Quantitation of articular surface topography and cartilage thickness in knee joints using stereophotogrammetry

An analytical stereophotogrammetry (SPG) technique has been developed based upon some of the pioneering work of Selvik [Ph.D. thesis, University of Lund, Sweden (1974)] and Huiskes and coworkers [J. Biomechanics 18, 559-570 (1985)], and represents a fundamental step in the construction of biomechanical models of diarthrodial joints. Using this technique, the precise three-dimensional topography of the cartilage surfaces of various diarthrodial joints has been obtained. The system presented in this paper delivers an accuracy of 90 microns in the least favorable conditions with 95% coverage using the same calibration method as Huiskes et al. (1985). In addition, a method has been developed, using SPG, to quantitatively map the cartilage thickness over the entire articular surface of a joint with a precision of 134 microns (95% coverage). In the present study, our SPG system has been used to quantify the topography, including surface area, of the articular surfaces of the patella, distal femur, tibial plateau, and menisci of the human knee. Furthermore, examples of cartilage thickness maps and corresponding thickness data including coefficient of variation, minimum, maximum, and mean cartilage thickness are also provided for the cartilage surfaces of the knee. These maps illustrate significant variations over the joint surfaces which are important in the determination of the stresses and strains within the cartilage during diarthrodial joint function. In addition, these cartilage surface topographies and thickness data are essential for the development of anatomically accurate finite element models of diarthrodial joints.(ABSTRACT TRUNCATED AT 250 WORDS)     

A chondral modeling theory revisited

The mechanical environment of limb joints constantly changes during growth due to growth-related changes in muscle and tendon lengths, long bone dimensions, and body mass. The size and shape of limb joint surfaces must therefore also change throughout post-natal development in order to maintain normal joint function. Frost's (1979, 1999) chondral modeling theory proposed that joint congruence is maintained in mammalian limbs throughout postnatal ontogeny because cartilage growth in articular regions is regulated in part by mechanical load. This paper incorporates recent findings concerning the distribution of stress in developing articular units, the response of chondrocytes to mechanically induced deformation, and the development of articular cartilage in order to expand upon Frost's chondral modeling theory. The theory presented here assumes that muscular contraction during post-natal locomotor development produces regional fluctuating, intermittent hydrostatic pressure within the articular cartilage of limb joints. The model also predicts that peak levels of hydrostatic pressure in articular cartilage increase between birth and adulthood. Finally, the chondral modeling theory proposes that the cell-cell and cell-extracellular matrix interactions within immature articular cartilage resulting from mechanically induced changes in hydrostatic pressure regulate the metabolic activity of chondrocytes. Site-specific rates of articular cartilage growth are therefore regulated in part by the magnitude, frequency, and orientation of prevailing loading vectors. The chondral modeling response maintains a normal kinematic pathway as the magnitude and direction of joint loads change throughout ontogeny. The chondral modeling theory also explains ontogenetic scaling patterns of limb joint curvature observed in mammals. The chondral modeling response is therefore an important physiological mechanism that maintains the match between skeletal structure, function, and locomotor performance throughout mammalian ontogeny and phylogeny.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

A surface roughness comparison of cartilage in different types of synovial joints

The naturally occurring structure of articular cartilage has proven to be an effective means for the facilitation of motion and load support in equine and other animal joints. For this reason, cartilage has been extensively studied for many years. Although the roughness of cartilage has been determined from atomic force microscopy (AFM) and other methods in multiple studies, a comparison of roughness to joint function has not be completed. It is hypothesized that various joint types with different motions and regimes of lubrication have altered demands on the articular surface that may affect cartilage surface properties. Micro- and nanoscale stylus profilometry was performed on the carpal cartilage harvested from 16 equine forelimbs. Eighty cartilage surface samples taken from three different functioning joint types (radiocarpal, midcarpal, and carpometacarpal) were measured by a Veeco Dektak 150 Stylus Surface Profilometer. The average surface roughness measurements were statistically different for each joint. This indicates that the structure of cartilage is adapted to, or worn by, its operating environment. Knowledge of cartilage micro- and nanoscale roughness will assist the future development and design of treatments for intra- articular substances or surfaces to preserve joint integrity and reduce limitations or loss of joint performance.     

