Kinematics of the human ankle complex in passive flexion; a single degree of freedom system

The restoration of original range and pattern of motion is the primary goal of joint replacement and ligament reconstruction. The objective of the present work is to investigate whether or not a preferred path of joint motion at the intact human ankle complex is exhibited during passive flexion. A rig was built to move the ankle complex through its range of flexion while applying only the minimum necessary load to drive ankle flexion. Joint motion was constrained only by the articular surfaces and the ligaments. The movements of the calcaneus, talus and fibula relative to the stationary tibia in seven cadaveric specimens were tracked with a stereophotogrammetric system. It was shown that the calcaneus follows a unique path of unresisted coupled motion relative to the tibia and that most of the motion occurred at the ankle, with little motion at the subtalar level. The calcaneofibular and the tibiocalcaneal ligaments showed near-isometric pattern of rotations. All specimens showed motion of the axis of rotation relative to the bones. Deviations from the unique path due to the application of load involved mostly subtalar motion and were resisted. The ankle complex exhibits one degree of unresisted freedom, the ankle behaving as a single degree of freedom mechanism and the subtalar as a flexible structure. We deduced that the calcaneofibular and tibiocalcaneal ligaments together with the articular surfaces guide ankle passive motion, other ligaments limit but do not guide motion.     

Biomechanical properties of human lumbar spine ligaments.

Biomechanical properties of the six major lumbar spine ligaments were determined from 38 fresh human cadaveric subjects for direct incorporation into mathematical and finite element models. Anterior and posterior longitudinal ligaments, joint capsules, ligamentum flavum, interspinous, and supraspinous ligaments were evaluated. Using the results from in situ isolation tests, individual force-deflection responses from 132 samples were transformed with a normalization procedure into mean force-deflection properties to describe the nonlinear characteristics. Ligament responses based on the mechanical characteristics as well as anatomical considerations, were grouped into T12-L2, L2-L4, and L4-S1 levels maintaining individuality and nonlinearity. A total of 18 data curves are presented. Geometrical measurements of original length and cross-sectional area for these six major ligaments were determined using cryomicrotomy techniques. Derived parameters including failure stress and strain were computed using the strength and geometry information. These properties for the lumbar spinal ligaments which are based on identical definitions used in mechanical testing and geometrical assay will permit more realistic and consistent inputs for analytical models.     

A geometric model of the human ankle joint.

A two-dimensional four-bar linkage model of the ankle joint is formulated to describe dorsi/plantarflexion in unloaded conditions as observed in passive tests on ankle complex specimens. The experiments demonstrated that the human ankle joint complex behaves as a single-degree-of-freedom system during passive motion, with a moving axis of rotation. The bulk of the movement occurred at the level of the ankle. Fibres within the calcaneofibular and tibiocalcaneal ligaments remained approximately isometric. The experiments showed that passive kinematics of the ankle complex is governed only by the articular surfaces and the ligaments. It was deduced that the ankle is a single-degree-of-freedom mechanism where mobility is allowed by the sliding of the articular surfaces upon each other and the isometric rotation of two ligaments about their origins and insertions, without tissue deformation. The linkage model is formed by the tibia/fibula and talus/calcaneus bone segments and by the calcaneofibular and tibiocalcaneal ligament segments. The model predicts the path of calcaneus motion, ligament orientations, instantaneous axis of rotation, and conjugate talus surface profile as observed in the experiments. Many features of ankle kinematics such as rolling and multiaxial rotation are elucidated. The geometrical model is a necessary preliminary step to the study of ankle joint stability in response to applied loads and can be used to predict the effects of changes to the original geometry of the intact joint. Careful reconstruction of the original geometry of the ligaments is necessary after injury or during total ankle replacement.     

A new one-DOF fully parallel mechanism for modelling passive motion at the human tibiotalar joint

