Joint moment and muscle power output characteristics of below knee amputees during running: the influence of energy storing prosthetic feet

Stance phase joint moments, muscle power outputs and mechanical energy characteristics were determined in five normal and five below knee amputee subjects running at 2.8 m s-1. The amputees were studied sequentially on three different prosthetic feet: the SACH foot (solid ankle cushion heel), and two energy storing feet, Seattle and Flex. While wearing the SACH foot, the amputees exhibited major alterations in the distribution and magnitude of muscle power output and muscle work: (1) the total work done by the lower extremity was reduced; (2) the hip extensors became the main source of energy absorption and generation, while in normal subjects the ankle plantarflexors were the major energy generators and the knee extensors the major energy absorbers; (3) the eccentric and concentric knee extensor power outputs were reduced and an abnormal concentric knee flexor power output was noted immediately after heel contact. In four of the amputees, energy storing feet resulted in improvements in the power output and mechanical work characteristics of the lower extremity: (1) the energy storing prosthetic feet generated 2-3 times greater energy than the SACH foot; (2) with the Flex foot the amputees exhibited a more normal pattern and magnitude of hip and knee extensor muscle work. One of the subjects, however, exhibited increased abnormalities with the energy storing prosthetic feet. The amount of energy restored relative to the amount of energy absorbed by each of the prosthetic feet was greater with the energy storing feet than the SACH foot (Flex 84%, Seattle 52%, SACH 31%).     

Significance of nonsagittal power terms in analysis of a dynamic elastic response prosthetic foot.

Dynamic elastic response prosthetic feet generally utilize a solid ankle, limiting dominant motion to the sagittal plane. However, researchers often use total rotational ankle joint power in the analysis of these feet. This investigation measured joint power terms in each plane for the Carbon Copy High Performance prosthetic foot. The significance of the frontal and transverse plane terms was assessed. Addition of these terms to the dominant sagittal power term revealed only slight differences, indicating that the sagittal power term is likely sufficient.     

Finite element analysis as a tool for parametric prosthetic foot design and evaluation. Technique development in the solid ankle cushioned heel (SACH) foot

In this study, we developed an approach for prosthetic foot design incorporating motion analysis, mechanical testing and computer analysis. Using computer modeling and finite element analysis, a three-dimensional (3D), numerical foot model of the solid ankle cushioned heel (SACH) foot was constructed and analyzed based upon loading conditions obtained from the gait analysis of an amputee and validated experimentally using mechanical testing. The model was then used to address effects of viscoelastic heel performance numerically. This is just one example of the type of parametric analysis and design enabled by this approach. More importantly, by incorporating the unique gait characteristics of the amputee, these parametric analyses may lead to prosthetic feet more appropriately representing a particular user's needs, comfort and activity level.     

Ankle and foot power in gait analysis: Implications for science,technology and clinical assessment

In human gait analysis studies, the entire foot is typically modeled as a single rigid-body segment; however, this neglects power generated/absorbed within the foot. Here we show how treating the entire foot as a rigid body can lead to misunderstandings related to (biological and prosthetic) foot function, and distort our understanding of ankle and muscle-tendon dynamics. We overview various (unconventional) inverse dynamics methods for estimating foot power, partitioning ankle vs. foot contributions, and computing combined anklefoot power. We present two case study examples. The first exemplifies how modeling the foot as a single rigid-body segment causes us to overestimate (and overvalue) muscle-tendon power generated about the biological ankle (in this study by up to 77%), and to misestimate (and misinform on) foot contributions; corroborating findings from previous multi-segment foot modeling studies. The second case study involved an individual with transtibial amputation walking on 8 different prosthetic feet. The results exemplify how assuming a rigid foot can skew comparisons between biological and prosthetic limbs, and lead to incorrect conclusions when comparing different prostheses/interventions. Based on analytical derivations, empirical findings and prior literature we recommend against computing conventional ankle power (between shank-foot). Instead, we recommend using an alternative estimate of power generated about the ankle joint complex (between shank-calcaneus) in conjunction with an estimate of foot power (between calcaneus-ground); or using a combined anklefoot power calculation. We conclude that treating the entire foot as a rigid-body segment is often inappropriate and ill-advised. Including foot power in biomechanical gait analysis is necessary to enhance scientific conclusions, clinical evaluations and technology development.     

