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.     

In-vitro measurement of the human knee joint motion during quadriceps leg raising

This paper represents a three-dimensional motion analysis of the human knee joint under given conditions of loading and constraint. As the knee is extended by a known force applied to the quadriceps tendon, relative displacements of the femur, tibia, and patella are measured using a video motion analysis system. The most prominent motion of the tibia is external rotation and anterior displacement relative to the femur during knee extension. The patellar flexion angle decreases from 70° to 0°. The moment arm of the knee extensor mechanism exhibits a characteristic bell shape which peaks somewhere in the 40°–60° region of flexion. In general, the quadriceps force results primarily from an increase in the torque exerted by the weight of the lower leg. In the range of 20°–60°, the quardricep force needed to extend the leg remains relatively constant. As the knee approaches full extension, the moment arm decreases due to the fact that the posterior capsule and the ACL begin to tighten in this region. Consequently, the quadriceps force increases rapidly.     

Three-dimensional contact dynamic model of the human knee joint during walking

It is well known that the geometry of the articular surface has a major role in determining the position of articular contact and the lines of action for the contact forces. The contact force calculation of the knee joint under the effect of sliding and rolling is one of the most challenging issues in this field. We present a 3-D human knee joint model including sliding and rolling motions and major ligaments to calculate the lateral and medial condyle contact forces from the recovered total internal reaction force using inverse dynamic contact modeling and the Least-Square method. As results, it is believed that the patella, muscles and tendon affect a lot for the internal reaction forces at the initial heel contact stage. With increasing flexion angles during gait, the decreasing contact area is progressively shifted to the posterior direction on the tibia plateau. In addition, the medial side contact force is larger than the lateral side contact force in the knee joint during normal human walking. The total internal forces of the knee joint are reasonabe compared to previous studies.     

Measurement of laxity in the anterior cruciate ligament-deficient knee: a comparison of three different methods in vitro

The aim of this study was to compare in-vitro measurements of anteroposterior laxity in the anterior cruciate ligament (ACL)-deficient knee using three different methods: an Instron materials-testing machine, then a KT-2000 arthrometer, and finally by Roentgen stereophotogrammetric analysis (RSA). Eight ACL-deficient human cadaver knees were used. Total displacement was measured between 90 N anterior and 90 N posterior tibiofemoral drawer forces at both 20 degrees and 90 degrees knee flexion. Laxity ranged from 11.5 to 27.6 mm at 20 degrees and from 8.7 to 23.9 mm at 90degrees. A statistically significant difference was not found between the mean RSA and KT-2000 measurements. However, the mean Instron measurements of laxity were significantly (3-4 mm) higher than both RSA and KT-2000 measurements. The clinical methods of RSA and the KT-2000 measurements agreed well but appeared to underestimate tibiofemoral anteroposterior laxity compared with the materials-testing machine. These findings may be helpful in the future comparison of different studies.     

双足机器人腿部新构型设计与试验研究

探究高动态性能双足机器人对腿部设计的要求,阐明机器人腿部设计准则、设计方案和实现措施。提出一种腿部串并联新构型方案,膝关节驱动器上移到髋关节,踝关节驱动器上移到膝关节,膝关节驱动器通过简化五连杆机构将运动传递到膝部,踝关节驱动器通过并联四连杆机构将运动传递到踝部。对踝关节并联机构和整个腿部关节进行运动学正逆解,建立新构型机器人的仿真模型。考虑运动控制算法,完成机器人动力学仿真。测试准直驱驱动器性能,并完成串并联构型腿部样机试验验证,机器人可实现0.4m/s的行走速度。结果表明,提出的腿部串并联新构型与传统串联构型比具有更高的运动性能,新构型机器人性能在真机测试中得到验证。该串并联新构型方案在双足机器人和其它服务机器人领域具有广阔的应用前景。     

Knee and hip joint forces--sensitivity to the degrees of freedom classification at the knee

Previous research has demonstrated that the number of degrees of freedom (DOF) modelled at a given joint affects the antagonistic muscle activity predicted by inverse dynamics optimization techniques. This higher level of muscle activity in turn results in greater joint contact forces. For instance, modelling the knee as a 3 DOF joint has been shown to result in higher hip and knee joint forces commensurate with a higher level of muscular activity than when the knee is modelled with 1 DOF. In this study, a previously described musculoskeletal model of the lower limb was used to evaluate the sensitivity of the knee and hip joint contact forces to the DOF at the knee during vertical jumping in both a 1 and a 3 DOF knee model. The 3 DOF knee was found to predict higher tibiofemoral and hip joint contact forces and lower patellofemoral joint contact forces. The magnitude of the difference in hip contact force was at least as significant as that found in previous research exploring the effect of subject-specific hip geometry on hip contact force. This study therefore demonstrates a key sensitivity of knee and hip joint contact force calculations to the DOF at the knee. Finally, it is argued that the results of this study highlight an important physiological question with practical implications for the loading of the structures of the knee; that is, the relative interaction of muscular, ligamentous, and articular structures in creating moment equilibrium at the knee.     