Knowledge on how ligaments and articular surfaces guide passive motion at the human ankle joint complex is fundamental for the design of relevant surgical treatments. The paper presents a possible improvement of this knowledge by a new kinematic model of the tibiotalar articulation. Passive motion, i.e. in virtually unloaded conditions, was captured in vitro in four lower leg specimens by means of a surgical navigation system with cluster of active markers attached to the tibia and talus. The anatomical geometry of the passive structures, i.e. articular surfaces and attachment areas of the ligaments, were taken by digitisation with a pointer. An equivalent spatial mechanism for the passive motion simulation was defined by three sphere-to-sphere contact points and two rigid links. These contact points were identified at the lateral talo-fibular articulation and at the medial and lateral aspects of the articulation between tibial mortise and trochlea tali. The two rigid links were identified by the isometric fibres at the calcaneofibular and tibiocalcaneal ligaments. An optimisation algorithm was developed for the identification of the final geometrical parameters resulting from an iterative refining process, which targets best matching between model predictions and corresponding experimental measurements of the spatial motion. The specimen-specific equivalent spatial mechanisms replicated the original passive motion very well, with mean discrepancies in position smaller than 2.5 mm and in rotation smaller than 1°. The study demonstrates that the articular surfaces and the ligaments, acting together as a mechanism, control the passive kinematics of the ankle joint.     

A global verification study of a quasi-static knee model with multi-bundle ligaments

The ligaments of the knee consist of fiber bundles with variable orientations, lengths and mechanical properties. In concept, however, these structures were too often seen as homogeneous structures, which are either stretched or slack during knee motions. In previous studies, we proposed a new structural concept of the ligaments of the knee. In this concept, the ligaments were considered as multi-bundle structures, with nonuniform mechanical properties and zero force lengths. The purpose of the present study was to verify this new concept.

For this purpose, laxity characteristics of a human knee joint were compared as measured in an experiment and predicted in a model simulation study. In the experiment, the varus-valgus and anterior-posterior laxities of a knee-joint specimen containing the ligaments and the articular surfaces only, were determined. From this knee-joint, geometric and mechanical parameters were derived to supply the parameters for a three-dimensional quasi-static knee-joint model. These parameters included (i) the three-dimensional insertion points of bundles, defined in the four major knee ligaments, (ii) the mechanical properties of these ligament, as functions of their relative insertion orientations and (iii) three-dimensional representations of the articular surfaces. With this model the experiments were simulated. If knee-model predictions and experimental results agree, then the multi-bundle ligament models are validated, at least with respect to their functional role in anterior-posterior and varus-valgus loading of the joint.

The model described the laxity characteristics in AP-translation and VV-rotation of the cadaveric knee-joint specimen reasonably well. Both display the same patterns of laxity changes during knee flexion. Only if a varus moment of 8 N m was applied and if the tibia was posteriorly loaded, did the model predict a slightly higher laxity than that measured experimentally.

From the model-experiment comparisons it was concluded that the proposed structural representations of the ligaments and their mechanical property distributions seem to be valid for studying the anterior-posterior and varus-valgus laxity characteristics of the human knee-joint.     

Ligament fibre recruitment at the human ankle joint complex in passive flexion

Knowledge of ligament fibre recruitment at the human ankle joint complex is a fundamental prerequisite for analysing mobility and stability. Previous experimental and modelling studies have shown that ankle motion must be guided by fibres within the calcaneofibular and tibiocalcaneal ligaments, which remain approximately isometric during passive flexion. The purpose of this study was to identify these fibres.

Three below-knee amputated specimens were analysed during passive flexion with combined radiostereometry for bone pose estimation and 3D digitisation for ligament attachment area identification. A procedure based on singular value decomposition enabled matching bone pose with digitised data and therefore reconstructing position in space of ligament attachment areas in each joint position. Eleven ordered fibres, connecting corresponding points on origin and insertion curves, were modelled for each of the following ligaments: posterior talofibular, calcaneofibular, anterior talofibular, posterior tibiotalar, tibiocalcaneal, and anterior tibiotalar.

The measured changes in length for the ligament fibres revealed patterns of tightening and slackening. The most anterior fibre of the calcaneofibular and the medio-anterior fibre of the tibiocalcaneal ligament exhibited the most isometric behaviour, as well as the most posterior fibre of the anterior talofibular ligament. Fibres within the calcaneofibular ligament remain parallel in the transverse plane, while those within the tibiocalcaneal ligament become almost parallel in joint neutral position. For both these ligaments, fibres maintain their relative inclination in the sagittal plane throughout the passive flexion range.

The observed significant change in both shape and orientation of the ankle ligaments suggest that this knowledge is fundamental for future mechanical analysis of their response to external forces.     

