Position dependence of ankle joint dynamics--I. Passive mechanics

System identification techniques were used to examine the position dependence of passive ankle joint mechanics. The relaxed ankle was stochastically perturbed about different angles in the range of motion (ROM). The linear dynamic relation between ankle position and torque was identified and modelled as a second-order underdamped system, having inertial (I), viscous (B) and elastic (K) parameters. Mean joint torque changed as the ankle was rotated through the ROM; it was small at mid-range and became much larger toward either extreme. While I remained constant both B and K changed as a function of ankle angle. At the extremes of the ROM, K was much larger than previously assumed and the relation between stiffness and the passive torque generated when the ankle was placed at different mean positions was linear. These results show that large variations in joint mechanics are possible even in the absence of voluntary muscle contraction. Moreover, these changes appear to be related to the torque generated when passive joint structures are stretched.     

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.     

Active auditory mechanics in mosquitoes

In humans and other vertebrates, hearing is improved by active contractile properties of hair cells. Comparable active auditory mechanics is now demonstrated in insects. In mosquitoes, Johnston's organ transduces sound-induced vibrations of the antennal flagellum. A non-muscular 'motor' activity enhances the sensitivity and tuning of the flagellar mechanical response in physiologically intact animals. This motor is capable of driving the flagellum autonomously, amplifying sound-induced vibrations at specific frequencies and intensities. Motor-related electrical activity of Johnston's organ strongly suggests that mosquito hearing is improved by mechanoreceptor motility.     

Subject-specific axes of the ankle joint complex

The aim of this study was to use a two-axis ankle joint model and an optimisation process (van den Bogert et al., 1994) to calculate and compare the talocrural and subtalar hinge axes for non-weight-bearing ankle motion, weight-bearing ankle motion, and walking in normal, healthy adult subjects and to see which of the first two sets of axes better fit the walking data. Motion data for the foot and shank were collected on eight subjects whilst they performed the activities mentioned. After choosing the best marker sets for motion tracking, a two-hinge ankle joint model was fit to the motion data. Ankle joint ranges of motion were also calculated. It was found that the model fit the experimental data well, with non-weight-bearing motion achieving the best fit. Despite this, the calculated axis orientations were highly variable both between motion types and between subjects. No significant difference between the fit of the non-weight-bearing and weight-bearing models to the walking data was found, which implies that either set of functional axes is adequate for modeling walking; however, the subtalar deviation angle was significantly closer for the weight-bearing activity and walking than for the non-weight-bearing activity and walking, which suggests that it is marginally better to use the weight-bearing functional motions. The results lead to questions about the appropriateness of the two-hinge ankle model for use in applications in which the behaviour of the individual joints of the ankle complex, rather than simply the relative motion of the leg and foot, is important.     

Mathematical model of the human ankle joint

It has been suspected that the mechanical environment in which a particular joint functions has an effect on the initiation or progression of degenerative joint disease. The objective of this study is to define the mechanical environment of the ankle joint, specifically, the contact areas and pressure distributions, through the development and analysis of a simplified mathematical model. Since the state of pressure across articular surfaces during function is influenced by joint incongruity, cartilage thickness profile and the geometry of the opposing surfaces, these factors have been incorporated into the model formulation. Mathematical analysis of the model has resulted in pressure distributions in both the anterior-posterior and medial-lateral directions and contact area growth plots which correlate well with observed ankle contact patterns obtained from in vitro investigations. The significance of joint incongruity to these pressure distributions and to the relative immunity of the ankle joint to primary osteoarthritis is discussed.     

Mechanomyogram amplitude vs. isometric ankle plantarflexion torque of human medial gastrocnemius muscle at different ankle joint angles

