Effect of boot shaft stiffness on stability joint energy and muscular co-contraction during walking on uneven surface

Increased boot shaft stiffness may have a noticeable impact on the range of motion of the ankle joint. Therefore, the ability of the ankle joint to generate power for propulsion might be impaired. This might result in compensatory changes at the knee and hip joint. Besides, adaptability of the subtalar joint to uneven surface might be reduced, which could in turn affect stability. The aim of the study was therefore to investigate the influence of boot shaft stiffness on biomechanical gait parameters.Fifteen healthy young adults walked over coarse gravel wearing two different hiking boots that differed by 50% in passive shaft stiffness. Leg kinematics, kinetics and electromyography were measured. Gait velocity and indicators for stability were not different when walking with the hard and soft boot shaft over the gravel surface. However, the hard boot shaft decreased the ankle range of motion as well as the eccentric energy absorbed at the ankle joint. As a consequence, compensatory changes at the knee joint were observed. Co-contraction was increased, and greater eccentric energy was absorbed. Therefore, the efficiency of gait with hard boots might be decreased and joint loading at the knee might be increased, which might cause early fatigue of knee muscles during walking or hiking. The results of this study suggest that stiffness and blocking of joint motion at the ankle should not be equated with safety. A trade-off between lateral stiffness and free natural motion of the ankle joint complex might be preferable.     

Human ankle joint stiffness over the full range of muscle activation levels

System identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels. Subjects lay supine on an experimental table with their left foot encased in a rigid, low-inertia cast which was fixed to an electro-hydraulic actuator operating as a position servo. Subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions (MVC) during repeated presentations of a stochastic ankle angular position perturbation. Compliance impulse response functions (IRF) were determined from every 2.5 s perturbation sequence. The gain (G), natural frequency (omega n), and damping (zeta) parameters of the second-order model providing the best fit to each IRF were determined and used to compute the corresponding inertial (I), viscous (B) and elastic (K) stiffness parameters. The behaviour of these parameters with mean torque was found to follow two simple rules. First, the elastic parameter (K) increased in proportion to mean ankle torque as it was varied from rest to MVC; these changes were considerable involving increases of more than an order of magnitude. Second, the damping parameter (zeta) remained almost invariant over the entire range of contractions despite the dramatic changes in K.     

Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults

The generation of muscle-actuated simulations that accurately represent the movement of old adults requires a model that accounts for changes in muscle properties that occur with aging. An objective of this study was to adjust the parameters of Hill-type musculo-tendon models to reflect nominal age-related changes in muscle mechanics that have been reported in the literature. A second objective was to determine whether using the parametric adjustments resulted in simulated dynamic ankle torque behavior similar to that seen in healthy old adults. The primary parameter adjustment involved decreasing maximum isometric muscle forces to account for the loss of muscle mass and specific strength with age. A review of the literature suggested the need for other modest adjustments that account for prolonged muscular deactivation, a reduction in maximum contraction velocity, greater passive muscle stiffness and increased normalized force capacity during lengthening contractions. With age-related changes incorporated, a musculo-tendon model was used to simulate isometric and isokinetic contractions of ankle plantarflexor and dorsiflexor muscles. The model predicted that ankle plantarflexion power output during 120 deg/s shortening contractions would be over 40% lower in old adults compared to healthy young adults. These power losses with age exceed the 30% loss in isometric strength assumed in the model but are comparable to 39-44% reductions in ankle power outputs measured in healthy old adults of approximately 70 years of age. Thus, accounting for age-related changes in muscle properties, other than decreased maximum isometric force, may be particularly important when simulating movements that require substantial power development.     

The effects of articulated figure skates on jump landing forces

Lower extremity injuries in figure skating have long been linked to skating boot stiffness, and recent increases in jump practice time may be influencing the frequency and seriousness of these injuries. It is hypothesized that stiff boots compromise skaters' abilities to attenuate jump landing forces. Decreasing boot stiffness by adding an articulation at the ankle may reduce the rate and magnitude of landing forces. Prototype articulated figure skating boots were tested in this study to determine their effectiveness in enabling skaters to land with lower peak impact forces. Nine competitive figure skaters, who trained in standard boots and subsequently in articulated boots, performed off-ice jump simulations and on-ice axels, double toe loops, and double axels. Analysis of the off-ice simulations showed decreases in peak heel force and loading rate with use of the articulated boot, although the exact kinematic mechanisms responsible for these decreases are still unclear. Analysis of the on-ice jumps revealed few kinematic differences between boot types, implying that the skaters did not use the articulation. Greater adaptation and training time is likely needed for the results seen off-ice to transfer to difficult on-ice jumps.     