Mobility of the subtalar joint in the intact ankle complex

A previous study by these authors showed that the calcaneus follows a unique path of unresisted coupled motion relative to the tibia during passive flexion and that most of this motion occurred at the ankle level. Subtalar motion in the intact ankle complex was observed only when perturbations from this path were induced by the application of force to the calcaneus. Relative motion of the bones of the ankle complex was tracked by stereophotogrammetry in seven specimens. Anatomical landmarks, reference frames and joint angles were defined by standard techniques. Sequential moments were applied to the calcaneus about the long axis of the tibia. Measured movements at subtalar level demonstrated plantarflexion coupled to supination and internal rotation (inversion) and dorsiflexion coupled to pronation and external rotation (eversion). These movements were resisted and were fully recovered when the external load was removed. Subtalar motion diminished as the ankle approached maximal dorsi- and plantarflexion. Two clearly distinguished mean axes of rotation were observed for inversion and eversion runs. The axes of inversion and eversion of the subtalar complex changed orientation along a preferred and repeatable path. The subtalar joint complex occupied only a single stable position in the unloaded state and with no range of unresisted motion. It is inferred that mobility was possible only by the stretching and lengthening of the ligaments and the indentation of the articular surfaces, requiring the application of loads. The subtalar joint complex behaves like a flexible structure.     

Biomechanical behaviour of ankle ligaments: constitutive formulation and numerical modelling

This study was aimed at the definition of a constitutive formulation of ankle ligaments and of a procedure for the constitutive parameters evaluation, for the biomechanical analysis by means of numerical models. To interpret the typical features of ligaments mechanical response, as anisotropic configuration, geometric non-linearity, non-linear elasticity and time-dependent behaviour, a specific fibre-reinforced visco-hyperelastic model is provided. The identification of constitutive parameters is performed by a stochastic–deterministic procedure that minimises the discrepancy between experimental and computational results. A preliminary evaluation of parameters is performed by analytical models in order to define reference values. Afterwards, solid models are developed to consider the complex histo-morphometric configuration of samples as a basis for the definition of numerical models. The results obtained are adopted for upgrading parameter values by comparison with specific mechanical tests. Assuming the new parameters set, the final numerical results are compared with the overall set of experimental data, to assess the reliability and efficacy of the analysis developed for the interpretation of the mechanical response of ankle ligaments.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Post-mortem timing of skeletal muscle biochemical and mechanical degradation

Fresh cadaveric human tissue is a valuable resource that is used to address important clinical questions. However, it is unknown how post-mortem time impacts skeletal muscle mechanical and biochemical properties. We simulated morgue conditions in rabbits and tested the passive mechanical properties of muscle bundles, and the degradation of myosin heavy chain, collagen, and titin at specific intervals up to 7 days post-mortem. While a great deal of inter-specimen variability was observed, it was independent of post-mortem time. Passive mechanics, myosin heavy chain, and collagen content were all unaffected while the titin protein degraded up to 80% over 7 days post-mortem. These data indicate that fresh cadaveric tissue may be used for passive mechanical testing and that certain biochemical properties are unchanged up to 7 days after death.     

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Mechanics of the ankle and subtalar joints revealed through a 3D quasi-static stress MRI technique

A technique to study the three-dimensional (3D) mechanical characteristics of the ankle and of the subtalar joints in vivo and in vitro is described. The technique uses an MR scanner compatible 3D positioning and loading linkage to load the hindfoot with precise loads while the foot is being scanned. 3D image processing algorithms are used to derive from the acquired MR images bone morphology, hindfoot architecture, and joint kinematics. The technique was employed to study these properties both in vitro and in vivo. The ankle and subtler joint motion and the changes in architecture produced in response to an inversion load and an anterior drawer load were evaluated. The technique was shown to provide reliable measures of bone morphology. The left-to-right variations in bone morphology were less than 5%. The left-to-right variations in unloaded hindfoot architecture parameters were less than 10%, and these properties were only slightly affected by inversion and anterior drawer loads. Inversion and anterior drawer loads produced motion both at the ankle and at the subtalar joint. In addition, high degree of coupling, primarily of internal rotation with inversion, was observed both at the ankle and at the subtalar joint. The in vitro motion produced in response to inversion and anterior drawer load was greater than the in vivo motion. Finally, external motion, measured directly across the ankle complex, produced in response to load was much greater than the bone movements measured through the 3D stress MRI technique indicating the significant effect of soft tissue and skin interference.     