Maximum finger force prediction using a planar simulation of the middle finger

Maximum isometric finger-grip forces were predicted using a biomechanical model for plane motion of the middle finger. In the course of this study, mathematical representations of tendon displacement, the moment arm of tendon at the finger joints and muscle force-length relationship were investigated. The information gathered was applied to the model to estimate the maximum grip force of the middle finger gripping cylinders of different sizes. Muscle force per unit physiological cross-section area of 30 N/cm2 resulted in good agreement with measured force. However, for finger postures having an acute proximal interphalangeal joint angle, the estimated force was greater than that measured. Various joint angles were applied to the model to simulate the wrist and finger postures not limited to the cylinder grip. In general the finger force was greatest with the wrist in its extended position and at acute flexion of the proximal interphalangeal joint. The maximum finger force occurred at reduced metacarpophalangeal joint angles as the wrist joint changed from an extended position to a flexed one. It is also postulated that muscle force-length relationship is an important factor in muscle force predictions. The data obtained by this research are useful for the design of handles and the current model is applicable to the analysis of hand postures for workers using hand tools.     

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.     

A position based kinematic method for the analysis of human gait

Human joint motion can be kinematically described in three planes, typically the frontal, sagittal, and transverse, and related to experimentally measured data. The selection of reference systems is a prerequisite for accurate kinematic analysis and resulting development of the equations of motion. Moreover, the development of analysis techniques for the minimization of errors, due to skin movement or body deformation, during experiments involving human locomotion is a critically important step, without which accurate results in this type of experiment are an impossibility. The traditional kinematic analysis method is the Angular-based method (ABM), which utilizes the Euler angle or the Bryant angle. However, this analysis method tends to increase cumulative errors due to skin movement. Therefore, the objective of this study was to propose a new kinematic analysis method, Position-based method (PBM), which directly applies position displacement data to represent locomotion. The PBM presented here was designed to minimize cumulative errors via considerations of angle changes and translational motion between markers occurring due to skin movements. In order to verify the efficacy and accuracy of the developed PBM, the mean value of joint dislocation at the knee during one gait cycle and the pattern of three dimensional translation motion of the tibiofemoral joint at the knee, in both flexion and extension, were accessed via ABM and via new method, PBM, with a Local Reference system (LRS) and Segmental Reference system (SRS), and then the data were compared between the two techniques. Our results indicate that the proposed PBM resulted in improved accuracy in terms of motion analysis, as compared to ABM, with the LRS and SRS.     

Objective measurement of knee laxity and stiffness with reference to knee injury diagnosis. Part 2: Results

Equipment capable of objective knee analysis has been used to obtain data from 85 'normal' healthy knees, 47 patients suffering with knee disorders, and three cadaveric knee joints. Among the 'normals' it was found that there was a correlation between body weight and stiffness and laxity. A lower stiffness and higher laxity was recorded at 20 degrees of knee flexion than at 90 degrees. Using relative-paired difference analysis the variables affected by different injuries in patients were identified and are presented. In a separate analysis a multi-variate technique is used to interpret the data. The technique could be used to predict or diagnose knee injury, and as such may be highly useful to clinicians.     

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 comparison of various loading configurations of the proximal femur for the evaluation of reconstructive surgical procedures.

The study was designed to evaluate the effect of different loading configurations on stem and bone stresses in simulated total hip arthroplasty. The traditional experiment design of loading the model through the head of the prosthesis by the resultant joint force was compared with a more realistic model which included an abductor strap to simulate the abductor muscle force. In addition, an alternative experiment design was evaluated in which a loading arm was clamped directly on to the head of the prosthesis. The results show that loading the model by the resultant joint force not only changes the magnitude of the stresses but also the stress distribution compared to the abductor muscle model. The new experiment design closely approximates stresses seen in the abductor muscle model below the lesser trochanter. In the proximal region, the stresses are increased on the medial side and decreased on the lateral side. The advantages of the proposed loading model are: (a) easy and reproducible set-up and alignment is facilitated, (b) different positions of the femur (flexion, extension) can be simulated and (c) a more realistic stress distribution and magnitude is achieved.     

