Muscle-ligament interactions at the human knee (I)

A three-dimensional dynamic model of the knee was developed to study the interactions between the articulating surfaces of the bones and the geometrical and mechanical properties of the ligaments. The contact-surface geometry of the distal femur, proximal tibia, and patella was modeled by fitting polynomials to each of the eight articular surfaces. Twelve elastic elements were used to describe the function of the ligamentous and capsular structures of the knee. The origin and insertion sites of each model ligament were obtained from cadaveric data reported for an average-size knee. The response of the model to both anterior-posterior drawer and axial rotation suggests that the geometrical and mechanical properties of the model ligaments approximate the behavior of real ligaments in the intact knee. Comparison of the model’s response with experimental data obtained from cadaveric knee extension indicate further that the three-dimensional model reproduces the response of the real knee during movement.     

An optimal control model for determining articular contact forces at the human knee during rising from a static squat position

A two-dimensional dynamic model of the knee joint was incorporated into a four-segment, eight-muscle model of the human body to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans stand up from a static squatting position. Our optimal control model predicted peak tibiofemoral contact forces 8 times as high as body weight. Furthermore, ligament forces, especially those in the anterior-cruciate, were nearly body weight as knee flexion approached 90 degrees. Ligament and tibiofemoral contact loads were dominated by the forces exerted by muscles during the movement.     

Muscle-ligament interactions at the knee during walking.

A two-dimensional mathematical model of the knee is used with gait analysis to calculate muscle, cruciate ligament and tibio-femoral contact forces developed at the knee during normal level walking. Ten normal adult subjects--four females and six males--participated. The knee model is based upon a four-bar linkage comprising the femur, tibia and two cruciate ligaments. It takes account of the rolling and sliding of the femur on the tibia during flexion/extension and the changes in direction of the ligaments and muscle tendons. We considered forces transmitted by six elements: quadriceps, hamstrings, gastrocnemius, anterior and posterior cruciate ligaments, and tibio-femoral contact. The equations of mechanics can be used to determine the absolute values of only three of the knee forces simultaneously, so that twenty limiting solutions of three of the six forces were considered. A limiting solution was rejected if any of the three forces were negative, corresponding to compressive muscle or ligament forces, or tensile contact forces. These constraints always reduced and at times removed the redundancy of the knee structures. The high incidence of predicted single muscle activity, supported by electromyography, suggested that the ligaments play a significant role in load transmission during gait. The temporal patterns of muscle and ligament activity and ligament force magnitudes were sensitive to the choice of model parameters. The analysis showed that each of four possible minimum principles of muscle selection--minimal muscle force, muscle stress, ligament force and contact force--was unlikely to be valid throughout the walking cycle.     

A model of human knee ligaments in the sagittal plane. Part 1: Response to passive flexion.

The development of a mathematical model of the knee ligaments in the sagittal plane is presented. Essential features of the model are (a) the representation of selected cruciate ligament fibres as isometric links in a kinematic mechanism that controls passive knee flexion and (b) the mapping of all other ligament fibres between attachments on the tibia and femur. Fibres slacken and tighten as the ligament attachment areas on the bones move relative to each other. The model is used to study the shape and fibre length changes of the cruciate and collateral ligaments in response to passive flexion/extension of the knee. The model ligament shape and fibre length changes compare well qualitatively with experimental results reported in the literature. The results suggest that when designing and implanting a ligament replacement with the aim of reproducing the natural fibre strain patterns, the surgeon must not only implant through the natural attachment areas but must also maintain the natural fibre mapping and render all fibres just tight at the appropriate flexion angle.     

A sequentially-defined stiffness model of the knee

A new procedure is proposed to obtain a stiffness model of the knee, i.e. a model of the joint when static external loads are applied to the tibia and femur. A sequential approach is used to generalise a kinematic model of the passive motion of the articulation previously presented by the authors. The procedure is devised in such a way that the restraining function of the articular components which guide the passive motion of the joint is preserved after generalisation. As a result, the new stiffness model can replicate the passive motion with the same accuracy as the previous kinematic model, and it can also replicate the relative motion of the tibia and femur when the knee is loaded by static external loads. The proposed procedure is applied to a specimen and the relevant stiffness model is devised. The motion of the model under several loading conditions is then compared with the original motion of the specimen and with data obtained from the literature, in order to show the accuracy of the model and the potential of the proposed procedure.     

