Kinematic models of lower limb joints for musculo-skeletal modelling and optimization in gait analysis

Kinematic models of lower limb joints have several potential applications in musculoskeletal modelling of the locomotion apparatus, including the reproduction of the natural joint motion. These models have recently revealed their value also for in vivo motion analysis experiments, where the soft-tissue artefact is a critical known problem. This arises at the interface between the skin markers and the underlying bone, and can be reduced by defining multibody kinematic models of the lower limb and by running optimization processes aimed at obtaining estimates of position and orientation of relevant bones. With respect to standard methods based on the separate optimization of each single body segment, this technique makes it also possible to respect joint kinematic constraints. Whereas the hip joint is traditionally assumed as a 3 degrees of freedom ball and socket articulation, many previous studies have proposed a number of different kinematic models for the knee and ankle joints. Some of these are rigid, while others have compliant elements. Some models have clear anatomical correspondences and include real joint constraints; other models are more kinematically oriented, these being mainly aimed at reproducing joint kinematics. This paper provides a critical review of the kinematic models reported in literature for the major lower limb joints and used for the reduction of soft-tissue artefact. Advantages and disadvantages of these models are discussed, considering their anatomical significance, accuracy of predictions, computational costs, feasibility of personalization, and other features. Their use in the optimization process is also addressed, both in normal and pathological subjects.     

Simulation of quadrupedal locomotion using a rigid body model

Locomotion of the horse is simulated using a mathematical model based on rigid body dynamics. A general method to generate the equations of motion for a two-dimensional rigid body model with an arbitrary number of hinge joints is presented and a numerical solution method, restricted to tree-structured models, is described. Joint movements originating from muscular forces or moments are simulated, but the method also allows that parts of the model follow strictly the pattern of kinematic data. Moment-generators with first-order linear feedback were used as a rotational muscle-equivalent. Ground-hoof interaction forces are approximated by a viscoelastic model and pseudo-Coulomb friction in vertical and horizontal directions respectively. Results of model simulations are compared to experimentally recorded data. Subsequently, adjustments are made to improve the agreement between simulation and experimental results.     

Virtual power based algorithm for decoupling large motions from infinitesimal strains: application to shoulder joint biomechanics

New trends of numerical models of human joints require more and more computation of both large amplitude joint motions and fine bone stress distribution. Together, these problems are difficult to solve and very CPU time consuming. The goal of this study is to develop a new method to diminish the calculation time for this kind of problems which include calculation of large amplitude motions and infinitesimal strains. Based on the Principle of Virtual Power, the present method decouples the problem into two parts. First, rigid body motion is calculated. The bone micro-deformations are then calculated in a second part by using the results of rigid body motions as boundary conditions. A finite element model of the shoulder was used to test this decoupling technique. The model was designed to determine the influence of humeral head shape on stress distribution in the scapula for different physiological motions of the joint. Two versions of the model were developed: a first version completely deformable and a second version based on the developed decoupling method. It was shown that biomechanical variables, as mean pressure and von Mises stress, calculated with the two versions were sensibly the same. On the other hand, CPU time needed for calculating with the new decoupled technique was more than 6 times less than with the completely deformable model.     

Muscle mass in musculoskeletal models

Most current models of musculoskeletal dynamics lump a muscle's mass with its body segment, and then simulate the dynamics of these body segments connected by joints. As shown here, this popular approach leads to errors in the system's inertia matrix and hence in all aspects of the dynamics. Two simplified mathematical models were created to capture the relevant features of monoarticular and biarticular muscles, and the errors were analyzed. The models were also applied to two physiological examples: the triceps surae muscles that plantar flex the human ankle and the biceps femoris posterior muscle of the rat hind limb. The analysis of errors due to lumping showed that these errors can be large. Although the errors can be reduced in some postures, they cannot be easily eliminated in models that use segment lumping. Some options for addressing these errors are discussed.     

Virtual Power Based Algorithm for Decoupling Large Motions from Infinitesimal Strains: Application to Shoulder Joint Biomechanics

New trends of numerical models of human joints require more and more computation of both large amplitude joint motions and fine bone stress distribution. Together, these problems are difficult to solve and very CPU time consuming. The goal of this study is to develop a new method to diminish the calculation time for this kind of problems which include calculation of large amplitude motions and infinitesimal strains. Based on the Principle of Virtual Power, the present method decouples the problem into two parts. First, rigid body motion is calculated. The bone micro-deformations are then calculated in a second part by using the results of rigid body motions as boundary conditions. A finite element model of the shoulder was used to test this decoupling technique. The model was designed to determine the influence of humeral head shape on stress distribution in the scapula for different physiological motions of the joint. Two versions of the model were developed: a first version completely deformable and a second version based on the developed decoupling method. It was shown that biomechanical variables, as mean pressure and von Mises stress, calculated with the two versions were sensibly the same. On the other hand, CPU time needed for calculating with the new decoupled technique was more than 6 times less than with the completely deformable model.     