The purpose of this study was to investigate the influence of changes in ankle joint angle on the mechanomyogram (MMG) amplitude of the human medial gastrocnemius (MG) muscle during voluntary isometric plantarflexion contractions. Ten healthy individuals were asked to perform voluntary isometric contractions at six different contraction intensities (from 10% to 100%) and at three different ankle joint angles (plantarflexion of 26°; plantarflexion of 10°; dorsiflexion of 3°). MMG signals were recorded from the surface over the MG muscle, using a 3-axis accelerometer. The relations between root mean square (RMS) MMG and isometric plantarflexion torque at different ankle joint angles were characterized to evaluate the effects of altered muscle mechanical properties on RMS MMG.We found that the relation between RMS MMG and plantarflexion torque is changed at different ankle joint angles: RMS MMG increases monotonically with increasing the plantarflexion torque but decreases as the ankle joint became dorsiflexed. Moreover, RMS MMG shows a negative correlation with muscle length, with passive torque, and with maximum voluntary torque, which were all changed significantly at different ankle joint angles.Our findings demonstrate the potential effects of changing muscle mechanical properties on muscle vibration amplitude. Future studies are required to explore the major sources of this muscle vibration from the perspective of muscle mechanics and muscle activation level, attributable to changes in the neural command.     

Kinematics of the ankle joint complex in snowboarding

Because snowboarders are known to injure their ankles more often than Alpine skiers, it has been postulated that stiffer snowboard boots would provide better protection to the ankle than current soft boots do. Snowboarders are also known to injure their front ankle more often than their back ankle, presumably because of the asymmetrical rotations of the ankles due to asymmetrical binding adjustement. To test these hypotheses, we measured the kinematics of the feet and legs of 5 snowboarders wearing soft boots and stiffer step-in boots during snowboarding maneuvers using an electromagnetic motion tracking system. The results were expressed in anatomically relevant rotations of the ankle joint complex, namely dorsi-/plantar flexion, eversion/inversion, and internal/external rotation. The measured ankle rotations show differences in the movement patterns of the front and back legs. Step-in boots were shown to allow less dorsiflexion, eversion, and external rotation than softer boots, possibly explaining why they are associated with a lower rate of fractures of the talus than soft boots.     

Active stiffness of the ankle in response to inertial and elastic loads.

Effective stiffness of the musculoskeletal system was examined as a function of the characteristics of an external load. Thirteen healthy subjects provided active contraction of the ankle plantarflexion musculature in a neutral ankle posture to support an external load. Musculoskeletal stiffness was computed from kinetic data recorded in response to dorsiflexion/plantarflexion perturbations. Ankle dynamics were recorded while supporting external loads of 19 and 38 kg with and without antagonistic co-contraction. External loads were applied using pure gravitational mass. In separate trials external loads were applied from stretch of steel springs in parallel with the plantarflexion musculature that also provided added parallel stiffness to the system. Adding external stiffness of 4.9 and 8.1 kN/m surprisingly failed to significantly change the stiffness of the ankle-plus-spring system. This suggests contributions from intrinsic muscle stiffness and reflex stiffness declined in response to added external stiffness. This could not be explained by load magnitudes, ankle postures, or co-activation as these were similar between the inertial and elastic loading conditions. However, non-linear parametric analyses suggest mean intrinsic stiffness of 35.5 kN/m and reflex gain of 11.6 kN/m with a constant reflex delay of 70 ms accurately described the empirical results. The phase response between the mechanical dynamics of the musculoskeletal system and delayed neuromotor feedback combine to provide robust control of system behavior.     

Effects of joint angle and age on ankle dorsi- and plantar-flexor strength.

This study aimed at examining the effects of joint angle and age on the maximal voluntary contraction (MVC) torque, for the agonist and antagonist muscle groups around the ankle, i.e., the dorsi- and plantar-flexors. To this aim, neural and muscular factors were investigated in two groups of healthy men: 11 young (mean age, 24 years) and 18 older (mean age, 78 years). Plantar-flexion (PF) and dorsiflexion (DF) isometric MVC torques were measured in three different ankle joint angles and surface electromyographic activities of the triceps surae and of the tibialis anterior muscles were recorded. The main findings were that the DF-to-PF MVC torque ratio varied with joint angle and age, indicating that aging affected at different rates the two muscle groups: this ratio was always higher in older adults because of the PF strength decline with aging. Furthermore, the DF MVC torque-angle relationship appeared to be especially explained by neural factors, whereas the relationship in PF seemed to be mainly due to muscular parameters. These relationships would not be a discriminating factor between the two age groups. As a consequence, measurements at one ankle joint angle, whatever the angle, are thus enough to examine the differences within age groups and to perform a rapid assessment of the imbalance at the ankle joint.     