Finite Element Analysis as a Tool for Parametric Prosthetic Foot Design and Evaluation. Technique Development in the Solid Ankle Cushioned Heel (SACH) Foot

In this study, we developed an approach for prosthetic foot design incorporating motion analysis, mechanical testing and computer analysis. Using computer modeling and finite element analysis, a three-dimensional (3D), numerical foot model of the solid ankle cushioned heel (SACH) foot was constructed and analyzed based upon loading conditions obtained from the gait analysis of an amputee and validated experimentally using mechanical testing. The model was then used to address effects of viscoelastic heel performance numerically. This is just one example of the type of parametric analysis and design enabled by this approach. More importantly, by incorporating the unique gait characteristics of the amputee, these parametric analyses may lead to prosthetic feet more appropriately representing a particular user's needs, comfort and activity level.     

A framework for parametric modeling of ankle ligaments to determine the in situ response under gross foot motion

Ligament sprains account for a majority of injuries to the foot and ankle complex, but ligament properties have not been understood well due to the difficulties in replicating the complex geometry, in situ stress state, and non-uniformity of the strain. For a full investigation of the injury mechanism, it is essential to build up a foot and ankle model validated at the level of bony kinematics and ligament properties. This study developed a framework to parameterize the ligament response for determining the in situ stress state and heterogeneous force–elongation characteristics using a finite element ankle model. Nine major ankle ligaments and the interosseous membrane were modeled as discrete elements corresponding functionally to the ligamentous microstructure of collagen fibers and having parameterized toe region and stiffness at the fiber level. The range of the design variables in the ligament model was determined from existing experimental data. Sensitivity of the bony kinematics to each variable was investigated by design of experiment. The results highlighted the critical role of the length of the toe region of the ligamentous fibers on the bony kinematics with the cumulative influence of more than 95%, while the fiber stiffness was statistically insignificant with an influence of less than 1% under the given variable range and loading conditions. With the flexibility of variable adjustment and high computational efficiency, the presented ankle model was generic in nature so as to maximize its applicability to capture the individual ligament behaviors in future studies.     

Lower-limb amputee recovery response to an imposed error in mediolateral foot placement

Despite walking with a wider step width, amputees remain 20% more likely to fall than non-amputees. Since mediolateral (ML) balance is critical for ambulation and contingent on ML foot placement, we used a ML disturbance to perturb walking balance and explore the influence of prosthetic foot stiffness on balance recovery. Ten transtibial amputees were fit with two commonly prescribed prosthetic feet with differing stiffness characteristics; 12 non-amputees also participated. A perturbation device that released an air burst just before heel strike imposed a repeatable medial or lateral disturbance in foot placement. After a medial disturbance, the first recovery step width was narrowed (p<0.0001) for the prosthetic limb (−103%), the sound limb (−51%) and non-amputees (−41%) and more than twice as variable. The ML inclination angle remained reduced (−109%) for the prosthetic limb, while the sound limb and non-amputees approached undisturbed levels (p<0.0004). Amputees required five steps to return to undisturbed step width after a prosthetic medial disturbance versus two steps for the sound limb and for non-amputees. After a lateral disturbance, the first recovery step was widened for the prosthetic limb (+82%), sound limb (+75%), and wider than non-amputees (+51%; p<0.0001), with all participants requiring three steps to return to undisturbed step width. Amputees also exhibited a similar upper torso response compared to the non-amputees for both disturbances. Prosthetic feet with different stiffness properties did not have a significant effect. In conclusion, amputee balance was particularly challenged by medial disturbances to the prosthetic limb implying a need for improved interventions that address these balance deficits.     

A methodology for studying the effects of various types of prosthetic feet on the biomechanics of trans-femoral amputee gait.

