The effect of speed on leg stiffness and joint kinetics in human running

The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.     

Chondrocyte damage and contact pressures following impact on the rabbit tibiofemoral joint

Epidemiological studies show that tibial plateau fractures comprise about 10% of all below-knee injuries in car crashes. Studies from this laboratory document that impacts to the tibiofemoral (TF) joint at 50% of the energy producing gross fracture can generate cartilage damage and microcracks at the interface between calcified cartilage and underlying subchondral bone in the tibial plateau. These injuries are suggestive of the initiation for a long term chronic disease, such as osteoarthritis. The disease process may be further encouraged by acute damage to chondrocytes in the cartilage overlying areas of occult microcracking. The hypothesis of the current study was that significant damage to chondrocytes in tibial plateau cartilage could be generated in areas of high contact pressure by a single impact delivered to the rabbit TF joint, without a gross fracture of bone. Three rabbits received a single, 13 J of energy blunt insult to the TF joint, while another three animals were used as controls. Cell viability analyses compared chondrocyte damage in impacted versus control cartilage. Two additional rabbits were impacted to document contact pressures generated in the TF joint. The study showed high contact pressures in uncovered areas of the plateau, with a trend for higher pressures in the lateral versus medial facets. A significantly higher percentage of damaged chondrocytes existed in impacted versus the opposite, nonimpacted limbs. Additionally, more chondrocyte damage was documented in the superficial zone (top 20% of cartilage thickness) of the cartilage compared to middle (middle 50% of thickness) and deep (bottom 30% of thickness) zones. This study showed that a single blunt insult to the in situ rabbit TF joint, generating large areas of contact pressure exceeding 20 MPa, produces significant chondrocyte damage in the tibial articular cartilage, especially in the superficial zone, without gross fracture of bone. Future studies will be needed to investigate the long term, chronic outcome of this blunt force joint trauma.     

The underestimation of Young's modulus in compressive testing of cancellous bone specimens

In order to determine the accuracy of measurements of Young's modulus of cancellous bone by conventional compression testing, two independent strain measurements were made simultaneously during non-destructive uniaxial compression to 0.8% strain of rectangular specimens (n = 18). Strain was measured by an extensometer attached to the compression anvils close to the specimen and by an optical system covering the central half of the specimens. Mean Young's modulus determined by the extensometer technique was 689 MPa, but was 871 MPa when determined by the optical technique (mean difference = 182 MPa, SED = 50 MPa, p less than 0.002). Uneven strain distribution due to lack of support of cut vertical trabeculae at the anvil-specimen interface is believed to be causing the underestimation of Young's modulus measured by the extensometer technique. The influence of friction at the specimen-anvil interface was studied by performing a finite element analysis. It is concluded that Young's modulus of specimens of the chosen geometry on average is underestimated by about 20% by conventional compressing testing. The underestimation seems not to be dependent upon specimen density.     

Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces

Estimating tibiofemoral joint contact forces is important for understanding the initiation and progression of knee osteoarthritis. However, tibiofemoral contact force predictions are influenced by many factors including muscle forces and anatomical representations of the knee joint. This study aimed to investigate the influence of subject-specific geometry and knee joint kinematics on the prediction of tibiofemoral contact forces using a calibrated EMG-driven neuromusculoskeletal model of the knee. One participant fitted with an instrumented total knee replacement walked at a self-selected speed while medial and lateral tibiofemoral contact forces, ground reaction forces, whole-body kinematics, and lower-limb muscle activity were simultaneously measured. The combination of generic and subject-specific knee joint geometry and kinematics resulted in four different OpenSim models used to estimate muscle–tendon lengths and moment arms. The subject-specific geometric model was created from CT scans and the subject-specific knee joint kinematics representing the translation of the tibia relative to the femur was obtained from fluoroscopy. The EMG-driven model was calibrated using one walking trial, but with three different cost functions that tracked the knee flexion/extension moments with and without constraint over the estimated joint contact forces. The calibrated models then predicted the medial and lateral tibiofemoral contact forces for five other different walking trials. The use of subject-specific models with minimization of the peak tibiofemoral contact forces improved the accuracy of medial contact forces by 47% and lateral contact forces by 7%, respectively compared with the use of generic musculoskeletal model.     

Experimental validation of a tibiofemoral model for analyzing joint force distribution

A computational model of the tibiofemoral joint utilizing the discrete element analysis method has been developed and validated with human cadaveric knees. The computational method can predict load distributions to within a root mean square error (RMSE) of 3.6%. The model incorporates subject-specific joint geometry and the health of the subjects’ articular cartilage to determine the cartilage stiffness. It also includes the collateral and cruciate ligaments and utilizes stiffness values derived from literature for these elements. Comparisons of the total load, peak load, and peak load location for axial, varus, and valgus loading conditions confirmed that there was less than 4% RMSE between the analytical and experimental results. The model presented in this paper can generate results with minimal computational time and it can be used as a non-invasive method for characterizing and monitoring subject-specific knee loading patterns.     

Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint

Most tissue-engineered cartilage constructs are more compliant than native articular cartilage (AC) and are poorly integrated to the surrounding tissue. To investigate the effect of an implanted tissue-engineered construct (TEC) with these inferior properties on the mechanical environment of both the engineered and adjacent native tissues, a finite element study was conducted. Biphasic swelling was used to model tibial cartilage and an implanted TEC with the material properties of either native tissue or a decreased elastic modulus and fixed charged density. Creep loading was applied with a rigid impermeable indenter that represented the femur. In comparison with an intact joint, compressive strains in the transplant, surface contact stress in the adjacent native AC and load partitioning between different phases of cartilage were affected by inferior properties of TEC. Results of this study may lead to a better understanding of the complex mechanical environment of an implanted TEC.     

The regional contribution of glycosaminoglycans to temporomandibular joint disc compressive properties

Understanding structure-function relationships in the temporomandibular joint (TMJ) disc is a critical first step toward creating functional tissue replacements for the large population of patients suffering from TMJ disc disorders. While many of these relationships have been identified for the collagenous fraction of the disc, this same understanding is lacking for the next most abundant extracellular matrix component, sulfated glycosaminoglycans (GAGs). Though GAGs are known to play a major role in maintaining compressive integrity in GAG-rich tissues such as articular cartilage, their role in fibrocartilaginous tissues in which GAGs are much less abundant is not clearly defined. Therefore, this study investigates the contribution of GAGs to the regional viscoelastic compressive properties of the temporomandibular joint (TMJ) disc. Chondroitinase ABC (C-ABC) was used to deplete GAGs in five different disc regions, and the time course for >95% GAG removal was defined. The compressive properties of GAG depleted regional specimens were then compared to non-treated controls using an unconfined compression stress-relaxation test. Additionally, treated and non-treated specimens were assayed biochemically and histologically to confirm GAG removal. Compared to untreated controls, the only regions affected by GAG removal in terms of biomechanical properties were in the intermediate zone, the most GAG-rich portion of the disc. Without GAGs, all intermediate zone regions showed decreased tissue viscosity, and the intermediate zone lateral region also showed a 12.5% decrease in modulus of relaxation. However, in the anterior and posterior band regions, no change in compressive properties was observed following GAG depletion, though these regions showed the highest compressive properties overall. Although GAGs are not the major extracellular matrix molecule of the TMJ disc, they are responsible for some of the viscoelastic compressive properties of the tissue. Furthermore, the mechanical role of sulfated GAGs in the disc varies regionally in the tissue, and GAG abundance does not always correlate with higher compressive properties. Overall, this study found that sulfated GAGs are important to TMJ disc mechanics in the intermediate zone, an important finding for establishing design characteristics for future tissue engineering efforts.     

Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint

Most tissue-engineered cartilage constructs are more compliant than native articular cartilage (AC) and are poorly integrated to the surrounding tissue. To investigate the effect of an implanted tissue-engineered construct (TEC) with these inferior properties on the mechanical environment of both the engineered and adjacent native tissues, a finite element study was conducted. Biphasic swelling was used to model tibial cartilage and an implanted TEC with the material properties of either native tissue or a decreased elastic modulus and fixed charged density. Creep loading was applied with a rigid impermeable indenter that represented the femur. In comparison with an intact joint, compressive strains in the transplant, surface contact stress in the adjacent native AC and load partitioning between different phases of cartilage were affected by inferior properties of TEC. Results of this study may lead to a better understanding of the complex mechanical environment of an implanted TEC.     

Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors

The apparent stiffness tensor is an important mechanical parameter for characterizing trabecular bone. Previous studies have modeled this parameter as a function of mechanical properties of the tissue, bone density, and a second-order fabric tensor, which encodes both anisotropy and orientation of trabecular bone. Although these models yield strong correlations between observed and predicted stiffness tensors, there is still space for reducing accuracy errors. In this paper, we propose a model that uses fourth-order instead of second-order fabric tensors. First, the totally symmetric part of the stiffness tensor is assumed proportional to the fourth-order fabric tensor in the logarithmic scale. Second, the asymmetric part of the stiffness tensor is derived from relationships among components of the harmonic tensor decomposition of the stiffness tensor. The mean intercept length (MIL), generalized MIL (GMIL), and fourth-order global structure tensor were computed from images acquired through microcomputed tomography of 264 specimens of the femur. The predicted tensors were compared to the stiffness tensors computed by using the micro-finite element method (\(\upmu \)FE), which was considered as the gold standard, yielding strong correlations (\(R^2\) above 0.962). The GMIL tensor yielded the best results among the tested fabric tensors. The Frobenius error, geodesic error, and the error of the norm were reduced by applying the proposed model by 3.75, 0.07, and 3.16 %, respectively, compared to the model by Zysset and Curnier (Mech Mater 21(4):243–250, 1995) with the second-order MIL tensor. From the results, fourth-order fabric tensors are a good alternative to the more expensive \(\upmu \)FE stiffness predictions.     

