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.     

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.     

Analysis of the assistance characteristics for the knee extension motion of knee orthosis using muscular stiffness force feedback

In this paper, we are interested in the characteristics of a knee joint when the knee extension motion was assisted by a powered knee orthosis using a muscular stiffness force feedback. For this purpose, we developed the powered knee orthosis with an artificial pneumatic actuator, which is intended for the assistance and the enhancement of muscular activities of lower limbs. The objective of this study was to confirm the effectiveness of the powered knee orthosis that generated a knee extension torque in the motion related to a knee joint. Twenty healthy subjects participated in this study and their lower limb muscular activities were measured to identify the effectiveness of the powered knee orthosis during sit-to-stand (STS) and squat motion. The muscular activities between with and without assistance of knee extension motion were compared and analyzed for the assistance characteristics of the powered knee orthosis. To generate the knee extension torque, the knee orthosis was controlled using muscular stiffness force (MSF) feedback that is controlled by muscular activities of the vastus intermedius muscle that mainly related to the knee extension motion. For analysis of muscular activities, the surface electromyography of the muscles related to the knee extension motion, i.e., RF, vastus lateralis, vastus medialis and vastus intermedius muscles in lower limbs of the right side were recorded and biodex dynamometer was used to measure the maximal concentric isokinetic strength of the knee extensors. The experimental result showed that muscular activities in lower limbs with the assistance of the powered knee orthosis was reduced by 25.62% in rectus femoris muscle and 29.82% in biceps femoris muscle, respectively and knee extension torque of an knee joint wearing knee orthosis was increased by 17.68% in averaged peak torque. Based on the effectiveness of the powered knee orthosis, weaken elder people may have benefited from the knee extension motion augmented by the powered knee orthosis during activity of daily living, e.g., stair ascent.     

Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait

Several three-dimensional (3D) lower-limb musculo-skeletal models have been developed for gait analysis and different hip, knee and ankle joint models have been considered in the literature. Conversely to the influence of the musculo-tendon geometry, the influence of the joint models--i.e. number of degrees of freedom and passive joint moments--on the estimated musculo-tendon forces and 3D joint reaction forces has not been extensively examined. In this paper musculo-tendon forces and 3D joint reaction forces have been estimated for one subject and one gait cycle with nine variations of a musculoskeletal model and outputs have been compared to measured electromyographic signals and knee joint contact forces. The model outputs are generally in line with the measured signals. However, the 3D joint reaction forces were higher than published values and the contact forces measured for the subject. The results of this study show that, with more degrees of freedom in the model, the musculo-tendon forces and the 3D joint reaction forces tend to increase but with some redistribution between the muscles. In addition, when taking into account passive joint moments, the 3D joint reaction forces tend to decrease during the stance phase and increase during the swing phase. Although further investigations are needed, a five-degree-of-freedom lower-limb musculo-skeletal model with some angle-dependent joint coupling and stiffness seems to provide satisfactory musculo-tendon forces and 3D joint reaction forces.     

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 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.     

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.     

Influence of the varus-valgus instability on the contact of the femoro-tibial joint

The varus-valgus instability of the knee joint is mainly due to ruptured or lax collateral ligaments. The purpose of this investigation was to study the influence of the varus-valgus instability on the contact pressures of the femoro-tibial joint. Six fresh knee specimens of human cadavers were tested to measure the contact pressure on the tibia plateau of the knee joint at varus or valgus alignment under various loads and at full extension. Pressure transducers and Bourdon tube pressure gauges were used simultaneously for recording pressure. At neutral alignment of the knee with the menisci intact, the peak pressure increased linearly with forces up to 4 MPa. With increasing varus alignment, the peak contact pressure on the medial plateau not covered by the menisci increased up to a maximum of 7.3 MPa at 5 degrees varus, and at 5 degrees valgus, the peak pressure on the lateral plateau was 7.8 MPa. After total meniscectomy, the contact pressure increased up to a maximum of 7.4 MPa at a force of 2700 N. With increasing varus alignment, the contact pressure on the medial plateau increased to 8.1 MPa at 5 degrees varus and on the lateral plateau 9.2 MPa at 5 degrees valgus.     