KIN-Nav navigation system for kinematic assessment in anterior cruciate ligament reconstruction: features, use, and perspectives

In this paper a new navigation system, KIN-Nav, developed for research and used during 80 anterior cruciate ligament (ACL) reconstructions is described. KIN-Nav is a user-friendly navigation system for flexible intraoperative acquisitions of anatomical and kinematic data, suitable for validation of biomechanical hypotheses. It performs real-time quantitative evaluation of antero-posterior, internal-external, and varus-valgus knee laxity at any degree of flexion and provides a new interface for this task, suitable also for comparison of pre-operative and post-operative knee laxity and surgical documentation. In this paper the concept and features of KIN-Nav, which represents a new approach to navigation and allows the investigation of new quantitative measurements in ACL reconstruction, are described. Two clinical studies are reported, as examples of clinical potentiality and correct use of this methodology. In this paper a preliminary analysis of KIN-Nav's reliability and clinical efficacy, performed during blinded repeated measures by three independent examiners, is also given. This analysis is the first assessment of the potential of navigation systems for evaluating knee kinematics.     

Unlockable knee joint mechanism for powered gait orthosis

Walking with the knee joint locked increases the amplitude of pelvic tilt and results in an unnatural gait. This paper introduces a powered gait orthosis with a moveable knee joint designed to improve the gait speed of patients with spinal cord injury (SCI). The unlockable knee joint powered gait orthosis (UKJ-PGO) uses a gas spring cylinder and a solenoid locking device to enable flexion of the joint, while the rigidity of the hip-joint device is enhanced using air muscles. A gait analysis was conducted to evaluate the performance of the UKJ-PGO, and the kinematic parameters obtained were compared with those of a standard PGO. In the gait of SCI patients using the UKJ-PGO, the new knee-joint device enabled flexion during the swing phase and showed a decrease in pelvic tilt compared with the standard PGO gait. As greater flexion was possible at the knee joint, the duration of the stance phase substantially decreased to near to the normal value, and the duration of the swing phase increased accordingly. In addition, the gait using the UKJ-PGO was faster than that with the standard PGO.     

Muscle-ligament interactions at the human knee (II)

In part I of this paper, a three-dimensional model of the human knee joint was incorporated into a detailed human musculoskeletal lower extremity model. The model was used to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans extend/flex in an isometric state. Part II investigates the sensitivity of the model calculations to changes in the parameters which describe the mechanical behavior of cartilage and the ligaments of the knee. The ligament function in the real knee was most sensitive to changes in ligament reference lengths or strains, less sensitive to changes in cartilage stiffness, and least sensitive to changes in ligament stiffness.     

2URR-SRR-RUPUR并联式腿部康复机器人机构设计与运动性能分析

基于腿部关节康复机理,提出了一种2URR-SRR-RUPUR 4自由度并联式腿部康复机器人,该机构能够实现踝关节的外展和内收运动、膝关节的屈伸运动、髋关节的内旋和外旋运动以及腿部的牵伸运动。基于螺旋理论分析了该机构在一般位型和初始位型下的约束螺旋系和自由度性质。建立了2URR-SRR-RUPUR并联机构的运动学模型,采用闭环矢量法求解机构的运动学逆解并分析了机构的速度雅可比矩阵,在此基础上,对机构的工作空间和奇异性进行研究,得到了机构的工作空间图和奇异位型。基于腿部关节康复运动路径对机构进行轨迹规划,将规划结果采用SolidWorks Motion软件进行运动仿真分析,仿真结果表明,机构运动连续平滑,适合腿部康复运动训练,具备良好的应用潜力。     

变载荷作用下柔性关节板弹簧的大变形分析与强度计算

提出一种由气缸驱动的柔性机械手关节,关节采用板弹簧作为骨架。板弹簧的变形等效于自由端受特殊变载荷作用的弹性悬臂梁的大变形,其特殊变载荷是一个方向和大小都随气缸压力而变化的载荷。建立了悬臂梁静态变形的微分方程,采用简单的微分计算方法得出不同气缸压力下板弹簧任意位置的变形倾角、变形位移及应力的数值解。绘制其变形曲线和应力曲线,分析板弹簧的变形和应力分布情况,并校核了板弹簧最大应力处的强度。     

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.     

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.     

Objective measurement of knee laxity and stiffness with reference to knee injury diagnosis. Part 1: Design considerations and apparatus

Apparatus capable of objectively evaluating the laxity of the knee in vivo has been developed. The equipment consisted of a microcomputer-controlled machine, into which the leg was firmly clamped. The mechanical properties of the knee were measured by slowly applying a load to the tibia, while the femur was held stationary, and monitoring the resulting displacement of the tibia. Three separate tests could be performed: anterior-posterior drawing, varus-valgus rotation and tibial rotation. The tests were carried out on both legs of each subject, making six tests in all. The forces versus displacement (or torque versus rotation) took the form of a hysteresis loop. From these a total of 24 variables describing the stiffness, laxity and visco-elastic properties of the knee were calculated.