knees. Higher correlation was found between variables for males than between variables for females. Overall, the patellar dimensions were seen to correlate least well with other anatomical variables. High correlation between femoral variables supports current femoral sizing procedure, although routine patellar resection practices are called into question. Average values for the 70 knees with extensive cartilage degeneration were significantly smaller (P < 0.01) than their counterparts for the other 126 knees. For a measurement not containing cartilage, such as femoral epicondylar width, this difference cannot be accounted for by the loss of cartilage owing to wear. This suggests that, for similar height and weight, a naturally narrower femoral epicondylar width may be associated with severe osteoarthritis.     

Mechanics of the passive knee joint. Part 1: The role of the tibial articular surfaces in guiding the passive motion

The motion of the unloaded knee is associated with tibial internal rotation and femoral posterior translation. Although it is known that the passive motion is the result of the interaction between the articular surfaces and the ligaments, the mechanism through which the particular pattern of motion is guided is not completely understood. The goal of this study was to focus on the tibial geometry and to identify the roles that its geometric features have in guiding the passive knee motion. The method used in this study simplified the geometry of the tibial plateaux and the menisci into basic features that could be eliminated individually. The generated tibial geometry was implemented in a computer model to simulate the passive motion. Different parts of the geometry were eliminated individually and the comparison between the simulation results was used to identify the role that each part of the geometry had in guiding the passive motion. The medial meniscus was found as the feature that promoted the tibial internal rotation and restrained the femoral posterior translation. The lateral meniscus and the medial aspect of the tibial eminence, on the other hand, were found as the elements that confined the tibial internal rotation.     

A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect

A single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal Euler-Bernoulli, Timoshenko, and higher order beams. The beams are assumed to be elastically supported and attached to continuous lateral and rotational springs to take into account the effects of the surrounding matrix. The discrete equations of motion associated with free transverse vibration of each model are established in the context of the nonlocal continuum mechanics of Eringen using Hamilton's principle and an efficient meshless method. The effects of slenderness ratio of the nanotube, small scale effect parameter, initial axial force and the stiffness of the surrounding matrix on the natural frequencies of various beam models are investigated for different boundary conditions. The capabilities of the proposed nonlocal beam models in capturing the natural frequencies of the nanotube are also addressed.     

In vitro characterization of the relationship between the Q-angle and the lateral component of the quadriceps force

Although the Q-angle is routinely measured, the relationship between the Q-angle and the lateral component of the quadriceps force acting on the patella is unknown. Five cadaver knees were flexed on a knee simulator with a normal Q-angle, and flexed after increasing and decreasing the Q-angle by shifting the quadriceps origin laterally and medially, respectively. The motion of the femur, tibia and patella was tracked from 20 to 90 degrees of flexion using electromagnetic sensors. The motion of landmarks used to quantify the Q-angle was tracked to determine the 'dynamic Q-angle' during flexion. The lateral component of the force applied by the actuator secured to the quadriceps tendon was also quantified throughout flexion. Increasing the initial Q-angle significantly (p < 0.05) increased the dynamic Q-angle and the lateral force exerted through the quadriceps tendon throughout flexion. Decreasing the initial Q-angle significantly decreased the dynamic Q-angle at 90 degrees of flexion and significantly decreased the lateral force exerted through the quadriceps tendon from 20 to 40 degrees of flexion. Even though the dynamic Q-angle changes during flexion, an abnormally large initial Q-angle can be an indicator of an abnormally large lateral force acting on the patella during flexion.     

The effect of glycosaminoglycan depletion on the friction and deformation of articular cartilage

Glycosaminoglycans (GAGs) have been shown to be responsible for the interstitial fluid pressurization of articular cartilage and hence its compressive stiffness and load-bearing properties. Contradictory evidence has been presented in the literature on the effect of depleting GAGs on the friction properties of articular cartilage. The aim of this study was to investigate the effect of depleting GAGs on the friction and deformation characteristics of articular cartilage under different tribological conditions. A pin-on-plate machine was utilized to measure the coefficient of friction of native and chondroitinase ABC (CaseABC)-treated articular cartilage under two different models: static (4 mm/s start-up velocity) and dynamic (4 mm/s sliding velocity; 4 mm stroke length) under a load of 25 N (0.4 MPa contact stress) and with phosphate-buffered saline as the lubricant. Indentation tests were carried out at 1 N and 2 N loads (0.14 MPa and 0.28 MPa contact stress levels) to study the deformation characteristics of both native and GAG-depleted cartilage samples. CaseABC treatment rendered the cartilage tissue soft owing to the loss of compressive stiffness and a sulphated-sugar assay confirmed the loss of GAGs from the cartilage samples. CaseABC treatment significantly increased (by more than 50 per cent) the friction levels in the dynamic model (p < 0.05) at higher loading times owing to the loss of biphasic lubrication. CaseABC treatment had no effect on friction in the static model in which the cartilage surfaces did not have an opportunity to recover fluid because of static loading unlike the cartilage tissue in the dynamic model, in which translation of the cartilage surfaces was involved, ensuring effective biphasic lubrication. Therefore the depletion of GAGs had a smaller effect on the coefficient of friction for the static model. Indentation tests showed that GAG-depleted cartilage samples had a lower elastic modulus and higher permeability than native tissue. These results corroborate the role of GAGs in the compressive and friction properties of articular cartilage and emphasize the need for developing strategies to control GAG loss from diseased articular cartilage tissue.     