Exploring novel objective functions for simulating muscle coactivation in the neck

Musculoskeletal modeling allows for analysis of individual muscles in various situations. However, current techniques to realistically simulate muscle response when significant amounts of intentional coactivation is required are inadequate. This would include stiffening the neck or spine through muscle coactivation in preparation for perturbations or impacts. Muscle coactivation has been modeled previously in the neck and spine using optimization techniques that seek to maximize the joint stiffness by maximizing total muscle activation or muscle force. These approaches have not sought to replicate human response, but rather to explore the possible effects of active muscle. Coactivation remains a challenging feature to include in musculoskeletal models, and may be improved by extracting optimization objective functions from experimental data. However, the components of such an objective function must be known before fitting to experimental data. This study explores the effect of components in several objective functions, in order to recommend components to be used for fitting to experimental data. Four novel approaches to modeling coactivation through optimization techniques are presented, two of which produce greater levels of stiffness than previous techniques. Simulations were performed using OpenSim and MATLAB cooperatively. Results show that maximizing the moment generated by a particular muscle appears analogous to maximizing joint stiffness. The approach of optimizing for maximum moment generated by individual muscles may be a good candidate for developing objective functions that accurately simulate muscle coactivation in complex joints. This new approach will be the focus of future studies with human subjects.     

Some effects of global joint morphology on local stress aberrations near imprecisely reduced intra-articular fractures

Cadaver models of contact pressure aberration near displaced intra-articular fractures complement clinical experience, but inter-specimen variability often complicates interpretation of in vitro data. A contact finite element formulation is here used to study juxta-articular stress distributions in a plane strain model of tibial plateau step-off incongruity. Attention is focused on the influence of global morphologic parameters: intact joint surface curvatures, cartilage thickness, and cartilage stiffness. The computed stress distributions agreed well with experimental recordings for a typical 3 mm incongruity in an otherwise normal joint. Both decreased cartilage thickness and increased cartilage modulus led to elevations in the peak local contact stress, and to concentration of contact stress near the edge of the step-off incongruity. Similar effects were seen when reduction of global joint congruency was modelled by decreasing the concavity of the tibial plateau. While the observed degree of coupling between global morphology and local stress aberration was by no means negligible, the sensitivity of the stresses to variations in individual parameters was relatively mild. This suggests that the finite element results will be useful for experimental data interpretation.     

Articular size and curvature as determinants of carpal joint mobility and stability in strepsirhine primates

Theoretical and empirical evidence suggest that limb joint surface morphology is mechanically related to joint mobility, stability, and strength. This study tests hypotheses relating aspects of joint surface shape to joint function by comparing carpal joint size and curvature among strepsirhine primates that differ significantly in their positional behaviors and hand postures: vertical clingers, active arboreal quadrupeds, and slow cautious climbers. Joints that are very mobile are expected to have increased size and curvature of male joint mating surfaces, whereas those that function primarily in weight-bearing are expected to have relatively expanded female joint mating surfaces. Results show that 1) high male joint mating surface curvature is related to increased joint mobility and 2) increased female joint mating surface curvature is related to increased joint stability under loads of different orientation. Arc lengths of both male and female joint mating surfaces do not differ significantly between locomotor groups. Moreover, carpal joint curvature is not significantly correlated with either joint size (arc length) or body size, but carpal joint size and body size are highly correlated with one another. Relative to body size, articular arc lengths scale close to isometry (geometric similarity) both within and among groups. These results suggest that structural changes leading to increased joint mobility involve modifying joint surface curvature, and in the case of the carpal joints do not include altering joint size. Curvature of female joint mating surfaces appears related to variation in load orientation, but not necessarily load magnitude and frequency. © 1996 Wiley-Liss, Inc.     

Load sharing between solid and fluid phases in articular cartilage: I--Experimental determination of in situ mechanical conditions in a porcine knee.