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 two-degree-of-freedom motor-powered gait orthosis for spinal cord injury patients

A number of orthoses have been developed to restore stance and walking in paraplegic subjects. Compliance, however, has been limited, mainly owing to walking effort. Use of the forces produced by actuators is an effective way to solve the problem of the considerable effort required for orthotic gait, namely high muscular effort and high energy expenditure. The purpose of the present study was to investigate the effects of assistance by external actuators on the orthotic gait of spinal cord injury (SCI) patients. Two kinds of linear actuator were developed by using direct current (d.c.) motors for assisting the knee and hip joint of a gait orthosis. They were mounted on the knee and hip joint of a commercial advanced reciprocating gait orthosis (ARGO), and a new two-degree-of-freedom externally powered gait orthosis was thus developed. The orthosis was assessed through inter-subject experiments on five male adult complete SCI patients. Owing to the short training period available for the assisted gait, simultaneous operation of both joint actuators was not conducted: either the knee actuation or the hip actuation was executed only. Thus, the knee actuator and the hip actuator were assessed with a T12 subject and with subjects for T5, T8, T11, and T12 respectively. The motions of the gaits, assisted by the linear actuators, were measured by a Vicon 370 system, and the general gait parameters and compensatory motions were evaluated. Results demonstrated that (a) all subjects could walk without falling, assisted either by the knee or the hip actuator; (b) both the knee and hip joint actuator increased the gait speed and the step length; (c) the knee flexion produced by the orthosis improved the dynamic cosmesis of walking; and (d) lateral compensatory motions as well as vertical ones tended to decrease when the hip joint was assisted, which could contribute to a reduction in walking effort.     

A general axisymmetric contact mechanics model for layered surfaces, with particular reference to artificial hip joint replacements

A general axisymmetric contact mechanics model for layered surfaces is considered in this study, with particular reference to artificial hip joint replacements. The indenting surface, which represents the femoral head, was modelled as an elastic solid with or without coating, while the other contacting surface, which represents the acetabular cup, was modelled as a two-layered solid. It is shown that this model is applicable to current total hip joint prostheses employing ultra-high molecular weight polyethylene (UHMWPE) acetabular cups against metallic, metallic with coating or ceramic femoral heads as well as metal-on-metal combinations. The effect of cement is also investigated for these prostheses using this model. The use of a metallic bearing surface bonded to a UHMWPE substrate for acetabular cups is particularly examined for metal-on-metal hip joint replacements. Both the contact radius and the contact pressure distribution are predicted for examples of these total hip joint replacements, under typical conditions. Application of contact mechanics to the design of artificial hip joint replacements employing various material combinations is discussed.     

Intersegmental dynamics of the lower limb in vertical jumps

The purpose of this study was to investigate changes in intersegmental dynamics of the lower limb at the instant of push-off in vertical jumps. Using a mathematical model including dynamic equations, the net joint moment (NET) was decomposed into a muscle moment (MUS), gravitational moment, and interaction moment (INT) in terms of joint acceleration and velocity. Ten subjects performed two submaximal jumps(60% and 80% of maximal height) and one maximal jump. Results showed that the hip and ankle joints mainly utilized MUS to generate NET at the push-off instant, while the knee joint primarily used INT at the instant of push-off. The hip MUS increased with increasing jump height because the deep countermovement (larger flexion angle of hip and knee joint at the push-off instant) in maximal jump was a disadvantage from intersegmental dynamics, but may be neurophysiologically advantageous.     