Effect of simulated joint instability and bracing on ankle and subtalar joint flexibility

It is clinically challenging to distinguish between ankle and subtalar joints instability in vivo. Understanding the changes in load-displacement at the ankle and subtalar joints after ligament injuries may detect specific changes in joint characteristics that cannot be detected by investigating changes in range of motion alone. The effect of restricting joints end range of motion with ankle braces was already established, but little is known about the effect of an ankle brace on the flexibility of the injured ankle and subtalar joints. Therefore, the purposes of this study were to (1) understand how flexibility is affected at the ankle and subtalar joints after sectioning lateral and intrinsic ligaments during combined sagittal foot position and inversion and during internal rotation and (2) investigate the effect of a semi-rigid ankle brace on the ankle and subtalar joint flexibility. Kinematics and kinetics were collected from nine cadaver feet during inversion through the range of ankle flexion and during internal rotation. Motion was applied with and without a brace on an intact foot and after sequentially sectioning the calcaneofibular ligament (CFL) and the intrinsic ligaments. Segmental flexibility was defined as the slope of the angle-moment curve for each 1 Nm interval. Early flexibility significantly increased at the ankle and subtalar joint after CFL sectioning during inversion. The semi-rigid ankle brace significantly decreased early flexibility at the subtalar joint during inversion and internal rotation for all ligament conditions and at the ankle joint after all ligaments were cut.     

Orientation dependence of the fracture mechanics of cortical bone

The fracture mechanics parameter of the critical stress intensity factor (Kc) was determined by a modified compact tension test method, for the fracture of bovine tibia cortical bone at orientations of 0 degrees, 15 degrees, 30 degrees, 45 degrees, 75 degrees and 90 degrees to the bone axis. It was established that, for a given loading rate, a variation in orientation from 0-90 degrees produced average increases in Kc from 3.2 to 6.5 MN m-3/2.     

Directional dependence of hydroxyapatite-collagen interactions on mechanics of collagen

Bone is a biological nanocomposite composed primarily of collagen and hydroxyapatite. The collagen molecules self-assemble to from a structure known as a fibril that comprises of about 85–95% of the total bone protein. In a fibril, the molecular level interactions at the interface between molecular collagen and hydroxyapatite nanocrystals have a significant role on its mechanical response. In this study, we have used molecular dynamics and steered molecular dynamics to study directional dependence of deformation response of collagen with respect to the hydroxyapatite surface. We have also studied mechanical response of collagen in the proximity of (0 0 0 1) and (1 0 1¯0) surfaces of hydroxyapatite. Our simulations indicate that the mechanics of collagen pulled in different directions with respect to hydroxyapatite is significantly different. Similar results were obtained for collagen pulled in the proximity of different crystallographic surfaces of hydroxyapatite.     

Active and passive respiratory mechanics in anesthetized dogs

In six spontaneously breathing anesthetized dogs (pentobarbital sodium, 30 mg/kg) airflow, volume, and tracheal and esophageal pressures were measured. The active and passive mechanical properties of the total respiratory system, lung, and chest wall were calculated. The average passive values of respiratory system, lung, and chest wall elastances amounted to, respectively, 50.1, 32.3, and 17.7 cmH2O X l-1. Resistive pressure-vs.-flow relationships for the relaxed respiratory system, lung, and chest wall were also determined; a linear relationship was found for the former (the total passive intrinsic resistance averaged 4.1 cmH2O X l-1 X s), whereas power functions best described the others: the pulmonary pressure-flow relationship exhibited an upward concavity, which for the chest wall presented an upward convexity. The average active elastance and resistance of the respiratory system were, respectively, 64.0 cmH2O X l-1 and 5.4 cmH2O X l-1 X s. The greater active impedance reflects pressure losses due to force-length and force-velocity properties of the inspiratory muscles and those due to distortion of the respiratory system from its relaxed configuration.     