The in situ mechanical conditions of cartilage in the articulated knee were quantified during joint loading. Six porcine knees were subjected to a 445 N compressive load while cartilage deformations and contact pressures were measured. From roentgenograms, cartilage thickness before and during loading allowed the calculation of tissue deformation on the lateral femoral condyle at different times during the loading process. Contact pressures on the articular surface were measured with miniature fiber-optic pressure transducers. Results showed that the medial side of the lateral femoral condyle had higher contact pressures, as well as deformations. To begin to correlate the pressures and resulting deformations, the intrinsic material properties of the cartilage on the lateral condyle were obtained from indentation tests. Data from four normal control specimens indicated that the aggregate modulus of the medial side was significantly higher than in other areas of the condyle. These experimental measures of the in situ mechanical conditions of articular cartilage can be combined with theoretical modeling to obtain valuable information about the relative contributions of the solid and fluid phases to supporting the applied load on the cartilage surface (see Part II).     

Acupuncture reduces pain in rats with osteoarthritis by inhibiting MCP2/CCR2 signaling pathway

Acupuncture is an emerging alternative therapy that has been beneficial for the pain of osteoarthritis (OA). However, the underlying mechanism of protective effect remains unclear. MCP1/CCR2 axis can be stimulated in various periods of OA, and we hypothesize that acupuncture may treat OA by regulating the MCP1/CCR2 axis. This study aimed to explore the effect of acupuncture at points ST35 and ST36 on the effects of hyperalgesia and cartilage in OA rats including the expression of chemokines, nerve growth factor (NGF), and inflammatory-related proteins. OA was induced in male Sprague–Dawley rats by anterior cruciate ligament transection at the right knee. The first acupuncture intervention was performed on the seventh day after surgery and once a day for seven weeks. The knee-pain-related behaviors, histology, and related protein were examined in this study. We have found that electroacupuncture at ST35 and ST36 can significantly alleviate the hyperalgesia and cartilage degeneration as well as reducing nerve sprouting in OA knee joint. Moreover, acupuncture treatment may inhibit the MCP1/CCR2 axis as well as down-regulate inflaming factor and NGF in cartilage and synovial tissue. The data presented here indicate that acupuncture exerts a protective effect against hyperalgesia and cartilage degeneration, and the mechanism might involve in chemokines and NGF pathway.     

A computer model of human thermoregulation for a wide range of environmental conditions: the passive system.

A dynamic model predicting human thermal responses in cold, cool, neutral, warm, and hot environments is presented in a two-part study. This, the first paper, is concerned with aspects of the passive system: 1) modeling the human body, 2) modeling heat-transport mechanisms within the body and at its periphery, and 3) the numerical procedure. A paper in preparation will describe the active system and compare the model predictions with experimental data and the predictions by other models. Here, emphasis is given to a detailed modeling of the heat exchange with the environment: local variations of surface convection, directional radiation exchange, evaporation and moisture collection at the skin, and the nonuniformity of clothing ensembles. Other thermal effects are also modeled: the impact of activity level on work efficacy and the change of the effective radiant body area with posture. A stable and accurate hybrid numerical scheme was used to solve the set of differential equations. Predictions of the passive system model are compared with available analytic solutions for cylinders and spheres and show good agreement and stable numerical behavior even for large time steps.     

In vivo patellar tracking and patellofemoral cartilage contacts during dynamic stair ascending

The knowledge of normal patellar tracking is essential for understanding the knee joint function and for diagnosis of patellar instabilities. This paper investigated the patellar tracking and patellofemoral joint contact locations during a stair ascending activity using a validated dual-fluoroscopic imaging system. The results showed that the patellar flexion angle decreased from 41.9° to 7.5° with knee extension during stair ascending. During first 80% of the activity, the patella shifted medially about 3.9mm and then slightly shifted laterally during the last 20% of the ascending activity. Anterior translation of 13mm of the patella was measured at the early 80% of the activity and the patella slightly moved posteriorly by about 2mm at the last 20% of the activity. The path of cartilage contact points was slightly lateral on the cartilage surfaces of patella and femur. On the patellar cartilage surface, the cartilage contact locations were about 2mm laterally from heel strike to 60% of the stair ascending activity and moved laterally and reached 5.3mm at full extension. However, the cartilage contact locations were relatively constant on the femoral cartilage surface (～5mm lateral). The patellar tracking pattern was consistent with the patellofemoral cartilage contact location pattern. These data could provide baseline knowledge for understanding of normal physiology of the patellofemoral joint and can be used as a reference for clinical evaluation of patellofemoral disorders.     