Analytical decomposition can help to interpret ankle joint moment-angle relationship

Moment-angle relationship (dynamic joint stiffness)--the relationship between changes in joint moment and changes in joint angle--is useful for demonstrating interaction of kinematics and kinetics during gait. However, the individual contributors of dynamic joint stiffness are not well studied and understood, which has thus far limited its clinical application. In this study, ankle dynamic joint stiffness was analyzed and decomposed into three components in thirty able-bodied children during the stance phase of the gait. To verify the accuracy of the decomposition, the sum of decomposed components was compared to stiffness computed from experimental data, and good to very good agreement was found. Component 1, the term associated with changes in ground reaction force moment, was the dominant contribution to ankle dynamic joint stiffness. Retrospective data from eight children with juvenile idiopathic arthritis and idiopathic toe-walking was examined to explore the potential utility of analytical decomposition in pathological gait. Compared to controls, component 1 was the source of highest deviation in both pathological groups. Specifically, ankle dynamic joint stiffness differences can be further identified via two sub-components of component 1 which are based on magnitudes and rates of change of the ground reaction force and of its moment arm, and differences between the two patient groups and controls were most evident and interpretable here. Findings of the current study indicate that analytical decomposition can help identify the individual contributors to joint stiffness and clarify the sources of differences in patient groups.     

Mechanics of the anterior drawer test at the ankle: the effects of ligament viscoelasticity

The anterior drawer test at the human ankle joint is a routine clinical examination. The relationship between the mechanical response of this joint and the flexion angle was elucidated by a recent mathematical model, using purely elastic mechanical characteristics for the ligament fibres. The objective of the present work was to assess the effect of ligament viscoelasticity on the force response of the ankle joint for anterior displacements of the foot relative to the tibia, at different ankle flexion positions. A viscoelastic model of the ligaments from the literature was included in the recently proposed mathematical model. Drawer tests were simulated at several flexion angles and for increasing velocities of the imposed anterior displacement. The stiffness of the model ankle joint increased only modestly with velocity. The response force found for a 6mm displacement at 20 degrees plantarflexion increased by only 13% for a one hundred-fold increase in velocity from 0.1 to 10 mm/s. The flexion angle was confirmed as the most influential parameter in the mechanical response of the ankle to anterior drawer test.     

Subject-specific finite element modelling of the human foot complex during walking: sensitivity analysis of material properties,boundary and loading conditions

The objective of this study was to develop and validate a subject-specific framework for modelling the human foot. This was achieved by integrating medical image-based finite element modelling, individualised multi-body musculoskeletal modelling and 3D gait measurements. A 3D ankle–foot finite element model comprising all major foot structures was constructed based on MRI of one individual. A multi-body musculoskeletal model and 3D gait measurements for the same subject were used to define loading and boundary conditions. Sensitivity analyses were used to investigate the effects of key modelling parameters on model predictions. Prediction errors of average and peak plantar pressures were below 10% in all ten plantar regions at five key gait events with only one exception (lateral heel, in early stance, error of 14.44%). The sensitivity analyses results suggest that predictions of peak plantar pressures are moderately sensitive to material properties, ground reaction forces and muscle forces, and significantly sensitive to foot orientation. The maximum region-specific percentage change ratios (peak stress percentage change over parameter percentage change) were 1.935–2.258 for ground reaction forces, 1.528–2.727 for plantar flexor muscles and 4.84–11.37 for foot orientations. This strongly suggests that loading and boundary conditions need to be very carefully defined based on personalised measurement data.     

Determination of dynamic ankle ligament strains from a computational model driven by motion analysis based kinematic data

External rotation of the foot has been implicated in high ankle sprains. Recent studies by this laboratory, and others, have suggested that torsional traction characteristics of the shoe-surface interface may play a role in ankle injury. While ankle injuries most often involve damage to ligaments due to excessive strains, the studies conducted by this laboratory and others have largely used surrogate models of the lower extremity to determine shoe-surface interface characteristics based on torque measures alone. The objective of this study was to develop a methodology that would integrate a motion analysis-based kinematic foot model with a computational model of the ankle to determine dynamic ankle ligament strains during external foot rotation. Six subjects performed single-legged, internal rotation of the body with a planted foot while a marker-based motion analysis was conducted to track the hindfoot motion relative to the tibia. These kinematic data were used to drive an established computational ankle model. Ankle ligament strains, as a function of time, were determined. The anterior tibiofibular ligament (ATiFL) experienced the highest strain at 9.2±1.1%, followed by the anterior deltoid ligament (ADL) at 7.8±0.7%, averaged over the six subjects. The peak ATiFL strain occurred prior to peak strain in the ADL in all subjects. This novel methodology may provide new insights into mechanisms of high ankle sprains and offer a basis for future evaluations of shoe-surface interface characteristics using human subjects rather than mechanical surrogate devices.     