The variation in the orientations and moment arms of the knee extensor and flexor muscle tendons with increasing muscle force: a mathematical analysis

The orientations and moment arms of the knee extensor and flexor muscle tendons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal plane was used to define the motion of the joint in the unloaded state during 0-120 degrees flexion. The cruciate and collateral ligaments were represented by arrays of elastic fibres, which were recruited sequentially under load or remained buckled when slack. A bi-articular model of the patello-femoral joint was used. Simple straight-line representation was used for the lines of action of the forces transmitted by the model muscle tendons. The effects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the maximum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degree flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tendon was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the maximum change in moment arm of the hamstrings tendon was 8 per cent at 60 degrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum change for the gastrocnemious tendon was 3 per cent at 0 degree. The orientations of the flexor muscle tendons in this range of force either remained constant or changed by 1 degree or less at any flexion angle. The general trend at any flexion angle was that, as the muscle force was increased, the moment arms and the orientations approached nearly constant values, showing asymptotic behaviour. It is concluded that experimental simulations of knee muscle action with low values of the externally applied load, of the order of 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.     

A viscoelastic analysis of the tensile weakening of deep femoral head articular cartilage

Articular cartilage from below the surface of the femoral head of the hip joint shows a profound age-dependent weakening in its tensile mechanical properties. This ageing is also associated with a reduced viscoelastic response in the older tissue. A constitutive model of the viscoelastic behaviour of deep articular cartilage (as discussed by Egan in 1988) is used to generate a graphical pattern which represents the mechanical behaviour. This constitutive approach suggests that the tensile weakening of the older cartilage is due to an age-related reduction in the recruitment of load-carrying structures as the tissue is deformed. The viscoelastic constitutive model also predicts a reduction in the tensile strength of deep articular cartilage with rate of deformation. This prediction is supported by experimental fracture stress data. A weakening of the tensile integrity of the microstructure of articular cartilage could make the tissue less able to sustain normal compressive physiological loading without damage and thus make the tissue more susceptible to osteoarthritic degeneration. The constitutive approach indicates that the weakening of the older tissue may be related to changes within the microstructure which determine how applied mechanical energy is stored and dissipated.     

Morphology of the stifle in agouti (Dasyprocta prymnolopha,Wagler 1831)

The agouti (Dasyprocta prymnolopha, Wagler 1831) is a wild rodent of great zootechnical potential, a fact that enables anatomical and morphological studies to support management actions with this animal. In this perspective, this study aimed to describe the anatomy and histology of the agouti stifle joint. Four adult agoutis were used, two females and two males. The animals were submitted to dissection and identification of the structures of the stifle joint. For light microscopy study, samples of the patellar ligament, cranial and caudal cruciate ligaments, medial and lateral collateral ligaments were used. Agouti has a highly congruent patellofemoral joint; elongated patella; medial and lateral fabellae at the proximal insertion of the gastrocnemius muscle; medial and lateral meniscus with lunula; in addition to the presence of the following ligament structures: patellar ligament, cranial and caudal cruciate ligaments, medial and lateral collateral ligaments, meniscofemoral ligament, caudal meniscal ligament of the medial meniscus, and medial and lateral cranial ligaments. The patellar ligament presents bundles of parallel collagen fibers with a straight path and coated fibroblasts; collateral and cruciate ligaments had loose and dense connective tissue, coated fibroblasts and collagen bundle undulations, the latter most expressive in the caudal cruciate ligament. Thus, except for the shape and angulation of the stifle, which allows specific movements, the agouti stifle has structures analogous to that of other rodents and domestic animals.     

Prolonged ethanol replacement by CO2 increases splits on articular cartilage surface after critical point drying

Ethanol replacement by CO₂ of glutaraldehyde-fixed and ethanol-dehydrated rabbit articular cartilage specimens was monitored with both gas chromatograph and alcometer prior to critical point drying (CPD). The surface structure of the patellar specimens was also systematically registered with a semiquantitative scanning electron microscopic method. After a 2 h interval, when about 28 μl of ethanol/15 min CO₂ extract was removed, the articular surface was smooth, although small areas of striated surface and superficial splits were present. A long-term CO₂ treatment (16 h) removed ethanol completely, but increased superficial splitting of the articular surface after CPD. Air-drying of the specimens gave rise to inferior preservation of the cartilage: large areas with pitted and leafy surface qualities, but no superficial splits, were present on the surface. It was evident that prolonged ethanol replacement by CO₂, prior to CPD, degraded surface structure of the articular cartilage which should be taken into consideration in the planning and design of experiments. Ethanol removal by CO₂ could conveniently be monitored by an alcometer.     

Application of design‐based stereology for estimation of absolute volume and surface area of the articular and calcified cartilage compartments of undecalcified human femoral heads

Design‐based stereological methods using systematic uniform random sampling, the Cavalieri estimator and vertical sections are used to investigate undecalcified human femoral heads. Ten entire human femoral heads, obtained from normal women and normal men, were systematically sampled and thin undecalcified vertical sections were obtained. Absolute volumes and surface areas of the entire femoral head, the articular cartilage and the calcified cartilage compartments were estimated. In addition, the average thickness of the articular cartilage and the calcified cartilage were calculated. The stereological procedures applied to the human femoral heads resulted in average coefficient of errors, which were 0.03–0.06 for the volume estimates and 0.03–0.04 for the surface area estimates. We conclude that design‐based stereology using the Cavalieri estimator and vertical sections can successfully be used in large undecalcified tissue specimens, like the human femoral head, to estimate the absolute volume and surface area of macroscopic as well as of microscopic tissue compartments. The application of well‐known design‐based stereological methods carries potential advantage for investigating the pathology in inflammatory and degenerative joint diseases.