Sensitivities of medial meniscal motion and deformation to material properties of articular cartilage, meniscus and meniscal attachments using design of experiments methods

This study investigated the role of the material properties assumed for articular cartilage, meniscus and meniscal attachments on the fit of a finite element model (FEM) to experimental data for meniscal motion and deformation due to an anterior tibial loading of 45 N in the anterior cruciate ligament-deficient knee. Taguchi style L18 orthogonal arrays were used to identify the most significant factors for further examination. A central composite design was then employed to develop a mathematical model for predicting the fit of the FEM to the experimental data as a function of the material properties and to identify the material property selections that optimize the fit. The cartilage was modeled as isotropic elastic material, the meniscus was modeled as transversely isotropic elastic material, and meniscal horn and the peripheral attachments were modeled as noncompressive and nonlinear in tension spring elements. The ability of the FEM to reproduce the experimentally measured meniscal motion and deformation was most strongly dependent on the initial strain of the meniscal horn attachments (epsilon(1H)), the linear modulus of the meniscal peripheral attachments (E(P)) and the ratio of meniscal moduli in the circumferential and transverse directions (E(theta)E(R)). Our study also successfully identified values for these critical material properties (epsilon(1H) = -5%, E(P) = 5.6 MPa, E(theta)E(R) = 20) to minimize the error in the FEM analysis of experimental results. This study illustrates the most important material properties for future experimental studies, and suggests that modeling work of meniscus, while retaining transverse isotropy, should also focus on the potential influence of nonlinear properties and inhomogeneity.     

Swelling and curling behaviors of articular cartilage.

A new experimental method was developed to quantify parameters of swelling-induced shape change in articular cartilage. Full-thickness strips of cartilage were studied in free-swelling tests and the swelling-induced stretch, curvature, and areal change were measured. In general, swelling-induced stretch and curvature were found to increase in cartilage with decreasing ion concentration, reflecting an increasing tendency to swell and "curl" at higher swelling pressures. An exception was observed at the articular surface, which was inextensible for all ionic conditions. The swelling-induced residual strain at physiological ionic conditions was estimated from the swelling-induced stretch and found to be tensile and from 3-15 percent. Parameters of swelling were found to vary with sample orientation, reflecting a role for matrix anisotropy in controlling the swelling-induced residual strains. In addition, the surface zone was found to be a structurally important element, which greatly limits swelling of the entire cartilage layer. The findings of this study provide the first quantitative measures of swelling-induced residual strain in cartilage ex situ, and may be readily adapted to studies of cartilage swelling in situ.     

Probing the Conformation of FhaC with Small-Angle Neutron Scattering and Molecular Modeling

Probing the solution structure of membrane proteins represents a formidable challenge, particularly when using small-angle scattering. Detergent molecules often present residual scattering contributions even at their match point in small-angle neutron scattering (SANS) measurements. Here, we studied the conformation of FhaC, the outer-membrane, β-barrel transporter of the Bordetella pertussis filamentous hemagglutinin adhesin. SANS measurements were performed on homogeneous solutions of FhaC solubilized in n-octyl-d17-βD-glucoside and on a variant devoid of the α helix H1, which critically obstructs the FhaC pore, in two solvent conditions corresponding to the match points of the protein and the detergent, respectively. Protein-bound detergent amounted to 142 ± 10 mol/mol as determined by analytical ultracentrifugation. By using molecular modeling and starting from three distinct conformations of FhaC and its variant embedded in lipid bilayers, we generated ensembles of protein-detergent arrangement models with 120–160 detergent molecules. The scattered curves were back-calculated for each model and compared with experimental data. Good fits were obtained for relatively compact, connected detergent belts, which occasionally displayed small detergent-free patches on the outer surface of the β barrel. The combination of SANS and modeling clearly enabled us to infer the solution structure of FhaC, with H1 inside the pore as in the crystal structure. We believe that our strategy of combining explicit atomic detergent modeling with SANS measurements has significant potential for structural studies of other detergent-solubilized membrane proteins.     