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.     

Translational stiffness of the replaced shoulder joint

Results after a total shoulder arthroplasty in rheumatoid patients are poor, indicated by loosening of especially the glenoid component, bad joint functionality and the possibility of a joint dislocation. The failure mechanisms behind this are multiple, including patient, surgical and design factors. These results must be improved. At present, the optimal geometrical prosthesis component design, focused on joint conformity and constraint, still has to be investigated.

Proper understanding of the effect of geometrical design parameters on the theoretical relationship between joint translations and joint forces may contribute to improved designs. The main objective of this study is to theoretically describe this relationship and to investigate the joint translational stiffness, which can be used to investigate the effect of design parameters on joint motion. Joint translational stiffness is the gradient of the subluxation force with respect to the humeral head displacement.

For this static analysis a potential field is introduced, as the result of a joint compressive force (muscle forces) and a subluxation force (external forces). The positive and negative stiffness during articulation inside and subluxation outside the glenoid cavity, lead to stable and unstable equilibrium joint positions, respectively. A most lateral position of the humeral head centre coincides with a zero subluxation force; at this position the humerus is dislocated and a restoring force is needed to relocate the humeral head.

Joint conformity and compression force influence the joint translational stiffness during articulation inside the glenoid cavity, whereas during articulating outside the glenoid cavity this is influenced by the joint compression force and humeral radius of curvature. The glenoid radius of curvature influences the contact point and, in combination with the glenoid superior–inferior chord length, it also influences the constraintness angle, which influences the maximum allowable subluxation load to prevent a joint dislocation. This constraintness angle together with the joint conformity also influences maximum joint translations before articulation outside the glenoid cavity. Furthermore, the sign of the joint translational stiffness determines the stability of shoulder motion, which is stable and unstable if this stiffness is positive and negative, respectively.     

Short range stiffness elastic limit depends on joint velocity

Muscles behave as elastic springs during the initial strain phase, indicated as short range stiffness (SRS). Beyond a certain amount of strain the muscle demonstrates a more viscous behavior. The strain at which the muscle transits from elastic- to viscous-like behavior is called the elastic limit and is believed to be the result of breakage of cross-bridges between the contractile filaments. The aim of this study was to test whether the elastic limit, measured in vivo at the wrist joint, depended on the speed of lengthening. Brief extension rotations were imposed to the wrist joint (n=8) at four different speeds and at three different levels of voluntary torque using a servo controlled electrical motor. Using a recently published identification scheme, we quantified the elastic limit from measured joint angle and torque. The results showed that the elastic limit significantly increased with speed in a linear way, indicating to a constant time of approximately 30 ms before cross-bridges break. The implications for movement control of the joint are discussed.     

Contribution of collagen fibers to the compressive stiffness of cartilaginous tissues

Cartilaginous tissues such as the intervertebral disk are predominantly loaded under compression. Yet, they contain abundant collagen fibers, which are generally assumed to contribute to tensile loading only. Fiber tension is thought to originate from swelling of the proteoglycan-rich nucleus. However, in aged or degenerate disk, proteoglycans are depleted, whereas collagen content changes little. The question then rises to which extend the collagen may contribute to the compressive stiffness of the tissue. We hypothesized that this contribution is significant at high strain magnitudes and that the effect depends on fiber orientation. In addition, we aimed to determine the compression of the matrix. Bovine inner and outer annulus fibrosus specimens were subjected to incremental confined compression tests up to 60 % strain in radial and circumferential direction. The compressive aggregate modulus was determined per 10 % strain increment. The biochemical composition of the compressed specimens and uncompressed adjacent tissue was determined to compute solid matrix compression. The stiffness of all specimens increased nonlinearly with strain. The collagen-rich outer annulus was significantly stiffer than the inner annulus above 20 % compressive strain. Orientation influenced the modulus in the collagen-rich outer annulus. Finally, it was shown that the solid matrix was significantly compressed above 30 % strain. Therefore, we concluded that collagen fibers significantly contribute to the compressive stiffness of the intervertebral disk at high strains. This is valuable for understanding the compressive behavior of collagen-reinforced tissues in general, and may be particularly relevant for aging or degenerate disks, which become more fibrous and less hydrated.     