This paper reports on a methodology developed for studying the effects of various types of prosthetic feet on the gait of trans-femoral amputees. It is shown that an analysis in three planes of motion of not only the prosthetic, but also the sound limb provides important information on the performance of prosthetic feet. Two male trans-femoral amputees were tested with four different prosthetic feet; the Springlite II, Carbon Copy III, Seattle LightFoot and the Multiflex foot. A detailed analysis of the results of one amputee and a summary of the most important results of a second subject is presented. The tests were carried out at normal (1.16 m s(-1)) and fast (1.56 m s(-1)) walking speeds. Three dimensional gait analysis was carried out to derive the time curves of the joint angles, intersegmental moments and power at the ankle, knee and hip joints at both the prosthetic and sound sides. A higher first peak of the ground reaction force at the sound side with the Seattle LightFoot compared to that with the Springlite II, may be the result of the lower late stance dorsiflexion angle with the former. Compared to the other two feet, the Carbon Copy III and the Springlite II showed higher prosthetic dorsiflexing moments and positive power at late stance, which could assist in the push-off. The 3D intersegmental loads at the ankle and knee can be used as a guide for design and for compilation of standards for testing of lower limb prostheses incorporating flexible feet.     

Comparison of methods for the calculation of energy storage and return in a dynamic elastic response prosthesis

The standard method used to calculate the ankle joint power contains deficiencies when applied to dynamic elastic response prosthetic feet. The standard model, using rotational power and inverse dynamics, assumes a fixed joint center and cannot account for energy storage, dissipation, and return. This study compared the standard method with new analysis models. First, assumptions of inverse dynamics were avoided by directly measuring ankle forces and moments. Second, the ankle center of rotation was corrected by including translational power terms. Analysis with below-knee amputees revealed that the conventional method overestimates ankle forces and moments as well as prosthesis energy storage and return. Results for efficiency of energy return were varied. Large differences between models indicate the standard method may have serious inadequacies in the analysis of certain prosthetic feet. This research is the first application of the new models to prosthetic feet, and suggests the need for additional research in gait analysis with energy-storing prostheses.     

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.     

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.     

A validated computational framework to evaluate the stiffness of 3D printed ankle foot orthoses

The purpose of this study was to create and validate a standardized framework for the evaluation of the ankle stiffness of two designs of 3D printed ankle foot orthoses (AFOs). The creation of four finite element (FE) models allowed patient-specific quantification of the stiffness and stress distribution over their specific range of motion during the second rocker of the gait. Validation was performed by comparing the model outputs with the results obtained from a dedicated experimental setup, which showed an overall good agreement with a maximum relative error of 10.38% in plantarflexion and 10.66% in dorsiflexion. The combination of advanced computer modelling algorithms and 3D printing techniques clearly shows potential to further improve the manufacturing process of AFOs.     

Comparative roll-over analysis of prosthetic feet

A prosthetic foot is a key element of a prosthetic leg, literally forming the basis for a stable and efficient amputee gait. We determined the roll-over characteristics of a broad range of prosthetic feet and examined the effect of a variety of shoes on these characteristics. The body weight of a person acting on a prosthetic foot during roll-over was emulated by means of an inverted pendulum-like apparatus. Parameters measured were the effective radius of curvature, the forward travel of the center of pressure, and the instantaneous radius of curvature of the prosthetic feet. Finally, we discuss how these parameters relate to amputee gait.     

The effect of speed on leg stiffness and joint kinetics in human running

The goals of this study were to examine the following hypotheses: (a) there is a difference between the theoretically calculated (McMahon and Cheng, 1990. Journal of Biomechanics 23, 65-78) and the kinematically measured length changes of the spring-mass model and (b) the leg spring stiffness, the ankle spring stiffness and the knee spring stiffness are influenced by running speed. Thirteen athletes took part in this study. Force was measured using a "Kistler" force plate (1000 Hz). Kinematic data were recorded using two high-speed (120 Hz) video cameras. Each athlete completed trials running at five different velocities (approx. 2.5, 3.5, 4.5, 5.5 and 6.5 m/s). Running velocity influences the leg spring stiffness, the effective vertical spring stiffness and the spring stiffness at the knee joint. The spring stiffness at the ankle joint showed no statistical difference (p < 0.05) for the five velocities. The theoretically calculated length change of the spring-mass model significantly (p < 0.05) overestimated the actual length change. For running velocities up to 6.5 m/s the leg spring stiffness is influenced mostly by changes in stiffness at the knee joint.     

Adaptative control of above knee electro-hydraulic prosthesis.