Non-destructive biomechanical analysis to evaluate surgical planning for hip joint diseases

The hip joint diseases have various kinds of origination, and they have multifarious forms according to the originations. One of the major concerns to plan the surgical operation for the hip diseases is the alternation of biomechanical environment, such as joint force and contact pressure. In this study, we analyzed the biomechanical effects of surgical techniques of the hip joint diseases by finite element analysis. We developed the finite element models of the pre-operative and post-operative hip joints for four children patients who have hip joint disease with abnormal joint anatomy. The models consist of two bones (pelvis and femur) reconstructed from CT images, and the articular cartilages on acetabulum and femoral head. Bones and cartilages were assumed having linear elastic material properties. The resultant joint force and the abductor force were calculated from 3-D static equilibrium in one-leg standing position. The calculated joint force was applied on the pelvis, the inferior plate of femur was fixed in all directions, and the medial edge of pelvis was constrained in vertical direction. Mechanical values such as contact force, pressure, and contact area on the hip joint were measured. The results of the finite element analysis were similar with those clinically estimated. The present non-destructive biomechanical evaluation method could be clinically useful for the optimal planning and selecting of surgical method by the rearrangement of contact pressure in the hip joint.     

Estimation of muscle and joint forces in the human lower extremity during rising motion from a seated position

Biomechanical models are often employed to predict in vivo muscle or joint forces in the human body because measuring these forces is difficult. Even though the rising motion from a seated position frequently occurs in daily life and the force acting on the knee joints during the motion is important for aged or infirmed people, limited studies related to the motion have been conducted. This study aims to propose a numerical procedure to estimate the muscle and joint forces in the human lower extremity during rising motion from a seated position. The human lower extremity is idealized as a multibody system in which the Hill-type muscle force model is employed. The multibody system consists of four bodies (shank, thigh, pelvis, and upper body), three revolute joints, and ten forces. The motion of the multibody system is assumed constrained to the sagittal plane, and the muscles in the human lower extremity are idealized by nine action/reaction forces. The nine forces are determined by minimizing the metabolic energy, which is consumed during the rising motion. Metabolic energy consists of the energy consumed by heat generation of muscles and the mechanical work done by muscles. For the accuracy validation of the proposed estimation method, numerical results obtained with the proposed method are compared with existing experimental results.     

Knee joint forces: prediction, measurement, and significance

Knee forces are highly significant in osteoarthritis and in the survival and function of knee arthroplasty. A large number of studies have attempted to estimate forces around the knee during various activities. Several approaches have been used to relate knee kinematics and external forces to internal joint contact forces, the most popular being inverse dynamics, forward dynamics, and static body analyses. Knee forces have also been measured in vivo after knee arthroplasty, which serves as valuable validation of computational predictions. This review summarizes the results of published studies that measured knee forces for various activities. The efficacy of various methods to alter knee force distribution, such as gait modification, orthotics, walking aids, and custom treadmills are analyzed. Current gaps in our knowledge are identified and directions for future research in this area are outlined.     

Glenohumeral contact forces

Glenohumeral contact forces have only been calculated previously either for simple abduction or for athletic activities. The objective of this study was to determine the glenohumeral contact forces for tasks which are demanding of the shoulder but which would commonly be performed by older people. The functional tasks chosen were using the arms to stand up from and sit down into a chair, walking with a cane, lifting a 5 kg box to shoulder height with both hands, and lifting a 10 kg suitcase. The trunk angles, arm angles and hand loads of six healthy subjects, average age 55 years, were recorded. This information was input into a biomechanical computer model which optimized the muscle force distribution by minimizing the sum of squared muscle stresses subject to constraints on the maximum muscle forces and maintaining the direction of the resultant force within the glenoid fossa. Average contact forces ranged from 1.3 to 2.4 times body weight (930-1720 N), the highest force being for lifting a suitcase. This latter value would be even higher if lifting either a greater load or to a greater height. Thus, contact forces at the shoulder should not be underestimated. This study provides functionally relevant contact forces which can be used for mechanical testing or finite element modelling of shoulder prostheses.     