Bone position estimation from skin marker co-ordinates using global optimisation with joint constraints

Widespread use of gait or motion analysis in the diagnosis of patients with locomotor pathology and the subsequent planning and assessment of treatment has been limited because of its reliability, particularly in evaluating frontal and transverse plane components. This is because spatial reconstruction of the musculoskeletal system and calculation of its kinematics and kinetics via a skin marker-based multi-link model are subject to marker skin movement artefacts. Traditional methods treat each body segment separately without imposing joint constraints, resulting in apparent dislocations at joints predominantly because of skin movement artefacts. An optimisation method for the determination of the positions and orientations of multi-link musculoskeletal models from marker co-ordinates is presented. It is based on the minimisation of the weighted sum of squared distances between measured and model-determined marker positions. The model imposes joint constraints. Numerical experiments were performed to show that the new method is capable of eliminating joint dislocations and giving more accurate model position and orientation estimations. It is suggested that, with joint constraints and a global error compensation scheme, the effects of measurement errors on the reconstruction of the musculoskeletal system and subsequent mechanical analyses can be reduced globally. The proposed method minimises errors in axial rotation and ab/adduction at the joints and may extend the applicability of gait analysis to clinical problems.     

Quantitative Method for Biomechanical Evaluation of Bedding Comfortableness

Comfortable bedding is usually designed subjectively because of the difficulty in performing a quantitative evaluation. This paper proposes a quantitative evaluation method of comfortableness of beddings. The bedding shape determining how comfortable an individual may feel in using it depends on the body shape and normal posture of individuals. The internal physical load is expected to relate to the comfortableness of bedding. However, only a few quantitative discussions exist on the relation between the comfortableness of bedding and physical load. This study proposes a new evaluation method of physical load in a relaxed posture. The strain energy of muscles and joints was used as an indicator of physical load. To estimate physical load, a neutral body position was simulated from a natural standing posture and was used as a reference posture with the neutral condition of muscle lengths. By considering individual differences, multiple models of neutral body position were provided. We simulated individual differences of a comfortable pillow height using the proposed models. Physical load in a relaxed posture was varied according to the models. Calculated results show that physical load becomes small when a pillow is comfortable. For both subjective pillow comfortableness and smallness of physical load, there is a similar tendency that the low pillow with the small height difference between head and neck is preferable if the concave depth of back shape of head and neck is small. Moreover, the results show that muscles and joints equally affect the comfortableness of designed pillow. This implies that less total energy required for maintaining the posture contributes to pillow comfortableness.     

Predicting the influence of hip and lumbar flexibility on lifting motions using optimal control

Computational models of the human body coupled with optimization can be used to predict the influence of variables that cannot be experimentally manipulated. Here, we present a study that predicts the motion of the human body while lifting a box, as a function of flexibility of the hip and lumbar joints in the sagittal plane. We modeled the human body in the sagittal plane with joints actuated by pairs of agonist-antagonist muscle torque generators, and a passive hamstring muscle. The characteristics of a stiff, average and flexible person were represented by co-varying the lumbar range-of-motion, lumbar passive extensor-torque and the hamstring passive muscle-force. We used optimal control to solve for motions that simulated lifting a 10 kg box from a 0.3 m height. The solution minimized the total sum of the normalized squared active and passive muscle torques and the normalized passive hamstring muscle forces, over the duration of the motion. The predicted motion of the average lifter agreed well with experimental data in the literature. The change in model flexibility affected the predicted joint angles, with the stiffer models flexing more at the hip and knee, and less at the lumbar joint, to complete the lift. Stiffer models produced similar passive lumbar torque and higher hamstring muscle force components than the more flexible models. The variation between the motion characteristics of the models suggest that flexibility may play an important role in determining lifting technique.     