A finite element model of an idealized diarthrodial joint to investigate the effects of variation in the mechanical properties of the tissues

The stiffness of articular cartilage increases dramatically with increasing rate of loading, and it has been hypothesized that increasing the stiffness of the subchondral bone may result in damaging stresses being generated in the articular cartilage. Despite the interdependence of these tissues in a joint, little is understood of the effect of such changes in one tissue on stresses generated in another. To investigate this, a parametric finite element model of an idealized joint was developed. The model incorporated layers representing articular cartilage, calcified cartilage, the subchondral bone plate and cancellous bone. Taguchi factorial design techniques, employing a two-level full-factorial and a four-level fractional factorial design, were used to vary the material properties and thicknesses of the layers over the wide range of values found in the literature. The effects on the maximum values of von Mises stress in each of the tissues are reported here. The stiffness of the cartilage was the main factor that determined the stress in the articular cartilage. This, and the thickness of the cartilage, also had the largest effect on the stresses in all the other tissues with the exception of the subchondral bone plate, in which stresses were dominated by its own stiffness. The stiffness of the underlying subchondral bone had no effect on the stresses generated in the cartilage. This study shows how stresses in the various tissues are affected by changes in their mechanical properties and thicknesses. It also demonstrates the benefits of a structured, systematic approach to investigating parameter variation in finite element models.     

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.     

Validation of the soft tissue restraints in a force-controlled knee simulator

In vitro testing of total knee replacements (TKRs) is important both at the design stage and after the production of the final components. It can predict long-term in vivo wear of TKRs. The two philosophies for knee testing are to drive the motion by displacement or to drive the motion by force. Both methods have advantages and disadvantages. For force control an accurate simulation of soft tissue restraints is required. This study was devised to assess the accuracy of the soft tissue restraints of the force-controlled Stanmore knee simulator in simulating the restraining forces of the anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL). In order to do this, human cadaver knee joints were subjected to the ISO Standard Walking Cycle. The resulting kinematics were monitored when the soft tissue structures were intact, when the ACL and PCL were resected, and when they were simulated by springs positioned anteriorly and posteriorly. The stiffness of the springs was determined from the literature. Two different stiffnesses of springs were used which were 7.24 N/mm (designated as soft springs) and 33.8 N/mm (designated as hard springs). All the intact knees showed displacements that were within the range of the machine. Cutting the ACL and PCL resulted in anterior and posterior motion and internal external rotation that were significantly greater than the intact knee. Results showed that when the ACL and PCL were cut hard springs positioned anterior and posterior to the knee returned the knee to near normal anterior-posterior (AP) motion. Using hard springs in the posterior position in any condition reduced rotational displacements. Therefore using springs in a force-controlled simulator is a compromise. More accuracy may be obtained using springs that are of intermediate stiffness.     

气动肌肉关节的刚度分析及变刚度运动控制

根据人腿髋关节、膝关节骨骼结构及拮抗肌肉运动发力特点,设计一种拮抗气动肌肉驱动的仿生单腿机器人;由三元素模型求单根肌肉及关节摆动下被动刚度特性,分析关节角度/刚度关系;为实现仿生腿膝关节刚度可控的角度控制,建立仿生关节关于角度/刚度的基本气压解算模型;基于计算力矩控制对非线性对象具有高度补偿线性化性,提出含力矩项补偿的改进气压解算模型。搭建仿真及样机实验平台,结果表明,含两种气压解算模型的双闭环控制算法均能较好跟随膝关节角度/刚度,含带力矩项补偿模型的双闭环控制算法对膝关节的角度/刚度控制精度优于含基本模型的双闭环控制算法。该算法适用拮抗气动肌肉关节的类人运动,可满足人机协作时可靠性、柔顺性、仿生性等要求。     

The effect of cartilage deformation on the laxity of the knee joint

In this paper, deformation of the articular cartilage layers is incorporated into an existing two-dimensional quasi-static model of the knee joint. The new model relates the applied force and the joint displacement, as measured in the Lachmann drawer test, and allows the effect of cartilage deformation on the knee joint laxity to be determined. The new model augments the previous knee model by calculating the tibio-femoral contact force subject to an approximate 'thin-layer' constitutive equation, and a method is described for finding the configuration of the knee under a specified load, in terms of a displacement from a zero-load reference configuration. The results show that inclusion of deformable cartilage layers can cause a reduction of between 10 and 35 per cent in the force required to produce a given tibial displacement, over the range of flexion angles considered. The presence of cartilage deformation was found to be an important modifier of the loading response but is secondary to the effect of ligamentous extension. The flexion angle dependence of passive joint laxity is much more strongly influenced by fibre recruitment in the ligaments than by cartilage deformation.     