The effect of ankle constraint on the torsional laxity of the knee during internal-external rotation of the foot

The in vivo torsional laxity and stiffness of the knee joint are usually determined by rotating the foot and measuring the torque generated at the knee. However, when rotation is applied to the foot, significant three-dimensional forces and moments are produced at the knee. These forces and moments depend upon the external constraint of the ankle complex, and as a result, the observed laxity of the knee also depends on the ankle constraint. Tests are conducted with the foot of a subject in a shoe, with and without the ankle taped, and in a buckled and unbuckled (ski) boot that can effectively constrain ankle rotation. The average laxity of the primary (linear) region of the axial moment vs internal-external rotation is 30% greater when the ankle is constrained by the buckled boot than it is in three other cases of lesser ankle constraint.     

Online estimation algorithm for a biaxial ankle kinematic model with configuration dependent joint axes

The kinematics of the human ankle is commonly modeled as a biaxial hinge joint model. However, significant variations in axis orientations have been found between different individuals and also between different foot configurations. For ankle rehabilitation robots, information regarding the ankle kinematic parameters can be used to estimate the ankle and subtalar joint displacements. This can in turn be used as auxiliary variables in adaptive control schemes to allow modification of the robot stiffness and damping parameters to reduce the forces applied at stiffer foot configurations. Due to the large variations observed in the ankle kinematic parameters, an online identification algorithm is required to provide estimates of the model parameters. An online parameter estimation routine based on the recursive least-squares (RLS) algorithm was therefore developed in this research. An extension of the conventional biaxial ankle kinematic model, which allows variation in axis orientations with different foot configurations had also been developed and utilized in the estimation algorithm. Simulation results showed that use of the extended model in the online algorithm is effective in capturing the foot orientation of a biaxial ankle model with variable joint axis orientations. Experimental results had also shown that a modified RLS algorithm that penalizes a deviation of model parameters from their nominal values can be used to obtain more realistic parameter estimates while maintaining a level of estimation accuracy comparable to that of the conventional RLS routine.     

Parameter identification of the human lower limb under dynamic, transient torsional loading

The response of the lower limb to dynamic, transient torsional loading applied at the foot has been measured for a male test subject. The dynamic loading was provided by a computer controlled pneumatic system which applied single haversine (i.e. half cycle of a sine wave) axial moment pulses of variable amplitude (0-100 Nm) and duration (50-600 ms). Potentiometers measured the absolute rotations of the three leg segments. Test variables included rotation direction, weight bearing and joint flexion. Two approaches were explored for specifying parameters (i.e. inertia, damping, stiffness) of a three degree-of-freedom dynamic system model which best duplicated the measured response. One approach involved identification of linear parameters by means of optimization while the other approach entailed estimation. Parameter estimates, which included non-linear, asymmetric stiffness functions, were derived from the literature. The optimization was undertaken so as to identify parameter dependence on test variables. Results indicate that parameter values are influenced by test variables. Results also indicate that the non-linear, estimated model better approximates the experimental data than the linear, identified model. In addition to identifying parameters of a three degree-of-freedom model, parameters were also identified for a single degree-of-freedom model where the motion variable was intended to indicate the rotation of the in vivo knee. It is concluded that the simpler model offers good accuracy in predicting both magnitude and time of occurrence of peak knee axial rotations. Model motion fails to track the measured knee rotation subsequent to the peak, however.     

Response properties of mouse trigeminal ganglion neurons

We used controlled whisker deflections to examine the response properties of 208 primary afferent neurons in the trigeminal ganglion of adult mice. Proportions of rapidly adapting (RA, 47%) and slowly adapting (SA, 53%) neurons were equivalent, and most cells had low or no spontaneous activity. We quantified angular tuning and sensitivity to deflection amplitude and velocity. Both RA and SA units fired more frequently to larger deflections and faster deflections, but RA units were more sensitive to differences in velocity whereas SA units were more sensitive to deflection amplitudes. Almost all neurons were tuned for deflection angle, and the average response to the maximally effective direction was more than fourfold greater than the average response in the opposite direction; SA units were more tuned than RA units. Responses of primary afferent whisker-responsive neurons are qualitatively similar to those of the rat. However, average firing rates of both RA and SA neurons in the mouse are less sensitive to differences in deflection velocity, and RA units, unlike those in the rat, display amplitude sensitivity. Subtle observed differences between mice and rats may reflect greater mechanical compliance in mice of the whisker hairs and of the tissue in which they are embedded.     