Locomotory mechanisms in Antarctic pycnogonids

Patterns of walking, modes of joint movement, and individual limb diversity were analysed with the aid of ciné film of several living Antarctic pycnogonids, including the 8-legged Colossendeis australis, C. angusta, Pallenopsis patagonica , and Nymphon sp., the 10-legged Decolopoda australis , and the 12-legged Dodecolopoda mawsoni. Appendage musculature of several of these species and also of the 10-legged Pentapycnon charcoti and Pentanymphon antarcticurn was dissected. At least two distinct morphotypes were identified: a short-legged, crawling variety ( P. charcoti ); and the more typical long-legged, large bodied, walking forms. No gross differences in musculature of joints were noted in the species examined. All joints are, at least superficially, hinge joints. The coxa-body joint is largely immobile, the coxa 1-coxa 2 joint alone exhibits promotion-remotion and all other joints are flexion-extension joints. The 8-legged forms move in an imprecise manner, there being irregularity of leg raising and lowering and where legs touch down in relation to the body and to other legs. The 10- and 12-legged forms exhibit more precise patterns of metachronal leg movements. Although legs move in a basic promotion-remotion, extension-flexion mode, there is a certain degree of twisting of a leg as it is picked up, brought forward, and set down; models indicating how such joint movement occurs were constructed. The possibility that hydrostatic pressure is employed in extension is considered and is found to be remote. Lateral placement of legs, orientated in almost all directions in the horizontal plane of the trunk, achieves a versatility of movement similar to that in crabs. Comments on pycnogonid taxonomic affinities are offered.     

Biomimetic Composite Structural T-joints

Biological structural fixed joints exhibit unique attributes,including highly optimized fiber paths which minimize stress concentrations.In addition,since the joints consist of continuous,uncut fiber architectures,the joints enable the organism to transport information and chemicals from one part of the body to the other.To the contrary,sections of man-made composite material structures are often joined using bolted or bonded joints,which involve low strength and high stress concentrations.These methods are also expensive to achieve.Additional functions such as fluid transport,electrical signal delivery,and thermal conductivity across the joints typically require parasitic tubes,wires,and attachment clips.By using the biomimetic methods,we seek to overcome the limitations which are present in the conventional methods. In the present work,biomimetic co-cured composite sandwich T-joints were constructed using unidirectional glass fiber,epoxy resin,and structural foam.The joints were fabricated using the wet lay-up vacuum bag resin infusion method.Foam sandwich T-joints with multiple continuous fiber architectures and sandwich foam thickness were prepared.The designs were tested in quasi-static bending using a mechanical load frame.The significantweight savings using the biomimetic approaches is discussed,as well as a comparison of failure modes versus architecture is described.     

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.     

Interdependency of the maximum range of flexion–extension of hand metacarpophalangeal joints

Mobility of the fingers metacarpophalangeal (MCP) joints depends on the posture of the adjacent ones. Current Biomechanical hand models consider fixed ranges of movement at joints, regardless of the posture, thus allowing for non-realistic postures, generating wrong results in reach studies and forward dynamic analyses. This study provides data for more realistic hand models. The maximum voluntary extension (MVE) and flexion (MVF) of different combinations of MCP joints were measured covering their range of motion. Dependency of the MVF and MVE on the posture of the adjacent MCP joints was confirmed and mathematical models obtained through regression analyses (RMSE 7.7°).     

Use of roentgen-television film for the analysis of physical exercises]

Biochemical investigation of movements of man is based on precise registration of movements of body links in space and time. The popular method of filming is almost unsuitable for studying exact movements in small joints, rotation movements and movements performed simultaneously in several joints. The use of rentgen-television filming of movement in the joints broadens the possibilities of biomechanical investigations of movements of man.     

A Lagrange-based generalised formulation for the equations of motion of simple walking models

Simple 2D models of walking often approximate the human body to multi-link dynamic systems, where body segments are represented by rigid links connected by frictionless hinge joints. Performing forward dynamics on the equations of motion (EOM) of these systems can be used to simulate their movement. However, deriving these equations can be time consuming. Using Lagrangian mechanics, a generalised formulation for the EOM of n-link open-loop chains is derived. This can be used for single support walking models. This has an advantage over Newton–Euler mechanics in that it is independent of coordinate system and prior knowledge of the ground reaction force (GRF) is not required. Alternative strategies, such as optimisation algorithms, can be used to estimate joint activation and simulate motion. The application of Lagrange multipliers, to enforce motion constraints, is used to adapt this general formulation for application to closed-loop chains. This can be used for double support walking models. Finally, inverse dynamics are used to calculate the GRF for these general n-link chains. The necessary constraint forces to maintain a closed-loop chain, calculated from the Lagrange multipliers, are one solution to the indeterminate problem of GRF distribution in double support models. An example of this method’s application is given, whereby an optimiser estimates the joint moments by tracking kinematic data.     