In situ mechanical behavior of posterior spinal ligaments in the lumbar region. An in vitro study

The posterior ligaments: ligamentum flavum, articular, interspinous and supraspinous ligaments of twenty five fresh cadaveric intervertebral segments, from T11-T12 to L4-L5, extracted from fourteen spines were tested in tension. A progressive dissection method was used, that is, each segment was tested after first resecting the disk with the ligaments intact and a force-elongation curve obtained. Then one ligament was cut and the test repeated, and so on. The most restrictive ligament was found to be the ligamentum flavum followed by the articular, interspinous, and supraspinous ligaments.     

Three-dimensional dynamical capabilities of the human masticatory muscles

Many habitual human jaw movements are non-symmetrical. Generally, it is observed that when the lower incisors move to one side the contralateral condyle moves forwards onto the articular eminence, whereas the ipsilateral condyle stays in the mandibular fossa, moving slightly to the ipsilateral side. These jaw movements are the result of contractions of active masticatory muscles and guided by the temporomandibular joints, their ligaments and passive elastic properties of the muscles. It is not known whether the movements are primarily dependent on passive guidance, active muscle control or both. Therefore, the objective of this study was to analyse the interplay between these factors during non-symmetrical jaw movements. A six-degrees-of-freedom dynamical biomechanical model of the human masticatory system was used. The movements were not restricted to a priori defined joint axes. Jaw movement simulations were performed by unilateral activity of the muscles. The ligaments or the passive elastic properties of the muscles could be removed during these simulations. Laterodeviations conform to naturally observed ones could be generated by unilateral muscle contractions. The movement of the lower incisors was hardly affected by the absence of passive elastic muscle properties or temporomandibular ligaments. The latter, however, influenced the movement of the condyles. The movements could be understood by analysing the combination of forces and torques with respect to the centre of gravity of the lower jaw. In addition, the loading of the condyles appeared to be an important determinant for the movement. This analysis emphasizes that the movements of the jaw are primarily dependent on the orientation of the contributing muscles with respect to this centre of gravity and not on the temporomandibular ligaments or passive elastic muscle properties.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion-extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

Hindlimb unloading alters ligament healing.

We investigated the hypothesis that hindlimb unloading inhibits healing in fibrous connective tissue such as ligament. Male rats were assigned to 3- and 7-wk treatment groups with three subgroups each: sham control, ambulatory healing, and hindlimb-suspended healing. Ambulatory and suspended animals underwent surgical rupture of their medial collateral ligaments, whereas sham surgeries were performed on control animals. After 3 or 7 wk, mechanical and/or morphological properties were measured in ligament, muscle, and bone. During mechanical testing, most suspended ligaments failed in the scar region, indicating the greatest impairment was to ligament and not to bone-ligament insertion. Ligament testing revealed significant reductions in maximum force, ultimate stress, elastic modulus, and low-load properties in suspended animals. In addition, femoral mineral density, femoral strength, gastrocnemius mass, and tibialis anterior mass were significantly reduced. Microscopy revealed abnormal scar formation and cell distribution in suspended ligaments with extracellular matrix discontinuities and voids between misaligned, but well-formed, collagen fiber bundles. Hence, stress levels from ambulation appear unnecessary for formation of fiber bundles yet required for collagen to form structurally competent continuous fibers. Results support our hypothesis that hindlimb unloading impairs healing of fibrous connective tissue. In addition, this study provides compelling morphological evidence explaining the altered structure-function relationship in load-deprived healing connective tissue.     

Details of human middle ear morphology based on micro‐CT imaging of phosphotungstic acid stained samples

A multitude of morphological aspects of the human middle ear (ME) were studied qualitatively and/or quantitatively through the postprocessing and interpretation of micro‐CT (micro X‐ray computed tomography) data of six human temporal bones. The samples were scanned after phosphotungstic acid staining to enhance soft‐tissue contrast. The influence of this staining on ME ossicle configuration was shown to be insignificant. Through postprocessing, the image data were converted into surface models, after which the approaches diverged depending on the topics of interest. The studied topics were: the ME ligaments; morphometric and mechanical parameters of the ossicles relating to inertia and the ossicular lever arm ratio; the morphology of the distal incus; the contact surface areas of the tympanic membrane (TM) and of the stapes footplate; and the thickness of the TM, round window of the cochlea, ossicle joint spaces, and stapedial annular ligament. Some of the resulting insights are relevant in ongoing discussions concerning ME morphology and mechanical functions, while other results provide quantitative data to add to existing data. All findings are discussed in the light of other published data and many are relevant for the construction of mechanical finite element simulations of the ME. J. Morphol. 276:1025–1046, 2015. © 2015 Wiley Periodicals, Inc.