Response properties of mouse trigeminal ganglion neurons

We used controlled whisker deflections to examine the response properties of 208 primary afferent neurons in the trigeminal ganglion of adult mice. Proportions of rapidly adapting (RA, 47%) and slowly adapting (SA, 53%) neurons were equivalent, and most cells had low or no spontaneous activity. We quantified angular tuning and sensitivity to deflection amplitude and velocity. Both RA and SA units fired more frequently to larger deflections and faster deflections, but RA units were more sensitive to differences in velocity whereas SA units were more sensitive to deflection amplitudes. Almost all neurons were tuned for deflection angle, and the average response to the maximally effective direction was more than fourfold greater than the average response in the opposite direction; SA units were more tuned than RA units. Responses of primary afferent whisker-responsive neurons are qualitatively similar to those of the rat. However, average firing rates of both RA and SA neurons in the mouse are less sensitive to differences in deflection velocity, and RA units, unlike those in the rat, display amplitude sensitivity. Subtle observed differences between mice and rats may reflect greater mechanical compliance in mice of the whisker hairs and of the tissue in which they are embedded.     

Diabetic neuropathy is related to joint stiffness during late stance phase

The majority of plantar ulcers in the diabetic population occur in the forefoot. Peripheral neuropathy has been related to the occurrence of ulcers. Long-term diabetes results in the joints becoming passively stiffer. This static stiffness may translate to dynamic joint stiffness in the lower extremities during gait. Therefore, the purpose of this investigation was to demonstrate differences in ankle and knee joint stiffness between diabetic individuals with and without peripheral neuropathy during gait. Diabetic subjects with and without peripheral neuropathy were compared. Subjects were monitored during normal walking with three-dimensional motion analysis and a force plate. Neuropathic subjects had higher ankle stiffness (0.236 N.m/deg) during 65 to 80% of stance when compared with non-neuropathic subjects (-0.113 N.m/deg). Neuropathic subjects showed a different pattern in ankle stiffness compared with non-neuropathic subjects. Neuropathic subjects demonstrated a consistent level of ankle stiffness, whereas non-neuropathic subjects showed varying levels of stiffness. Neuropathic subjects demonstrated lower knee stiffness (0.015 N.m/deg) compared with non-neuropathic subjects (0.075 N.m/deg) during 50 to 65% of stance. The differences in patterns of ankle and knee joint stiffness between groups appear to be related to changes in timing of peak ankle dorsiflexion during stance, with the neuropathic group reaching peak dorsiflexion later than the non-neuropathic subjects. This may partially relate to the changes in plantar pressures beneath the metatarsal heads present in individuals with neuropathy.     

Kinetic models for detection of toxicity in a microbial fuel cell based biosensor

Currently available models describing microbial fuel cell (MFC) polarization curves, do not describe the effect of the presence of toxic components. A bioelectrochemical model combined with enzyme inhibition kinetics, that describes the polarization curve of an MFC-based biosensor, was modified to describe four types of toxicity. To get a stable and sensitive sensor, the overpotential has to be controlled. Simulations with the four modified models were performed to predict the overpotential that gives the most sensitive sensor. These simulations were based on data and parameter values from experimental results under non-toxic conditions. Given the parameter values from experimental results, controlling the overpotential at 250 mV leads to a sensor that is most sensitive to components that influence the whole bacterial metabolism or that influence the substrate affinity constant (Km). Controlling the overpotential at 105 mV is the most sensitive setting for components influencing the ratio of biochemical over electrochemical reaction rate constants (K1), while an overpotential of 76 mV gives the most sensitive setting for components that influence the ratio of the forward over backward biochemical rate constants (K2). The sensitivity of the biosensor was also analyzed for robustness against changes in the model parameters other than toxicity. As an example, the tradeoff between sensitivity and robustness for the model describing changes on K1 (IK1) is presented. The biosensor is sensitive for toxic components and robust for changes in model parameter K2 when overpotential is controlled between 118 and 140 mV under the simulated conditions.     