The simulation of aerial movement--II. A mathematical inertia model of the human body

A mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described. The human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements. A 'stadium' solid is introduced for modelling the torso segments using perimeter and width measurements. This procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used. Inertia parameter values may be obtained for body models of up to 20 segments. Errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes.     

Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa

I used a simple mathematical model of the inverse dynamics of locomotion to estimate the minimum muscle masses required to maintain quasi-static equilibrium about the four main limb joints at mid-stance of fast running. Models of 10 extant taxa (a human, a kangaroo, two lizards, an alligator, and five birds) were analyzed in various bipedal poses to examine how anatomy, size, limb orientation, and other model parameters influence running ability. I examined how the muscle masses required for fast running compare to the muscle masses that are actually able to exert moments about the hip, knee, ankle, and toe joints, to see how support ability varies across the limb. I discuss the assumptions and limitations of the models, using sensitivity analysis to see how widely the results differed with feasible parameter input values. Even with a wide range of input values, the models validated the analysis procedure. Animals that are known to run bipedally were calculated as able to preserve quasi-static equilibrium about their hindlimb joints at mid-stance, whereas non-bipedal runners (iguanas and alligators) were recognized as having too little muscle mass to run quickly in bipedal poses. Thus, this modeling approach should be reliable for reconstructing running ability in extinct bipeds such as nonavian dinosaurs. The models also elucidated how key features are important for bipedal running capacity, such as limb orientation, muscle moment arms, muscle fascicle lengths, and body size. None of the animals modeled had extensor muscle masses acting about any one joint that were 7% or more of their body mass, which provides a reasonable limit for how much muscle mass is normally apportioned within a limb to act about a particular joint. The models consistently showed that a key biomechanical limit on running ability is the capacity of ankle extensors to generate sufficiently large joint moments. Additionally, the analysis reveals how large ratite birds remain excellent runners despite their larger size; they have apomorphically large extensor muscles with relatively high effective mechanical advantage. Finally, I reconstructed the evolution of running ability in the clade Reptilia, showing that the ancestors of extant birds likely were quite capable runners, even though they had already reduced key hip extensors such as M. caudofemoralis longus.     

An improved inverse dynamics formulation for estimation of external and internal loads during human sagittal plane movements

Planar musculoskeletal models are common in the inverse dynamics analysis of human movements such as walking, running and jumping. The continued interest in such models is justified by their simplicity and computational efficiency. Related to a human planar model, a unified formulation for both the flying and support phases of the sagittal plane movements is developed. The actuation involves muscle forces in the lower limbs and the resultant muscle torques in the other body joints. The dynamic equations, introduced in absolute coordinates of the segments, are converted into useful compact forms using the projective technique. The solution to a determinate inverse dynamics problem allows for the explicit determination of the external reactions (presumed to vanish during the flying phases) and the resultant muscle torques in all the model joints. The indeterminate inverse dynamics problem is then focused on the assessment of muscle forces and joint reaction forces selectively in the supporting lower limb. Numerical results of the inverse dynamics simulation of sample sagittal plane movements are reported to illustrate the validity and effectiveness of the improved formulation.     

Regulation of biomechanical signals by NF-kappaB transcription factors in chondrocytes

Physical therapies and exercise are beneficial not only for physiological recovery in inflamed or injured joints, but also for promoting a homeostatic equilibrium in healthy joints. Human joints provide the pivot points and physiological hinges essential for ambulation and movement to the body, and it is this mobility that in return promotes the health of the joints. But how mobilization regulates the joint microenvironment at the molecular level has remained enigmatic for many years. Recent advances in joint biomechanics and molecular approaches have facilitated an enriched understanding of how joints operate. Consequently, the mechanisms active during joint inflammation that lead to arthritic conditions, both in vivo in animal models, and in vitro at cell and tissue levels, have become increasingly detailed and defined. These efforts have produced mounting evidences supporting the premise that biomechanical signals play a fundamental role in both the etiopathogenesis of arthritic diseases and in the physiological restoration of joints. This report aims to summarize current peer-reviewed literature and available experimental data to explain how the signals generated by mechanical forces/joint mobilization generate beneficial effects on inflamed articular cartilage, and to propose the basis for using appropriate physical therapies for the optimal benefit to the patient suffering from joint associated injuries.