Hinged ankle braces do not alter knee mechanics during sidestep cutting

Lateral ankle sprains are common injuries in quick, dynamic movements and are caused by rapid ankle inversion. Ankle braces are used to reduce ankle inversion, while allowing normal plantar and dorsiflexion ranges of motion. Knee injuries, such as anterior cruciate ligament injuries, are also common in dynamic movements. It is important to understand how ankle braces affect injury risk at other proximal joints. There is limited and conflicting results on how ankle braces affect knee mechanics during these types of movements. Additionally, it is unknown if sex differences exist when using an ankle brace. Therefore, the purpose of this study was to determine the effects of a hinged ankle brace and sex during a 45° cutting movement. Three-dimensional kinematics and ground reaction forces were collected using a motion capture system and force plate on ten men and eight women during cutting trials. 2 × 2 repeated measures ANOVAs were used to detect differences in ground reaction forces, as well as knee and ankle kinematics between brace conditions and sex (p < 0.05). The brace condition exhibited greater initial contact ankle dorsiflexion (p = 0.011), decreased peak ankle inversion (p < 0.01), and increased vertical loading rate (p = 0.040). Females performed the cutting movement with less initial contact (p = 0.019) and peak knee flexion (p = 0.023) compared to males. Ankle bracing had no impact on the observed sex differences. Females exhibited decreased knee flexion compared to males, which has been well documented in the literature. The use of an ankle braces reduced ankle injury risk variables while not adversely impacting knee mechanics during a 45° sidecutting movement.     

Prestress revealed by passive co-tension at the ankle joint

This study was designed to test the assumption that elastic tissues of the ankle are prestressed, by investigating the presence of simultaneous opposite passive elastic moments and thus, passive co-tension, at the ankle joint. A prestressed two-spring model used to generate qualitative predictions of the effects of stretching the posterior elastic structures of the ankle on the net passive moment of this joint was used. Twenty-seven healthy individuals were subjected to passive evaluation of the net elastic moment of the ankle in the sagittal plane, with the knee positioned at 90°, 60°, 30° and 0° of flexion, in order to change the length of the posterior biarticular elastic structures. The placement of the knee in the more extended positions caused changes in the net passive moment as predicted by the prestressed model. The ankle position in which the net passive moment was equal to zero was shifted to more plantar flexed positions (p<0.001) and there was a global increase in ankle stiffness since both passive dorsiflexion stiffness (p≤0.037) and passive plantar flexion stiffness (p≤0.029) increased. The normalized terminal plantar flexion stiffness also increased (p≤0.047), suggesting that biarticular posterior elastic structures are pre-strained and still under tension when the ankle is maximally plantar flexed and the knee is positioned at 60° of flexion. Resting positions were indicative of equilibrium between opposite passive elastic moments. The results revealed that there is passive co-tension at the ankle, demonstrating the existence of prestress in elastic structures of this joint.     

The influence of body weight support on ankle mechanics during treadmill walking

The use of body weight support (BWS) systems during locomotor retraining has become routine in clinical settings. BWS alters load receptor feedback, however, and may alter the biomechanical role of the ankle plantarflexors, influencing gait. The purpose of this study was to characterize the biomechanical adaptations that occur as a result of a change in limb load (controlled indirectly through BWS) and gait speed during treadmill locomotion. Fifteen unimpaired participants underwent gait analysis with surface electromyography while walking on an instrumented dual-belt treadmill at seven different speeds (ranging from 0.4 to 1.6 m/s) and three BWS conditions (ranging from 0% to 40% BWS). While walking, spatiotemporal measures, anterior/posterior ground reaction forces, and ankle kinetics and muscle activity were measured and compared between conditions. At slower gait speeds, propulsive forces and ankle kinetics were unaffected by changing BWS; however, at gait speeds ≥approximately 0.8 m/s, an increase in BWS yielded reduced propulsive forces and diminished ankle plantarflexor moments and powers. Muscle activity remained unaltered by changing BWS across all gait speeds. The use of BWS could provide the advantage of faster walking speeds with the same push-off forces as required of a slower speed. While the use of BWS at slower speeds does not appear to detrimentally affect gait, it may be important to reduce BWS as participants progress with training, to encourage maximal push-off forces. The reduction in plantarflexor kinetics at higher speeds suggests that the use of BWS in higher functioning individuals may impair the ability to relearn walking.