The effect of Knee-Ankle-Foot orthosis stiffness on the parameters of walking

The purpose of this simulation study was to analyze the effect of variation in Knee-Ankle-Foot-Orthosis stiffness on the joint power and the energy cost of walking. The effect of contractile tissue was simulated using linear elastic spring and viscous dampers in knee and ankle joints. Then, joint angles, ground reaction force, were collected from Twenty chronic hemiparesis subjects (15 males and 5 females) and twenty control subjects (14 males and 6 females), and spring stiffness were considered as the inputs. In this new study, the generated muscle torques were optimized by changing the stiffness as the desired output in the mathematical model attained by the MATLAB SimMechanics toolbox. Finally, the simulated mathematical model was introduced as an appropriate substitute in obtaining the optimized stiffness with a more convenient and efficient designed orthosis.     

The effect of resorption cavities on bone stiffness is site dependent

Resorption cavities formed during the bone remodelling cycle change the structure and thus the mechanical properties of trabecular bone. We tested the hypotheses that bone stiffness loss due to resorption cavities depends on anatomical location, and that for identical eroded bone volumes, cavities would cause more stiffness loss than homogeneous erosion. For this purpose, we used beam–shell finite element models. This new approach was validated against voxel-based FE models. We found an excellent agreement for the elastic stiffness behaviour of individual trabeculae in axial compression (R² = 1.00) and in bending (R²>0.98), as well as for entire trabecular bone samples to which resorption cavities were digitally added (R² = 0.96, RMSE = 5.2%). After validation, this new method was used to model discrete cavities, with dimensions taken from a statistical distribution, on a dataset of 120 trabecular bone samples from three anatomical sites (4th lumbar vertebra, femoral head, iliac crest). Resorption cavities led to significant reductions in bone stiffness. The largest stiffness loss was found for samples from the 4th lumbar vertebra, the lowest for femoral head samples. For all anatomical sites, resorption cavities caused significantly more stiffness loss than homogeneous erosion did. This novel technique can be used further to evaluate the impact of resorption cavities, which are known to change in several metabolic bone diseases and due to treatment, on bone competence.     

The effect of cyclical compressive loading on gene expression in articular cartilage

Osteoarthritis (OA) develops as a consequence of articular cartilage degeneration possibly initiated by excessive or abnormal loading of the joint, and potentially mediated through a proteinase/proteinase inhibitor imbalance. We have shown previously that physiological loads (0.5 MPa, 1 Hz, 3 hour) elicit increased expression and activation of the matrix metalloproteinases (MMPs) in articular cartilage explants in vitro. The objective of this study was to identify mechanically-regulated genes involved in the observed induction of MMP expression and enhanced activation. Differential RNA Display (DRD) was used to identify mechanically-regulated genes by comparing DRD products derived from loaded and unloaded cartilage. One gene up-regulated in cartilage after 10, 30 and 60 minute loading revealed 83% homology with Mus musculus thymosin beta_4 which is known to induce MMP gene expression. The identification of mechanically regulated genes will greatly enhance our understanding of matrix turnover providing an exciting future in elucidating the role of mechanically-regulated genes in the development of OA.     

The effect of boundary condition on the biomechanics of a human pelvic joint under an axial compressive load: a three-dimensional finite element model

The finite element (FE) model of the pelvic joint is helpful for clinical diagnosis and treatment of pelvic injuries. However, the effect of an FE model boundary condition on the biomechanical behavior of a pelvic joint has not been well studied. The objective of this study was to study the effect of boundary condition on the pelvic biomechanics predictions. A 3D FE model of a pelvis using subject-specific estimates of intact bone structures, main ligaments and bone material anisotropy by computed tomography (CT) gray value was developed and validated by bone surface strains obtained from rosette strain gauges in an in vitro pelvic experiment. Then three FE pelvic models were constructed to analyze the effect of boundary condition, corresponding to an intact pelvic joint, a pelvic joint without sacroiliac ligaments and a pelvic joint without proximal femurs, respectively. Vertical load was applied to the same pelvis with a fixed prosthetic femoral stem and the same load was simulated in the FE model. A strong correlation coefficient (R(2)=0.9657) was calculated, which indicated a strong correlation between the FE analysis and experimental results. The effect of boundary condition changes on the biomechanical response depended on the anatomical location and structure of the pelvic joint. It was found that acetabulum fixed in all directions with the femur removed can increase the stress distribution on the acetabular inner plate (approximately double the original values) and decrease that on the superior of pubis (from 7 MPa to 0.6 MPa). Taking sacrum and ilium as a whole, instead of sacroiliac and iliolumber ligaments, can influence the stress distribution on ilium and pubis bone vastly. These findings suggest pelvic biomechanics is very dependent on the boundary condition in the FE model.