Experimental measurement and modeling analysis on mechanical properties of incudostapedial joint

The incudostapedial (IS) joint between the incus and stapes is a synovial joint consisting of joint capsule, cartilage, and synovial fluid. The mechanical properties of the IS joint directly affect the middle ear transfer function for sound transmission. However, due to the complexity and small size of the joint, the mechanical properties of the IS joint have not been reported in the literature. In this paper, we report our current study on mechanical properties of human IS joint using both experimental measurement and finite element (FE) modeling analysis. Eight IS joint samples with the incus and stapes attached were harvested from human cadaver temporal bones. Tension, compression, stress relaxation and failure tests were performed on those samples in a micro-material testing system. An analytical approach with the hyperelastic Ogden model and a 3D FE model of the IS joint including the cartilage, joint capsule, and synovial fluid were employed to derive mechanical parameters of the IS joint. The comparison of measurements and modeling results reveals the relationship between the mechanical properties and structure of the IS joint.     

Comparison of MRI-based estimates of articular cartilage contact area in the tibiofemoral joint

Knee osteoarthritis (OA) detrimentally impacts the lives of millions of older Americans through pain and decreased functional ability. Unfortunately, the pathomechanics and associated deviations from joint homeostasis that OA patients experience are not well understood. Alterations in mechanical stress in the knee joint may play an essential role in OA; however, existing literature in this area is limited. The purpose of this study was to evaluate the ability of an existing magnetic resonance imaging (MRI)-based modeling method to estimate articular cartilage contact area in vivo. Imaging data of both knees were collected on a single subject with no history of knee pathology at three knee flexion angles. Intra-observer reliability and sensitivity studies were also performed to determine the role of operator-influenced elements of the data processing on the results. The method's articular cartilage contact area estimates were compared with existing contact area estimates in the literature. The method demonstrated an intra-observer reliability of 0.95 when assessed using Pearson's correlation coefficient and was found to be most sensitive to changes in the cartilage tracings on the peripheries of the compartment. The articular cartilage contact area estimates at full extension were similar to those reported in the literature. The relationships between tibiofemoral articular cartilage contact area and knee flexion were also qualitatively and quantitatively similar to those previously reported. The MRI-based knee modeling method was found to have high intra-observer reliability, sensitivity to peripheral articular cartilage tracings, and agreeability with previous investigations when using data from a single healthy adult. Future studies will implement this modeling method to investigate the role that mechanical stress may play in progression of knee OA through estimation of articular cartilage contact area.     

Tensile properties of the mandibular condylar cartilage

Mandibular condylar cartilage plays a crucial role in temporomandibular joint (TMJ) function, which includes facilitating articulation with the temporomandibular joint disc and reducing loads on the underlying bone. The cartilage experiences considerable tensile forces due to direct compression and shear. However, only scarce information is available about its tensile properties. The present study aims to quantify the biomechanical characteristics of the mandibular condylar cartilage to aid future three-dimensional finite element modeling and tissue engineering studies. Porcine condylar cartilage was tested under uniaxial tension in two directions, anteroposterior and mediolateral, with three regions per direction. Stress relaxation behavior was modeled using the Kelvin model and a second-order generalized Kelvin model, and collagen fiber orientation was determined by polarized light microscopy. The stress relaxation behavior of the tissue was biexponential in nature. The tissue exhibited greater stiffness in the anteroposterior direction than in the mediolateral direction as reflected by higher Young's (2.4 times), instantaneous (1.9 times), and relaxed (1.9 times) moduli. No significant differences were observed among the regional properties in either direction. The predominantly anteroposterior macroscopic fiber orientation in the fibrous zone of condylar cartilage correlated well with the biomechanical findings. The condylar cartilage appears to be less stiff and less anisotropic under tension than the anatomically and functionally related TMJ disc. The anisotropy of the condylar cartilage, as evidenced by tensile behavior and collagen fiber orientation, suggests that the shear environment of the TMJ exposes the condylar cartilage to predominantly but not exclusively anteroposterior loading.