Tribological testing of articular cartilage of the medial compartment of the knee using a friction simulator

The aim of this study was to develop a tribological simulation of a unicondylar natural knee, to measure the friction and wear of articular cartilage (AC) against itself (AC-vs-AC) and against stainless steel (SS) simulating a hemiarthroplasty (AC-vs-SS). AC-vs-AC produced low levels of friction and no wear was found. AC-vs-SS showed higher levels of friction and significant AC wear. Using AC-vs-SS with elevated loading, the wear of AC was accelerated and through to bone. This study demonstrated the importance of contact stress in the design of a spacer hemiarthroplasty for the medial compartmental knee. Initial results showed the importance of contact mechanics, stress and biomaterial type in determining short-term tribological function and long-term clinical outcome of hemiarthroplasty.     

A model of human knee ligaments in the sagittal plane. Part 2: Fibre recruitment under load.

A mathematical model of the knee ligaments in the sagittal plane is used to study the forces in the cruciate and collateral ligaments produced by anterior/posterior tibial translation. The model is based on ligament fibre functional architecture. Geometric analysis of the deformed configurations of the model ligaments provides the additional compatibility conditions necessary for calculation of the statically indeterminate distributions of strain and stress within the ligaments and the sharing of load between ligaments. The investigation quantifies the process of ligament fibre recruitment, which occurs when fibres made slack by passive flexion/extension of the knee stretch and change their spatial positions in order to resist applied loads. The calculated ligament forces are in reasonable agreement with experimental results reported in the literature. The model explains some subtleties of ligament function not incorporated in models that represent the ligaments by a small number of lines.     

A three-dimensional dynamic finite element model of the prosthetic knee joint: simulation of joint laxity and kinematics

For testing purposes of prostheses at a preclinical stage, it is very valuable to have a generic modelling tool, which can be used to optimize implant features and to avoid poor designs being launched on to the market. The modelling tool should be fast, efficient, and multi-purpose in nature; a finite element model is well suited to the purpose. The question posed in this study was whether it was possible to develop a mathematically fast and stable dynamic finite element model of a knee joint after total knee arthroplasty that would predict data comparable with published data in terms of (a) laxities and ligament behaviour, and (b) joint kinematics. The soft tissue structures were modelled using a relatively simple, but very stable, composite model consisting of a band reinforced with fibres. Ligament recruitment and balancing was tested with laxity simulations. The tibial and patellar kinematics were simulated during flexion-extension. An implicit mathematical formulation was used. Joint kinematics, joint laxities, and ligament recruitment patterns were predicted realistically. The kinematics were very reproducible and stable during consecutive flexion-extension cycles. Hence, the model is suitable for the evaluation of prosthesis design, prosthesis alignment, ligament behaviour, and surgical parameters with respect to the biomechanical behaviour of the knee.     

Mechanics of the passive knee joint. Part 2: interaction between the ligaments and the articular surfaces in guiding the joint motion

The aim of this study was to examine how the interaction between ligament tensions and contact forces guides the knee joint through its specific pattern of passive motion. A computer model was built based on cadaver data. The passive motion and the ligament lengthening and force patterns predicted by the model were verified with data from the literature. The contribution of each ligament and contact force was measured in terms of the rotational moment that it produced about the tibial medial plateau and the anterior-posterior (AP) force that it exerted on the tibia. The high tension of the anterior cruciate ligament (ACL) and the geometric constraints of the anterior horns of the menisci were found to be key features that stabilized the knee at full extension. The mutual effect of the cruciates was found as the reason for the screw-home mechanism at early flexion. Past 300, the AP component of contact force on the convex geometry of the lateral tibial plateau and tension of the lateral collateral ligament (LCL) were identified as elements that control the joint motion. From 60 degrees to 90 degrees, reduction in the tension of the ACL was determined as a reason for continuation of the tibial anterior translation. From 90 degrees to 120 degrees, increase in the tension of the posterior cruciate ligament and the AP component of the contact force on the convex geometry of the lateral tibial plateau pushed the tibia more anteriorly. This anterior translation was limited by the constraining effects of the ACL tension and the AP component of the contact force on the medial meniscus. The important guiding role observed for the LCL suggests that it should not be overlooked in knee models.     

