Hubertus F.J.M. Koopman

Energy storage and release of prosthetic feet Part 1: biomechanical analysis related to user benefits

The energy storing and releasing behaviour of 2 energy storing feet (ESF) and 2 conventional prosthetic feet (CF) were compared (ESF: Otto Bock Dynamic Pro and Hanger Quantum; CF: Otto Bock Multi Axial and Otto Bock Lager). Ten trans-tibial amputees were selected. The study was designed as a double-blind, randomised trial. For gait analysis a VICON motion analysis system was used with 2 AMTI force platforms. A special measuring device was used for measuring energy storage and release of the foot during a simulated step. The impulses of the anteroposterior component of the ground force showed small, statistically non-significant differences (deceleration phase: 22.7–23.4 Ns; acceleration phase: 17.0–18.4 Ns). The power storage and release phases as well as the net results also showed small differences (maximum difference in net result is 0.03 J kg−1). It was estimated that these differences lead to a maximum saving of 3% of metabolic energy during walking. It was considered unlikely that the subjects would notice this difference. It was concluded that during walking differences in mechanical energy expenditure of this magnitude are probably not of clinical relevance. Ankle power, as an indicator for energy storage and release gave different results to the energy storage and release as measured with the special test device, especially during landing response. In the biomechanical model (based on inverse dynamics) used in the gait analysis the deformation of the material is not taken into consideration and hence this method of gait analysis is probably not suitable for calculation of shock absorption.

Multiple-step strategies to recover from stumbling perturbations.

This study has analysed the recovery from an induced stumble whilst walking on a treadmill. Four stumbling conditions were tested; at early swing with short and long durations and at mid and late swing with short duration. The experiment set-up, including the possibility of being stumbled, did not alter the normal gait patterns and the recovery strategies depended on the perturbation conditions. For the early swing perturbation, delayed lowering and elevating strategies were performed using the perturbed leg. A lowering strategy was seen for mid and late swing perturbations. An elevating strategy consisted of an elevation of the swing limb while a lowering one consisted of bringing the foot quickly to the ground. There were two groups of reactions to the experimental perturbation of gait. In the first, there was an effort to complete the disturbed step as normally as possible, so the following steps were less constrained to maintain treadmill speed. In the second group of reactions, the perturbed step was aborted and the recovery effort transferred to the contralateral limb. In many cases, several steps were needed to regain normal gait pattern. The study of recovery reactions from gait perturbations should include at least three steps after the perturbed one.

A Hill type model of rat medial gastrocnemius muscle that accounts for shortening history effects

The aim of the present study was to develop a Hill type muscle model that accounts for the effects of shortening history. For this purpose, a function was derived that relates force depression to starting length, shortening amplitude and contraction velocity. History parameters were determined from short-range isokinetic experiments on rat medial gastrocnemius muscle (GM). Simulations of isokinetic as well as isotonic experiments were performed with the new model and a standard Hill type model. The simulation results were compared with experimental results of rat GM to evaluate if incorporation of history effects leads to improvements in model predictions. In agreement with the experimental results, the new model qualitatively described force reduction during and after isokinetic shortening as well as the experimental observation that isometric endpoints of isotonic contractions are attained at higher muscle lengths than is expected from the fully isometric length-force curve. Consequently, the new model gave a better quantitative prediction of the experimental results compared to the standard model. It was concluded that incorporation of history effects can improve the predictive power of a Hill type model considerably. The applicability of the model to conditions other than those described in the present paper is discussed.

Stiffness and hysteresis properties of some prosthetic feet

A prosthetic foot is an important element of a prosthesis, although it is not always fully recognized that the properties of the foot, along with the prosthetic knee joint and the socket, are in part responsible for the stability and metabolic energy cost during walking. The stiffness and the hysteresis, which are the topics of this paper, are not properly prescribed, but could be adapted to improve the prosthetic walking performance. The shape is strongly related to the cosmetic appearance and so can not be altered to effect these improvements. Because detailed comparable data on foot stiffness and hysteresis, which are necessary to quantify the differences between different types of feet, are absent in literature, these properties were measured by the authors in a laboratory setup for nine different prosthetic feet, bare and with two different shoes. One test cycle consisted of measurements of load deformation curves in 66 positions, representing the range from heel strike to toe-off. The hysteresis is defined by the energy loss as a part of the total deformation energy. Without shoes significant differences in hysteresis between the feet exist, while with sport shoes the differences in hysteresis between the feet vanish for the most part. Applying a leather shoe leads to an increase of hysteresis loss for all tested feet. The stiffness turned out to be non-constant, so mean stiffness is used. Because very little is known about the optimal values of stiffness and hysteresis, and substantial differences in stiffness between different feet and shoes exist, further investigation into the importance of stiffness and hysteresis to the walking quality of a foot is necessary. Footwear counts too for this quality because it modifies the variation in stiffness among the feet.