Prediction of the loading along the leg during snow skiing.

The complete force and moment of each cross section of the leg between the ski boot top and the knee during normal skiing were predicted from measurements of the force and moment under the toe and heel of the boot and the flexion of the ankle. The force and moment components predicted at the base of the boot were significantly different from those predicted at sites of potential injury at the boot top and the knee. The maximum torsional and maximum varus-valgus moments predicted at the knee over all subjects tested were 70 Nm and 149 Nm, which are within the estimated range of the ultimate strength of the knee without support from contracted muscles crossing the knee. Regression analyses were used to find the force components at the base of the boot that best predict the bending and torsional moments at the boot top and knee. The torsional moments at the boot top and knee are best predicted by the medial-lateral force at the toe. The varus-valgus moment at the boot top and knee are best predicted by the resultant medial-lateral force component at the base of the boot. The set of best predictors of the anterior-posterior bending moments at the boot top and knee includes the vertical force at the toe, the vertical force at the heel and the component of the total vertical force directed perpendicular to the leg.     

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

     

A parameter optimization method to determine ski stiffness properties from ski deformation data

The deformation of skis and the contact pressure between skis and snow are crucial factors for carved turns in alpine skiing. The purpose of the current study was to develop and to evaluate an optimization method to determine the bending and torsional stiffness that lead to a given bending and torsional deflection of the ski. Euler-Bernoulli beam theory and classical torsion theory were applied to model the deformation of the ski. Bending and torsional stiffness were approximated as linear combinations of B-splines. To compute the unknown coefficients, a parameter optimization problem was formulated and successfully solved by multiple shooting and least squares data fitting. The proposed optimization method was evaluated based on ski stiffness data and ski deformation data taken from a recently published simulation study. The ski deformation data were used as input data to the optimization method. The optimization method was capable of successfully reproducing the shape of the original bending and torsional stiffness data of the ski with a root mean square error below 1 N m2. In conclusion, the proposed computational method offers the possibility to calculate ski stiffness properties with respect to a given ski deformation.     

Ankle intrinsic stiffness changes with postural sway

In standing, the human body is inherently unstable and its stabilization requires constant regulation of ankle torque, generated by a combination of ankle intrinsic properties, peripheral reflexes, and central contributions. Ankle intrinsic stiffness, which quantifies the joint intrinsic properties, has been usually assumed constant in standing; however, there is strong evidence that it is highly dependent on the joint torque, which changes significantly with sway in stance. In this study, we examined how ankle intrinsic stiffness changes with postural sway during standing. Ten subjects stood on a standing apparatus, while subjected to pulse perturbations of ankle position. The mean torque of a short period before the start of each pulse was used as a measure of background torque. Responses with similar background torques were grouped together and used to estimate the parameters of an intrinsic stiffness model. Stiffness estimates were normalized to the critical stiffness and the background torque was transformed to the center of pressure location. We found that in most subjects, the normalized stiffness increased linearly with the movement of center of pressure towards the toes, with an average slope of 2.11 ± 0.80 1/m·rad. This modulation of ankle intrinsic stiffness seems functionally appropriate, since the intrinsic stiffness increases quickly, as the center of pressure moves toward the toes and the limits of stability. These large changes of ankle intrinsic stiffness with postural sway must be incorporated in any model of stance control.     

A reproducibility study on musculotendinous stiffness quantification, using a new transportable ankle ergometer device

The use of biomechanical methods to quantify functional/physiological parameters in malnourished humans can provide new insights into the understanding of effects of malnutrition on human muscles. Therefore, a transportable ankle ergometer device was developed, which allows the quantification of mechanical properties of the human plantarflexor muscles in field experiments. More precisely, the ergometer quantifies isometric force in static conditions and musculotendinous stiffness in dynamic conditions. This latter parameter is obtained by the quick-release technique. The aim of the study was first to conduct a reproducibility study on musculotendinous stiffness. Seven healthy subjects were tested three times in alternate days. The results showed the well-known linear relationship between musculotendinous stiffness and torque, where the slope was used as a stiffness index (SI(MT)). Individual regression line comparison indicated that SI(MT) values were not significantly different between the three repeated measurements (P>0.05). Mean coefficient of variation was 4.5+/-1.0%. The individual SI(MT) data were within the range of those reported in the literature. The reproducibility study showed that the quantification of musculotendinous stiffness by means of the quick-release technique is a reliable method, using a transportable ankle ergometer device.