Spatial and temporal changes of subchondral bone proceed to articular cartilage degeneration in rats subjected to knee immobilization

This study was aimed to investigate the spatial and temporal changes of subchondral bone and its overlying articular cartilage in rats following knee immobilization. A total of 36 male Wistar rats (11–13 months old) were assigned randomly and evenly into 3 groups. For each group, knee joints in 6 rats were immobilized unilaterally for 1, 4, or 8 weeks, respectively, while the remaining rats were allowed free activity and served as external control groups. For each animal, femurs at both sides were dissected after sacrificed. The distal part of femur was examined by micro‐CT. Subsequently, femoral condyles were collected for further histological observation and analysis. For articular cartilage, significant changes were observed only at 4 and 8 weeks of immobilization. The thickness of articular cartilage and chondrocytes numbers decreased with time. However, significant changes in subchondral bone were defined by micro‐CT following immobilization in a time‐dependent manner. Immobilization led to a thinner and more porous subchondral bone plate, as well as a reduction in trabecular thickness and separation with a more rod‐like architecture. Changes in subchondral bone occurred earlier than in articular cartilage. More importantly, immobilization‐induced changes in subchondral bone may contribute, at least partially, to changes in its overlying articular cartilage. Microsc. Res. Tech. 79:209–218, 2016. © 2016 Wiley Periodicals, Inc.     

基因表达谱芯片用于小鼠膝关节炎组织的检测与分析

通过副韧带及半月板切除方法(MLI-OA)建立小鼠KOA模型,补肾活血方灌胃给药、常规抽提和纯化RNA,采用Agilent SurePrint G3 Mouse GE V2.0基因表达谱芯片检测小鼠膝OA关节组织的基因表达变化。检测结果显示补肾活血方对KOA组织基因表达具有明显调控作用补肾活血方有明显上调作用的基因中,中药组比模型组上调2倍以上的有56个;明显下调作用的基因中,中药组比模型组下调2倍以上的有119个。研究结果表明补肾活血方可能通过调控目前在KOA病变过程中作用尚不明确的基因,促进关节炎性因子代谢,延缓软骨退变,治疗骨关节炎的作用。     

A study on the influence of the seat and head restraint foam stiffnesses on neck injury in low speed offset rear impacts

Soft tissue neck injury (STNI) is thought to be related to automotive seat characteristics, and it is important to know how the stiffness of the seatback and head restraint foam affect the occupant’s motions in low speed rear impacts. The combined MADYMO(MAthematical DYnamic MOdel, TNO) 50th percentile facet male human body model with a detailed neck model was selected for this analysis. In order to determine the relationship between the occupant’s motions and seatback and head restraint foam stiffnesses, 40% offset rear impact simulations were performed by changing the stiffness of seatback and head restraint. Simulated results show that the maximum acceleration of head and trunk would tend to increase with those stiffnesses. Increased stiffness of the seatback and head restraint resulted in increased ligament and disc forces. On the other hand a proper combination of seatback and head restraint stiffness can reduce a possible neck injury. It is clear that an appropriate combination of stiffnesses between seatback and head restraint allows to minimize a neck injury.     

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.     

Effect of twisting hamstring tendon grafts on strength and joint laxity through the range of knee movement

Twisting or braiding of hamstring tendon grafts for use in anterior cruciate ligament reconstructions has been advocated to increase their strength and stiffness under load. In this study, a two-dimensional model was used to determine the failure strength of twisted and parallel grafts and associated knee laxity under simulated physiological loading conditions. For validation, mechanical tests of tendon grafts were also simulated with these models. The simulated physiological loading of the graft models showed that knees with twisted grafts had greater laxity than knees with parallel grafts, although there was little difference in failure load between the two graft configurations. The tensile loading of the graft models showed little difference in failure load when the tendons were modelled using line segments. When the tendons were considered as three-dimensional helical elements, which more accurately describe the tendon structure, the failure load of the twisted graft decreased significantly. This research provided no evidence to support the belief that a twisted tendon graft is a superior graft configuration relative to a parallel tendon graft.     

A Model for Intra-Articular Heat Exchange in a Knee Joint

A mathematical model has been developed for the understanding of temperature distribution in knee joint. Temperature rises in knee joint as a result of frictional energy. This heated synovial fluid enters into the articular cartilage by the process of filtration and supplies heat to cartilage and bone. This cooled fluid again mixes well with the lubricant in the joint cavity. The problem is formulated as a two-region flow and diffusion model: flow and thermal diffusion within the intra-articular gap; and within the porous matrix covering the approaching bones at the joint. The solution of the coupled mixed boundary value problem is solved by using perturbation method. It has been observed that, in certain diseased and or old synovial joints, the movement of the fluid into or out of the cartilage resisted, and therefore, the temperature does rise. The temperature does rise in old and diseased joints as observed by varying the values of parameters from its normal values. These values refer to old age and/or diseases affecting degeneration of synovial fluid and or cartilage.