Energy efficient and robust rhythmic limb movement by central pattern generators

Humans show great energy efficiency and robustness in rhythmic tasks, such as walking and arm swinging. In this study a mathematical model of rhythmic limb movement is presented, which shows that tight local coupling of Central Pattern Generators (CPGs) to limbs could explain part of this behavior. Afferent feedback to flexor and extensor centers of the CPG is crucial in providing energy efficiency by means of resonance tuning. Feedback of positional information provides resonance tuning above the endogenous frequency of the CPG. Integral feedback provides resonance tuning at and below the endogenous frequency. Feedback of velocity information is necessary to compensate for the time delay in the loop, coupling limb to CPG; without velocity feedback bi-stability occurs and resonance tuning is not possible at high movement frequencies. The concepts of energy efficient and robust control of rhythmic limb movements are also applicable to robotics. It is the first CPG model, which provides resonance tuning at natural limb frequencies above and below its endogenous frequency.

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.

Prediction of ground reaction forces and moments during various activities of daily living

Inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement. Due to inaccuracies in the kinematic and force plate data, and a mismatch between the model and the subject, the equations of motion are violated when solving the inverse dynamics problem. As a result, dynamic inconsistency will exist and lead to residual forces and moments. In this study, we present and evaluate a computational method to perform inverse dynamics-based simulations without force plates, which both improves the dynamic consistency as well as removes the model׳s dependency on measured external forces. Using the equations of motion and a scaled musculoskeletal model, the ground reaction forces and moments (GRF&Ms) are derived from three-dimensional full-body motion. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and, in contrast to previously proposed techniques, does not require training or empirical data. The method was applied to nine healthy subjects performing several Activities of Daily Living (ADLs) and evaluated with simultaneously measured force plate data. Except for the transverse ground reaction moment, no significant differences (P>0.05) were found between the mean predicted and measured GRF&Ms for almost all ADLs. The mean residual forces and moments, however, were significantly reduced (P>0.05) in almost all ADLs using our method compared to conventional inverse dynamic simulations. Hence, the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics.

Resonance tuning in a neuro-musculo-skeletal model of the forearm

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior—such as resonance tuning—in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which—according to literature—is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.

Modelling functional effects of muscle geometry.

Muscle architecture is an important aspect of muscle functioning. Hence, geometry and material properties of muscle have great influence on the force-length characteristics of muscle. We compared experimental results for the gastrocnemius medialis muscle (GM) of the rat to model results of simple geometric models such as a planimetric model and three-dimensional versions of this model. The capabilities of such models to adequately calculate muscle geometry and force-length characteristics were investigated. The planimetric model with elastic aponeurosis predicted GM muscle geometry well: maximal differences are 6, 1, 4 and 6% for fiber length, aponeurosis length, fiber angle and aponeurosis angle respectively. A slanted cylinder model with circular fiber cross-section did not predict muscle geometry as well as the planimetric model, whereas the geometry results of a second slanted cylinder model were identical to the planimetric model. It is concluded that the planimetric model is capable of adequately calculating the muscle geometry over the muscle length range studied. However, for modelling of force-length characteristics more complex models are needed, as none of the models yielded results sufficiently close to experimental data. Modelled force-length characteristics showed an overestimation of muscle optimum length by 2 mm with respect to experimental data, and the force at the ascending limb of the length force curve was underestimated. The models presented neglect important aspects such as non-linear geometry of muscle, certain passive material properties and mechanical interactions of fibers. These aspects may be responsible for short-comings in the modelling. It is argued that, considering the inability to adequately model muscle length-force characteristics for an isolated maximally activated (in situ) muscle, it is to be expected that prediction will fail for muscle properties in conditions of complex movement with many interacting factors. Therefore, modelling goals should be limited to the heuristic domain rather than expect to be able to predict or even approach medical or biological reality. However, the increased understanding about muscular mechanisms obtained from heuristic use of such simple models may very well be used in creating progress in, for example, clinical applications.

Sensitivity of subject-specific models to errors in musculo-skeletal geometry

Subject-specific musculo-skeletal models of the lower extremity are an important tool for investigating various biomechanical problems, for instance the results of surgery such as joint replacements and tendon transfers. The aim of this study was to assess the potential effects of errors in musculo-skeletal geometry on subject-specific model results. We performed an extensive sensitivity analysis to quantify the effect of the perturbation of origin, insertion and via points of each of the 56 musculo-tendon parts contained in the model. We used two metrics, namely a Local Sensitivity Index (LSI) and an Overall Sensitivity Index (OSI), to distinguish the effect of the perturbation on the predicted force produced by only the perturbed musculo-tendon parts and by all the remaining musculo-tendon parts, respectively, during a simulated gait cycle. Results indicated that, for each musculo-tendon part, only two points show a significant sensitivity: its origin, or pseudo-origin, point and its insertion, or pseudo-insertion, point. The most sensitive points belong to those musculo-tendon parts that act as prime movers in the walking movement (insertion point of the Achilles Tendon: LSI=15.56%, OSI=7.17%; origin points of the Rectus Femoris: LSI=13.89%, OSI=2.44%) and as hip stabilizers (insertion points of the Gluteus Medius Anterior: LSI=17.92%, OSI=2.79%; insertion point of the Gluteus Minimus: LSI=21.71%, OSI=2.41%). The proposed priority list provides quantitative information to improve the predictive accuracy of subject-specific musculo-skeletal models.