Assistance of the elbow flexion motion on the active elbow orthosis using muscular stiffness force feedback

An elbow orthosis with pneumatic artificial muscles has been developed to assist and enhance upper limbs movements and has been examined for effectiveness. The effectiveness of the elbow orthosis was examined by comparing muscular activities during alternate dumbbell curl motion wearing and without wearing the orthosis. The subjects participating in the experiment were young adults in their twenties. The subjects were instructed to perform a dumbbell curl motion in a sitting position with and without wearing an orthosis in turn, and a dynamometer was used to measure elbow joint torque in isokinetic mode. The measurements were done with four various dumbbell loads: 0, 1, 3, and 5 kg. We examined the effectiveness of the elbow orthosis in two control methods. First, the orthosis was pneumatically actuated and controlled in the passive control mode. Then, it was controlled in the active control mode using the muscular stiffness force of the muscle that is measured from a force sensor through a cDAQ-9172 board. For the analysis of muscular power, the muscular activities of the subject were measured during alternate dumbbell curl motion using MP150 (BIOPAC Systems, Inc.). The muscles of interest were biceps brachii muscle, triceps brachii muscle, brachioradialis muscle, and flexor carpi ulnaris muscle in the upper limbs of the right side. The elbow joint torque was measured during elbow flexion motion using a dynamometer at 60° per second for isokinetic strength. The experimental result showed that the muscular activities wearing the elbow orthosis were reduced and elbow joint torque wearing the elbow orthosis was higher because of the assist of the orthosis. As a result of this experiment, the effectiveness of the developed elbow orthosis was confirmed and the level of assistance was quantified. With this, we confirmed the effectiveness of the developed elbow orthosis.     

Muscle forces analysis in the shoulder mechanism during wheelchair propulsion

This study combines an ergometric wheelchair, a six-camera video motion capture system and a prototype computer graphics based musculoskeletal model (CGMM) to predict shoulder joint loading, muscle contraction force per muscle and the sequence of muscular actions during wheelchair propulsion, and also to provide an animated computer graphics model of the relative interactions. Five healthy male subjects with no history of upper extremity injury participated. A conventional manual wheelchair was equipped with a six-component load cell to collect three-dimensional forces and moments experienced by the wheel, allowing real-time measurement of hand/rim force applied by subjects during normal wheelchair operation. An ExpertVision six-camera video motion capture system collected trajectory data of markers attached on anatomical positions. The CGMM was used to simulate and animate muscle action by using an optimization technique combining observed muscular motions with physiological constraints to estimate muscle contraction forces during wheelchair propulsion. The CGMM provides results that satisfactorily match the predictions of previous work, disregarding minor differences which presumably result from differing experimental conditions, measurement technologies and subjects. Specifically, the CGMM shows that the supraspinatus, infraspinatus, anterior deltoid, pectoralis major and biceps long head are the prime movers during the propulsion phase. The middle and posterior deltoid and supraspinatus muscles are responsible for arm return during the recovery phase. CGMM modelling shows that the rotator cuff and pectoralis major play an important role during wheelchair propulsion, confirming the known risk of injury for these muscles during wheelchair propulsion. The CGMM successfully transforms six-camera video motion capture data into a technically useful and visually interesting animated video model of the shoulder musculoskeletal system. The CGMM further yields accurate estimates of muscular forces during motion, indicating that this prototype modelling and analysis technique will aid in study, analysis and therapy of the mechanics and underlying pathomechanics involved in various musculoskeletal overuse syndromes.     

穿戴式机器人髋膝关节协调自律控制方法

针对步行辅助中人机交互柔顺性和髋膝关节协调自律控制的问题,提出一种新型多关节协调自律控制方法,该方法基于中枢模式发生器（Central pattern generator,CPG）网络,同时具备单关节人机交流和多关节协调运动特性。建立左右侧髋、膝关节4个CPG单元及其对外交流机制,改善了各关节处的人机交互柔顺性;建立左右髋关节、左右膝关节CPG单元间的对称抑制连接及同侧髋膝关节CPG单元间的非对称内部抑制连接,获得双侧髋膝关节间的逆相位及同侧髋膝关节的自然相位,实现了人机交互环境下稳定的步行辅助。穿戴式步行试验证明了该方法对生成步行中自然髋、膝关节协调运动的有效性。最后,采用肌肉活动强度、步长和步行速度三个指标,运用对比试验的方法讨论和分析了步行辅助效果。