Conventional designs of an above-knee prosthesis are based on mechanisms with mechanical properties (such as friction, spring and damping coefficients) that remain constant during changing cadence. These designs are unable to replace natural legs due to the lack of active knee joint control. Since the nonlinear and time-varying dynamic coupling between the thigh and the prosthetic limb is high during swing phase, an adaptive control is employed to control the knee joint motion. Two dimensional simulation indicates that the adaptive controller can improve the appearance of gait pattern. It is adaptable to walking speed and can compensate for the variations of hip moment, hip trajectory and toe-off conditions.     

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.     

Trajectory of the center of rotation in non-articulated energy storage and return prosthetic feet

Non-articulated energy storage and return prosthetic feet lack any true articulation or obvious point of rotation. This makes it difficult to select a joint center about which to estimate their kinetics. Despite this absence of any clear point of rotation, methods for estimating the kinetic performance of this class of prosthetic feet typically assume that they possess a fixed center of rotation and that its location is well approximated by the position of the contralateral lateral malleolus. To evaluate the validity of this assumption we used a finite helical axis approach to determine the position of the center of rotation in the sagittal plane for a series of non-articulated energy storage and return prosthetic feet. We found that over the course of stance phase, the sagittal finite helical axis position diverged markedly from the typically assumed fixed axis location. These results suggest that researchers may need to review center of rotation assumptions when assessing prosthetic foot kinetics, while clinicians may need to reconsider the criteria by which they prescribe these prosthetic feet.     

Rotational stiffness of football shoes influences talus motion during external rotation of the foot

Shoe-surface interface characteristics have been implicated in the high incidence of ankle injuries suffered by athletes. Yet, the differences in rotational stiffness among shoes may also influence injury risk. It was hypothesized that shoes with different rotational stiffness will generate different patterns of ankle ligament strain. Four football shoe designs were tested and compared in terms of rotational stiffness. Twelve (six pairs) male cadaveric lower extremity limbs were externally rotated 30 deg using two selected football shoe designs, i.e., a flexible shoe and a rigid shoe. Motion capture was performed to track the movement of the talus with a reflective marker array screwed into the bone. A computational ankle model was utilized to input talus motions for the estimation of ankle ligament strains. At 30 deg of rotation, the rigid shoe generated higher ankle joint torque at 46.2?±?9.3 Nm than the flexible shoe at 35.4?±?5.7 Nm. While talus rotation was greater in the rigid shoe (15.9?±?1.6 deg versus 12.1?±?1.0 deg), the flexible shoe generated more talus eversion (5.6?±?1.5 deg versus 1.2± 0.8 deg). While these talus motions resulted in the same level of anterior deltoid ligament strain (approxiamtely 5%) between shoes, there was a significant increase of anterior tibiofibular ligament strain (4.5± 0.4% versus 2.3?±?0.3%) for the flexible versus more rigid shoe design. The flexible shoe may provide less restraint to the subtalar and transverse tarsal joints, resulting in more eversion but less axial rotation of the talus during foot∕shoe rotation. The increase of strain in the anterior tibiofibular ligament may have been largely due to the increased level of talus eversion documented for the flexible shoe. There may be a direct correlation of ankle joint torque with axial talus rotation, and an inverse relationship between torque and talus eversion. The study may provide some insight into relationships between shoe design and ankle ligament strain patterns. In future studies, these data may be useful in characterizing shoe design parameters and balancing potential ankle injury risks with player performance.     

The validity of stability measures: A modelling approach

Measures calculated from unperturbed walking patterns, such as variability measures and maximum Floquet multipliers, are often used to study the stability of walking. However, it is unknown if, and to what extent, these measures correlate to the probability of falling.We studied whether in a simple model of human walking, i.e., a passive dynamic walker, the probability of falling could be predicted from maximum Floquet multipliers, kinematic state variability, and step time variability. We used an extended version of the basic passive dynamic walker with arced feet and a hip spring. The probability of falling was manipulated by varying the foot radius and hip spring stiffness, or varying these factors while co-varying the slope to keep step length constant.The simulation data indicated that Floquet multipliers and kinematic state variability correlated inconsistently with probability of falling. Step time variability correlated well with probability of falling, but a more consistent correlation with the probability of falling was found by calculating the variability of the log transform of the step time. Our findings speak against the use of maximum Floquet multipliers and suggest instead that variability of critical variables may be a good predictor of the probability to fall.